what is logic in essay

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Logic in Argumentative Writing

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This handout is designed to help writers develop and use logical arguments in writing. This handout helps writers analyze the arguments of others and generate their own arguments. However, it is important to remember that logic is only one aspect of a successful argument. Non-logical arguments , statements that cannot be logically proven or disproved, are important in argumentative writing—such as appeals to emotions or values. Illogical arguments , on the other hand, are false and must be avoided.

Logic is a formal system of analysis that helps writers invent, demonstrate, and prove arguments. It works by testing propositions against one another to determine their accuracy. People often think they are using logic when they avoid emotion or make arguments based on their common sense, such as "Everyone should look out for their own self-interests" or "People have the right to be free." However, unemotional or common sense statements are not always equivalent to logical statements. To be logical, a proposition must be tested within a logical sequence.

The most famous logical sequence, called the syllogism , was developed by the Greek philosopher Aristotle. His most famous syllogism is:

Premise 1: All men are mortal. Premise 2: Socrates is a man. Conclusion: Therefore, Socrates is mortal.

In this sequence, premise 2 is tested against premise 1 to reach the logical conclusion. Within this system, if both premises are considered valid, there is no other logical conclusion than determining that Socrates is a mortal.

This guide provides some vocabulary and strategies for determining logical conclusions.

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1 What is Logic?

Matthew Knachel

There’s an ancient view, still widely held, that what makes human beings special—what distinguishes us from the “beasts of the field”—is that we are rational. What does rationality consist in? That’s a vexed question, but one possible response goes roughly like this: we manifest our rationality by engaging in activities that involve reasoning —making claims and backing them up with reasons, acting in accord with reasons and beliefs, drawing inferences from available evidence, and so on.

This reasoning activity can be done well and it can be done badly; it can be done correctly or incorrectly. Logic is the discipline that aims to distinguish good reasoning from bad.

Good reasoning is not necessarily effective reasoning. In fact, as we shall see in a subsequent chapter on logical fallacies, bad reasoning is pervasive and often extremely effective—in the sense that people are often persuaded by it. In logic, the standard of goodness is not effectiveness in the sense of persuasiveness, but rather correctness according to logical rules.

For example, consider Hitler. He persuaded an entire nation to go along with a variety of proposals that were not only false but downright evil. You won’t be surprised to hear that if you examine it critically, his reasoning does not pass logical muster. Hitler’s arguments were effective, but not logically correct. Moreover, his persuasive techniques go beyond reasoning in the sense of backing up claims with reasons. Hitler relied on threats, emotional manipulation, unsupported assertions, etc. There are many rhetorical tricks one can use to persuade.

In logic, we study the rules and techniques that allow us to distinguish good, correct reasoning from bad, incorrect reasoning.

Since there are a variety of different types of reasoning and methods with which to evaluate each of these types, plus various diverging views on what constitutes correct reasoning, there are many approaches to the logical enterprise. We talk of logic, but also of logics . A logic is just a set of rules and techniques for distinguishing good reasoning from bad. A logic must formulate precise standards for evaluating reasoning and develop methods for applying those standards to particular instances.

Basic Notions

Reasoning involves claims or statements—making them and backing them up with reasons, drawing out their consequences. Propositions are the things we claim, state, assert.

Propositions are the kinds of things that can be true or false. They are expressed by declarative sentences . We use such sentences to make all sorts of assertions, from routine matters of fact (“the Earth revolves around the Sun”), to grand metaphysical theses (“reality is an unchanging, featureless, unified Absolute”), to claims about morality (“it is wrong to eat meat”).

It is important to distinguish sentences in the declarative mood, which express propositions, from sentences in other moods, which do not. Interrogative sentences, for example, ask questions (“Is it raining?”), and imperative sentences issue commands (“Don’t drink kerosene.”). It makes no sense to ask whether these kinds of sentences express truths or falsehoods, so they do not express propositions.

We also distinguish propositions from the sentences that express them, because a single proposition can be expressed by different sentences. “It’s raining” and “es regnet” both express the proposition that it’s raining; one sentence does it in English, the other in German. Also, “John loves Mary” and “Mary is loved by John” both express the same proposition.

The fundamental unit of reasoning is the argument. In logic, by “argument” we don’t mean a disagreement, a shouting match; rather, we define the term precisely:

Argument = a set of propositions, one of which, the conclusion, is (supposed to be) supported by  the others, the premises.

If we’re reasoning by making claims and backing them up with reasons, then the claim that’s being backed up is the conclusion of an argument; the reasons given to support it are the argument’s premises. If we’re reasoning by drawing an inference from a set of statements, then the inference we draw is the conclusion of an argument, and the statements from which it’s drawn are the premises.

We include the parenthetical hedge—“supposed to be”—in the definition to make room for bad arguments. A bad argument, very roughly speaking, is one where the premises fail to support the conclusion; a good argument’s premises actually do support the conclusion.

Analysis of Arguments

The following passage expresses an argument:

So does this passage:

Again, the ultimate purpose of logic is to evaluate arguments—to distinguish the good from the bad. To do so requires distinctions, definitions, principles, and techniques that will be outlined in subsequent chapters. For now, we will focus on identifying and reconstructing arguments.

The first task is to explicate arguments—to state explicitly their premises and conclusions. A perspicuous way to do this is simply to list declarative sentences expressing the relevant propositions, with a line separating the premises from the conclusion, thus:

• McDonald’s pays their workers very low wages.
• The animals that provide McDonald’s meat are raised in deplorable conditions.
• McDonald’s food is very unhealthy.
• [latex]/ \therefore[/latex] You shouldn’t eat at McDonald’s. [1]

This is an explication of the first argumentative passage above. To identify the conclusion of an argument, it is helpful to ask oneself, “What is this person trying to convince me to believe by saying these things? What is the ultimate point of this passage?” The answer is pretty clear in this case. Another clue as to what’s going on in the passage is provided by the word “because” in the third sentence. Along with other words, like “since” and “for,” it indicates the presence of a premise. We can call such words premise markers . The symbol “/∴” can be read as shorthand for “therefore.” Along with expressions like “consequently,” “thus,” “it follows that” and “which implies that,” “therefore” is an indicator that the argument’s conclusion is about to follow. We call such locutions conclusion markers . Such a marker is not present in the first argument, but we do see one in the second, which may be explicated thus:

• The universe is vast and complex.
• The universe displays an astonishing degree of order.
• The planets orbit the sun according to regular laws.
• Animals’ minutest parts are arranged precisely to serve their purposes.
• Such order and complexity cannot arise at random.
• [latex]/ \therefore[/latex] The universe must be the product of a designer of enormous power and intellect: God.

Several points of comparison to our first explication are worthy of note here. First, as mentioned, we were alerted of the conclusion by the word “therefore.” Second, this passage required much more paraphrase than the first. The second sentence is interrogative, not declarative, and so it does not express a proposition. Since arguments are, by definition, collections of propositions, we must restrict ourselves to declarative sentences when explicating them. Since the answer to the second sentence’s rhetorical question is clearly “yes,” we paraphrase as shown. The third sentence expresses two propositions, so in our explication we separate them; each one is a premise.

So sometimes, when we explicate an argument, we have to take what’s present in the argumentative passage and change it slightly, so that all of the sentences we write down express the propositions present in the argument. This is paraphrasing. At other times, we have to do even more. For example, we may have to introduce propositions which are not explicitly mentioned within the argumentative passage, but are undoubtedly used within the argument’s reasoning.

There’s a Greek word for argumentative passages that leave certain propositions unstated: enthymemes . Here’s an example:

There’s an implicit premise lurking in the background here—something that hasn’t been said, but which needs to be true for the argument to go through. We need a claim that connects the premise to the conclusion—that bridges the gap between them. Something like this: An all-loving God would not allow innocent people to suffer. Or maybe: widespread suffering is incompatible with the idea of an all-loving deity. The premise points to suffering, while the conclusion is about God; these propositions connect those two claims. A complete explication of the argumentative passage would make a proposition like this explicit:

• Many innocent people all over the world are suffering.
• An all-loving God would not allow innocent people to suffer.
• [latex]/ \therefore[/latex] There cannot be an all-loving God.

This is the mark of the kinds of tacit premises we want to uncover: if they’re false, they undermine the argument. Often, premises like this are unstated for a reason: they’re controversial claims on their own, requiring evidence to support them; so the arguer leaves them out, preferring not to get bogged down. [2] When we draw them out, however, we can force a more robust dialectical exchange, focusing the argument on the heart of the matter. In this case, a discussion about the compatibility of God’s goodness and evil in the world would be in order. There’s a lot to be said on that topic. Philosophers and theologians have developed elaborate arguments over the centuries to defend the idea that God’s goodness and human suffering are in fact compatible. [3]

So far, our analysis of arguments has not been particularly deep. We have noted the importance of identifying the conclusion and clearly stating the premises, but we have not looked into the ways in which sets of premises can support their conclusions. We have merely noted that, collectively, premises provide support for conclusions. We have not looked at how they do so, what kinds of relationships they have with one another. This requires deeper analysis.

Often, different premises will support a conclusion—or another premise—individually, without help from any others. Consider this simple argument:

Propositions 1 and 2 support the conclusion, proposition 3—and they do so independently. Each gives us a reason for believing that the war was unjust, and each stands as a reason even if we were to suppose that the other were not true; this is the mark of independent premises .

It can be helpful, especially when arguments are more complex, to draw diagrams that depict the relationships among premises and conclusion. We could depict the argument above as follows:

In such a diagram, the circled numbers represent the propositions and the arrows represent the relationship of support from one proposition to another. Since propositions 1 and 2 each support 3 independently, they get their own arrows.

Other relationships among premises are possible. Sometimes, premises provide support for conclusions only indirectly, by giving us a reason to believe some other premise, which is intermediate between the two claims. Consider the following argument:

In this example, proposition 1 provides support for proposition 2 (the word “hence” is a clue), while proposition 2 directly supports the conclusion in 3. We would depict the relationships among these propositions thus:

Sometimes premises must work together to provide support for another claim, not because one of them provides reason for believing the other, but because neither provides the support needed on its own; we call such propositions joint premises . Consider the following:

In this argument, neither premise 1 nor premise 2 supports the conclusion on its own; rather, the second premise, as it were, provides a key that unlocks the conclusion from the conditional premise 1. We can indicate such interdependence diagrammatically with brackets, thus:

Diagramming arguments in this way can be helpful both in understanding how they work and informing any attempt to critically engage with them. One can see clearly in the first argument that any considerations put forward contrary to one of the independent premises will not completely undermine support for the conclusion, as there is still another premise providing it with some degree of support. In the second argument, though, reasons telling against the second premise would cut off support for the conclusion at its root; and anything contrary to the first premise will leave the second in need of support. And in the third argument, considerations contrary to either of the joint premises will undermine support for the conclusion. Especially when arguments are more complex, such visual aids can help us recognize all of the inferences contained within the argument.

Perhaps it will be useful to conclude by considering a slightly more complex argument. Let’s consider the nature of numbers:

The conclusion of this argument is the last proposition, that numbers are abstract objects. Notice that the first premise gives us a choice between this claim and an alternative—that they are concrete. The second premise denies that alternative, and so premises 1 and 2 are working together to support the conclusion:

Now we need to make room in our diagram for propositions 3 and 4. They are there to give us reasons for believing that numbers are not concrete objects. First, by asserting that numbers aren’t located in space like concrete objects are, and second by asserting that numbers don’t interact with other objects, like concrete objects do. These are separate, independent reasons for believing they aren’t concrete, so we end up with this diagram:

Logic and Philosophy

At the heart of the logical enterprise is a philosophical question: What makes a good argument? That is, what is it for a set of claims to provide support for some other claim? Or maybe: When are we justified in drawing inferences? To answer these questions, logicians have developed a wide variety of logical systems, covering different types of arguments, and applying different principles and techniques. Many of the tools developed in logic can be applied beyond the confines of philosophy. The mathematician proving a theorem, the computer scientist programming a computer, the linguist modeling the structure of language—all these are using logical methods. Because logic has such wide application, and because of the formal/mathematical sophistication of many logical systems, it occupies a unique place in the philosophical curriculum. A class in logic is typically unlike other philosophy classes in that very little time is spent directly engaging with and attempting to answer the “big questions”; rather, one very quickly gets down to the business of learning logical formalisms. The questions logic is trying to answer are important philosophical questions, but the techniques developed to answer them are worthy of study on their own.

This does not mean, however, that we should think of logic and philosophy as merely tangentially related; on the contrary, they are deeply intertwined. For all the formal bells and whistles featured in the latest high-end logical system, at bottom it is part of an effort to answer the fundamental question of what follows from what. Moreover, logic is useful to the practicing philosopher in at least three other ways.

Philosophers attempt to answer deep, vexing questions—about the nature of reality, what constitutes a good life, how to create a just society, and so on. They give their answers to these questions, and they back those answers up with reasons. Then other philosophers consider their arguments and reply with elaborations and criticisms—arguments of their own. Philosophy is conducted and makes progress by way of exchanging arguments. Since they are the primary tool of their trade, philosophers better know a little something about what makes for good arguments! Logic, therefore, is essential to the practice of philosophy.

But logic is not merely a tool for evaluating philosophical arguments; it has altered the course of the ongoing philosophical conversation. As logicians developed formal systems to model the structure of an ever-wider range of discursive practices, philosophers have been able to apply their insights directly to traditional philosophical problems and recognize previously hidden avenues of inquiry. Since the turn of the 20th century especially, the proliferation of novel approaches in logic has sparked a revolution in the practice of philosophy. It is not too much of an exaggeration to say that much of the history of philosophy in the 20th century constituted an ongoing attempt to grapple with new developments in logic, and the philosophical focus on language that they seemed to demand. No philosophical topic—from metaphysics to ethics to epistemology and beyond—was untouched by this revolution.

Finally, logic itself is the source of fascinating philosophical questions. The basic question at its heart—what is it for a claim to follow from others?—ramifies out in myriad directions, providing fertile ground for philosophical speculation. There is logic, and then there is philosophy of logic . Logic is said to be “formal,” for example. What does that mean? It’s a surprisingly difficult question to answer. [5] Our simplest logical formulations of conditional sentences (those involving “if”), lead to apparent paradoxes. [6] How should those be resolved? Should our formalisms be altered to better capture the natural-language meanings of conditionals? What is the proper relationship between logical systems and natural languages, anyway?

Traditionally, most logicians have accepted that logic should be “bivalent”: every proposition is either true or false. But natural languages contain vague terms whose boundaries of applicability are not always clear. For example, “bald”: for certain subjects, we might be inclined to say that they’re well on their way to full-on baldness, but not quite there yet; on the other hand, we would be reluctant to say that they’re not-bald. There are in-between cases. For such cases, we might want to say, for example, that the proposition that Fredo is bald is neither true nor false. Some logicians have developed logics that are not bivalent, to deal with this sort of linguistic phenomenon. Some add a third truth-value: “neither” or “undetermined,” for instance. Others introduce infinite degrees of truth (this is called “fuzzy logic”). These logics deviate from traditional approaches. Are they therefore wrong in some sense? Or are they right, and the traditionalists wrong? Or are we even asking a sensible question when we ask whether a particular logical system is right or wrong? Can we be so-called logical “pluralists,” accepting a variety of incompatible logics, depending, for example, on whether they’re useful?

These sorts of questions are beyond the scope of this introductory text, of course. They’re included to give you a sense of just how far one can take the study of logic. The task for now, though, is to begin that study.

First, explicate the following arguments, paraphrasing as necessary and only including tacit premises when explicitly instructed to do so. Next, diagram the arguments.

• Numbers, if they exist at all, must be either concrete or abstract objects. Concrete objects–like planets and people–are able to interact with other things in cause-and-effect relations. Numbers lack this ability. Therefore, numbers are abstract objects. [ You will need to add an implicit intermediate premise here! ]
• Abolish the death penalty! Why? It is immoral. Numerous studies have shown that there is racial bias in its application. The rise of DNA testing has exonerated scores of inmates on death row; who knows how many innocent people have been killed in the past? The death penalty is also impractical. Revenge is counterproductive: “An eye for an eye leaves the whole world blind,” as Gandhi said. Moreover, the costs of litigating death penalty cases, with their endless appeals, are enormous.
• A just economic system would feature an equitable distribution of resources and an absence of exploitation. Capitalism is an unjust economic system. Under capitalism, the typical distribution of wealth is highly skewed in favor of the rich. And workers are exploited: despite their essential role in producing goods for the market, most of the profits from the sales of those goods go to the owners of firms, not their workers.
• The mind and the brain are not identical. How can things be identical if they have different properties? There is a property that the mind and brain do not share: the brain is divisible, but the mind is not. Like all material things, the brain can be divided into parts—different halves, regions, neurons, etc. But the mind is a unity. It is my thinking essence, in which I can discern no separate parts. [7]
• Every able-bodied adult ought to participate in the workforce. The more people working, the greater the nation’s wealth, which benefits everyone economically. In addition, there is no replacement for the dignity workers find on the job. The government should therefore issue tax credits to encourage people to enter the workforce. [ Include in your explication a tacit premise, not explicitly stated in the passage, but necessary to support the conclusion. ]
• The symbols preceding the conclusion, "[latex]/ \therefore[/latex]" represent the word "therefore." ↵
• This is not always the reason. Some claims are left tacit simply because everybody accepts them and to state them explicitly would be a waste of time. If we argue, “Elephants are mammals, and so warm-blooded,” we omit the claim that all mammals are warm-blooded for this innocent reason. ↵
• These arguments even have a special name: they’re called “theodicies.” ↵
• An extremely compressed version of Plato’s objections to poetry in Book X of The Republic . ↵
• John MacFarlane, in his widely read PhD dissertation, spends over 300 pages on that question. See: MacFarlane, J. 2000. “What Does It Mean to Say That Logic Is Formal?” University of Pittsburgh. ↵
• For a concise explanation, see the Wikipedia entry on paradoxes of material implication . ↵
• A simplified version of an argument from Rene Descartes. ↵

The unambiguated meaning of declarative sentences.

Sentences which communicate that something is, or is not, the case. For example, “Bob won the 50m freestyle.” Declarative sentences can be contrasted with those that pose questions, called interrogative sentences , and those which deliver commands, known as imperative sentences . (Declarative sentences are also known as indicative  sentences)

Words that generally indicate what follows is a premise, e.g. “given that,” “as,” “since.”

Words that generally indicate that what follows is a conclusion, e.g. “therefore,” “thus,” “consequently.”

Arguments which leave certain premises unstated.

Premises which aim to provide sufficient support on their own for the truth of the conclusion.

Premises which attempt to directly support not the conclusion of an argument, but another premise.

Premises which only provide support for the truth of the conclusion when combined.

What is Logic? Copyright © 2020 by Matthew Knachel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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24 What is Logic?

Kirsten DeVries

Logic, in its most basic sense, is the study of how ideas reasonably fit together.  In other words, when you apply logic, you must be concerned with analyzing ideas and arguments by using reason and rational thinking, not emotions or mysticism or belief.  As a dedicated field of study, logic belongs primarily to math, philosophy, and computer science; in these fields, one can get professional training in logic.  However,  all  academic disciplines employ logic: to evaluate evidence, to analyze arguments, to explain ideas, and to connect evidence to arguments.  One of the most important uses of logic is in composing and evaluating arguments.

The study of logic divides into two main categories: formal and informal.   Formal logic  is the formal study of logic.  In other words, in math or philosophy or computer science, if you were to take a class on logic, you would likely be learning formal logic.  The purpose of formal logic is to eliminate any imprecision or lack of objectivity in evaluating arguments.  Logicians, scholars who study and apply logic, have devised a number of formal techniques that accomplish this goal for certain classes of arguments. These techniques can include truth tables, Venn diagrams, proofs, syllogisms, and formulae.  The different branches of formal logic include, but are not limited to, propositional logic, categorical logic, and first order logic.

Informal logic  is logic applied outside of formal study and is most often used in college, business, and life.  According to  The Stanford Encyclopedia of Philosophy ,

For centuries, the study of logic has inspired the idea that its methods might be harnessed in efforts to understand and improve thinking, reasoning, and argument as they occur in real life contexts: in public discussion and debate; in education and intellectual exchange; in interpersonal relations; and in law, medicine, and other professions. Informal logic is the attempt to build a logic suited to this purpose. It combines the study of argument, evidence, proof and justification with an instrumental outlook which emphasizes its usefulness in the analysis of real life arguing.

When people apply the principles of logic to employ and evaluate arguments in real life situations and studies, they are using informal logic.

Why Is Logic Important?

Logic is one of the most respected elements of scholarly and professional thinking and writing.  Consider that logic teaches us how to recognize good and bad arguments—not just arguments about logic,  any  argument.  Nearly every undertaking in life will ultimately require that you evaluate an argument, perhaps several. You are confronted with a question: “Should I buy this car or that car?”  “Should I go to this college or that college?” “Did that scientific experiment show what the scientist claims it did?” “Should I vote for the candidate who promises to lower taxes, or for the one who says she might raise them?” Your life is a long parade of choices.

When answering such questions, to make the best choices, you often have only one tool: an argument. You listen to the reasons for and against various options and must choose among them. Thus, the ability to evaluate arguments is an ability useful in everything that you will do—in your work, your personal life, and your deepest reflections.  This is the job of logic.

If you are a student, note that nearly every discipline–be it a science, one of the humanities, or a study like business–relies upon arguments. Evaluating arguments is the most fundamental skill common to math, physics, psychology, history, literary studies, and any other intellectual endeavor. Logic alone tells you how to evaluate the arguments of  any  discipline.

The alternative to developing logic skills is to be always at the mercy of bad reasoning and, as a result, bad choices. Worse, you can be manipulated by deceivers. Speaking in Canandaigua, New York, on August 3, 1857, the escaped slave and abolitionist leader Frederick Douglass observed,

Power concedes nothing without a demand. It never did and it never will. Find out just what any people will quietly submit to and you have found out the exact measure of injustice and wrong which will be imposed upon them, and these will continue till they are resisted with either words or blows, or with both. The limits of tyrants are prescribed by the endurance of those whom they oppress.

Add this to Frederick Douglass’s words: If you find out just how much a person can be deceived, that is just how far she will be deceived. The limits of tyrants are also prescribed by the reasoning abilities of those they aim to oppress. What logic teaches you is how to demand and recognize good reasoning, and, hence, avoid deceit. You are only as free as your powers of reasoning enable.

The remaining part of this logic section will concern two types of logical arguments— inductive  and  deductive —and the tests of those arguments, including  validity ,  soundness ,  reliability , and  strength , so that you can check your own arguments and evaluate the arguments of others, no matter if those arguments come from the various academic disciplines, politics, the business world, or just discussions with friends and family.

What Is Deductive Argument?

A  deductive argument  is an argument whose conclusion is supposed to follow from its premises with absolute certainty, thus leaving no possibility that the conclusion doesn’t follow from the premises. If a deductive argument fails to guarantee the truth of the conclusion, then the deductive argument can no longer be called a deductive argument.

The Tests of Deductive Arguments: Validity and Soundness

So far in this chapter, you have learned what arguments are and how to determine their structure, including how to reconstruct arguments in standard form.  But what makes an argument good or bad?  There are four main ways to test arguments, two of which are for deductive arguments.  The first test for deductive arguments is  validity , a concept that is central to logical thinking. Validity relates to how well the premises support the conclusion and is the golden standard that every deductive argument should aim for. A  valid argument  is an argument whose conclusion cannot possibly be false, assuming that the premises are true.  Another way to put this is as a conditional statement: A valid argument is an argument in which  if  the premises are true, the conclusion  must  be true.  Here is an example of a valid argument:

• Violet is a dog.
• Therefore, Violet is a mammal. (from 1)

You might wonder whether it  is  true that Violet is a dog (maybe she’s a lizard or a buffalo—you have no way of knowing from the information given). But, for the purposes of validity, it doesn’t matter whether premise 1 is  actually  true or false. All that matters for validity is whether the conclusion follows from the premise. You can see that the conclusion—that Violet is a mammal—does seem to follow from the premise—that Violet is a dog. That is, given the truth of the premise, the conclusion has to be true. This argument is clearly valid because  if  you assume that “Violet is a dog” is true, then, since all dogs are mammals,  it follows  that “Violet is a mammal” must also be true. Thus, whether an argument is valid has nothing to do with whether the premises of the argument are actually true. Here is an example where the premises are clearly false, yet the argument is valid:

• Everyone born in France can speak French.
• Barack Obama was born in France.
• Therefore, Barack Obama can speak French. (from 1-2)

This is a valid argument. Why? Because when you  assume  the truth of the premises (everyone born in France can speak French, and Barack Obama was born in France) the conclusion (Barack Obama can speak French)  must  be true. Notice that this is so even though none of these statements is  actually  true. Not everyone born in France can speak French (think about people who were born there but then moved somewhere else where they didn’t speak French and never learned it), and Barack Obama was not born in France, but it is also false that Obama can speak French. However, the argument is still valid even though neither the premises nor the conclusion is actually true. That may sound strange, but if you understand the concept of validity, it is not strange at all. Remember:  validity describes the relationship between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true.

To better understand the concept of validity, examine this example of an  invalid  argument:

• George was President of the United States.
• Therefore, George was elected President of the United States. (from 1)

This argument is  invalid  because it is possible for the premise to be true and yet the conclusion false. Here is a counterexample to the argument. Gerald Ford was President of the United States, but he was never elected president because Ford replaced Richard Nixon when Nixon resigned in the wake of the Watergate scandal. Therefore, it does not follow that just because someone is President of the United States that he was  elected  President of the United States. In other words, it is possible for the premise of the argument to be true and yet the conclusion false. This means that the argument is invalid. If an argument is invalid, it will always be possible to construct a counterexample to show that it is invalid (as demonstrated in the Gerald Ford scenario). A  counterexample  is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false.

Determine whether the following arguments are valid by using an informal test of validity. In other words, ask whether you can imagine a scenario in which the premises are both true and yet the conclusion is false. For each argument do the following: (1) If the argument is valid, explain your reasoning, and (2) if the argument is invalid, provide a counterexample.  Remember, this is a test of validity, so you may assume all premises are true (even if you know or suspect they are not in real life) for the purposes of this assignment.

1. Katie is a human being. Therefore, Katie is smarter than a chimpanzee.

2. Bob is a fireman. Therefore, Bob has put out fires.

3. Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.

4. Monica is a French teacher. Therefore, Monica knows how to teach French.

5. Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie.

6. Craig loves Linda. Linda loves Monique. Therefore, Craig loves Monique.

7. Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God.

8. All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah.

9. Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals.

10. Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside.

A good deductive argument is not only valid but also  sound . A  sound argument  is a valid argument that has all true premises. That means that the conclusion, or claim, of a sound argument will always be true because if an argument is valid, the premises transmit truth to the conclusion on the assumption of the truth of the premises. If the premises are actually true, as they are in a sound argument, and since all sound arguments are valid, we know that the conclusion of a sound argument is true.  The relationship between soundness and validity is easy to specify:  all sound arguments are valid arguments, but not all valid arguments are sound arguments .

Professors will expect sound arguments in college writing.  Philosophy professors, for the sake of pursuing arguments based on logic alone, may allow students to pursue unsound arguments, but nearly all other professors will want sound arguments.  How do you make sure that all the premises of your argument are true?  How can we know that Violet is a dog or that littering is harmful to animals and people?  Answers to these questions come from  evidence , often in the form of research.

One way to counter another’s argument is to question his premises and test them for soundness.  If you find that one or more premise is unsound, you can add that information–and your explanations–to the support of your own argument.

One way to test the accuracy of a premise is to apply the following questions:

• Is there a sufficient amount of data?
• What is the quality of the data?
• Has additional data been missed?
• Is the data relevant?
• Are there additional possible explanations?

Determine whether the starting claim is based upon a sample that is both representative and sufficiently large, and ask yourself whether all relevant factors have been taken into account in the analysis of data that leads to a generalization.

Another way to evaluate a premise is to determine whether its source is credible.  Ask yourself,

• Are the authors identified?
• What are their backgrounds?
• Was the claim something you found on an undocumented website?
• Did you find it in a popular publication or a scholarly one?
• How complete, how recent, and how relevant are the studies or statistics discussed in the source?

What Is Inductive Argument?

In contrast to a deductive argument, an  inductive argument  is an argument whose conclusion is supposed to follow from its premises with a high level of probability, which means that although it is possible that the conclusion doesn’t follow from its premises, it is unlikely that this is the case. Here is an example of an inductive argument:

Tweets is a healthy, normally functioning bird and since most healthy, normally functioning birds fly, Tweets most likely flies.

Notice that the conclusion, “Tweets probably flies,” contains the words “most likely.” This is a clear indicator that the argument is supposed to be inductive, not deductive. Here is the argument in standard form:

• Tweets is a healthy, normally functioning bird. ( premise )
• Most healthy, normally functioning birds fly. ( premise )
• Therefore, Tweets probably flies. ( conclusion )

Given the information provided by the premises, the conclusion does seem to be well supported. That is, the premises provide strong reasons for accepting the conclusion. The inductive argument’s conclusion is a strong one, even though we can imagine a scenario in which the premises are true and yet the conclusion is false.

Remember, inductive arguments cannot guarantee the truth of the conclusion, which means they will look like invalid deductive arguments. Indeed, they are. There  will  be counterexamples for inductive arguments because an inductive argument never promises absolute truth. We measure inductive arguments by degrees of  probability  and  plausibility , not absolute categories like validity and soundness. Validity and soundness do not allow for a sliding scale of degrees. They are absolute conditions: There is no such thing as being partially valid or somewhat sound.

Do not let this difference between deductive and inductive arguments cause you to privilege deductive and revile inductive because inductive arguments cannot guarantee truth. That is an unfair measure, and it is not practical. The truth is that most arguments we create and evaluate in life are inductive arguments. It might be helpful to think of deductive arguments as those created in perfect lab conditions, where all the ideal parameters can be met. Life is much messier than that, and we rarely get ideal conditions. One main reason is that we rarely ever have all the information we need to form an absolutely true conclusion. When new information is discovered, a scientist or historian or psychologist or business executive or a college student should investigate how it affects previous ideas and arguments, knowing that those previous ideas may need to be adjusted based on new information. For example, suppose that we added the following premise to our earlier argument:

Tweets is 6 feet tall and can run 30 mph. ( premise )

When we add this premise, the conclusion that Tweets can fly would no longer be likely because any bird that is 6 feet tall and can run 30 mph, is not a kind of bird that can fly. That information leads us to believe that Tweets is an ostrich or emu, which are not kinds of birds that can fly.

The Tests of Inductive Arguments: Reliability and Strength

Inductive arguments can never lead to absolute certainty, which is one reason scholars keep studying and trying to add to knowledge. This does not mean, however, that any inductive argument will be a good one. Inductive arguments must still be evaluated and tested, and the two main tests are  reliability  and  strength .

Test of  reliability , much like that of validity for deductive arguments, tests an inductive argument’s reason, its internal logic. In other words, just because an inductive argument cannot guarantee a true conclusion doesn’t mean that it should not be logically constructed. One cannot make just any sort of claim, particularly one that does not have a reliable basis. Reliability, unlike validity, can be measured by degree. More reliable arguments are ones that have a more solid basis in reason. Consider this example:

Ninety-seven percent of Banana TM  computers work without any glitches. ( premise )

Max has a Banana TM  computer. ( premise )

Therefore, Max’s computer works without any glitches. ( conclusion )

This argument has a high degree of reliability. While it may well be true that Max has one of the three percent of computers that have glitches, it is much more likely, given the initial premise that he does not. If the initial premise changes, however, so does the reliability of the argument:

Thirty-three percent of Banana TM  computers work without any glitches.

Max has a Banana TM  computer.

Therefore, Max’s computer works without any glitches.

Note how the degree of reliability has gone done dramatically. The argument can now be considered unreliable since the conclusion that Max’s computer will work without glitches is improbable given the premises provided. The conclusion still could be true, but it has tipped toward unlikely.

The second test of inductive arguments is  strength . Strength, like reliability, can be measured by degree. Strong arguments must have the following conditions: (1) They must be reliable arguments; (2) they draw upon multiple lines of reasoning as support and/or a collection of data. Indeed, the more the data and the more the reasons for a conclusion, the stronger the argument. Consider the following argument:

Susie has walked by Mack the dog every day for ten days. ( premise )

Mack the dog has never bitten Susie. ( premise )

Thus, when Susie walks by Mack the dog today, he will not bite her. ( conclusion )

This argument is reasonable; we can see that the premises may logically lead to the conclusion. However, the argument is not very strong as Susie has only walked by the dog for ten days. Is that enough data to make the conclusion a likely one? What if we had more data, like so—

Susie has walked by Mack the dog every day for five years.

Mack the dog has never bitten Susie.

Thus, when Susie walks by Mack the dog today, he will not bite her.

This argument, with more data to consider (five years of information instead of just ten days), is much stronger. An argument also gets stronger when reasons are added:

Mack’s owners trained him to be friendly to people. ( additional premise )

Mack the dog’s breed is not known for aggression. ( additional premise )

This argument is even stronger. Not only does it have more data, but it also has additional reasons for Mack’s gentle nature.

Remember these tests when writing your own essays. You are most likely going to be using inductive arguments, and you should make them as reliable and strong as you can because you can bet your professors will be evaluating your arguments by those criteria as well.

What Are Logical Fallacies, and Why Should You Avoid Them?

Fallacies  are errors or tricks of reasoning. A fallacy is an  error  of reasoning if it occurs accidentally; it is a  trick  of reasoning if a speaker or writer uses it to deceive or manipulate his audience. Fallacies can be either  formal  or  informal .

Whether a fallacy is an error or a trick, whether it is formal or informal, its use undercuts the validity and soundness of any argument. At the same time, fallacious reasoning can damage the credibility of the speaker or writer and improperly manipulate the emotions of the audience or reader.  This is a consideration you must keep in mind as a writer who is trying to maintain credibility ( ethos ) with the reader.  Moreover, being able to recognize logical fallacies in the speech and writing of others can greatly benefit you as both a college student and a participant in civic life. Not only does this awareness increase your ability to think and read critically—and thus not be manipulated or fooled—but it also provides you with a strong basis for counter arguments.

Even more important, using faulty reasoning is unethical and irresponsible.  Using logical fallacies can be incredibly tempting.  The unfortunate fact is they work.  Every day—particularly in politics and advertising—we can see how using faults and tricks of logic effectively persuade people to support certain individuals, groups, and ideas and, conversely, turn them away from others.  Furthermore, logical fallacies are easy to use.  Instead of doing the often difficult work of carefully supporting an argument with facts, logic, and researched evidence, the lazy debater turns routinely to the easy path of tricky reasoning.  Human beings too often favor what is easy and effective, even if morally questionable, over what is ethical, particularly if difficult.  However, your college professors’ task is not to teach you how to join the Dark Side. Their job is to teach you how to write, speak, and argue effectively and  ethically .  To do so, you must recognize and avoid the logical fallacies.

What Are Formal Fallacies?

Most  formal fallacies  are errors of logic: The conclusion does not really “follow from” (is not supported by) the premises. Either the premises are untrue, or the argument is invalid. Below is an example of an invalid deductive argument:

Premise : All black bears are omnivores.

Premise : All raccoons are omnivores.

Conclusion : All raccoons are black bears.

Bears are a subset of omnivores. Raccoons also are a subset of omnivores. But these two subsets do not overlap, and that fact makes the conclusion illogical. The argument is invalid—that is, the relationship between the two premises does not support the conclusion.

“Raccoons are black bears” is instantaneously recognizable as fallacious and may seem too silly to be worth bothering about. However, that and other forms of poor logic play out on a daily basis, and they have real world consequences. Below is an example of a common fallacious argument:

Premise : All Arabs are Muslims.

Premise : All Iranians are Muslims.

Conclusion : All Iranians are Arabs.

This argument fails on two levels. First, the premises are untrue because, although many Arabs and Iranians are Muslim, not all are. Second, the two ethnic groups (Iranians and Arabs) are sets that do not overlap; nevertheless, the two groups are confounded because they (largely) share one quality in common (being Muslim). One only has to look at comments on the web to realize that the confusion is widespread and that it influences attitudes and opinions about US foreign policy.  The logical problems make this both an invalid and an unsound argument.

What Are Informal Fallacies?

Informal fallacies  take many forms and are widespread in everyday discourse. Very often they involve bringing irrelevant information into an argument, or they are based on assumptions that, when examined, prove to be incorrect. Formal fallacies are created when the relationship between premises and conclusion does not hold up or when premises are unsound; informal fallacies are more dependent on misuse of language and of evidence.

It is easy to find lists of informal fallacies, but that does not mean that it is always easy to spot them.

How Can You Check for Logical Fallacies?

One way to go about evaluating an argument for fallacies is to return to the concept of the three fundamental appeals:  ethos ,  logos , and  pathos .  As a quick reminder,

• Ethos  is an appeal to ethics, authority, and/or credibility.
• Logos  is an appeal to logic.
• Pathos  is an appeal to emotion.

Once you have refreshed your memory of the basics, you may begin to understand how ethos, logos, and pathos can be used appropriately to strengthen your argument or inappropriately to manipulate an audience through the use of fallacies. Classifying fallacies as fallacies of ethos, logos, or pathos will help you to understand their nature and to recognize them. Please keep in mind, however, that some fallacies may fit into multiple categories.  For more details and examples on errors in the rhetorical appeals, see  Chapter 2, “Rhetorical Analysis.”

Fallacies of ethos  relate to credibility. These fallacies may unfairly build up the credibility of the author (or his allies) or unfairly attack the credibility of the author’s opponent (or her allies). Some fallacies give an unfair advantage to the claims of the speaker or writer or an unfair disadvantage to his opponent’s claims. These are  fallacies of logos .  Fallacies of pathos  rely excessively upon emotional appeals, attaching positive associations to the author’s argument and negative ones to his opponent’s position.

Key Takeaways: Logic

• Logic —shows how ideas fit together by using reason.
• Formal Logic —a formal and rigorous study of logic, such as in math and philosophy.
• Informal Logic —the application of logic to arguments of all types: in scholarship, in business, and in life.  Informal logic is what this part of the chapter covers.
• Deductive Argument —guarantees a true conclusion based on the premises. The tests for deductive arguments are validity and soundness.
• Validity —a way to evaluate a deductive argument; a valid argument is one which,  if  the premises are true, the conclusion must be true.
• Soundness —the second way to evaluate a deductive argument; a sound argument is one where the argument is valid AND the premises have been shown to be true (via support).
• Inductive Argument —cannot guarantee a true conclusion but can only assert what is most likely to be true based on the premises and the support. The tests for inductive arguments are reliability and strength.
• Reliability —a test of reason for inductive arguments. Inductive arguments must still be reasonable, must still have a reliable basis in logic.
• Strength —another test for inductive arguments. Inductive arguments are stronger when they have more reasons and more data to support them.
• Logical Fallacy —a flaw or trick of logic to be avoided at all costs.  Fallacies can be formal or informal.  See the Repository of Logical Fallacies below for individual examples.

Let's Get Writing! Copyright © 2018 by Kirsten DeVries is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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11.1 Developing Your Sense of Logic

Learning outcomes.

By the end of this section, you will be able to:

• Identify key rhetorical concepts and thought patterns in a variety of texts.
• Explain how patterns of thought function for different audiences, purposes, and situations.

For the purposes of this course, logic means “reasoning based on thought and evidence.” In practical terms, logic is the ability to analyze and evaluate persuasive or argument writing for effectiveness. By extension, it also means that you can learn to use logic in your own argumentative writing. Like any other new skill, you are likely to learn best when you have a starting point. Here are some suggestions for how to begin thinking and writing logically:

• Approach a topic with an open mind.
• Consider what you already know about the topic.
• Consider what you want to know about the topic.
• Find credible information about the topic.
• Base your judgments of the topic on sound reasoning and evidence.

Once you have formed your opinions on a particular debatable subject, you must decide on the best way to organize them to share with others. Developing your skills in six widely used reasoning strategies , or patterns for thinking and writing, can help you determine the most logical and effective means of organizing information to make your points.

In this chapter, you will examine these six reasoning strategies—analogy, cause and effect, classification and division, comparison and contrast, problem and solution, and definition—that are often used in college classes. In addition, you will consider how writers’ personal views, cultural backgrounds, and purposes for writing help determine

• which reasoning strategy suits their needs; and
• what they decide to include in their writing.

As you progress in your college classes and beyond, you will find these reasoning strategies used in all genres of writing, both nonfiction (e.g., textbooks, how-to books) and fiction (e.g., novels, short stories). Understanding how these strategies work can help you recognize their common formats and analyze what you read; likewise, as a writer, understanding how these strategies work to reflect your thinking can help you determine the strategy you need to use.

Writers frequently use analogy as a strategy to compare two unlike subjects—one subject is familiar to readers, whereas the other is not. To explain or clarify the unfamiliar subject, the writer emphasizes the way or ways in which the two subjects are similar, even though they are dissimilar and unrelated in all other ways. Analogies are basically long forms of similes (short comparisons of unlike elements, based on the word like or as ) or metaphors (short comparisons without signal words). In the example paragraph, the writer explains unfamiliar aspects of the COVID-19 pandemic by comparing it with the more familiar concept of a robbery spree.

Model Paragraph

student sample text Examining COVID-19 is like examining a robbery case in this way: both require a great deal of investigation. Those investigating the causes behind the pandemic look for the history of how the virus spread, and those investigating a crime look for the backstory that might connect the victims and criminals. In addition, the two groups of investigators look at the reasons behind the focus of their study. Medical investigators look at why the virus spread throughout the world; police investigators look at why the crime spree took place in a particular area. Also, both types of investigators are trying to stop whatever or whoever is the focus of their investigation. Medical investigators want to stop the virus; police investigators want to stop the crimes. end student sample text

Cause and Effect

Cause-and-effect writing identifies and examines the reasons (causes) for and consequences (effects) of an action, event, or idea. Cause-and-effect writing often answers the question “Why?” and helps readers understand the connections between what happens because of—or as a result of—something else.

student sample text Ray’s grocery, Artie’s Hardware store, and Cradle and Teen department store all went out of business because a well-known superstore opened in Springdale. Customers who frequented Ray’s, an establishment that had been run by the same family for four generations, used to drive many miles to take advantage of the high quality of items in the meat and deli departments. After the opening of the superstore, however, those same customers found they could get similar items at a savings, even if the quality was not as high as the products at Ray’s. Customers at Artie’s Hardware often talked with owner Artie Shoeman about their hardware needs, but the store did not offer the same variety of items they could find in the superstore. The same was true for those who shopped at Cradle and Teen. The superstore featured lower prices and more variety, even if the items did not match the quality of the items at Cradle and Teen. end student sample text

Classification and Division

Classification and division are actually two closely related strategies, generally discussed together because of their similarity. When using the strategy of division, the writer identifies a single subject or group and explains categories within that subject or group. In other words, the writer divides the larger unit into component parts. When using the strategy of classification, writers do the opposite. They group various elements and place them into larger, more comprehensive categories rather than divide the whole into parts. In general, the reasoning strategy of classification and division looks at smaller elements as parts of a larger element and thus helps readers understand a general concept and the elements that it comprises.

Model Paragraphs

student sample text Extra material in the textbook can be divided into photographs, quotations, and tables. The photographs were all taken by the author and focus on various parts of the life cycle of the plants highlighted in the chapter. In addition, to add color and more information about the subject matter of each chapter, the author has inserted sidebar quotations from both famous and non-famous people. The tables the author has included help readers see more details about the progression of the plants’ spread across the country. end student sample text

student sample text After three months of training, the young dogs were placed into three categories: those who would go directly to permanent homes, those who would repeat the course, and those who would advance to the next level. The dogs that would be homed immediately were those who were far too social or far too active to be service dogs. The dogs that would repeat the course had possibilities as service dogs but needed more discipline and instruction. Their futures were yet to be decided. Those that advanced to the next level were obedient and focused and learned quickly. They displayed great promise as service dogs. end student sample text

Comparison and Contrast

Compare and contrast , one of the most frequently used reasoning strategies, analyzes two (sometimes more) subjects, examining the similarities (comparisons) and differences (contrasts) between them. Nearly everything you can think of can be a subject for comparison and contrast: objects, people, concepts, places, movies, literature, and styles, to name a few. To elaborate on the separate points, writers provide details about each element being compared or contrasted. Comparison and contrast helps readers analyze and evaluate subjects.

This strategy is helpful when the similarities or differences are not obvious and when a significant common thread exists between the subjects. For example, a contrast between an expensive, elegant restaurant and a fast-food restaurant would be useless because the differences are clearly obvious, despite the common thread—both are restaurants. However, not so obvious might be some similarities.

When subjects have no common thread or have obvious shared characteristics, any comparison or contrast makes little sense—like contrasting a fish and a shoe (no common thread) or comparing two fast-food restaurants (obvious similarities). However, a writer actually might find a common thread between a fish and a shoe (perhaps shine or texture or color), and a valid topic of contrast might be differences between the two fast-food restaurants.

student sample text Although they seem different on the surface, one way in which Romantic-period poetry and 1980s rap music are alike is the desire the writers had to create a new approach to their art. They wanted to represent simpler values that were more connected to the natural world, values to which a general audience could relate. For example, in William Wordsworth ’s “Daffodils,” the speaker can escape the depressing, industrialized urban world to find peace in nature by contemplating a field of flowers. Similarly, in the Sugarhill Gang ’s 1979 “Rapper’s Delight,” the band sings of how their beats can lift spirits and cause listeners to dance and forget their woes. However, Romantic-period poetry and 1980s rap music are different in the delivery style and form of the art; “Rapper’s Delight” is set to music, which is an integral part of the piece, but “Daffodils” is not. end student sample text

Problem and Solution

When using this reasoning strategy, writers introduce a predicament or challenging issue (the problem) and offer information about what was done or what should be done to remedy the predicament or issue (the solution). Problem-and-solution writing helps readers understand the complexities of some predicaments and the actions that can improve or eliminate them.

student sample text The issue of combating the spread of hate speech and misinformation on social media can be addressed if more social media providers improve their monitoring services. Aside from creating more algorithms that search for linked key words and phrases, social media providers should increase the number of professional monitors conducting active searches. Additionally, while many platforms such as Twitter and Facebook respond within a few days to reports of posts that violate their policies, more monitors could lessen the amount of time these posts are available. According to Facebook, inappropriate posts are investigated and removed within 24 to 48 hours (Facebook “Community Standards”). Some offenders have been reported multiple times for their platform violations, and social media sponsors should increase their monitoring of those offenders. Although such surveillance would increase the burden on the social media providers, it would help solve the growing challenge of online hate speech and misinformation. end student sample text

When using the reasoning strategy of definition , writers elaborate on the meaning of an idea, a word, or an expression, usually one that is controversial or that can be viewed in multiple ways. Beginning writers tend to think that definition writing looks only at the denotation , or dictionary definition. However, definition writing entails much more than relaying a dictionary definition. It also explains and elaborates on the connotations , the emotions and implications the topic evokes. Definition writing is especially useful for explaining and interpreting terms, ideas, or concepts that are easily or often confused or that have meanings beyond their denotations. Sometimes these meanings are personal interpretations and thus reflect a writer’s particular viewpoint. Additionally, this strategy is beneficial when writers want to explain or reinforce a term before making an argument about a larger concept.

student sample text In everyday speech, the word critical is often used to highlight negative aspects of a topic. If someone says a friend was critical of a new haircut, the implication is that the friend did not like the cut. However, when used in college classes, critical has an expanded meaning: noting both the negative and positive aspects of a topic, examining those aspects in depth, and then making decisions about the discoveries. Students directed to use critical thinking, critical reading, or critical writing should know they are expected to examine all sides of a topic fully, evaluate the validity of those sides, and then make sound judgments on the basis of their evaluation. end student sample text

In this chapter, you have learned about various reasoning strategies that you may use in academic and professional writing. Utilizing these strategies when you write can help you both evaluate and analyze text that you read and create more logical and persuasive arguments.

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Introduction to Logic and Critical Thinking

(10 reviews)

Matthew Van Cleave, Lansing Community College

Copyright Year: 2016

Publisher: Matthew J. Van Cleave

Language: English

Formats Available

Conditions of use.

Learn more about reviews.

Reviewed by "yusef" Alexander Hayes, Professor, North Shore Community College on 6/9/21

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness. read more

Comprehensiveness rating: 5 see less

Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness.

Content Accuracy rating: 5

The book is accurate.

Relevance/Longevity rating: 5

While many modern examples are used, and they are helpful, they are not necessarily needed. The usefulness of logical principles and skills have proved themselves, and this text presents them clearly with many examples.

Clarity rating: 5

It is obvious that the author cares about their subject, audience, and students. The text is comprehensible and interesting.

Consistency rating: 5

The format is easy to understand and is consistent in framing.

Modularity rating: 5

This text would be easy to adapt.

Organization/Structure/Flow rating: 5

The organization is excellent, my one suggestion would be a concluding chapter.

Interface rating: 5

I accessed the PDF version and it would be easy to work with.

Grammatical Errors rating: 5

The writing is excellent.

Cultural Relevance rating: 5

This is not an offensive text.

Reviewed by Susan Rottmann, Part-time Lecturer, University of Southern Maine on 3/2/21

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it... read more

Comprehensiveness rating: 4 see less

I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it fits better for a general critical thinking course than for a true logic course. I'm not sure that I'd agree. I have been using Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," and I think that book is a better introduction to critical thinking for non-philosophy majors. However, the latter is not open source so I will figure out how to get by without it in the future. Overall, the book seems comprehensive if the subject is logic. The index is on the short-side, but fine. However, one issue for me is that there are no page numbers on the table of contents, which is pretty annoying if you want to locate particular sections.

Content Accuracy rating: 4

I didn't find any errors. In general the book uses great examples. However, they are very much based in the American context, not for an international student audience. Some effort to broaden the chosen examples would make the book more widely applicable.

Relevance/Longevity rating: 4

I think the book will remain relevant because of the nature of the material that it addresses, however there will be a need to modify the examples in future editions and as the social and political context changes.

Clarity rating: 3

The text is lucid, but I think it would be difficult for introductory-level students who are not philosophy majors. For example, in Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," the sub-headings are very accessible, such as "Experts cannot rescue us, despite what they say" or "wishful thinking: perhaps the biggest single speed bump on the road to critical thinking." By contrast, Van Cleave's "Introduction to Logic and Critical Thinking" has more subheadings like this: "Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form" or "Propositional logic and the four basic truth functional connectives." If students are prepared very well for the subject, it would work fine, but for students who are newly being introduced to critical thinking, it is rather technical.

It seems to be very consistent in terms of its terminology and framework.

Modularity rating: 4

The book is divided into 4 chapters, each having many sub-chapters. In that sense, it is readily divisible and modular. However, as noted above, there are no page numbers on the table of contents, which would make assigning certain parts rather frustrating. Also, I'm not sure why the book is only four chapter and has so many subheadings (for instance 17 in Chapter 2) and a length of 242 pages. Wouldn't it make more sense to break up the book into shorter chapters? I think this would make it easier to read and to assign in specific blocks to students.

Organization/Structure/Flow rating: 4

The organization of the book is fine overall, although I think adding page numbers to the table of contents and breaking it up into more separate chapters would help it to be more easily navigable.

Interface rating: 4

The book is very simply presented. In my opinion it is actually too simple. There are few boxes or diagrams that highlight and explain important points.

The text seems fine grammatically. I didn't notice any errors.

The book is written with an American audience in mind, but I did not notice culturally insensitive or offensive parts.

Overall, this book is not for my course, but I think it could work well in a philosophy course.

Reviewed by Daniel Lee, Assistant Professor of Economics and Leadership, Sweet Briar College on 11/11/19

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument read more

Comprehensiveness rating: 3 see less

This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument

To the best of my ability, I regard this content as accurate, error-free, and unbiased

The book is broadly relevant and up-to-date, with a few stray temporal references (sydney olympics, particular presidencies). I don't view these time-dated examples as problematic as the logical underpinnings are still there and easily assessed

Clarity rating: 4

My only pushback on clarity is I didn't find the distinction between argument and explanation particularly helpful/useful/easy to follow. However, this experience may have been unique to my class.

To the best of my ability, I regard this content as internally consistent

I found this text quite modular, and was easily able to integrate other texts into my lessons and disregard certain chapters or sub-sections

The book had a logical and consistent structure, but to the extent that there are only 4 chapters, there isn't much scope for alternative approaches here

No problems with the book's interface

The text is grammatically sound

Cultural Relevance rating: 4

Perhaps the text could have been more universal in its approach. While I didn't find the book insensitive per-se, logic can be tricky here because the point is to evaluate meaningful (non-trivial) arguments, but any argument with that sense of gravity can also be traumatic to students (abortion, death penalty, etc)

No additional comments

Reviewed by Lisa N. Thomas-Smith, Graduate Part-time Instructor, CU Boulder on 7/1/19

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text,... read more

The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text, and the index is very thorough.

The content is excellent. The text is thorough and accurate with no errors that I could discern. The terminology and exercises cover the material nicely and without bias.

The text should easily stand the test of time. The exercises are excellent and would be very helpful for students to internalize correct critical thinking practices. Because of the logical arrangement of the text and the many sub-sections, additional material should be very easy to add.

The text is extremely clearly and simply written. I anticipate that a diligent student could learn all of the material in the text with little additional instruction. The examples are relevant and easy to follow.

The text did not confuse terms or use inconsistent terminology, which is very important in a logic text. The discipline often uses multiple terms for the same concept, but this text avoids that trap nicely.

The text is fairly easily divisible. Since there are only four chapters, those chapters include large blocks of information. However, the chapters themselves are very well delineated and could be easily broken up so that parts could be left out or covered in a different order from the text.

The flow of the text is excellent. All of the information is handled solidly in an order that allows the student to build on the information previously covered.

The PDF Table of Contents does not include links or page numbers which would be very helpful for navigation. Other than that, the text was very easy to navigate. All the images, charts, and graphs were very clear

I found no grammatical errors in the text.

Cultural Relevance rating: 3

The text including examples and exercises did not seem to be offensive or insensitive in any specific way. However, the examples included references to black and white people, but few others. Also, the text is very American specific with many examples from and for an American audience. More diversity, especially in the examples, would be appropriate and appreciated.

Reviewed by Leslie Aarons, Associate Professor of Philosophy, CUNY LaGuardia Community College on 5/16/19

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an... read more

This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an argument and an explanation; validity; soundness; and the distinctions between an inductive and a deductive argument in accessible terms in the first chapter. It also does a good job introducing and discussing informal fallacies (Chapter 4). The incorporation of opportunities to evaluate real-world arguments is also very effective. Chapter 2 also covers a number of formal methods of evaluating arguments, such as Venn Diagrams and Propositional logic and the four basic truth functional connectives, but to my mind, it is much more thorough in its treatment of Informal Logic and Critical Thinking skills, than it is of formal logic. I also appreciated that Van Cleave’s book includes exercises with answers and an index, but there is no glossary; which I personally do not find detracts from the book's comprehensiveness.

Overall, Van Cleave's book is error-free and unbiased. The language used is accessible and engaging. There were no glaring inaccuracies that I was able to detect.

Van Cleave's Textbook uses relevant, contemporary content that will stand the test of time, at least for the next few years. Although some examples use certain subjects like former President Obama, it does so in a useful manner that inspires the use of critical thinking skills. There are an abundance of examples that inspire students to look at issues from many different political viewpoints, challenging students to practice evaluating arguments, and identifying fallacies. Many of these exercises encourage students to critique issues, and recognize their own inherent reader-biases and challenge their own beliefs--hallmarks of critical thinking.

As mentioned previously, the author has an accessible style that makes the content relatively easy to read and engaging. He also does a suitable job explaining jargon/technical language that is introduced in the textbook.

Van Cleave uses terminology consistently and the chapters flow well. The textbook orients the reader by offering effective introductions to new material, step-by-step explanations of the material, as well as offering clear summaries of each lesson.

This textbook's modularity is really quite good. Its language and structure are not overly convoluted or too-lengthy, making it convenient for individual instructors to adapt the materials to suit their methodological preferences.

The topics in the textbook are presented in a logical and clear fashion. The structure of the chapters are such that it is not necessary to have to follow the chapters in their sequential order, and coverage of material can be adapted to individual instructor's preferences.

The textbook is free of any problematic interface issues. Topics, sections and specific content are accessible and easy to navigate. Overall it is user-friendly.

I did not find any significant grammatical issues with the textbook.

The textbook is not culturally insensitive, making use of a diversity of inclusive examples. Materials are especially effective for first-year critical thinking/logic students.

I intend to adopt Van Cleave's textbook for a Critical Thinking class I am teaching at the Community College level. I believe that it will help me facilitate student-learning, and will be a good resource to build additional classroom activities from the materials it provides.

Reviewed by Jennie Harrop, Chair, Department of Professional Studies, George Fox University on 3/27/18

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters... read more

While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters that are dense with statistical analyses and critical vocabulary. These topics are likely better broached in manageable snippets rather than hefty single chapters.

The ideas addressed in Introduction to Logic and Critical Thinking are accurate but at times notably political. While politics are effectively used to exemplify key concepts, some students may be distracted by distinct political leanings.

The terms and definitions included are relevant, but the examples are specific to the current political, cultural, and social climates, which could make the materials seem dated in a few years without intentional and consistent updates.

While the reasoning is accurate, the author tends to complicate rather than simplify -- perhaps in an effort to cover a spectrum of related concepts. Beginning readers are likely to be overwhelmed and under-encouraged by his approach.

Consistency rating: 3

The four chapters are somewhat consistent in their play of definition, explanation, and example, but the structure of each chapter varies according to the concepts covered. In the third chapter, for example, key ideas are divided into sub-topics numbering from 3.1 to 3.10. In the fourth chapter, the sub-divisions are further divided into sub-sections numbered 4.1.1-4.1.5, 4.2.1-4.2.2, and 4.3.1 to 4.3.6. Readers who are working quickly to master new concepts may find themselves mired in similarly numbered subheadings, longing for a grounded concepts on which to hinge other key principles.

Modularity rating: 3

The book's four chapters make it mostly self-referential. The author would do well to beak this text down into additional subsections, easing readers' accessibility.

The content of the book flows logically and well, but the information needs to be better sub-divided within each larger chapter, easing the student experience.

The book's interface is effective, allowing readers to move from one section to the next with a single click. Additional sub-sections would ease this interplay even further.

Grammatical Errors rating: 4

Some minor errors throughout.

For the most part, the book is culturally neutral, avoiding direct cultural references in an effort to remain relevant.

Reviewed by Yoichi Ishida, Assistant Professor of Philosophy, Ohio University on 2/1/18

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic,... read more

This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic, this textbook does not cover suppositional arguments, such as conditional proof and reductio ad absurdum. But other standard argument forms are covered. Chapter 3 covers inductive logic, and here this textbook introduces probability and its relationship with cognitive biases, which are rarely discussed in other textbooks. Chapter 4 introduces common informal fallacies. The answers to all the exercises are given at the end. However, the last set of exercises is in Chapter 3, Section 5. There are no exercises in the rest of the chapter. Chapter 4 has no exercises either. There is index, but no glossary.

The textbook is accurate.

The content of this textbook will not become obsolete soon.

The textbook is written clearly.

The textbook is internally consistent.

The textbook is fairly modular. For example, Chapter 3, together with a few sections from Chapter 1, can be used as a short introduction to inductive logic.

The textbook is well-organized.

There are no interface issues.

I did not find any grammatical errors.

This textbook is relevant to a first semester logic or critical thinking course.

Reviewed by Payal Doctor, Associate Professro, LaGuardia Community College on 2/1/18

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner... read more

This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner book, but seems to be a good text for a course that needs a foundation for arguments. There are exercises on creating truth tables and proofs, so it could work as a logic primer in short sessions or with the addition of other course content.

The books is accurate in the information it presents. It does not contain errors and is unbiased. It covers the essential vocabulary clearly and givens ample examples and exercises to ensure the student understands the concepts

The content of the book is up to date and can be easily updated. Some examples are very current for analyzing the argument structure in a speech, but for this sort of text understandable examples are important and the author uses good examples.

The book is clear and easy to read. In particular, this is a good text for community college students who often have difficulty with reading comprehension. The language is straightforward and concepts are well explained.

The book is consistent in terminology, formatting, and examples. It flows well from one topic to the next, but it is also possible to jump around the text without loosing the voice of the text.

The books is broken down into sub units that make it easy to assign short blocks of content at a time. Later in the text, it does refer to a few concepts that appear early in that text, but these are all basic concepts that must be used to create a clear and understandable text. No sections are too long and each section stays on topic and relates the topic to those that have come before when necessary.

The flow of the text is logical and clear. It begins with the basic building blocks of arguments, and practice identifying more and more complex arguments is offered. Each chapter builds up from the previous chapter in introducing propositional logic, truth tables, and logical arguments. A select number of fallacies are presented at the end of the text, but these are related to topics that were presented before, so it makes sense to have these last.

The text is free if interface issues. I used the PDF and it worked fine on various devices without loosing formatting.

1. The book contains no grammatical errors.

The text is culturally sensitive, but examples used are a bit odd and may be objectionable to some students. For instance, President Obama's speech on Syria is used to evaluate an extended argument. This is an excellent example and it is explained well, but some who disagree with Obama's policies may have trouble moving beyond their own politics. However, other examples look at issues from all political viewpoints and ask students to evaluate the argument, fallacy, etc. and work towards looking past their own beliefs. Overall this book does use a variety of examples that most students can understand and evaluate.

My favorite part of this book is that it seems to be written for community college students. My students have trouble understanding readings in the New York Times, so it is nice to see a logic and critical thinking text use real language that students can understand and follow without the constant need of a dictionary.

Reviewed by Rebecca Owen, Adjunct Professor, Writing, Chemeketa Community College on 6/20/17

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current... read more

This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current events, funny scenarios, or other interesting ways to evaluate argument structure and validity. The third section, which deals with logical fallacies, is very clear and comprehensive. My only critique of the material included in the book is that the middle section may be a bit dense and math-oriented for learners who appreciate the more informal, informative style of the first and third section. Also, the book ends rather abruptly--it moves from a description of a logical fallacy to the answers for the exercises earlier in the text.

The content is very reader-friendly, and the author writes with authority and clarity throughout the text. There are a few surface-level typos (Starbuck's instead of Starbucks, etc.). None of these small errors detract from the quality of the content, though.

One thing I really liked about this text was the author's wide variety of examples. To demonstrate different facets of logic, he used examples from current media, movies, literature, and many other concepts that students would recognize from their daily lives. The exercises in this text also included these types of pop-culture references, and I think students will enjoy the familiarity--as well as being able to see the logical structures behind these types of references. I don't think the text will need to be updated to reflect new instances and occurrences; the author did a fine job at picking examples that are relatively timeless. As far as the subject matter itself, I don't think it will become obsolete any time soon.

The author writes in a very conversational, easy-to-read manner. The examples used are quite helpful. The third section on logical fallacies is quite easy to read, follow, and understand. A student in an argument writing class could benefit from this section of the book. The middle section is less clear, though. A student learning about the basics of logic might have a hard time digesting all of the information contained in chapter two. This material might be better in two separate chapters. I think the author loses the balance of a conversational, helpful tone and focuses too heavily on equations.

Consistency rating: 4

Terminology in this book is quite consistent--the key words are highlighted in bold. Chapters 1 and 3 follow a similar organizational pattern, but chapter 2 is where the material becomes more dense and equation-heavy. I also would have liked a closing passage--something to indicate to the reader that we've reached the end of the chapter as well as the book.

I liked the overall structure of this book. If I'm teaching an argumentative writing class, I could easily point the students to the chapters where they can identify and practice identifying fallacies, for instance. The opening chapter is clear in defining the necessary terms, and it gives the students an understanding of the toolbox available to them in assessing and evaluating arguments. Even though I found the middle section to be dense, smaller portions could be assigned.

The author does a fine job connecting each defined term to the next. He provides examples of how each defined term works in a sentence or in an argument, and then he provides practice activities for students to try. The answers for each question are listed in the final pages of the book. The middle section feels like the heaviest part of the whole book--it would take the longest time for a student to digest if assigned the whole chapter. Even though this middle section is a bit heavy, it does fit the overall structure and flow of the book. New material builds on previous chapters and sub-chapters. It ends abruptly--I didn't realize that it had ended, and all of a sudden I found myself in the answer section for those earlier exercises.

The simple layout is quite helpful! There is nothing distracting, image-wise, in this text. The table of contents is clearly arranged, and each topic is easy to find.

Tiny edits could be made (Starbuck's/Starbucks, for one). Otherwise, it is free of distracting grammatical errors.

This text is quite culturally relevant. For instance, there is one example that mentions the rumors of Barack Obama's birthplace as somewhere other than the United States. This example is used to explain how to analyze an argument for validity. The more "sensational" examples (like the Obama one above) are helpful in showing argument structure, and they can also help students see how rumors like this might gain traction--as well as help to show students how to debunk them with their newfound understanding of argument and logic.

The writing style is excellent for the subject matter, especially in the third section explaining logical fallacies. Thank you for the opportunity to read and review this text!

Reviewed by Laurel Panser, Instructor, Riverland Community College on 6/20/17

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as... read more

This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as the 13th edition with the same title. Lori Watson is the second author on the 13th edition.

Competing with Hurley is difficult with respect to comprehensiveness. For example, Van Cleave’s book is comprehensive to the extent that it probably covers at least two-thirds or more of what is dealt with in most introductory, one-semester logic courses. Van Cleave’s chapter 1 provides an overview of argumentation including discerning non-arguments from arguments, premises versus conclusions, deductive from inductive arguments, validity, soundness and more. Much of Van Cleave’s chapter 1 parallel’s Hurley’s chapter 1. Hurley’s chapter 3 regarding informal fallacies is comprehensive while Van Cleave’s chapter 4 on this topic is less extensive. Categorical propositions are a topic in Van Cleave’s chapter 2; Hurley’s chapters 4 and 5 provide more instruction on this, however. Propositional logic is another topic in Van Cleave’s chapter 2; Hurley’s chapters 6 and 7 provide more information on this, though. Van Cleave did discuss messy issues of language meaning briefly in his chapter 1; that is the topic of Hurley’s chapter 2.

Van Cleave’s book includes exercises with answers and an index. A glossary was not included.

Reviews of open source textbooks typically include criteria besides comprehensiveness. These include comments on accuracy of the information, whether the book will become obsolete soon, jargon-free clarity to the extent that is possible, organization, navigation ease, freedom from grammar errors and cultural relevance; Van Cleave’s book is fine in all of these areas. Further criteria for open source books includes modularity and consistency of terminology. Modularity is defined as including blocks of learning material that are easy to assign to students. Hurley’s book has a greater degree of modularity than Van Cleave’s textbook. The prose Van Cleave used is consistent.

Van Cleave’s book will not become obsolete soon.

Van Cleave’s book has accessible prose.

Van Cleave used terminology consistently.

Van Cleave’s book has a reasonable degree of modularity.

Van Cleave’s book is organized. The structure and flow of his book is fine.

Problems with navigation are not present.

Grammar problems were not present.

Van Cleave’s book is culturally relevant.

Van Cleave’s book is appropriate for some first semester logic courses.

Table of Contents

Chapter 1: Reconstructing and analyzing arguments

• 1.1 What is an argument?
• 1.2 Identifying arguments
• 1.3 Arguments vs. explanations
• 1.4 More complex argument structures
• 1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form
• 1.6 Validity
• 1.7 Soundness
• 1.8 Deductive vs. inductive arguments
• 1.9 Arguments with missing premises
• 1.10 Assuring, guarding, and discounting
• 1.11 Evaluative language
• 1.12 Evaluating a real-life argument

Chapter 2: Formal methods of evaluating arguments

• 2.1 What is a formal method of evaluation and why do we need them?
• 2.2 Propositional logic and the four basic truth functional connectives
• 2.3 Negation and disjunction
• 2.4 Using parentheses to translate complex sentences
• 2.5 “Not both” and “neither nor”
• 2.6 The truth table test of validity
• 2.7 Conditionals
• 2.8 “Unless”
• 2.9 Material equivalence
• 2.10 Tautologies, contradictions, and contingent statements
• 2.11 Proofs and the 8 valid forms of inference
• 2.12 How to construct proofs
• 2.13 Short review of propositional logic
• 2.14 Categorical logic
• 2.15 The Venn test of validity for immediate categorical inferences
• 2.16 Universal statements and existential commitment
• 2.17 Venn validity for categorical syllogisms

Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies

• 3.1 Inductive arguments and statistical generalizations
• 3.2 Inference to the best explanation and the seven explanatory virtues
• 3.3 Analogical arguments
• 3.4 Causal arguments
• 3.5 Probability
• 3.6 The conjunction fallacy
• 3.7 The base rate fallacy
• 3.8 The small numbers fallacy
• 3.9 Regression to the mean fallacy
• 3.10 Gambler's fallacy

Chapter 4: Informal fallacies

• 4.1 Formal vs. informal fallacies
• 4.1.1 Composition fallacy
• 4.1.2 Division fallacy
• 4.1.3 Begging the question fallacy
• 4.1.4 False dichotomy
• 4.1.5 Equivocation
• 4.2 Slippery slope fallacies
• 4.2.1 Conceptual slippery slope
• 4.2.2 Causal slippery slope
• 4.3 Fallacies of relevance
• 4.3.1 Ad hominem
• 4.3.2 Straw man
• 4.3.3 Tu quoque
• 4.3.4 Genetic
• 4.3.5 Appeal to consequences
• 4.3.6 Appeal to authority

Answers to exercises Glossary/Index

Ancillary Material

About the book.

This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.”

About the Contributors

Matthew Van Cleave ,   PhD, Philosophy, University of Cincinnati, 2007.  VAP at Concordia College (Moorhead), 2008-2012.  Assistant Professor at Lansing Community College, 2012-2016. Professor at Lansing Community College, 2016-

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• March 8, 2018

Human beings have been thinking logically (and sometimes illogically) since the earliest era of human existence. However, they have not always been aware of the general principles that distinguish logical from illogical forms of thought. Logic, as an academic subject, is the systematic study of those principles. The logician asks, Which rules should we follow if we want our reasoning to be the best possible?

The rules of logic are guides to correct reasoning just as the rules of arithmetic are guides to correctly adding, subtracting, multiplying, and dividing numbers, the principles of photography are guides to taking good photos, and so on. You can improve your reasoning by studying the principles of logic, just as you can improve your number-crunching abilities by studying the principles of mathematics. Because correct reasoning can be applied to any subject matter whatsoever, the number of potential applications of logical theory is practically unlimited.

The Greek philosopher Aristotle (384–322 BC) wrote the first book on the standards of correct reasoning and later wrote four additional treatises on the subject. Thus, in five highly original (and extremely complex) works, collectively known as the Organon (Greek for “tool,” as in “general tool of thought”), Aristotle launched the study of the principles of correct reasoning and earned the title historians have conferred on him: founder of logic. [i] The noted twentieth-century logician and philosopher Benson Mates writes:

[W]e can say flatly that the history of logic begins with the Greek philosopher Aristotle . . . Although it is almost a platitude among historians that great intellectual advances are never the work of only one person (in founding the science of geometry Euclid made use of the results of Eudoxus and others; in the case of mechanics Newton stood upon the shoulders of Descartes, Galileo, and Kepler; and so on), Aristotle, according to all available evidence, created the science of logic absolutely ex nihilo. [ii]

Logic was first taught as an academic subject in the universities of ancient Athens, Greece during the fourth century BC, making it one of the oldest of all academic subjects. For twenty-five hundred years, it has been considered a core academic requirement at institutions of higher learning around the world. Logic remains part of the core curriculum around the world today because the principles of correct reasoning can help anyone reason more accurately, no matter what subject, making it an all-purpose “tool kit” for your mind.

Major Divisions of Logic

Formal logic studies the abstract patterns or forms of correct reasoning. Here the focus is on form rather than content, that is, on the logical structure of reasoning apart from what it is specifically about. Since ancient times, logicians have used special symbols and formulas, similar to those used in mathematics, to record the abstract logical forms they have discovered. This is why formal logic is sometimes also called “symbolic logic” or “mathematical logic.”

Informal logic studies the non-formal aspects of reasoning—qualities that cannot be accurately translated into abstract symbols. This is why informal logic for the most part dispenses with special symbols and formulas. In this division of logic, the focus is often reasoning expressed within everyday language.

Logical theory begins with the notion of an argument , which is defined as one or more statements, called “premises,” offered as evidence, or reason to believe, that a further statement, called the “conclusion,” is true. In plain terms, an argument is reasoning offered in support of a conclusion. Arguments are part of everyday life. You present one every time you put your reasoning into words to share it with others. In the following example, the premises are marked P1 and P2, and the conclusion is labeled C.

• P1: All songwriters are poets.
• P2: Bob Dylan is a songwriter.
• C: Therefore, Bob Dylan is a poet.

The second building block of logical theory is the distinction, first noted by Aristotle, between deductive and inductive reasoning. A deductive argument aims to establish its conclusion with complete certainty, in such a way that if its premises all are true, then its conclusion must be true. Put another way, the underlying claim in the case of a deductive argument is that it is not even possible the premises all are true and the conclusion is false. For example:

• P1. Tiny Tim played the ukulele.
• P2. Anyone who plays the ukulele is a musician.
• C. Consequently, Tiny Tim was a musician.

Deductive arguments aim for certainty and nothing less. If a deductive argument succeeds in its aim, it is a valid deductive argument. If it does not, it is an invalid deductive argument. A deductive argument is said to be sound if it is (a) valid and (b) all of its premises are true. The following deductive argument is clearly valid although it is not sound.

• P1. All students are millionaires.
• P2. All millionaires drink vodka.
• C. Therefore, necessarily, all students drink vodka.

In contrast, the following argument is invalid (and hence also unsound).

• P1. Ann and Sue are cousins.
• P2. Sue and Rita are cousins.
• C. So, Ann and Rita must be cousins.

The following argument hits the target—it is both valid and sound.

• P1. All whales are mammals.
• P2. All mammals are warm-blooded.
• C. Ergo, all whales are warm-blooded.

Deductive logic is the study of the standards of correct deductive reasoning. Here is an example of a law of deductive logic. Let A, B, and C be variables ranging over terms that stand for categories—words such as cats, dogs, people, trucks, and so forth. Aristotle proved that the following form or pattern of reasoning, named Barbara by logicians in Europe during the Middle Ages, is a valid form, meaning that any argument—about any subject—that exactly follows this pattern is valid.

The Barbara Argument Form

• All B are C.
• All A are B.
• Therefore, necessarily, all A are C.

Let’s test Barbara. If we replace the variable A with sparrows , the variable B with birds , and substitute animals for the variable C, we get the following “substitution instance” of the corresponding form:

• P1. All birds are animals.
• P2. All sparrows are birds.
• C. Therefore, necessarily, all sparrows are animals.

This argument is clearly valid. Aristotle proved that any argument that exactly follows this form of reasoning is valid. For instance:

• P1. All mammals are animals.
• P2. All cats are mammals.
• C. Therefore, necessarily, all cats are animals.

To return to Barbara for a moment, notice that the form is not about any particular subject—it is an abstract pattern with no material content. Barbara is all form and no content. Aristotle discovered that an argument’s validity is always a function of its form rather than its content. You can learn a lot about reasoning by studying valid argument forms. Logicians have catalogued hundreds of them. The study of logical forms is valuable, for if your argument follows a valid form, then it is guaranteed to be valid and therefore your conclusion must be true if your premises are true. As you may have guessed, formal logic and deductive logic overlap in the study of valid patterns of reasoning, of which there are many.

An inductive argument, on the other hand, does not aim to show that its conclusion is certain. Rather it aims to show that its conclusion is probably, though not definitely, true so that if its premises are true, it is likely that its conclusion is true. This argument aims to establish its conclusion with a probability less than one:

• P1. Joe has eaten a Dick’s Deluxe burger for lunch every day for the past month.
• C. So, it is very probable that he will have a Dick’s Deluxe for lunch tomorrow.

If an inductive argument achieves its aim, it is a strong argument . An inductive argument that does not achieve its aim is a weak argument . An inductive argument is said to be cogent if it is (a) strong, and (b) all of its premises are true. The following inductive argument is strong although it is surely not cogent:

• P1. We interviewed one thousand people from all walks of life and every social group all over Seattle over a ten-week period, and 90 percent said they do not drink coffee.
• C. Therefore, probably about 90 percent of Seattleites do not drink coffee.

The following argument is clearly weak:

• P1. We interviewed one thousand people from all walks of life as they exited coffee shops in Seattle, and 98 percent said they drink coffee.
• C. Therefore, probably about 98 percent of Seattleites drink coffee.

The following argument is better—it is strong as well as cogent:

• P1. NASA announced that it found evidence of water on Mars.
• P2. NASA is a scientifically reliable agency.
• C. Therefore it is likely there is or was water on Mars.

Inductive logic is the study of the standards of good inductive reasoning. One inductive standard pertains to analogical arguments —arguments that take the following form:

• A and B have many features in common.
• A has attribute x and B is not known not to have attribute x .
• Therefore, B probably has attribute x as well.

For instance:

• P1. Monkey hearts are very similar to human hearts.
• P2. Drug X cures heart disease in monkeys.
• P3. Drug x is not known to not cure heart disease in humans.
• C.Therefore, drug X will probably cure heart disease in humans.

Analogical arguments can be evaluated rationally. Here are three principles commonly used to judge their strength:

• The more attributes A and B have in common, the stronger the argument, provided the common features are relevant to the conclusion.
• The more differences there are between A and B, the weaker the argument, provided the differences are relevant to the conclusion.
• The more specific or narrowly drawn the conclusion, the weaker the argument. The more general or widely drawn the conclusion, the stronger the argument.

Informal and inductive logic overlap in the study of the many non-formal aspects of inductive reasoning, which include guides to help us improve our assessments of probability.

Information Spillover

The history of ideas is fascinating because often one idea leads to another which leads to a completely unexpected discovery. Economists call this “information spillover” because freely traded ideas tend to give birth to new ideas that give birth to still more ideas that spill from mind to mind as the process cascades into ever widening circles of knowledge and understanding. Aristotle discovered logical principles so exact they could be expressed in symbols like those used in mathematics. Because they could be expressed so precisely, he was able to develop a system of logic similar to geometry. Recall that geometry begins with statements, called “axioms,” asserted as self-evident. With the addition of precise definitions, the geometer uses precise reasoning to derive further statements, called “theorems.” Aristotle’s system began in a similar way, with precise definitions and exact formulas asserted as self-evident. With the base established, he derived a multitude of theorems that branched out in many directions. When he was finished, his system of logical principles was as exact, and proven, as any system of mathematics of the day.

Some observers thought the rules of his system were too mechanical and abstract to be of any practical use. They were mistaken. Aristotle’s system of logic was actually the first step on the path to the digital computer. The first person to design a computing machine was a logician who, after reflecting on the exact and mechanical nature of Aristotle’s system of logical principles, raised one of the most seminal questions ever: Is it possible to design a machine whose gears, by obeying the “laws” of Aristotle’s logic, compute for us the exact, logically correct answer every time?

The logician who first asked the question that connected logic and computing was Raymond Lull (1232–1315), a philosopher, Aristotelian logician, and Catholic priest. Lull has been called the “father of the computer” because he was the first to conceive and design a logical computing machine. Lull’s device consisted of rotating cogwheels inscribed with logical symbols from Aristotle’s system, aligned to move in accord with the rules of logic. In theory, the operator would enter the premises of an argument by setting the dials, and the machine’s gears would then accurately crank out the logically correct conclusion.

Lull’s design may have been primitive, but for the first time in history someone had the idea of a machine that takes inputs, processes them mechanically on the basis of exact rules of logic, and outputs a logically correct answer. We usually associate computing with mathematics, but the first design for a computer was based not on math but on logic—the logic of Aristotle.

Ideas have consequences, and sometimes ideas that seem impractical have consequences that are quite practical. Lull was the first in a long succession of logical tinkerers, each seeking to design a more powerful computing machine. You have a cell phone in your hand right now thanks to the efforts of these innovators, each trained in logical theory. In addition to Lull, the list includes computer pioneers Leonardo da Vinci (1452–1519), Wilhelm Schickard (1592–1635), William Oughtred (1574–1660), Blaise Pascal (1623–1662), Gottfried Leibniz (1646–1716), Charles Babbage (1791–1871), Vannevar Bush (1890–1974), Howard Aiken (1900–1973), and Alan Turing (1912–1954).

Thus, a continuous line of thought can be traced from Aristotle’s logical treatises to the amazing advances in logic and computing theory of the nineteenth and twentieth centuries which led to the completion of the world’s first digital computer (at Iowa State College in 1937) and from there to the much smaller yet more powerful devices of today. It is no coincidence that the circuits inside every digital computer are called “logic gates.” In the logic classroom, this is my answer to those who suppose that abstract logical theory has no practical applications.

Computer science is only one spin-off of logical theory. The subject Aristotle founded remains as vital today as it was in ancient Athens. Aristotle probably had no idea how important his new subject would be—or how long the spillover and information overflow would continue.

What does all of this have to do with anything? In everyday life as well as in every academic subject, reason is our common currency. It follows that the ability to reason well is an essential life skill. But skills require knowledge as well as practice. Since logic is the study of the principles of correct reasoning, a familiarity with elementary logic and its applications can help anyone improve his or her life. Some people suppose logic is a useless subject; the truth may be the reverse—it may be the most useful subject of all.

[i] An editor applied the name Organon (“tool”) to Aristotle’s logical works after his death. The name reflects Aristotle’s claim that logic is an all-purpose tool of thought, a guide to the precise thinking needed to attain solidly proven truth on any subject.

[ii] Benson Mates, Elementary Logic , 2nd ed. (New York: Oxford University Press, 1972), 206. Ex nihilo is Latin for “out of nothing” and means “from scratch” in this context.

For a deeper look at the fundamentals of this subject, check out the free course “ Short Little Lessons in Logic ” published by Philosophy News. This course will teach you the fundamentals of logic in bite-sized lessons that you can learn at your own pace.

About the author

Paul Herrick received his Ph.D in philosophy from the University of Washington. Since 1983 he has taught philosophy at Shoreline Community College, in Shoreline, Washington, near Seattle. He is the author of Reason and Worldview. An Introduction to Western Philosophy , Think with Socrates: An Introduction to Critical Thinking, The Many Worlds of Logic, and Introduction to Logic .

Other articles by Paul Herrick

Books by paul herrick.

This is a comprehensive introduction to the fundamentals of logic (both formal logic and critical reasoning), with exceptionally clear yet conversational explanations and a multitude of engaging examples and exercises. Herrick’s examples are on-point and fun, often bringing in real-life situations and popular culture. And more so than other logic textbooks, Introduction to Logic brings in the history of philosophy and logic through interesting boxes/sidebars and discussions, showing logic’s relation to philosophy.

Brief yet comprehensive, Think with Socrates: An Introduction to Critical Thinking uses the methods, ideas, and life of Socrates as a model for critical thinking. It offers a more philosophical, historical, and accessible introduction than longer textbooks while still addressing all of the key topics in logic and argumentation. Applying critical thinking to the Internet, mass media, advertising, personal experience, expert authority, the evaluation of sources, writing argumentative essays, and forming a worldview, Think with Socrates resonates with today’s students and teaches them how to apply critical thinking in the real world. At the same time, it covers the ancient intellectual roots and history of the field, placing critical thinking in its larger context to help students appreciate its perennial value.

A comprehensive look at major movements in philosophy and how those movements helped shape the way we think and behave.

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9.3: The Argumentative Essay

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Learning Objectives

• Examine types of argumentative essays

Argumentative Essays

You may have heard it said that all writing is an argument of some kind. Even if you’re writing an informative essay, you still have the job of trying to convince your audience that the information is important. However, there are times you’ll be asked to write an essay that is specifically an argumentative piece.

An argumentative essay is one that makes a clear assertion or argument about some topic or issue. When you’re writing an argumentative essay, it’s important to remember that an academic argument is quite different from a regular, emotional argument. Note that sometimes students forget the academic aspect of an argumentative essay and write essays that are much too emotional for an academic audience. It’s important for you to choose a topic you feel passionately about (if you’re allowed to pick your topic), but you have to be sure you aren’t too emotionally attached to a topic. In an academic argument, you’ll have a lot more constraints you have to consider, and you’ll focus much more on logic and reasoning than emotions.

Argumentative essays are quite common in academic writing and are often an important part of writing in all disciplines. You may be asked to take a stand on a social issue in your introduction to writing course, but you could also be asked to take a stand on an issue related to health care in your nursing courses or make a case for solving a local environmental problem in your biology class. And, since argument is such a common essay assignment, it’s important to be aware of some basic elements of a good argumentative essay.

When your professor asks you to write an argumentative essay, you’ll often be given something specific to write about. For example, you may be asked to take a stand on an issue you have been discussing in class. Perhaps, in your education class, you would be asked to write about standardized testing in public schools. Or, in your literature class, you might be asked to argue the effects of protest literature on public policy in the United States.

However, there are times when you’ll be given a choice of topics. You might even be asked to write an argumentative essay on any topic related to your field of study or a topic you feel that is important personally.

Whatever the case, having some knowledge of some basic argumentative techniques or strategies will be helpful as you write. Below are some common types of arguments.

Causal Arguments

• In this type of argument, you argue that something has caused something else. For example, you might explore the causes of the decline of large mammals in the world’s ocean and make a case for your cause.

Evaluation Arguments

• In this type of argument, you make an argumentative evaluation of something as “good” or “bad,” but you need to establish the criteria for “good” or “bad.” For example, you might evaluate a children’s book for your education class, but you would need to establish clear criteria for your evaluation for your audience.

Proposal Arguments

• In this type of argument, you must propose a solution to a problem. First, you must establish a clear problem and then propose a specific solution to that problem. For example, you might argue for a proposal that would increase retention rates at your college.

Narrative Arguments

• In this type of argument, you make your case by telling a story with a clear point related to your argument. For example, you might write a narrative about your experiences with standardized testing in order to make a case for reform.

Rebuttal Arguments

• In a rebuttal argument, you build your case around refuting an idea or ideas that have come before. In other words, your starting point is to challenge the ideas of the past.

Definition Arguments

• In this type of argument, you use a definition as the starting point for making your case. For example, in a definition argument, you might argue that NCAA basketball players should be defined as professional players and, therefore, should be paid.

https://assessments.lumenlearning.co...essments/20277

Essay Examples

• Click here to read an argumentative essay on the consequences of fast fashion . Read it and look at the comments to recognize strategies and techniques the author uses to convey her ideas.
• In this example, you’ll see a sample argumentative paper from a psychology class submitted in APA format. Key parts of the argumentative structure have been noted for you in the sample.

Link to Learning

For more examples of types of argumentative essays, visit the Argumentative Purposes section of the Excelsior OWL .

Contributors and Attributions

• Argumentative Essay. Provided by : Excelsior OWL. Located at : https://owl.excelsior.edu/rhetorical-styles/argumentative-essay/ . License : CC BY: Attribution
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Using Logical Reasoning in Academic Writing

The model we were taught in school for writing an effective essay has some good bones: Create a thesis. Present several claims and argue for those statements. Tie those arguments back to the thesis with supporting evidence to show your reader that what you're saying is true. If any of your arguments fall apart, your entire work will unravel faster than the scarf I made during my first attempt at learning to crochet. If you're creating a work of academic writing, you will need to follow a pattern of clearly defined logic to reinforce and support your argument.

Logic refers to the process of making a conclusion under valid laws of inference. Through this process, a writer makes arguments using statements to explain why these arguments are true. Logical reasoning is the act of settling on a viewpoint and then expressing to others why you selected that opinion over all other available conclusions.

Apply logical reasoning in your academic writing, and you'll be on your way to creating a strong conclusion with supporting evidence. Here are some tips on constructing a perfectly logical argument in your work.

Define your thoughts

Before you even start composing your text, clarify your own thoughts on the subject. You already have a solid idea that you want to illustrate for your readers. It makes perfect sense to you, because you have access to all the good arguments, supporting evidence, and gut feelings you've accumulated during your research at the forefront of your brain. Unfortunately, you can't open your brain and instantly share your certainty of an idea with others. This problem is especially apparent every time you have a misunderstanding with another person. You might feel passionate about an idea, but when you try to communicate your point, your mannerisms might portray petulance and impatience, which can cloud the perception of the other person. Maybe you feel frustrated that your significant other leaves the door open, and you are worried that your dog will run away forever. Your approach to the situation can be clouded by your delivery, which is heavy with the emotion connected to the issue, and your significant other can miss your message entirely if it is framed in a way that makes him/her defensive. If we could see a situation from the complete point of view as our friends and neighbors, the world might be a much more peaceful place!

Of course, sadly, the only way to express your thoughts and feelings is through the use of language and expression. While there is no perfect way to bring others into your world to share your thoughts, you can create the best-case scenario by mapping out your idea and why you feel it is true before you begin writing. Write out your idea and the supporting arguments. How do you know they are true? Seeing your points laid out on paper can help you remove your own perspective in a small way and view them as others might. Do your points represent logical connections between ideas, or are you depending on leaps in logic that will be too wide for your readers to navigate?

Gather irrefutable evidence to support your claim

When using logical reasoning, you draw conclusions whose evidence to support the claim creates a guarantee of a specific result. Look for concrete facts backed by studies and expert inquiries. If you are publishing a paper on your own research, aim to represent your work clearly and thoroughly by outlining the steps you took to create a conclusion. Ask yourself these questions:

• At the beginning of your research, what did you think would happen?
• How did you set out to prove/disprove this assertion?
• What result did you observe, and was it in line with your previous expectations?

As most researchers will attest, the greater the scope of your study, the more irrefutable your evidence will be, and you can be more confident that your conclusions can be considered facts.

Avoid logical fallacies

A logical fallacy is false reasoning that leads your argument to become unreliable or untrue. When your readers encounter a logical fallacy, you lose their trust in your argument. Be aware of these fallacies and take measures to avoid them within your argument.

• The bandwagon fallacy: Under this fallacy, you might claim that an idea is true simply because the majority of the people believe it. The common advertising claim , "4 out of 5 dentists prefer this toothpaste" draws on the bandwagon fallacy with the hope that its audience will believe that this toothpaste brand is the best on the market, whereas it is not necessarily true.
• The correlation/causation fallacy: Just because two elements seem to be connected doesn't mean one directly leads to another. For example, if you changed the font on your company website last month, and then website hits were down during that same month, you might apply the correlation/causation fallacy and state that the font was detrimental to business without any other evidence supporting this claim.
• Ignoratio elenchi (Latin for "ignoring refutation"): If your argument has an opposing side (and most do, of course), you will need to address that opposition with convincing logic. This fallacy arises when you respond to a counterargument without properly addressing the point of the argument. Let's say I am presenting the benefits of building a new bike trail in my city. My opponents assert that the city just doesn't have the budget to fund this project, while I claim that the advantages of a bike trail far outweigh any cost incurred. My claim is that cost is irrelevant to the project. In doing so, I fail to present a solution to the lack of money needed to build the path.
• The straw man fallacy: This fallacy arises when you oversimplify your opposing argument and thus misrepresent it, thereby presenting your argument as the more obvious choice in the matter. In the debate on whether schools should implement school uniforms, an opponent of the school uniform might claim, "Schools that enforce dress codes discourage students' individuality." Such an argument dismisses any benefits of the opposing argument and boils down the claim to a simplified form that might not be fully true.
• The anecdotal evidence fallacy: Under this fallacy, instead of applying logical evidence to your argument, you cite a story of one instance in which something happened, seeming to support a claim. Maybe your aunt tried a certain type of dryer sheet and the next day her dryer went up in flames. Does this mean that type of dryer sheet causes people's clothes dryers to ignite? This fallacy is also related to the correlation/causation fallacy.

Consider the opposition

An effectively formulated argument must acknowledge that the viewpoint presented is not shared by everyone, and some opposing arguments exist with relation to the topic. Imagine you are preparing for a debate; an effective approach include preparing your demonstration based on what you might expect your opponent to argue. For example, let's say I'm asserting that plastic bags should be banned. In addition to collecting data on the detrimental effects of plastic bags on the environment and the species of animals that suffer as a result of their invention, I should also consider who stands to benefit from plastic bags. I should investigate the low cost of producing and offering plastic bags from the perspective of businesses and stores in relation to alternative options and the effects those alternatives would have on my customer base. In order to present an effective argument against plastic bags, I should create strong data regarding the cost of alternatives and reveal statistics to show that their use is not as cost effective as previously considered. By anticipating the opposing view, I can create an argument to refute it.

By applying logical reasoning in your academic writing, you can present a strong argument on your subject. Create a stance that you can support with irrefutable evidence, having already mapped out your personal views in order to organize your desired viewpoint. Also, when you know what types of logical fallacies can exist, you can keep your eyes open for any problems in your logic and thereby avoid them. Following these tips can help you achieve a solid piece of writing that will earn you a good grade in class, convince your mentor that your thesis is bulletproof, or charm the socks off the editors at the journal in which you seek to be published.

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Unit 6: Argumentative Essay Writing

42 Logical Fallacies

Logical fallacies are errors in reasoning based on faulty logic . Good writers want to convince readers to agree with their arguments—their reasons and conclusions. If your arguments are not logical, readers won’t be convinced. Logic can help prove your point and disprove your opponent’s point—and perhaps change a reader’s mind about an issue. If you use faulty logic (logic not based on fact), readers will not believe you or take your position seriously.

Read about five of the most common logical fallacies and how to avoid them below:

• Generalizations
• Loaded words
• Inappropriate authority figures
• Either/or arguments
• Slippery slope

Common Logical Fallacies

Below are five of the most common logical fallacies.

#1 Generalizations

Explanation: Hasty generalizations are just what they sound like—making quick judgments based on inadequate information. This kind of logical fallacy is a common error in argumentative writing.

Example 1: Ren didn’t want to study at a university. Instead, Ren decided to go to a technical school. Ren is now making an excellent salary repairing computers. Luis doesn’t want to study at a university. Therefore, Luis should go to a technical school to become financially successful.

Analysis: While they have something in common (they both want to go to school and earn a high salary), this fact alone does not mean Luis would be successful doing the same thing that their friend Ren did. There may be other specific information which is important as well, such as the fact that Ren has lots of experience with computers or that Luis has different skills.

Example 2: If any kind of gun control laws are enacted, citizens will not be allowed to have any guns at all.

Analysis: While passing new gun control laws may result in new restrictions, it is highly unlikely the consequences would be so extreme; gun control is a complex issue and each law that may be passed would have different outcomes. Words such as “all,” “always,” “never,” “everyone,” “at all” are problematic because they cannot be supported with evidence. Consider making less sweeping and more modest conclusions.

Suggestions for Avoiding Generalizations

Replace “absolute” expressions with more “softening” expressions.

• Replace words like “all” or “everyone” with “most people.” Instead of “no one” use “few people.”
• Replace “always” with “typically” or “usually” or “often.”
• Replace “never” with “rarely” or “infrequently” or the “to be verb” + “unlikely.”
• Replace “will” with “may or might or could” or use the “to be verb” + “likely.”

Example 1 revised: Luis could consider going to a technical school. This education track is more likely to lead to financial success.

Example 2 revised: If extensive gun control laws are enacted, some citizens may feel their constitutional rights are being limited.

#2 Loaded Words

Explanation: Some words contain positive or negative connotations, which may elicit a positive or negative emotional response. Try to avoid them in academic writing when making an argument because your arguments should be based on reason (facts and evidence), not emotions.  In fact, using these types of words may cause your reader to react against you as the writer, rather than being convincing as you hoped.  Therefore they can make your argument actually weaker rather than stronger.

Example 1: It is widely accepted by reasonable people that free-trade has a positive effect on living standards, although some people ignorantly disagree with this.

Analysis: The words “reasonable” (positive) and “ignorantly” (negative) may bias the readers about the two groups without giving any evidence to support this bias.

Example 2: This decision is outrageous and has seriously jeopardized the financial futures for the majority of innocent citizens.

Analysis: The words “outrageous,” “seriously,” and “innocent” appeal to readers’ emotions in order to persuade them more easily. However, the most persuasive arguments in academic writing will be supported with evidence instead of drawing on emotions.

Suggestions for Avoiding Loaded Words

Choose appropriate vocabulary.

• Omit adjectives and adverbs, especially if they carry emotion, value, or judgment.
• Replace/add softeners like, “potentially” or modals like “might” or “may.”

Example 1 revised: It is widely accepted by many people that free-trade may have a positive effect on living standards, although some people may disagree with this.

Example 2 revised: This decision has potentially serious consequences for the financial futures for the majority of citizens.

#3 Inappropriate authority figures

Explanation: Using famous names may or may not help you prove your point. However, be sure to use the name logically and in relation to their own area of authority.

Example 1: Albert Einstein , one of the fathers of atomic energy, was a vegetarian and believed that animals deserved to be treated fairly. In short, animal testing should be banned.

Analysis: While Einstein is widely considered one of the great minds of the 20th century, he was a physicist , not an expert in animal welfare or ethics.

Example 2: Nuclear power is claimed to be safe because there is very little chance for an accident to happen, but little chance does not have the same meaning as safety. Riccio (2013), a news reporter for the Wisconsin State Journal, holds a strong opinion against the use of nuclear energy and constructions of nuclear power plants because he believes that the safety features do not meet the latest standards.

Analysis: In order to provide strong evidence to support the claim regarding the safety features of nuclear power plants, expert opinion is needed ; the profession of a reporter does not provide sufficient expertise to validate the claim.

Suggestions for Avoiding Inappropriate Authority Figures

Replace inappropriate authority figures with credible experts.

• Read through your sources and look for examples of experts. Pay attention to their credentials. (See examples below.)
• Find new sources written by or citing legitimate experts in the field.
• Google the authority figure you wish to use to determine if they are an expert in the field. Use the Library Databases to locate a substantive or scholarly article related to your topic. Cite the author of one of these articles or use an indirect citation to cite an expert mentioned in the article.

Example 1 revised: Kitty Block, president and CEO of the Humane Society of the U.S. , emphasizes the need for researchers to work with international governments and agencies to follow new guidelines to protect animals and minimize their use in animal testing.

Example 2 revised: Edwin Lyman, senior scientist of the Global Security Program, points out that while the U.S. has severe-accident management programs, these plans are not evaluated by the Nuclear Regulatory Commission, and therefore may be subject to accidents or sabotage.

#4 Either/Or Arguments

Explanation: When you argue a point, be careful not to limit the choices to only two or three. This needs to be qualified.

Example 1: Studying abroad either increases job opportunities or causes students to become depressed.

Analysis: This statement implies that only two things may happen, whereas in reality these are two among many possible outcomes.

Example 2: People can continue to spend countless amounts of tax dollars fighting the use of a relatively safe drug, or they can make a change, legalize marijuana, and actually see a tax and revenue benefit for our state. (owl.excels ior.edu)

Analysis: Most issues are very complex and hardly ever either/or, i.e. they rarely have only two opposing ways of looking at them or two possible outcomes. Instead, use language that acknowledges the complexity of the issue.

Suggestions for Avoiding Either/Or Arguments

Offer more than one or two choices, options, or outcomes.

• If relevant for your essay focus, offer more than one or two choices, options, or outcomes.
• Acknowledge that multiple outcomes or perspectives exist.

Example 1 revised: Studying abroad may have a wide spectrum of outcomes , both positive and negative, from increasing job opportunities to leading to financial debt and depression.

Example 2 revised: There are a number of solutions for mitigating the illegal sale of marijuana, including legalizing the use of the drug in a wider range of contexts, increasing education about the drug and its use, and creating legal businesses for the sale, among other business related solutions.

#5 Slippery Slope

Explanation: When you argue that a chain reaction will take place, i.e. say that one problem may lead to a greater problem, which in turn leads to a greater problem, often ending in serious consequences. This way of arguing exaggerates and distorts the effects of the original choice. If the series of events is extremely improbable, your arguments will not be taken seriously.

Example 1: Animal experimentation reduces society’s respect for life. If people don’t respect life, they are likely to be more and more tolerant of violent acts like war and murder. Soon society will become a battlefield in which everyone constantly fears for their lives.

Analysis: This statement implies that allowing animal testing shows a moral problem which can lead to completely different, greater outcomes: war, death, the end of the world!  Clearly an exaggeration.

Example 2: If stricter gun control laws are enacted, the right of citizens to own guns may be greatly restricted, which may limit their ability to defend themselves against terrorist attacks. When that happens, the number of terrorist attacks in this country may increase. Therefore, gun control laws may result in higher probability of widespread terrorism. (owl.excelsior.edu)

Analysis: The issue of gun control is exaggerated to lead into a very different issue. Check your arguments to make sure any chains of consequences are reasonable and still within the scope of your focused topic. (writingcenter.unc.edu)

Suggestions for Avoiding Slippery Slope

Think through the chain of events.

• Carefully think about the chain of events and know when to stop to make sure these events are still within the narrowed focus of your essay.

Example 1 revised: If animal experimentation is not limited, an increasing number of animals will likely continue to be hurt or killed as a result of these experiments.

Example 2 revised: With stricter gun laws, the number of citizens who are able to obtain firearms may be reduced, which could lead to fewer deaths involving guns.

As you read your own work, imagine you are reading the draft for the first time. Look carefully for any instances of faulty logic and then use the tips above to eliminate the logical fallacies in your writing.

Adapted from Great Essays by Folse, Muchmore-Vokoun, & Soloman

For more logical fallacies, watch this video.

from GCFLearnFree.org

Academic Writing I Copyright © by UW-Madison ESL Program is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License , except where otherwise noted.

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77 Logic Essay Topic Ideas & Examples

🏆 best logic topic ideas & essay examples, 📌 simple & easy logic essay titles, 👍 good essay topics on logic.

• Language and Logic: The Similarities and Differences A major function of language is that the symbols are subjective. There are various areas of study that will allow one to get the right interpretation of language and logic.
• Rene Descartes: Education and Rules of Logic I believe it is a considerable drawback of schooling, and it should be fixed in the near future, as young adults need to learn how to apply the knowledge they get.
• The Logic: Model and Evaluation At the initiation stage of the project, the targeted indicators and deliverables of the project are s sufficiently drawn by the project staff according to the basic needs assessments already conducted.
• Propositional and First-Order Logic in Artificial Intelligence Artificial intelligence’s propositional logic analyzes sentences as variables, and in the event of complicated sentences, the first phase is to deconstruct the sentence into its component variables.
• Aristotle’s View on the Concept of Logic Thus, it was shown that logic is not just a specific doctrine of specific things or terms, but the science of the laws of syllogisms, such as modus ponens or modus tollens, expressed in variables. […]
• Is Female Thinking and Logic Truly Different From the Male’s One It is necessary to analyze this question from a scientific point of view and to understand whether the thought processes of different genders are different.
• Mathematical Platonism: Philosophy’s Loss of Logic In 1953, Gottlob Frege posted a strong argument that the language of mathematics tends to refer to and quantify the mathematical objects and the corresponding theories are true. Frege argues that mathematical language is quantifiable, […]
• Logic and Design: Flowcharts and Pseudocode The basic understanding of logic and design is that processes should be presented in a way that demonstrates certain algorithms, i.e.the description of a process should be precise and should contain detailed instructions on what […]
• Feelings and Logic in the Literature Works In his short story, Poe covers the side of the senses and the rigor of the mind. Another metaphor is the combination of the heart and the clock that beat in the head of the […]
• Dangers of Logic and Artificial Intelligence The following are the dangers of logic and artificial intelligence when applied in various areas. The last danger of logic and artificial intelligence relates to autonomous weapons.
• Postmodernism, or, the Cultural Logic of Late Capitalism I agree with the statement because people with different cultures have different ways of doing things and architecture is one of the crucial tools used to express the culture of the people.
• NGO Logic Model: Review The successful implementation of the proposed project depends on the stakeholders’ ability to be involved and focus on the anticipated short-term and long-term goals.
• Logic and Philosophy Relations Aristotle is reputed to be the first man to study the logic concept although there have been other numerous contributions to the concept over the years.
• Importance to Reason and Logic Prior to evaluating the strengths and weaknesses of reason as a way of knowing, we should first discuss such concept as knowledge, because even now philosophers and scholars have not come to the agreement as […]
• Logic Dialectic and Rhetoric: Compare and Contrast In addition, the prominent thinker estimated rhetoric in the context of logic, because logic, as well as rhetoric and dialectic, point out the studying of persuasion methods.
• History of Logic: Brief Review of Inferences or Judgments The history of logic relates to the progress of the science of valid inference. The logic of Aristotle was of importance during the period of the Renaissance too.
• Women, Instagram and Calligraphy: Neoliberal Logic in Production of Aesthetic Objects Such a reality imposes the need for the research of a valuable topic that deals with the role of women in the creation of aesthetic content for online commerce on social media.
• The Use of Logic in the Declaration of Independence: Following Jefferson’s Argument By emphasizing the notions of egalitarianism and the principles of natural law, Jefferson successfully appeals to logic and makes a convincing presentation of the crucial social and legal principles to his opposition.
• Relational Logic in “I-It” and “I-You” Relations While considering the concept of “I-It”, specific attention should be paid to the perception of the self through It unless a person is not involved in relation with another thing or object.
• Logic and Philosophy Questions As a rule, a traditional logical inference has two basic elements, i.e, a premise and a conclusion. Therefore, A.
• Say “Stop” to Childhood Obesity: Logic Model The company is related to the priority population since it aims at reducing the rates of childhood obesity among Hispanic children.
• The Logic of Modern Physics The purpose of this paper is to reflect on the writings of these three scholars and generate three questions that can be discussed in class.
• Radix Sort Algorithm, Its Logic and Applications The sorting process starts from the rightmost digit based on the key or the positions of the numbers being sorted. LSD radix sorts the integers from the least to the most significant digit.
• Work and Family: Institutional Logic The recognition of the practical and theoretical benefits of the institutional approach led to the creation of the notion of institutional logic, which comprises “the socially constructed, historical patterns of material practices, assumptions, values, beliefs, […]
• Yield Management and Service Dominant Logic The reduction in the price of the goods offered means that loyal customer are now able to enjoy the product during different seasons in a year.
• The Logic of Using Quantitative Data As far as the types of quantitative data required to show the results of an intervention are concerned, it can be suggested that the information including the grades that the students receive for their performance, […]
• Programming Logic – File Processing for Game Design In most of cases, the PLD used for a given prototyping, is the same PLD that will be put into use in the final invention of the end equipment, like games.
• Programming Logic and Design – Program Change In the online processing method, processing of data takes place as it is input into the program, that is, unlike in batch processing it does not wait for the data to be organized into a […]
• Strategic Planning and Performance Measurement: Logic Model Short-term outcomes are influenced by two major factors, which are awareness and knowledge base of the affected. Conversely, intermediate-term outcomes are identified after a certain program has changed the practices that are common to clients […]
• Understanding Economics: The Nature and Logic of Capitalism These profits are determined by the prices of the commodities and the cost of production that the producer incurred during the whole process of production and creation of goods and services[3].
• Analyzing the Logic of an Article: Cultural Authenticity and Recovery Maintenance in a Rural First Nation Community The key question of the article is how culture may bolster resilience in substance abuse recovery as well as what constitutes “cultural authenticity” for both indigenous and non-indigenous residents of a remote community.
• Logic in Islam and Number of Islamic Theologians Combination of the diverse philosophical ideologies resulted into Islamic logic, which has made marked contribution in the Islamic philosophy.”Historians of logic have long recognized that the medieval Muslim philosophers and philosophical theologians rendered variously as […]
• Informal Logic-Fallacies Definition Syntactic ambiguity is the second type of ambiguity and is normally identified by the presence of ambiguous grammar usage or the general structure of the statement. Hence, the ambiguity of this sentence is in the […]
• Value Innovation: The strategic Logic of High Growth
• Virtual to Virtuous Money: A Virtue Ethics Perspective on Video Game Business Logic
• The Prevailing Logic Of Global Microbial Diversity
• The Nature Of Logic As It Relates To Critical Thinking
• Understanding the Source and Logic Behind Violent Conflicts
• The Ramist Logic of Edward Taylor’s Upon a Spider Catching a Fly
• The Pure Logic of Accounting: A Critique of the Fair Value Revolution
• The Relevance of Logic in Our Everyday Lives
• Use of Logic in Monty Python and the Holy Grail
• The Undercover Parent: Coben’s Spyware Logic
• Zen Action, Zen Person And Nagarjuna: The Logic Of Emptiness
• The Teachings of Christ: The Logic to Morality
• Use of Programmable Logic Control in Modern Vehicle
• The Strategic Logic of Suicide Terrorism
• Understanding Logic: Inductive or Deductive
• Value, Price and Exploitation: The Logic of the Transformation Problem
• The Threat From Logic And Compassion
• The Symbolism of the Costume of Anita in Dog Logic
• What Is The Fundamental Economic Logic Of Minoli’s Turnaround
• What Love & Logic Means to Effective Parenting
• Verifying Logic Circuits by Benders Decomposition
• To What Extent Can Logic, Math or Music Be Classified as a Language?
• Value Co Creation And Service Dominant Logic
• Using A Logic Table For More Efficient Research
• Theory Ok Knowledge: Emotion’s Role in Logic and Reason
• The Moral Logic and Growth of Suicide Terrorism
• What Did Aristotle Contribute to the Discipline of Logic
• The Role Of Cognitive Development, Logic, And Emotionality
• Understanding the Logic of Learned Education
• What Logic Was Forwarded by Schwcitzguebel in Support of Tourism
• The Sanctions Debate and the Logic of Choice/Diplomacy
• The Theory of Fuzzy Logic and its Application to Real Estate Valuation
• The Notion of Hyperreality in Frederic Jameson’s Cultural Logic of Late Capitalism
• Use Of Logic To Seduce Women In John Donne’s ‘The Flea’ And Andrew Marvell’s ‘To His Coy Mistress’
• The World Religion Dataset, 1945–2010: Logic, Estimates, and Trends
• Understanding The Logic Between Material And Ideological
• Vocab: Logic and Sounds. Deductive Reasoning
• The Reason And Logic Behind The Law
• The Nature of Logic and Perception
• The Nature and Logic of Capitalism by Heilbroner
• The Political-Economic Logic of World Governance
• The New Growth Theory: Its Logic and Trade Policy Implications
• Virtue Essay Ideas
• Urban Planning Research Ideas
• Virtual Reality Topics
• Theology Topics
• Video Game Topics
• Technology Essay Ideas
• Structuralism Essay Topics
• Philosophy of Education Paper Topics
• Chicago (A-D)
• Chicago (N-B)

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IvyPanda . "77 Logic Essay Topic Ideas & Examples." February 28, 2024. https://ivypanda.com/essays/topic/logic-essay-topics/.