Why Study Logic?
7
Why Study Logic?
Vladimir Godnik/Photolibrary
Logic is the beginning of wisdom, not the end.
—Leonard Nimoy
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CHAPTER 7Section 7.1 Logic as the Study of Reasoning
As we have seen, logic investigates various kinds of arguments, both deductive and inductive, and offers ways of evaluating those arguments. We have seen good (valid) deductive arguments, as well as strong inductive arguments. We have also seen bad argu- ments, many of which commit fallacies by drawing inferences that are not well supported. Being aware of how to construct good arguments and how to detect (and avoid) bad argu- ments has several advantages in situations where we encounter arguments.
What Have We Discovered?
• We saw that arguments are constructed from sentences. • We examined how sentences can be used as premises and conclusions. • We identified a number of commonly made fallacies, both informal and formal. • We applied logical techniques to explore arguments from everyday life, ethics, science, and philosophy. • We introduced some elementary symbolism to make clearer the logical structure of deductive
arguments.
7.1 Logic as the Study of Reasoning
We encounter arguments with some frequency. I may argue with my spouse about who should do the dishes. A child may argue with her parents about how late she can stay up. A couple on a date may argue about what movie they wish to see. A boss may argue with her employee about working overtime. Two politicians may argue about how to generate revenue without raising taxes. In all of these arguments, one person is trying to persuade another of something; we can call that thing a claim, or a conclusion. And in all of these arguments, those conclusions are based on reasons, or premises. If the premises are seen to be true, they support the conclusion. Sometimes that support comes in the form of a valid deductive argument, where, if the premises are accepted as true, the conclusion must be accepted as true. Other times, the conclusion is supported on the basis of an inductive argument, where, if the premises are accepted as true, the conclusion is seen to be more likely or more probable.
Logicians often deal with the kinds of arguments listed in the previous paragraph, using the term argument in the sense of a dispute or conflict, often involving the emotions and sometimes generating anger and even violence. But logicians also broaden the notion of argument to include any sequence of sentences that looks like this:
Reason (or reasons)
therefore
Conclusion
As we have seen, any conclusion that is claimed to follow on the basis of one or more reasons is an argument. And logicians focus on how to construct good arguments—valid deductive arguments and strong inductive arguments—and how to avoid bad arguments.
Logicians regard almost any statement put forth on the basis of reasons to be the source of an argument. These arguments can be rather trivial, but they can also involve some of the most important topics we ever deal with: how we are treated, how we treat others, what happens to us after our physical death, and many other significant issues. While it is often said that one can’t do anything about death or taxes, logicians insist that we can at least
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CHAPTER 7Section 7.1 Logic as the Study of Reasoning
discuss them and try to make our reasoning about such fundamental questions as clear as possible.
Indeed, if one were to ask, “Why study logic?” perhaps the best response is to ask what would be the alternative. Would you rather be able to articulate those things that you believe, or not be able to? Would it be advantageous to offer good, solid reasons to support those things you believe, or be unable or unwilling to do so? Should you simply believe what someone else tells you, or is it useful to consider whether that person is cred- ible, or reliable? And even if that person gener- ally offers good information, can you still benefit from taking the time to consider whether or not the specific reasons offered support, or fail to sup- port, the specific conclusion being put forth? Who is more persuasive: a person who is unwilling or unable to support his or her beliefs, or the person who can provide convinc- ing support and a powerful defense of his or her beliefs? Logic examines these reasons, and the support they offer for various conclusions, in order to make it less likely that we are persuaded of something we should not be and in order to provide the best reasons and the best arguments for our own views. Whether one is discussing science and mathemat- ics, or morality and ethics, or religion and death, it is an enormous advantage to be able to identify the specific questions involved, make precise the language we use in investigat- ing them, and provide the best defense we can in support of our own views and beliefs.
Being able to construct good arguments and to identify and avoid bad arguments— whether our own or those of others—will probably not turn us into the sort of “logical machine” that Mr. Spock of Star Trek represents. Rather, being able to articulate our beliefs, support them with good reasons, and defend them with good arguments is just an abil- ity that provides, as we have seen, rather obvious advantages. It doesn’t mean that we eliminate our feelings, emotions, and passion from our discussions with others; it does mean that those discussions do not have to rest solely on feelings, emotions, and passions. After all, we don’t want to claim that the person who shouts the loudest or makes the most potent threats has—for that reason—the best argument. To avoid that, we turn to logic, adding a degree of calm, rational debate to situations that often benefit from its introduc- tion. You can probably remember a number of situations where introducing logic into an argument might have been helpful.
One other fundamental aspect of logic is its role in criticism. Often the term criticism has a negative tone, as when one criticizes something in order to reject it. Again, just as with the term argument, logicians and philosophers do not see criticism as necessarily negative; criticism can also be indispensable for making something better. A mother may criticize her son’s behavior, not to be negative, but in the hope that her son’s behavior will improve. Artists often want constructive, informed criticism; it can make their art better. Similarly, if we try to convince someone of something on the basis of a bad argument, it really is to our benefit to have it pointed out that we are, in fact, using a bad argument. This doesn’t mean that we abandon the claim for which we are arguing; it means we need a better argument. We want our arguments to be the best that we can make them, if only because that makes them considerably more difficult to challenge and defeat.
GoGo Images/Photolibrary
Wouldn’t you like to know if a speaker is making a salient point? If you were speaking, wouldn’t you like to have the tools to convince your audience?
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CHAPTER 7Further Reading
In the same way, logic helps us be more aware of arguments when someone else is trying to convince us of something. A politician may run an advertisement that says things about his or her own record, or an opponent’s record, that seem persuasive and may make us think we should vote for that candidate. But logic reminds us to take a little time to examine the information and the arguments. Are the facts correctly stated and fairly interpreted? Do they offer reasons to support this candidate, or are there some tricks involved? Taking this time to consider the arguments can be of great benefit in making the correct decision and reaching a justified conclusion. Often, we don’t actually need to do this, nor do we have the time; after all, we don’t sit down and carefully scrutinize our reasons for going to the mall instead of staying home and watching TV. But it is good to know that we have the capabil- ity, particularly when the decisions are very significant. Logic helps develop our abilities in this area, and while our logical skills—like most skills—can continue to be strengthened, sharpened, and improved, it is clear that, given the alternative, logic offers enormous ben- efits in understanding our own reasoning and the reasoning we engage in with others.
Some Final Questions
• If someone asks you why you took a logic class, what reasons (beyond, for instance, it being a requirement) might you offer? Why is logic the kind of thing from which more people would benefit?
• For what kinds of beliefs might one not be willing to give an argument? What does logic have to say about how we support such beliefs? How can we respond to someone who views such beliefs as wrong?
• If logic is part of what some call “intellectual self-defense,” what does it offer in helping us articulate our beliefs? How can logic make our conversations—and arguments—with others more productive?
Further Reading Here are some suggested readings in logic, arranged by the topics they cover. Within each subsection, texts are listed in order of increasing difficulty.
Logic Puzzles; Paradoxes
Carroll, L. “What the Tortoise Said to Achilles” [in many collections]
Gardner, M. Entertaining Mathematical Puzzles
New Mathematical Diversions: More Puzzles, Problems, Games, and Other Mathematical Diversions
Smullyan, R. What Is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles
Sainsbury, R. M. Paradoxes
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CHAPTER 7Further Reading
Symbolic Logic
Quine, W. V. Methods of Logic
Crossley, J. N. (et al.) What Is Mathematical Logic?
Mates, B. Elementary Logic
Hunter, G. Metalogic: An Introduction to the Metatheory of Standard First Order Logic
Enderton, H. A Mathematical Introduction to Logic
Mendelson, E. Introduction to Mathematical Logic
Philosophy of Logic
Haack, S. Philosophy of Logics
Strawson, P. F. Introduction to Logical Theory
Engel, P. The Norm of Truth
The Foundation of Mathematics
Russell, B. Introduction to Mathematical Philosophy
Kitcher, P. The Nature of Mathematical Knowledge
Körner, S. The Philosophy of Mathematics
Benacerraf, P. & Putnam, H. Philosophy of Mathematics: Selected Readings
Wittgenstein, L. Remarks on the Foundations of Mathematics
van Heijenoort, J. From Frege to Gödel
Krivine, J. L. Introduction to Axiomatic Set Theory
Inductive Logic; Philosophy of Science; Miscellaneous
Poundstone, W. Labyrinths of Reason
Skyrms, B. Choice and Chance
Carnap, R. An Introduction to the Philosophy of Science
Cherniak, C. Minimal Rationality
Goodman, N. Fact, Fiction and Forecast
Jeffrey, R. The Logic of Decision
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