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Basic Tools for Argument

1. 1.1 Arguments, premises, and conclusions
2. 1.2 Deduction
3. 1.3 Induction
4. 1.4 Validity and soundness
5. 1.5 Invalidity
6. 1.6 Consistency
7. 1.7 Fallacies
8. 1.8 Refutation
9. 1.9 Axioms
10. 1.10 Definitions
11. 1.11 Certainty and probability
12. 1.12 Tautologies, self-contradictions, and the law of non-contradiction

1.1 Arguments, premises, and conclusions

Philosophy is for nit-pickers. That's not to say it is a trivial pursuit. Far from it. Philosophy addresses some of the most important questions human beings ask themselves. The reason philosophers are nit-pickers is that they are commonly concerned with the ways in which the claims and beliefs people hold about the world either are or are not rationally supported, usually by rational argument. Because their concern is serious, it is important for philosophers to demand attention to detail. People reason in a variety of ways using a number of techniques, some legitimate and some not. Often one can discern the difference between good and bad reasoning only if one scrutinises the content and structure of arguments with supreme and uncompromising diligence.

Argument and inference

What, then, is an 'argument' proper? For many people, an argument is a contest or conflict between two or more people who disagree about something. An argument in this sense might involve shouting, name-calling, and even a bit of shoving. It might also - but need not - include reasoning.

Philosophers, in contrast, use the term 'argument' in a very precise and narrow sense. For them, an argument is the most basic complete unit of reasoning - an atom of reasoning. An 'argument' understood this way is an inference from one or more starting points (truth claims called a 'premise' or 'premises') to an end point (a truth claim called a 'conclusion'). All arguments require an inferential movement of this sort. For this reason, arguments are called discursive.

Argument vs explanation

'Arguments' are to be distinguished from 'explanations'. A general rule to keep in mind is that arguments attempt to demonstrate that something is true, while explanations attempt to show how something is true. For example, consider encountering an apparently dead woman. An explanation of the woman's death would undertake to show how it happened. ('The existence of water in her lungs explains the death of this woman.') An argument would undertake to demonstrate that the person is in fact dead ('Since her heart has stopped beating and there are no other vital signs, we can conclude that she is in fact dead.') or that one explanation is better than another ('The absence of bleeding from the laceration on her head combined with water in the lungs indicates that this woman died from drowning and not from bleeding.')

The place of reason in philosophy

It's not universally realised that reasoning comprises a great deal of what philosophy is about. Many people have the idea that philosophy is essentially about ideas or theories about the nature of the world and our place in it that amount just to opinions. Philosophers do indeed advance such ideas and theories, but in most cases their power, their scope, and the characteristics that distinguish them from mere opinion stem from their having been derived through rational argument from acceptable premises. Of course, many other regions of human life also commonly involve reasoning, and it may sometimes be impossible to draw clean lines demarcating philosophy from them. (In fact, whether or not it is possible to demarcate philosophy from non-philosophy is itself a matter of heated philosophical debate!)

The natural and social sciences are, for example, fields of rational inquiry that often bump up against the borders of philosophy (especially in inquiries into the mind and brain, theoretical physics, and anthropology). But theories composing these sciences are generally determined through certain formal procedures of experimentation and reflection to which philosophy has little to add. Religious thinking sometimes also enlists rationality and shares an often-disputed border with philosophy. But while religious thought is intrinsically related to the divine, sacred, or transcendent - perhaps through some kind of revelation, article of faith, or ritualistic practice - philosophy, by contrast, in general is not.

Of course, the work of certain prominent figures in the Western philosophical tradition presents decidedly non-rational and even anti-rational dimensions (for example, that of Heraclitus, Kierkegaard, Nietzsche, Heidegger, and Derrida). We will examine the non-argumentative philosophical methods of these authors in what follows of this book. Furthermore, many include the work of Asian (Confucian, Taoist, Shinto), African, Aboriginal, and Native American thinkers under the rubric of philosophy, even though they seem to make little use of argument and have generally not identified their work as philosophical.

But, perhaps despite the intentions of its authors, even the work of non-standard thinkers involves rationally justified claims and subtle forms of argumentation too often missed. And in many cases, reasoning remains on the scene at least as a force with which thinkers must reckon.

Philosophy, then, is not the only field of thought for which rationality is important. And not all that goes by the name of philosophy is argumentative. But it is certainly safe to say that one cannot even begin to master the expanse of philosophical thought without learning how to use the tools of reason. There is, therefore, no better place to begin stocking our philosophical toolkit than with rationality's most basic components, the subatomic particles of reasoning - 'premises' and 'conclusions'.

Premises and conclusions

For most of us, the idea of a 'conclusion' is as straightforward as a philosophical concept gets. A conclusion is just that with which an argument concludes, the product and result of an inference or a chain of inferences, that which the reasoning claims to justify and support. What about 'premises', though? Premises are defined in relation to the conclusion. They are, of course, what do the justifying. There is, however, a distinctive and a bit less obvious property that all premises and conclusions must possess.

In order for a sentence to serve either as a premise or as a conclusion, it must exhibit this essential property: it must make a claim that is either true or false. A sentence that does that is in logical terms called a statement or proposition.

Sentences do many things in our languages, and not all of them possess that property and thence not all of them are statements. Sentences that issue commands, for example ('Forward march, soldier!'), or ask questions ('Is this the road to Edinburgh?'), or register exclamations ('Wow!'), are neither true nor false. Hence, it's not possible for sentences of those kinds to serve as premises or as conclusions.

This much is pretty easy, but things can get sticky in a number of ways. One of the most vexing issues concerning arguments is the problem of implicit claims. That is, in many arguments, key premises or even the conclusion remain unstated, implied or masked inside other sentences. Take, for example, the following argument: 'Socrates is a man, so Socrates is mortal.' What's left implicit is the claim that 'all men are mortal'. Arguments with unstated premises like this are often called enthymemes or enthymemetic.

It's also the case that sometimes arguments nest inside one another so that in the course of advancing one, main conclusion several ancillary conclusions are proven along the way. Untangling arguments nested in others can get complicated, especially as those nests can pile on top of one another and interconnect. It often takes a patient, analytical mind to sort it all out (just the sort of mind you'll encounter among philosophers).

In working out precisely what the premises are in a given argument, then, ask yourself first what the principal claim is that the argument is trying to demonstrate. Then ask yourself what other claims the argument relies upon (implicitly or explicitly) in order to advance that demonstration. Sometimes certain words and phrases will explicitly indicate premises and conclusions. Phrases like 'therefore', 'in conclusion', 'it follows that', 'we must conclude that', and 'from this we can see that' often indicate conclusions. ('The DNA, the fingerprints, and the eyewitness accounts all point to Smithers. It follows that she must be the killer.') Words like 'because' and 'since', and phrases like 'for this reason' and 'on the basis of this', on the other hand, often indicate premises. (For example,...