First Philosophy
Introduction to Arguments
The main tool of philosophy is the argument. An argument is any sequence of statements intended to establish—or at least to make plausible—some particular claim. For example, if I say that Vancouver is a better place to live than Toronto because it has a beautiful setting between the mountains and the ocean, is less congested, and has a lower cost of living, then I am making an argument. The claim which is being defended is called the conclusion, and the statements which together are supposed to show that the conclusion is (likely to be) true are called the premises.
Often arguments will be strung together in a sequence, with the conclusions of earlier arguments featuring as premises of the later ones. For example, I might go on to argue that since Vancouver is a better place to live than Toronto, and since one's living conditions are a big part of what determines one's happiness, then the people who live in Vancouver must, in general, be happier than those living in Toronto. Usually, a piece of philosophy is primarily made up of chains of argumentation: good philosophy consists of good arguments; bad philosophy contains bad arguments.
What makes the difference between a good and a bad argument? It's important to notice, first of all, that the difference is not that good arguments have true conclusions and bad arguments have false ones. A perfectly good argument might, unluckily, happen to have a conclusion that is false. For example, you might argue that you know this rope will bear my weight because you know that the rope's rating is greater than my weight, you know that the rope's manufacturer is a reliable one, you have a good understanding of the safety standards which are imposed on rope makers and vendors, and you have carefully inspected this rope for flaws. Nevertheless, it still might be the case that this rope is the one in 50 million that has a hidden defect causing it to snap. If so, that makes me unlucky, but it doesn't suddenly make your argument a bad one—we were still being quite reasonable when we trusted the rope. On the other hand, it is very easy to give appallingly bad arguments for true conclusions:
Every sentence beginning with the letter c is true;
Chickens lay eggs begins with the letter c;
Therefore, chickens lay eggs.
But there is a deeper reason why the evaluation of arguments doesnt begin by assessing the truth of the conclusion. The whole point of making arguments is to establish whether or not some particular claim is true or false. An argument works by starting from some claims which, ideally, everyone is willing to accept as true—the premises—and then showing that something interesting—something new—follows from them: i.e., an argument tells you that if you believe these premises, then you should also believe this conclusion. In general, it would be unfair, therefore, to simply reject the conclusion and suppose that the argument must be a bad one—in fact, it would often be intellectually dishonest. If the argument were a good one, then it would show you that you might be wrong in supposing its conclusion to be false; and to refuse to accept this is not to respond to the argument but simply to ignore it.
It follows that there are exactly two reasonable ways to criticize an argument: the first is to question the truth of the premises; and the second is to question the claim that if the premises are true then the conclusion is true as well—that is, one can critique the strength of the argument. Querying the truth of the premises (i.e., asking whether its really true that Vancouver is less congested or cheaper than Toronto) is fairly straightforward. The thing to bear in mind is that you will usually be working backwards down a chain of argumentation: that is, each premise of a philosopher's main argument will often be supported by sub-arguments, and the controversial premises in these sub-arguments might be defended by further arguments, and so on. Normally it is not enough to merely demand to know whether some particular premise is true: one must look for why the arguer thinks it is true, and then engage with that argument.
Understanding and critiquing the strength of an argument (either your own or someone elses) is somewhat more complex. In fact, this is the main subject of most books and courses in introductory logic. When dealing with the strength of an argument, it is usual to divide arguments into two classes: deductive arguments and inductive arguments. Good deductive arguments are the strongest possible kind of argument: if their premises are true, then their conclusion must necessarily be true. For example, if all bandicoots are rat-like marsupials, and if Billy is a bandicoot, then it cannot possibly be false that Billy is a rat-like marsupial. On the other hand, good inductive arguments establish that, if the premises are true, then the conclusion is highly likely (but not absolutely certain) to be true as well. For example, I may notice that the first bandicoot I see is rat-like, and the second one is, and the third, and so on; eventually, I might reasonably conclude that all bandicoots are rat-like. This is a good argument for a probable conclusion, but nevertheless the conclusion can never be shown to be necessarily true. Perhaps a non-rat-like bandicoot once existed before I was born, or perhaps there is one living now in an obscure corner of New Guinea, or perhaps no bandicoot so far has ever been non-rat-like but at some point, in the future, a mutant bandicoot will be born that in no way resembles a rat, and so on.
The strength of deductive arguments is an on/off affair, rather than a matter of degree. Either these arguments are such that if the premises are true then the conclusion necessarily must be, or they are not. Strong deductive arguments are called valid; otherwise, they are called invalid.
The main thing to notice about validity is that its definition is an if / then statement: if the premises were true, then the conclusion would be. For example, an argument can be valid even if its premises and its conclusion are not true: all that matters is that if the premises had been true, the conclusion necessarily would have been as well. This is an example of a valid argument:
1. Either bees are rodents or they are birds.
2. Bees are not birds.
3. Therefore bees are rodents.
If the first premise were true, then (since the second premise is already true), the conclusion would have to be true—that' s what makes this argument valid. This example makes it clear that validity, though a highly desirable property in an argument, is not enough all by itself to make a good argument: good deductive arguments are both valid and have true premises. When arguments are good in this way they are called sound: sound arguments have the attractive feature that they necessarily have true conclusions. To show that an argument is unsound, it is enough to show that it is either invalid or has a false premise.
It bears emphasizing that even arguments which have true premises and a true conclusion can be unsound. For example:
1. Only US citizens can become the President of America.
2. George W. Bush is a US citizen.
3. Therefore, George W. Bush was elected President of America.
This argument is not valid, and therefore it should not convince anyone who does not already believe the conclusion to start believing it. It is not valid because the conclusion could have been false even though the premises were true: Bush could have lost to Gore in 2000, for example. The question to ask, in thinking about the validity of arguments is this: Is there a coherent possible world, which I can even imagine, in which the premises are true and the conclusion false? If there is, then the argument is invalid.
When assessing the deductive arguments that you encounter in philosophical work, it is often useful to try to lay out, as clearly as possible, their structure. A standard and fairly simple way to do this is simply to pull out the logical connecting phrases and to replace, with letters, the sentences they connect. Five of the most common and important 'logical operators' are and, or, it is not the case that, if... then, and if and only if....
The structure of a deductive argument could be laid bare as follows:
1. If (O and G) then not-E.
2. E.
3. Therefore not-(O and G).
4. Therefore either not-O or not-G.
Revealing the structure in this way can make it easier to see whether or not the argument is valid. And in this case, it is valid. In fact, no matter what O, G, and E stand for—no matter how we fill in the blanks—any argument of this form must be valid. You could try it yourself: invent random sentences to fill in for O, G, and E, and no matter how hard you try, you will never produce an argument with all true premises and a false conclusion.
What this shows is that validity is often a property of the form or structure of an argument. (This is why deductive logic is known as formal logic. It is not formal in the sense that it is stiff and ceremonious, but because it has to do with argument forms.)
Using this kind of shorthand, therefore, it is possible to describe certain general argument forms which are invariably valid and which—since they are often used in philosophical writing—it can be handy to look out for. For example, a very common and valuable form of argument looks like this: if P then Q; P; therefore Q. This form is often called modus ponens. Another—which appears in the previous argument about God and evil—is modus tollens: if P then Q; not-Q; therefore not-P. A disjunctive syllogism works as follows: either P or Q; not-P; therefore Q. A hypothetical syllogism has the structure: if P then Q; if Q then R; therefore if P then R. Finally, a slightly more complicated but still common argument structure is sometimes called a constructive dilemma: either P or Q; if P then R; if Q then R; therefore R.
I noted above that the validity of deductive arguments is a yes/no affair—that a deductive argument is either extremely strong or it is hopelessly weak. This is not true for inductive arguments. The strength of an inductive argument—the amount of support the premises give to the conclusion—is a matter of degree, and there is no clear dividing line between the 'strong' inductive arguments and the 'weak' ones. Nevertheless, some inductive arguments are obviously much stronger than others, and it is useful to think a little bit about what factors make a difference.
There are lots of different types and structures of inductive arguments; here I will briefly describe four which are fairly representative and commonly encountered in philosophy. The first is inductive generalization. This type of argument is the prototype inductive argument—indeed, it is often what people mean when they use the term induction—and it has the following form:
1. x per cent of observed Fs are G.
2. Therefore x per cent of all Fs are G.
That is, inductive generalizations work by inferring a claim about an entire population of objects from data about a sample of those objects.
For Example:
(a) Every swan I have ever seen is white, so all swans (in the past and future, and on every part of the planet) are white.
(b) Every swan I have ever seen is white, so probably all the swans around here are white.
(c) 800 of the 1,000 rocks we have taken from the Moon contain silicon, so probably around 80% of the Moon's surface contains silicon.
(d) We have tested two very pure samples of copper in the lab and found that each sample has a boiling point of 2,567°C; we conclude that 2,567°C is the boiling point for copper.
(e) Every intricate system I have seen created (such as houses and watches) has been the product of intelligent design, so therefore all intricate systems (including, for example, frogs and volcanoes) must be the product of intelligent design.
The two main considerations when assessing the strength of inductive generalizations are the following. First, ask how representative is the sample? How likely is it that whatever is true of the sample will also be true of the population as a whole?
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A second type of inductive argument is an argument from analogy. It most commonly has the following form:
1. Object (or objects) A and object (or objects) B are alike in having features F, G, H,
2. B has feature X.
3. Therefore A has feature X as well.
Put together the following arguments from analogy.
The strength of an argument from analogy depends mostly on two things: first, the degree of positive relevance that the noted similarities (F, G, H) have to the target property X; and second, the absence of relevant dissimilarities—properties which A has but B does not, which make it less likely that A is X.
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A third form of inductive argument is often called inference to the best explanation or sometimes abduction. This kind of argument works in the following way. Suppose we have a certain quantity of data to explain (such as the behavior of light in various media, or facts about the complexity of biological organisms, or a set of ethical claims). Suppose also that we have a number of theories which account for this data in different ways (e.g., the theory that light is a particle, or the theory that light is a wave, or the theory that it is somehow both). One way of arguing for the truth of one of these theories, over the others, is to show that one theory provides a much better explanation of the data than the others. What counts as making a theory a better explanation can be a bit tricky, but some basic criteria would be:
1. The theory predicts all the data we know to be true.
2. The theory explains all this data in the most economical and theoretically satisfying way (scientists and mathematicians often call this the most beautiful theory).
3. The theory predicts some new phenomena which turn out to exist and which would be a big surprise if one of the competing theories were true. (For example, one of the clinchers for Einstein's theory of relativity was the observation that starlight is bent by the suns gravity. This would have been a big surprise under the older Newtonian theory, but was predicted by Einstein's theory.)
Here are some examples of inferences to the best explanation:
(a) When I inter-breed my pea plants, I observe certain patterns in the properties of the plants produced (e.g., in the proportion of tall plants, or of plants which produce wrinkled peas). If the properties of pea plants were generated randomly, these patterns would be highly surprising. However, if plants pass on packets of information (genes) to their offspring, the patterns I have observed would be neatly explained. Therefore, genes exist.
(b) The biological world is a highly complex and inter-dependent system. It is highly unlikely that such a system would have come about (and would continue to hang together) from the purely random motions of particles. It would be much less surprising if it were the result of conscious design from a super-intelligent creator. Therefore, the biological world was deliberately created (and therefore, God exists).
(c) The biological world is a highly complex and inter-dependent system. It is highly unlikely that such a system would have come about (and would continue to hang together) from the purely random motions of particles. It would be much less surprising if it were the result of an evolutionary process of natural selection which mechanically preserves order and eliminates randomness, and which (if it existed) would produce a world much like the one we see around us. Therefore, the theory of evolution is true.
The final type of inductive argument that I want to mention here is usually called reductio ad absurdum, which means reduction to absurdity.
It is always a negative argument, and has this structure:
1. Suppose (for the sake of argument) that position p were true.
2. If p were true then something else, q, would also have to be true.
3. However q is absurd—it can't possibly be true.
4. Therefore p can't be true either.
In fact, this argument style can be either inductive or deductive, depending on how rigorous the premises 2 and 3 are. If p logically implies q, and if q is a logical contradiction, then it is deductively certain that p can't be true (at least, assuming the classical laws of logic).
On the other hand, if q is merely absurd but not literally impossible, then the argument is inductive: it makes it highly likely that p is false, but does not prove it beyond all doubt.
(a) Suppose that gun control were a good idea. That would mean it's a good idea for the government to gather information on anything we own which, in the wrong hands could be a lethal weapon, such as kitchen knives and baseball bats. But that would be ridiculous. This shows gun control cannot be a good idea.
(b) If you think that foetuses have a right to life because they have hearts and fingers and toes, then you must believe that anything with a heart, fingers, and toes has a right to life. But that would be absurd. Therefore, a claim like this about foetuses cannot be a good argument against abortion.
(c) Suppose, for the sake of argument, that this is not the best possible world. But that would mean God had either deliberately chosen to create a sub-standard world or had failed to notice that this was not the best of all possible worlds, and either of these options is absurd. Therefore, it must be true that this is the best of all possible worlds.
(d) The anti-vitalist says that there is no such thing as vital spirit. But this claim is self-refuting. The speaker can be taken seriously only if his claim cannot. For if the claim is true, then the speaker does not have vital spirit and must be dead. But if he is dead, then his statement is a meaningless string of noises, devoid of reason and truth. (If you want more information, see Paul Churchland's "Eliminative Materialism and the Propositional Attitudes," Journal of Philosophy 78 [1981].)
The critical questions to ask about reductio arguments are simply: Does the supposedly absurd consequence follow from the position being attacked? and Is it really absurd?
1. Suppose some deductive argument has a premise which is necessarily false. Is it a valid argument?
2. Suppose some deductive argument has a conclusion which is necessarily true. Is it a valid argument? From this information alone, can you tell whether it is sound?
3. Is the following argument form valid: if P then Q; Q; therefore P? How about: if P then Q; not-P; so not-Q?
4. No inductive argument is strong enough to prove that its conclusion is true: the best it can do is to show that the conclusion is highly probable. Does this make inductive arguments bad or less useful? Why don't we restrict ourselves to using only deductive arguments?
5. Formal logic provides mechanical and reliable methods for assessing the validity of deductive arguments. Do you think there might be some similar system for evaluating the strength of inductive arguments?
6. I have listed four important fallacies; can you identify any other common patterns of poor reasoning?