Recommended Reading

Cederblom, J. & D.W. Paulsen, (2001) Critical Reasoning, Wadswoth, 5^th ed.

Copi, I. & C. Cohen, (1994), Introduction to Logic, Macmillan, 9th ed.

Fogelin, R.J. & W. Sinnott-Armstrong (2001) Understanding Arguments, Harcourt Brace, 6th ed.

Introduction

Philosophy depends almost totally upon argument: there are no experiments and very few observations that are directly pertinent to any philosopher’s claims about truth, goodness, beauty, consciousness, and so on. Therefore we need to know about arguments: we need to know what sorts of arguments are good ones, how should we test arguments to see whether they are good ones, and what are the most common errors that are committed by people in forming arguments. There used to be a course on Critical Reasoning which covered these topics in depth over a semester, but we can get the bare basics I think in one lecture.

Arguments

Parts of Arguments

The first thing we’ll need to do is to say what we mean by an argument. There are books written about this, but I think it will be enough for us to say that:

An argument is a set of claims put forward as reasons to believe some statement.

The ideal form of an argument is to have the reasons, which we call premisses, given explicitly, followed by the conclusion, which is the statement they are supposed to support, also given explicitly. For example:

if children like ice-cream and Bob is a child, then Bob likes ice-cream

If we want to make the structure of this argument as plain as possible we’ll rewrite it like this:

            P1        Children like ice-cream

            P2        Bob is a child               

            C          Bob likes ice-cream

You’re going to see this a lot in this course, so get used to it.

Kinds of Arguments

When we look at arguments more closely we see that they are not all of the same kind. Philosophers have divided them into two large classes: deductive arguments and inductive arguments. The difference between the two is basically that in a deductive argument the conclusion does not pretend to tell us more about the world than the premisses taken together do, whereas an inductive argument makes claims about the world that do go beyond the information conveyed in the premisses. Before we go any further, here are two examples to illustrate what we’re talking about.

1.             A deductive argument

If children like ice-cream and Bob is a child, then Bob likes ice cream

2.             An inductive argument

All the swans I have seen are black. Therefore all swans are black.

You can see that the conclusion for the deductive argument gives us no more information about the world than the premisses did. It’s just a matter of arranging it so that it emphasises some part of that information. On the other hand the conclusion to the inductive argument tells us about swans never seen. It gives us extra information.

It’s one of the consequences of that informational distinction that a deductive argument, if it is a good one, will remain a good one no matter what extra premisses are supplied, whereas a good inductive argument can be made useless by extra information. For example: we could add the premiss that ‘Bob is a white swan’, or that ‘ice-creams are produced by putting puppies in blenders’ or any ridiculous premiss at all, and it would make no difference to the strength of the deductive argument. On the other hand, if we add the premiss ‘Bob is a white swan’ to the inductive argument we make the conclusion obviously false.

Obviously, our use and critcism of the different kinds of arguments are going to have to be sensitive to these differences; so let’s look at them now.

Deductive Arguments

Validity and Soundness

The first point to make about deductive arguments is that when they are good, they are as good as they can be. In the example that I gave of the boy who likes ice-cream, for example, it is clear that if the premisses are true then the conclusion must be true. We call an argument like this a valid argument.

Now note an important point here: just because an argument is valid doesn’t mean that its conclusion is true. Why not? Because all validity says is that IF the premisses are true then the conclusion is true. But if the premisses are not true, then the fact that the argument is valid doesn’t tell you anything about the conclusion – it may be true or it may be false, we just can’t tell from the argument. Consider the example:

If children like ice-cream and Bob is a child, then Bob likes ice cream

A valid argument, as I say. But suppose it’s actually false that Bob is a child, suppose that Bob is actually a white swan; then the argument tells us nothing. We cannot tell anything about whether Bob does or does not like ice-cream.

What we want for a good deductive argument therefore is for the argument to be valid and for the premisses to be true, because in that case the conclusion is necessarily true. We call an argument like this a sound argument.

Logic

A second point to make about deductive arguments is that they also have different kinds Some valid arguments are valid just because of the form of the statements that occur in them. For example, the argument that:

All men are mortal

Socrates is a man

Socrates is mortal

is valid: and any argument that has the form

            All A are B

            C is an A

            C is a B

is going to be valid whenever the A, B, and C are uniformly replaced by some appropriate phrases or names. It is arguments of this sort that form the subject matter of Logic And we can think of them as the logical arguments. They are a very important type of argument because – if they are done right – they can be shown to be as strong as any argument can be, and there are lots of tools for handling this sort of argument, because they’ve been a main focus of philosophical study for the 2300 years since Aristotle.

Arguments of that sort seem to be quite different from a valid argument such as:

            Socrates is a bachelor

Socrates is unmarried.

Where there doesn’t seem to be any information about the validity of that argument in its form. Replacing the major terms in that argument isn’t guaranteed to preserve its validity. Arguments like this are much harder to handle.

Criticizing Deductive Arguments

When we want to criticize a deductive argument there are just two options. Either we can show that the argument is not, in fact, valid, and therefore the truth of the premisses does not guarantee the truth of the conclusion; or we can show that whether it is valid or not, the premisses aren’t all true, and therefore the conclusion can’t be supported by the reasons given. There’s not much to say in a general way about showing that the premisses aren’t all true – that’s going to require different approaches for every case; but there are a couple of useful ways of approaching the question of showing invalidity that we can introduce here.

A.            Method 1 — The Counterexample Method

To show an argument X is invalid we can simply point to arguments having the same structure as X which are clearly invalid — i.e. find an argument with the same structure which has obviously true premises and an obviously false conclusion. This will show that argument X has an invalid

form and so is invalid. In other words, to show that argument X is invalid — that the conclusion does not follow from the premises — we need only show that argument X is just like arguing according to some argument Y, where Y is clearly invalid.

So, applying this, consider the argument:

       If God created the universe then the theory of evolution is wrong

       The theory of evolution is wrong                                                

       God created the universe

If this is valid then it must be because it has a valid logical structure or form. So, any argument of this form will be valid. But arguing that way is just like arguing:

       If Dominic is a wombat then Dominic is a mammal

       Dominic is a mammal                                                   

       Dominic is a wombat

This latter argument has the same structure and is obviously invalid. Premises are obviously true and conclusion is obviously false! So it follows that that argument does not have valid logical structure and so is invalid.

B.            Method 2 — Invalidating Possible Situations

Another method for showing that an argument is invalid establishes directly that it is not impossible for the premises to true and the conclusion false by showing how it is possible for the premises to be true and the conclusion false.

Consider some argument:

       A                     It can be shown to be                           'A' can be true,

       B              ®    invalid if we can show that        ®        'B' can be true,

       C                                                                                  and 'C' can be false

in the same situation.

The claim that an argument is valid amounts to the claim that any situation which makes the premises true makes the conclusion true, so, pointing to a possible or conceivable situation that makes the premises obviously true yet the conclusion obviously false will clearly show that the argument is invalid.

E.g.      Fallacy of affirming the consequent

                   If my car is out of fuel, it won't start

                   My car won't start                                      

                   My car is out of fuel.

Consider now the following possible situation.

My car will indeed not start without fuel (it is a fuel-driven car) and the electrical system needed to start the car has been taken out for repairs (so it won't start). Yet the car has a full tank of petrol.

The premises are obviously true in this situation and the conclusion is obviously false.

The situation is not impossible (i.e. it is possible).                        

So, it is not impossible for the premises to be true and the conclusion false.

So, the argument is invalid.

E.g.      Fallacy of denying the antecedent

                   If the Committee addresses wilderness value then it must address naturalness.

                   It will not address wilderness value.                                                                   

                   It need not address naturalness.

       Consider now the following possible situation.

Wilderness value involves, amongst other things, naturalness (Federal legislation actually defines 'wilderness value' this way). Moreover, the Committee's terms of reference do not include consideration of wilderness value (so it won't address it). Yet the Committee is explicitly formed to consider naturalness (to feed their findings into those of other Committees, so that a joint finding can be made regarding wilderness values).

       The premises are obviously true in this situation and conclusion obviously false.

       The situation is not impossible (i.e. it is possible).                        

       So, it is not impossible for the premises to be true and the conclusion false.

       So, the argument is invalid.

Fallacies

There are very common errors that are made with deductive arguments. In the examples above I just showed how two of them could be shown to be errors. What makes these particularly important errors is that they look a lot like valid arguments and if you have a long and involved argument in real language it may be hard to recognise what’s going wrong.

The first fallacy was Affirming the Consequent. It had the form:

If P then Q

Q        

P

It is often mistaken for the perfectly acceptable Modus Ponens, which has the form:

If P then Q

P         

Q

And the second fallacy was Denying the Antecedent, with the form:

If P then Q

Not P  

Not Q

Which is often mistaken for a valid Modus Tollens argument, with the form:       

If P then Q

Not Q  

Not P

If you can recognise a fallacious argument by its mere form that’s a very easy way of discounting an argument that you want to disagree with.

Inductive Arguments

That’ll do for deductive arguments; now let’s look at the good arguments which are not deductive – the inductive arguments. In these arguments the reasons given for the conclusion are supposed to make it more likely to be true, but they don’t aspire to the absolute certainty that deductive arguments can achieve. There are quite a few different forms of inductive argument, but I think for philsophical purposes there are just two that are really important: the argument from analogy and the inference to the best explanation.

The Argument from Analogy

Here’s a famous example that we’ll look at again later in the course.

The Argument from Design for the Existence of God

Consider a watch. A watch exhibits (a) complexity of parts; (b) suitability to fulfill a certain function (i.e. telling the time); and (c) its complexity is what enables it to fulfill this function. These three features are extremely unlikely to have come about by accident. No one on seeing a watch would think it the product of chance. Even seeing it for the first time, one would conclude that it is the product of design by some intelligent being.

But many things in nature we observe (e.g. the eye) are similarly complex, fulfill a function (e.g. seeing) and their complexity enables them to fulfill this function.

         So it is reasonable to suppose that they too are made by an intelligent being.

This argument is a paradigmatic argument from analogy, its important parts can be summarized thus:

            P1        A watch has (a), (b), (c).

P2        The world has (a), (b), (c).

P3        Watches require a watch-maker            

            C          The world requires a world-maker

But that’s just one argument: the more general definition of an argument from analogy looks like this:

P1        It is claimed that the Object (an argument, or a natural phenomenon, or an idea, or what you will) has properties P₁, P₂, …, P_n.

P2        The Analogue also has properties P₁, P₂, …, P_n.

P3        The analogue has property P                                                                             

C          Therefore the object has property P.

We can see from this that an argument of this form could be treated as a type of deductively valid argument if we thought there was a hidden premiss that:

[5.  If two objects share properties P₁, P₂, …, P_n, they will also share property P.]

Arguments like this are fallacious if the hidden premiss is not true or if it is not obviously true and yet is not argued for.

Evaluating Arguments from Analogy

Whether an argument from analogy is a good argument or not depends on several things.

1.             Are the premises true?

2.             Is the analogy itself strong. It is weakened if:

a.             the similarities P₁, P₂, …, P_n cited are either irrelevant or unimportant in relation to P

b.             there are relevant disanalogies.

c.             the strength of the conclusion is too strong for the strength of the analogy

         The philosopher David Hume, in his Dialogues Concerning Natural Religion (1779) pointed to the fact that, even supposing the analogy were a strong one, it would only strongly support the very limited, much weaker conclusion that there are Gods (not necessarily one as required by advocates of the argument), that are very powerful (not necessarily all-powerful, all-good, all-knowing).

The Inference to Best Explanation

Here’s an example of the sort of thing that’s meant by this.

You return home to find your door broken and some valuable items missing. This cries out for explanation. Possible explanations include: (1)A meteorite struck your door and vaporised your valuables, (2) friends are playing a joke on you, (3) a police Tactical Response Group entered your house mistakenly, and (4) you were robbed. Explanation 4 seems the best, so you conclude you were robbed.

More generally, inferences to best explanation take the following form:

            P1        Phenomenon A is observed

            P2        Explanation X explains A and does so better than any rival explanation

            C          X is the case

The underlying assumption is that the best explanation of a phenomenon is likely to be true.

Evaluating Inferences to Best Explanation

There are a few obvious things to check when we’re evaluating an inference to best explanation.

1.                   Is there anything to explain?

People often believe things since they are thought necessary to explain some illusory phenomenon. They draw an inference to the best explanation of what they take to be a real phenomenon requiring explanation. In fact, they believe a falsehood inferred from the false claim that some phenomenon obtains (and is best explained by that which they come to believe).     
 

            Example.

I think that Phil always acts strangely in my presence. I take this to be a puzzling phenomenon requiring explanation. In the circumstances I reasonably suppose, say, that the best explanation of this is the idea that Phil dislikes me ... and so I go on to infer that Phil doesn't like me.
In fact, Phil does not always act strangely in my presence. I have a partial and defective recall of social situations we have been in together.

2.                   What do we mean by "best explanation"?

Under what conditions can we be confident in the truth of the second premise and thus be confident that the explanation is probably true?

a.       Firstly, how do we evaluate them for strength?

                                       i.            They should actually explain the event in question as opposed to merely shifting the burden of explanation onto something else itself needing explaining.

                                     ii.            They should be powerful (i.e. widely applicable).

                                    iii.            The simpler the better.

                                   iv.            They should be conservative with respect to prior beliefs.

(Compare creationism and evolutionary theory as rival explanations of the diversity of the biological world.)

b.       Secondly, we want to be as confident as possible that we have to hand all the "rival explanations" there might be ... or at least, all strong rivals.

End

This has just been a really, really brief overview of arguments and how to think about them. We’ll look at these things again as they come up, but it’s as well that you should know about them now to prepare yourself for the sorts of things that you’ll see when you read philosophy texts where arguments are being criticised.