The Similarity of Fallacies Fallacy

I hesitated about putting this in my blog, because it concerns material dealt with in my Philosophy Notes, but I decided to say something here because logic is so widely understood, even by people who are conscious of its importance and try to get it right; they frequently err by oversimplifying and a common oversimplification is to assume that errors in arguments are usually easily spotted.

If parts of this blog seem obscure, please refer to Chapter 2 (Logic) and Chapter 6 (Science) of my notes available on the Philosophy page of my web site.

Most people have at least a vague awareness of logic, but even among most of the well educated ideas are hazy, garnered mainly from little book abut clear thinking, and lectures on ‘Communication Studies’

Among the complicated tangle of aptitudes and skills that we call ‘intelligence’, two are particularly conspicuous. Ability to spot patterns and similarities, which I‘ll call ‘animal cunning‘, and ability to address a complicated problem by treating it as composed of interrelated parts and to explain the problem by tracing the relations and interactions of those pats. I call that ‘analysis’. Both are vital to our reasoning, but it is analysis that is dominant in Logic.

Unfortunately the popular introductions lean too heavily towards animal cunning, and to that bias I attribute
a widespread misconception, namely that fallacious arguments usually come in one or another of a few clearly defined types that are fairly easily spotted. The popular introductions support that misconception by concentrating on fallacious arguments that are what I call ‘near misses’, coming near to fitting some valid form, but not quite making it. Example: ‘The bank was brought down by short sellers; Fiona is a short seller; so she brought down the bank’

In fact it is unusual for fallacy to be so easily spotted, because there are few patterns that guarantee fallacy, and one of those is just the strategy I’m discussing, of arguing:

Argument A follows the same pattern as argument B; argument B is fallacious, therefore so is argument A.

To argue thus may wrongly condemn arguments that are in fact valid.

The fallacy of the intrusive ‘but'.

Quite a few fallacious arguments follow a pattern of using ‘but’, where all that is justified is ‘and’ . Frequently people do this to confer apparent validity on arguments of the form.

‘Some A are not B’ therefore reject ‘Most A are B’

For example:
X: ‘Most members of chess clubs wear glasses’

Y: ‘But Simon, Hilda and Montmorency all belong to chess clubs and none of them wear glasses’

That exchange may appear to resemble this one:

W: ‘Most native speakers of the Qulmyoi language of Eastern Rumblethump are pipe smokers’

Z: But Simon, Hilda and Montmorency are all native speakers of the Qulmyoi language of Eastern Rumblethump and none of them are pipe smokers’

However, it so happens that there are only five native speakers of that language so Simon, Hilda and Montmorency together form a majority, and their not smoking pipes does indeed refute the claim that most native speakers do.

There is a longer example taken from life in Chapter 2 of my Philosophy Notes.

Start from Validity
An understanding of logic has to start with validity, not fallacy. A valid argument in one that fits some pattern that guarantees validity. An argument is fallacious if it fits no such pattern.

However, a particular argument may fit many patterns (consider for example, someone arguing ‘I'm hungry, so it must be dinner time‘), so although we can establish validity by finding just one pattern that is valid, we can establish invalidity only be showing that no pattern matching the argument is valid.

It is therefore often easier to substantiate a valid argument than to refute one that is invalid. The contrary assumption, that error is easily spotted, is linked to another, the belief that the truth is manifest and clear to see, so that any who fails to see it is at least negligent, and at worst wicked.

The best way to show that a putatively analytic argument is invalid is to concentrate on that particular argument, and describe circumstances in which it’s premises could be true and its conclusion false.

Popular consideration of logic concentrates on deductive arguments, in which it is impossible for the premisses to be true and the conclusion false. Let’s call such arguments proofs. In practice proofs are very rare outside Mathematics and its applications in Science, and it is only in Mathematics that proofs are used to establish the truth of propositions. In Science proofs are used to deduce testable consequences from theories, but not to establish the truth of theories themselves.

Most arguments are not proofs and cite observations to justify more or less tentative conclusions about matters of fact. For instance, we notice that the bin men usually arrive between 9 and 10 on Tuesday mornings, and so expect they’ll continue to appear around that time. Of such arguments the popular logic books have little to say except that we should avoid generalising from samples that are too small, or unrepresentative, without tackling the very difficult matter of deciding what is too small or unrepresentative.

When chemists determine the melting point of a sample, they consider two readings adequate, but two instances of chess players who dislike chocolate would not be considered to establish ’no chess players like chocolate’.

When assessing the adequacy of evidence it is important to distinguish (1) cases provided as examples, (2) samples used to check a conclusion established on other grounds (3) cases put forward as the sole evidence for some generalisation. People commonly apply to cases (1) and (2) the more stringent criteria that would be applicable to (3).

Re-reading what I’ve just written I realise that it is very abstract and would benefit from half a dozen more examples, but that would make it very long for a blog, and there are examples in the Philosophy Notes on my web site.

I plan to comment here on individual samples of popular logic or illogic when I come across them in the media or in conversation.