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Thursday, April 24, 2014


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We cannot extract the logical form of an argument be examining its physical features. We have to understand what the constituent sentences mean, and to understand what they mean, we have to understand what their constituent terms mean.

We are entirely agreed then. Shock.


We can't say that an argument is invalid because it instantiates an invalid form. The argument Socrates is a man; all men are mortal; ergo Socrates is mortal instantiates the invalid form a is F; all Hs are G; ergo a is G, but modulo equivocation, it is truth-preserving. Instantiation of form is just pattern-matching, and the argument does match the pattern of the invalid form.

Returning to the Thames argument, we can split your second approach into two variants:

1. The argument is valid by virtue of instantiating a valid form; the premises are true; but the argument is unsound because of equivocation on 'bank'.
2. Equivocation on 'bank' invalidates the argument.
Which option we choose depends on how we want to extend the notion of validity of form to validity of argument. Both routes are feasible, I think, but we need to be consistent else confusion arises. My inclination is for (1). For me validity is about syntactic form. Soundness brings in truth. For this we have to have meaning, Hence equivocation on meaning falls under soundness.

I can't agree that 'We cannot extract the logical form of an argument be examining its physical features.' The only reason that the Thames argument is put forward as a truth-preserving inference is that its conclusion results from matching its premises to those of a valid inferential pattern. There is no valid argument form with premises This is an F; every H is G and conclusion This F is G. The form of the quoted argument has to be the one given.

Bill: “We cannot extract the logical form of an argument be [sic, = by] examining its physical features. “
I rarely correct your typos but I have a reason this time. More later.

This is just to note that Jan Lukasiewicz would have profoundly disagreed with this statement, holding that it is precisely the physical features, and only the physical features, that logical form is concerned with. Why? He says (see the first chapter of Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, 1951, that logic in the true sense must avoid any kind of psychologism. Logic is not ‘the law of the forms of thought’ or whatever. For thought is a psychological phenomenon and the thoughts of others are not accessible to us ‘unless we are clairvoyants’, which we generally aren’t. Logic should avoid ‘thought’ and ‘meaning’ entirely. The purpose of logic is to assign or categorise valid forms of expression, i.e. the outward manifestations of thought, namely visible signs or spoken words. Such signs are accessible to others. We can agree on their shape and order, we can agree (unless the writing is really poor) whether a letter is a token of ‘a’ or ‘b’ or whatever.

Lukasiewicz concedes that ordinary language is ambiguous, and for that very reason prefers truly ‘formal’ logic, i.e. a logic where the signs and syntax are completely unambiguous, such as predicate calculus or the ghastly Polish logic, which he developed. For him, logical ‘form’ is therefore precisely about the physical, i.e. perceptible features of argumentation. Validity cannot be guaranteed when it depends on partly or wholly unobservable items such as ‘thoughts’ or ‘meanings’ or ‘intentions’.

Returning to the typo. I altered your ‘be’ to ‘by’. Why? ‘Be’ was what you actually typed. However, I made a judgement about your intention. You meant to type ‘by’, correct? But the question is how I knew this. Am I a clairvoyant with access to your private mental states? Surely not. I looked at the sentence and it did not make sense. I found that I could make sense of it by altering the word in that way. So I made the judgment, and changed it. Without clairvoyance or telepathic powers.

Indeed, I could write a crude computer program to pick up typos like that. My word processor already has one. Yet a computer cannot access private mental states either.

In conclusion, perhaps Lukasiewicz is right. Logical form is about the outward manifestation of arguments as expressed in writing or speech. However, a more sophisticated approach would be to understand how we resolve ambiguity without the crude and literal approach advocated by Lukasiewicz. That is a matter for further investigation.


It looks like Lukasiewicz was deeply confused. Yes, psychologism is to be avoided. But how does it follow that logic is concerned precisely with physical features? The conclusion is absurd. Therefore, any argument to it must have one or more false premises.

Did L. reject psychologism only to fall into 'physicism'? I have argued in these pages that logic cannot be reduced to psychology. But it cannot be reduced to physics either, or to any empirical study of merely material things or processes.

One could study a complex pattern of bird droppings on a wall, noting all sorts of physical, including geometrical, features. But no such pattern expresses a proposition. And without propositions one cannot do logic. Logic is concerned with consistency, inconsistency, and entailment. But these are relations defined over propositions. These relations do not hold between or among merely physical things and processes.

Brightly: “We can't say that an argument is invalid because it instantiates an invalid form.”

I spotted that too.

“equivocation on meaning falls under soundness.” I can’t agree with that, neither I suspect would Bill.

Bill “how does it follow that logic is concerned precisely with physical features?”

L didn’t say that. He said that logical form is concerned with that. That is why it is called ‘form’.

“It looks like Lukasiewicz was deeply confused.”

Well he is a very famous and respected logician, and inventor of Polish logic. Perhaps I misread him. I shall read the chapter again and report back.

Lukasiewicz was quite a character. Someone told me a story about his obsession with the correct use of quotation marks, but I can’t remember it. He also argued that if the schema is ‘every A is a B’, we cannot substitute ‘all As are Bs’, because it is not precisely equiform.

He also fell into the class of ‘rude logicians’. There are some juicy quotes in the chapter which I can send. We were going to discuss this. Are logicians as a group more uncivil and generally more unpleasant than other professions? If so, why? Has anyone done a statistical survey?

I love you guys even though we disagree about almost everything. Amazing that you've stuck with me all these years.

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