Lukasiewicz on Logical Form

London Ed writes,

I read and excerpted the chapter. I am not mistaken. Also, what he says seems correct to me.

He claims that logic is not formal, insofar as it is concerned with the 'laws of thought'. He says "Thought is a psychical phenomenon, and psychical phenomena have no extension. What is meant by the form of an object that has no extension?"  I can't fault this.

I take it that the argument is this:

1. Only spatially extended objects have forms.
2. Neither acts of thinking, nor such objects of thought as propositions, are spatially extended.
Therefore
3. If logic studies either acts of thinking or objects of thought, then logic is not a formal study, a study of forms.

If this is the argument, I am not impressed. Premise (1) is false.  L.'s notion of form is unduly restrictive.  There are forms other than shapes. Consider a chord and an arpeggio consisting of the same notes.  The 'matter' is the same, the 'form' is different.  In a chord the notes sound at the same time; in an arpeggio at different times.  The arrangement of the notes is different.  Arrangement and structure are forms.  Examples are easily multiplied.

Nor, he says, is it the object of logic to investigate how we are thinking or how we ought to think. "The first task belongs to psychology, the second to a practical art of a similar kind to mnemonics". And then he says "Logic has no more to do with thinking than mathematics has". Isn't that correct?

We can agree that logic is not a branch of psychology: it is not an empirical study and its laws are not empirical generalizations.  LNC, for example, is not an empirical generalization.  But a case can be made for logic's being normative.  It does not describe how we do think, but it does prescribe how we ought to think if we are to arrive at truth.  If so, then logic does have a practical side and issues hypothetical imperatives, e.g., "If you want truth, avoid contradictions!"

In a similar vein he notes the formalism of Aristotelian logic. The whole Aristotelian theory of the syllogism is built up on the four expressions 'every' (A), 'no' (E), 'some' (I) and 'not every' (O). "It is obvious that such a theory has nothing more in common with our thinking than, for instance, the theory of the relations of greater and less in the field of numbers".  Brilliant.

Why do you call it "brilliant"?  Husserl and Frege said similar things.  It's old hat, isn't it?  Psychologism died with the 19th century at least in the mainstream.  Given propositions p, q, logic is concerned with such questions as: Does p entail q?  Are they consistent?  Are they inconsistent?  We could say that logic studies certain relations between and among propositions, which are the possible contents of judgings, but are not themselves judgings or entertainings or supposings or anything else that is mental or psychological.

Again, on the need for logic and science to focus on the expression of  thought rather than 'thought', he says "Modern formal logic strives to attain the greatest possible exactness. This aim can be reached only by means of a precise language built up of stable, visually perceptible signs. Such a language is indispensable for any science. Our own thoughts not formed in words are for ourselves almost inapprehensible and the thoughts of other people, when not bearing an external shape [my emphasis] could be accessible only to a clairvoyant. Every scientific truth in order to be perceived and verified, must be put into an external form [my emphasis] intelligible to everybody."

I can't fault any of this. What do you think?

Sorry, but I am not impressed.  It is fundamentally wrongheaded.  First of all this is a howling non sequitur:

1. Logic does not study mental processes;
Therefore
2. Logic studies visually perceptive signs.

Surely it is a False Alternative to suppose that logic must either study mental processes or else physical squiggles and such.  There is an easy way between the horns: logic studies propositions, which are neither mental nor physical. 

In my last post I can gave two powerful arguments why a perceptible string of marks is not identical to the proposition those marks are used to express.

L. speaks of an external form intelligible to everybody.  But what is intelligible (understandable) is not the physical marks, but the proposition they express.  We both can see this string:

Yash yetmis ish bitmish

but only I know what it means. (Assuming you don't know any Turkish.)  Therefore, the meaning (the proposition), is not identical to the physical string.

There is also an equivocation on 'thought' to beware of, as between thinking and object of thought.  As you well know, in his seminal essay Der Gedanke Frege was not referring to anything psychological.

I will grant L. this much, however.  Until one has expressed a thought, it is not fully clear what that thought is.  But I insist that the thought -- the proposition -- must not be confused with its expression.

The real problem here is that you wrongly think that one is multiplying entities beyond necessity if one makes the sorts of elementary distinctions that I am making. 

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Comments

[Ed]

>>First of all this is a howling non sequitur:

1. Logic does not study mental processes;
Therefore
2. Logic studies visually perceptive signs.
<<

Yes, but Lukasiewicz does not make this inference. He states (1) that logic is the not the science of the laws of thought, and that “the laws of logic do not concern your thoughts in a greater degree than do those of mathematics”.

And he does not say that “Logic studies visually perceptive signs”. Rather, that the aim of logic is to attain the greatest possible exactness by means of a precise language built up of stable, visually perceptible signs.

Expressing his argument as I understand it.

(A) The main object of logic is to establish criteria for valid reasoning.

(B) Such criteria are a body of scientific truth.

(C) Every scientific truth in order to be perceived and verified, must be put into an external form intelligible to everybody.

(C) Thought processes, when not formed in words and bearing an external shape, are accessible only to a clairvoyant, and thus not in a form intelligible to everybody.

(D) There can be no scientific truths about thought processes, unless they are formed in words and bearing an external shape.

(E) Logic, insofar as it is a science, is the science involving thoughts qua ‘bearing an external shape’. In particular, any ‘criterion of validity’ can be applied only to the form of external material such as written and spoken words.

>>The meaning (the proposition), is not identical to the physical string.

Correct. It is the form that thought takes when expressed in the physical string. But that form must be observable. Your example of the Turkish “Yash yetmis ish bitmish” is like colour-blindness. Some people cannot distinguish red from green. They are colour-blind. Sometimes they can learn to distinguish. Other times they can have medical treatment. The cure for meaning-blindness is simpler: learn the language. In this case, learn Turkish. Then you can perceive a form that was always there, but not apprehensible to all.