Myself is not Me, Formal Logic and Contradictions...

Question

If it is possible to decribe a contradiction via formal logic, how would you do it?

Could if I would like to say that "Myself is not me." Then would I simply diagram the sentence as A=~A? or would there be other things invovled? Like more details...

On a side note, Wittgenstein suggests that everyday language is much more significant and meaningful than the structure of formal logic, but how would you translate a contradiction [A=~A] into a formal statement and NOT have it diminsh its "common" meaning?

Hope this question is understandable...thanks for any help!

Answer 1

My boss seems to believe that the three of us,working together, should get more work done - Me, Myself and I, so why should he hire more help.

Answer 2

Any translation from a natural language into the language of symbolic logic is just that, a translation. The entirety of the meaning will not always translate effectively.

In the case of classical sentential logic, meaning is reflected only in the truth functional sentential connectives - and nothing else. So, obviously the language of classical sentential logic is not able to contain the extent of meaning contained in a natural language.

In the case of classical first order predicate logic, meaning is reflected in truth functional sentential connectives plus quantification of individual variables. Second order predicate logic adds meaning reflected in quantification over functions and relations (predicates).

Each of these types of logic, respectively, extend the capability of symbolic logic to reflect the meaning of other languages, such as natural languages or the language of mathematics. This doesn't end with second order predicate logic, higher order forms of logic attempt to reflect even more meaning. But as it stands now, Wittgenstein's view still holds.

Answer 3

Of course it is possible to describe contradictions in formal logic. Your example A=~A is a valid example, as is true = false.

When you try to attach meaning to this statement, or any other logical statement, though, you are inherently either making the statement more diffuse and general, and therefore not very valuable, or concrete, and therefore perhaps incorrect, at least in the generality that the logical statement expresses.

Going from normal spoken or written language to an axiomatic system such as formal logic can be seen as a projection, such as showing what is happening in three dimensions on a TV with just two dimensions. This is valid. However, if you were to "un-project" the picture on the TV from 2D back to 3D, you would have a problem of exactly finding where along the ray from the viewer, through the TV, a point would go. Does one person stand closer to the camera than a second? Without additional information, you cannot know.

At some point, I also see both of Goedel's incompleteness theorems coming into the mix. According to the first theorem, in any axiomatic system, there are true statements that simply cannot be proven. This suggests that there are things you cannot express using formal logic.

According to the second incompleteness theorem, a system can only make a statement about its own consistency if it is, in fact, inconsistent. That is the case for everyday language, but not for axiomatic systems.

All this taken together, it seems clear that spoken language is much richer than the axiomatic system of formal logic. Yes, you can express *a* contradiction, such as A=~A, but you may not be able to express exactly the contradiction you want to, or you may get the meaning wrong. With "I am not myself" (which is how I would phrase the statement; myself is used reflexively), people usually mean that they feel odd or unusual; they don't mean that aliens have snatched them up and replaced them with clones.

The consistency that an axiomatic system can give you comes with a price: lowered expressiveness.

Answer 4

yes

Answer 5

Well, in formal logic it's important to understand that it's more about structure than about interpretation. "Myself is not me" would certainly be A = ~A in formal logic. Formal logic is incredibly loose when it comes to what it may represent, but very strict on how it is formed. I don't see how it's possible to not diminish its common meaning when expressing it in formal logic. A=~A would represent any contradiction, from "myself is not me" to "a carrot is not a carrot".

Answer 6

Wow. A real question dealing with philosophy. 5 Stars just for knowing what philosophy really is.

The Law of Non-Contradiction:

"These truths hold good for everything that is, and not for some special genus apart from others. And all men use them, because they are true of being qua being . . . . For a principle which everyone must have who understands anything that is, is not a hypothesis . . . . Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect."

Aristotle, Metaphysics, IV, 3 (W. D. Ross, trans.)

Imagine this part in all in caps: "the same attribute cannot at the same time belong and not belong to the same subject and in the same respect."

They cannot, because contradiction cannot exist.

If you discover what appears to be a contradiction, it is only because two or more ideas are trying to exist in the same way at the same time. Maybe it is poor definitions. Maybe it is poor logic. Maybe it is a case of not seeing all the facts, that the key to unlocking the contradiction is missing.

But understand that if you see a contradiction, "the same attribute cannot at the same time belong and not belong to the same subject and in the same respect." So you must attempt to figure out what it is that is attempting to exist at the same time, in the same respect, within the same subject.

"[The] underscoring of primary facts is one of the crucial epistemological functions of axiomatic concepts. It is also the reason why they can be translated into a statement only in the form of a repetition (as a base and a reminder): Existence exists —Consciousness is conscious —A is A. (This converts axiomatic concepts into formal axioms.)"

Introduction to Objectivist Epistemology, 78; Ayn Rand

My own website adheres to the Law of Non-Contradiction, and to the ideas of Rand. But its primary purpose is to put those ideas into everyday thinking and everyday practice. Thanks for looking at it.

http://freeassemblage.blogspot.com/