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What is the O'ist view on the Liar's Paradox?

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I think what we're lacking here is a definition of the term "deduce." For the purposes of Godel's theorem, it means applying a set of deduction rules to a set of formalized premises (called "axioms") to yield other formalized statements that are logical consequences of the premises.

For example, you could formalize the premises in my earlier example (1, "John is a friend of mine" 2, "I don't have any Canadian friends") somehow like this:

  • John element-of Friends
  • not (exists f such that f element-of Canadians and f element-of Friends)

Then you (or a computer program, or an assistant you've hired) could take these formalized premises and follow a list of instructions which are the rules of deduction. This process would result in a number of formalized statements, such as:

  • John not-element-of Canadians

For every resulting statement, you can be certain that it is implied in the premises (provided that no error was made while you followed the rules of deduction).

This, and only this, is the process we call deduction when discussing Godel's theorem: a foolproof, completely automatable way of finding out whether a proposition is implied in a set of premises. Essentially, it is the sort of thing mathematicians do when they say they prove things.

Now, one might wonder, after we have followed the rules of deduction and listed all the statements those rules told us to list, do we know that we have listed all statements that are implied in the premises?

Godel proved that, if the premises ("axioms") are sophisticated enough to allow self-referential statements, as well as statements that reference the set of statements that can be deduced from the axioms using the rules of deduction, and if the axioms don't contradict themselves, then we know that we have not listed all implied statements.

Objectivism's EIC axioms are not formalized statements from which you (or a computer, or assistant) deduce things by following predefined instructions. They are simply a statement of common sense; a concise summary of the basis of objectivism, which is the rejection of mysticism, skepticism, determinism, materialism, the primacy of consciousness, and all the other irrational approaches to life.

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  • 1 year later...

Ayn Rand once wrote "there is no such thing as a contradiction, if you find yiourself with a contradiction, check your premises. One of them is faulty"(or something to that effect). But, if there is a liar who always lies, and says "this statement is false", is that true? :confused:

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Statements are not just true or false - they can also be arbitrary. Because "this statement is false" has no referent in reality, it's a statement of another kind - gibberish.

I'd go a step farther and say that "this statement is false" is not really a statement, because it doesn't state anything. Its only referent is itself -- or, more exactly, its only referent is its own referring. Sure, it's a grammatically correct sentence, but it's not a statement until it refers to something outside itself -- just as consciousness is not consciousness until it is conscious of something outside of itself. "A consciousness conscious of nothing but itself is a contradiction in terms" (Galt's Speech), and a statement that only states its own stating in a contradiction in terms. (See Harry Binswanger's lecture, "The Metaphysics of Consciousness," where he discusses self-referential pseudo-statements explicitly.)

It follows from this that "this statement is false" is not some sort of exception to the law of contradiction. For, the law of contradiction states that something cannot be both A and non-A at the same time and in the same respect. "This statement is false" is not both true and not true; it's simply not true, and it's not false either. It's not "truth-functional" at all. It is, as GreedyCapitalist said, gibberish.

And the same goes for most (if not all) of the paradoxes that analytic philosophy has bequeathed to us. They commit this same "fallacy of pure self-reference" (as Dr. Binswanger calls it), and thus merely serve as examples of the word games that analytic philosophers love to play.

--Alex

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And the same goes for most (if not all) of the paradoxes that analytic philosophy has bequeathed to us.  They commit this same "fallacy of pure self-reference" (as Dr. Binswanger calls it), and thus merely serve as examples of the word games that analytic philosophers love to play.

Amen to that! Objectivism's answer to the "paradox" under discussion here is surely testament to fact that Objectivism is a philosophical revolution in the deepest sense (as opposed to just a philosophical or ethical revolution). I didn't gain a true appreciation of this fact until I studied philosophy at a university level.

For those of you who haven't had the "pleasure" of taking philosophy courses in a university, it may be hard to fathom what is at stake here. This "paradox" isn't just some side issue that analytic philosophers dreamt up for fun. Entire systems of philosophy are built out of non-issues like this one! That is how Analytic philosophers work and it's disgusting. See the Gödel's Incompleteness Theorem entry in WikiPedia for illustration of this point.

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