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Can something be used to disprove itself?

Waxwing
Posts: 1
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9/1/2013 1:06:06 AM
Posted: 3 years ago
This is a logical riddle that occurred to me today while I was thinking about rationalism.

Without getting into excessive detail, if you were to have a premise such as, "Assume rationalism", for example, then use that premise to conclude that "rationalism is therefor false", in the sense that you start with some form of thought, show it to be contradictory and then conclude it must be false, what seems to happen is this: The conclusion that one of the premises required to reach that conclusion is false, means your very argument is false. Since one of your premises is now admittedly false, your conclusion is invalid. But this seems counter-intuitive on how logic should be able to invalidate something by demonstrating that it's contradictory.

Generic example:

1. A
2. A cannot be true when B
3. B
4. Therefor A is false.

On one hand it seems a perfectly legitimate way of demonstrating something is contradictory, but on the other hand, A, being a premise, must be valid for the conclusion to be valid, but the conclusion invalidates its very own premise. It just creates this strange logical viscous-circle, some sort of self-referencing infinite progression.

For a more specific example, let's look at what is probably the most common objection to Nihilism:

If nihilism is true, then nothing can be known.
If nothing can be known, something can be known (that nothing can be known)
If something can be known, nihilism is false.

The core problem is that when you begin an argument with "If nihilism is true", then nihilism can't be false. It can't be true and false simultaneously.

I expect this isn't an original observation, but I've never come across a discussion or text on it before.
Fractals
Posts: 38
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9/1/2013 2:14:12 AM
Posted: 3 years ago
It's a little round about, but Stephen Law's Evil God is a good use of using a set of standard assumptions to challenge those same assumptions.

http://journals.cambridge.org...
Fruitytree
Posts: 2,176
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9/1/2013 8:24:24 AM
Posted: 3 years ago
If the definition of A leads to a contradiction, than you can disprove the definition of A.

So if A has more than one definition, you could get rid of the false definitions of A, at least.

If all A definitions can be disproved this way, then yes you can disprove A.
wiploc
Posts: 1,485
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9/1/2013 11:47:20 AM
Posted: 3 years ago
At 9/1/2013 1:06:06 AM, Waxwing wrote:
On one hand it seems a perfectly legitimate way of demonstrating something is contradictory, but ... It just creates this strange logical viscous-circle, some sort of self-referencing infinite progression.

It's a standard technique for disproving things.

- If A then B.
- If A then not B.
- Therefore, not A.

on the other hand, A, being a premise, must be valid for the conclusion to be valid, but the conclusion invalidates its very own premise.

If A being true entails a contradiction, then A is false. That's not a "logical viscous-circle." It's just a fact.

You have some terminological difficulty, which may be contributing to your confusion:

Premises are true or false, not valid or invalid.

Arguments are valid or invalid. An argument can be valid when its premises are false. Example:

- This robot is a man.
- All men are mortal.
- This robot is mortal.

This argument is obviously valid, even though a premise and the conclusion are obviously false.
zmikecuber
Posts: 4,093
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9/12/2013 2:32:08 PM
Posted: 3 years ago
If something can be logically demonstrated to necessarily lead to self contradictions then it is false.

Take "Nothing can be known". If it leads to logical self contradictions, then it is false. If this statement is false, then the contradictory statement must be true. Clearly it's a false statement. Therefore "Some things can be known" is true.
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"primal man had the habit, when he came into contact with fire, of satisfying the infantile desire connected with it, by putting it out with a stream of his urine... Putting out the fire by micturating was therefore a kind of sexual act with a male, an enjoyment of sexual potency in a homosexual competition."