Is Logic Flawed by Paradoxes and Variables?

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Paradoxes are recognized as existing within logic but are not believed to manifest in the real world, suggesting potential flaws in our logical frameworks. Logic is intended to prescribe how the universe should function, yet it may not always align with observable reality. Discussions highlight that while simple logic suffices for everyday reasoning, more complex scenarios require advanced logical frameworks that include states beyond true and false. The conversation also touches on the distinction between different types of paradoxes, such as those arising from vagueness or self-reference, and emphasizes that theoretical physics may predict paradoxical effects, but these are often seen as indicators of errors in understanding. Ultimately, the existence of paradoxes in logic raises questions about the adequacy of our logical systems in accurately describing the universe.
  • #51
Imparcticle said:
How is a truth value defined? How is a false value defined?

As Omin has just demonstrated so well, we can use natural language to split semantical hairs ad infinitum and get nowhere, or we can even redefine words willy nilly and begin spouting nonsense poetry.

Once again with emphasis, words only have demonstrable meaning according to their function in a given context. In this case, I gave a specific context, that of formal logic. The following definition will serve as well as any other for this purpose.

Dictionary.com said:
truth ( P ) Pronunciation Key (trth)
n. pl. truths (trthz, trths)
Conformity to fact or actuality.
 
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  • #52
Symbols may only represent knowns.

How about variables? For example, in formulas like a2+b2=c2, the variables a, b, and c are symbols representing unknowns.
 
  • #53
Imparcticle said:
How about variables? For example, in formulas like a2+b2=c2, the variables a, b, and c are symbols representing unknowns.

I once thought things could be destroyed or things could be negated. I also thought things could be created out of nothing. I now only look at all things as being positioned here or there. Forms change, but there elements are not created or destroyed.

The essential meaning of unknown may be infered with these simple logic negations of an underlying positive statement.

The subject is in the color Sienna, the copula is in Dark Olive Green and predicate is in Dark Slate Blue. The first example is the negative form and the second (in parenthesis) is the positive form it really infers! All statements in language infer only positive. All things are only inside or outside something rather than created or destroyed. It seems a play on words, but I found it helpfull because inside and outside connotes existence vs. not, un, etc which seems to connote zero or nothing concepts, which can increase confusion thorugh paradoxical type expression.

The Positive Statement
Things I know are things I sense. The statement that is said over and over in the negatives below.

The Negatives Turned To Positives
Things I don't know are things I don't sense. (Things outside my knowledge are things outside my sense.)

Things I know aren't things I don't sense. (Things I know are things outside what is outside what I sense.)

Things unknown are things I don't sense. (Things outside what I know are outside what things I sense.)

Non-things I know are things I don't sense. (Things outside my knowledge are things outside my senses.)

Etc, etc... We could go on and on.

And there is also the appeal to ignorance...what could it possible mean?

Nothing does exist because you can't prove it doesn't exist.
Nothing doesn't exist because you you can't prove it exists.

I used the paradoxal words and their definitions for conviece of explanation.
 
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