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In short, the answer to your question is: No.

Have you looked at Godel's theorem? It shows that, from what I understand, that any axiomatic system has to be incomplete, in the sense that there will aways be true statements that you cannot derive within the system. There are probably people on this forum that have a better understanding of this than I do, so correct me if I'm wrong.

Oh, and also, an application of logic requires certainty as far as the premises go, so you can prove that IF you accept the axioms THEN you have to believe something else is true, but what necessitates us to accept one set of premises or axioms over another?

Have you looked at Godel's theorem? It shows that, from what I understand, that any axiomatic system has to be incomplete, in the sense that there will aways be true statements that you cannot derive within the system. There are probably people on this forum that have a better understanding of this than I do, so correct me if I'm wrong.

Oh, and also, an application of logic requires certainty as far as the premises go, so you can prove that IF you accept the axioms THEN you have to believe something else is true, but what necessitates us to accept one set of premises or axioms over another?

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Pengwuino

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@Prague

Get a girlfriend and then you wont even have to ask this question :P

Get a girlfriend and then you wont even have to ask this question :P

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honestrosewater

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Google Gödel'sC0mmie said:In short, the answer to your question is: No.

Have you looked at Godel's theorem? It shows that, from what I understand, that any axiomatic system has to be incomplete, in the sense that there will aways be true statements that you cannot derive within the system. There are probably people on this forum that have a better understanding of this than I do, so correct me if I'm wrong.

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A set of rules for deriving true statements.honestrosewater said:Google Gödel'sCompletenessTheorem. Do you know what an axiomatic system is? If not, that would be a good place to start.

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honestrosewater

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And how do you know if a statement is true? You need some other things too. Here's a quick outline.C0mmie said:A set of rules for deriving true statements.

You start with a language that contains a set of

You define a

You then define a

Everything above, minus the valuation and tautologies, is called a

Make sense? Do you have a statement of Gödel's Completeness or Incompleteness Theorems around? Edit: If not, you can search PF; They've been discussed many times here. Hurkyl and matt grime are reliable sources.

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I wasn't looking for an explanation of what logic is. I've studied it for quite a bit and I'm taking a symbolic logic course right now. I just wasn't sure if my understanding of Godel's Theorem was correct. Yes, the other posts on this subject did turn out to be helpful.

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honestrosewater

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Okay, great- you'll probably see a completeness proof soon then. I was just going on your earlier statements and considering the other people who might be reading the thread. Glad others were helpful.C0mmie said:

I wasn't looking for an explanation of what logic is. I've studied it for quite a bit and I'm taking a symbolic logic course right now. I just wasn't sure if my understanding of Godel's Theorem was correct. Yes, the other posts on this subject did turn out to be helpful.

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