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In a discussion about the logical validation of contingency argument (Necessary existence), One said that the contingency argument results in a contradictory (Inconsistent) system according to Godel's incompleteness theorem.

My doubt: Is it true that an argumentation can satisfy the hypothesis of incompleteness theorem? If so, how can we say that the premises ( of contingency argument) lies inside a system generated by a finite number of axioms (according to the hypothesis of incompleteness theorem)?

Mauro ALLEGRANZA
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RIYASUDHEEN T. K
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    Godels theorem is about arithmetic. No less, but no more. Each time someone tries to shut down the conversation by name dropping Godel on any other subject the appropriate response is a good laugh. – armand Aug 08 '21 at 10:32
  • It is interesting to me to know why the incompleteness theorem is not applicable to some areas like analysis, algebra, logical argumentation, etc. – RIYASUDHEEN T. K Aug 08 '21 at 10:40
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    Not clear at all... Do you know the hypothesis of [Gödel’s Incompleteness Theorems](https://plato.stanford.edu/entries/goedel-incompleteness/)? They apply to a wide range of **formal systems**: one of them is that the set of premises (axioms of the theory) must be finite or at least decidable. But there are others. – Mauro ALLEGRANZA Aug 08 '21 at 11:08
  • Ya...I want to know why this hypothesis cannot extend to the premises in a logical argumentation OR what are the consequences if one say the whole argumentaion is inconsistent (by relaxing the platform '' formal system for any branch of mathematics containing arithmetic'') ? – RIYASUDHEEN T. K Aug 08 '21 at 11:24
  • Is there any analog of incompleteness theorem in formal logic? – RIYASUDHEEN T. K Aug 08 '21 at 16:10
  • @armand "In modern mathematical logic, the Liar sentence is constructed in a more roundabout way: sentences are designated by Gödel numbers according to a coding scheme, and then a computable diagonalization function is used to achieve the self-reference needed for the Liar. ... there is really no cogent objection to the simpler expedient of simple stipulation. As Kripke remarks: “A simpler, and more direct, form of self-reference uses demonstratives and proper names: Let ‘Jack be a name of the sentence ‘Jack is short’, and we have a sentence that says of itself that it is short." T Maudlin – J Kusin Aug 08 '21 at 17:13
  • Properly speaking, Gödel's incompleteness theorems apply not just to arithmetic itself, but to any theory that is capable of interpreting arithmetic. This includes set theory, for example. Whether they apply to what you are calling the "contingency argument" rather depends on the details of that argument. We would need to see the workings. – Bumble Aug 08 '21 at 18:57
  • This is nothing but an argumentation with premise : 1. Every being that exists is either contingent or necessary. 2. Not every being can be contingent. 3. Therefore, there exists a necessary being on which the contingent beings depend. 4. A necessary being, on which all contingent things depend, is what we mean by “God”. CONCLUSION: Therefore, God exists. – RIYASUDHEEN T. K Aug 09 '21 at 05:24

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