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Questions tagged [goedel]

Questions related to the work of Kurt Gödel. Please mind the spelling of his last name: "Gödel". If you cannot or don't know how to create the "ö", you might also write his name as "Goedel". In all cases, please avoid "Godel". If you want to create a (hyper)link to, say, a Wikipedia entry, you might have to manually change the "ö" to "%F6".

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12
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1answer
1k views

Was Wittgenstein anticipating Gödel?

The Tractatus 6.123: 6.123 Clearly the laws of logic cannot in their turn be subject to laws of logic. (There is not, as Russell thought, a special law of contradiction for each 'type'; one law is ...
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Does Gödel's argument that minds are more powerful than computers have the inconsistency loophole?

In "Raatikainen, P., 2005, “On the Philosophical Relevance of Gödel's Incompleteness Theorems,” , the author argues that Penrose's and others use of Gödel's theorem as an argument against mechanism (...
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8answers
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Is Kurt Gödel's Incompleteness Theorem a “cheap trick”?

I found a throw-away critique of Kurt Gödel's Incompleteness Theorem in an essay about Deconstruction: The basic enterprise of contemporary literary criticism is actually quite simple. It is based on ...
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What are the philosophical implications of Gödel's First Incompleteness Theorem?

Gödel's First Incompleteness Theorem states Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any ...
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Did Russell understand Gödel's incompleteness theorems?

Russell was active in philosophy (although no longer in math) for many years after the Gödel's 1931 publication. Gödel's paper were not obscure, and Russell would have been aware of their effect on ...
13
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794 views

What sources discuss Russell's response to Gödel's incompleteness theorems?

In his book My Philosophical Development Russell writes, In my introduction to the Tractatus, I suggested that, although in any given language there are things which that language cannot express, ...
16
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666 views

What are the philosophical consequences of the undecidability of the spectral gap in quantum theory?

An article published in Nature yesterday proves that finding the spectral gap of a material based on a complete quantum level description of the material is undecidable (in the Turing sense). One of ...
6
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1answer
866 views

Why did Gödel believe that there was a conspiracy to suppress Leibniz's works?

It is known that Gödel was obsessed with Leibniz, and apparently he even believed that their was a worldwide conspiracy among academics to suppress Leibniz's works. Does anyone know where this came ...
16
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When it is correct to use Tarski's undefinability theorem versus Gödel's incompleteness theorem?

Smullyan (1991, 2001) has argued forcefully that Tarski's undefinability theorem deserves much of the attention garnered by Gödel's incompleteness theorems. That the latter theorems have much to say ...
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How does Gödel's incompleteness theorem apply to materialism and the mind

Assertion 1: Humans use some logical system to understand the universe Assertion 2: Gödel proved through a formal logic what is provable about a logical system is a subset of what is true about it, ...
5
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Does Gödel's second incompleteness theorem interact with logical positivism?

Gödel's second incompleteness theorem (GSIT), informally stated, says: For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal ...
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How does Gödel's theorem apply to daily life?

I came across a simplified description of Gödel's theorem and the discussion touches on a concept of honesty (truth?) and completeness. How does Gödel's theorem apply to everyday interactions?
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Where did Gödel write that first-order logic is the “true” logic?

In "On How Logic Became First-Order" Matti Eklund writes (p. 2/148): It appears to be widely held today that arguments from Skolem and Kurt Gödel, both alleged proponents of the thesis that ...
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What are the philosophical implications of the Halting Problem?

In a great answer, a community member gave the following proof sketch that the halting problem is undecidable: Proof that the halting problem is undecidable. If there were a computable procedure to ...
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How did the logical positivists respond to Gödel's incompleteness theorem?

In a lecture on philosophy of science I recently listened to, it was stated that Quine was the one who decisively refuted the logical positivist program. I've also read that Quine and Popper were ...
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Are axioms tautologies?

My understanding is that axioms are the unprovable statements upon which systems are built. Tautologies are in essence things that can't be false. Godel's Incompleteness Theorem, though, shows that ...
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Can Gödel's incompleteness theorems be applied to ethics?

It seems, that simplistically, that Gödel's incompleteness theorems can be applied to ethics in a very straightforward way by: Replacing "True" and "False" with "Right" and "Wrong" Assuming real ...
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615 views

Is Gödel's incompleteness theorem still valid if one uses a higher-order logic?

Gödel's incompleteness theorem is wholly formal (in my understanding), and relies on a proof system that I assume is first-order. Does it make any difference to the theorem if higher-order logic is ...
4
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Does the finitary proof of the consistency of relevant PA shows that first order PA is irrelevant?

Relevance logic takes a closer look at the implication operation in first-order logic. It suggests that implications such as: p and not p -> q cannot hold; in ordinary English, an example of this ...