Questions tagged [arithmetic]
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15 questions
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Is there any philosophical significance to the superexponential bound for Presburger Arithmetic?
Presburger Arithmetic is, roughly, the additive theory of the natural numbers. The Fischer-Rabin theorem asserts a superexponential lower bound e^{e^{cn}} for the worst-case scenario for the length ...
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Can we mathematically justify associating the concept of the imaginary unit with some kind of stagewise concept of negation?
By a "stagewise concept," I mean one that somehow "unfolds" or "grows out from" a seed concept. This need not be a recursive, but it might be a Hegelian-dialectical, ...
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Epimenides paradox inside arithmetic
I am currently reading "Gödel, Escher, Bach", and in the book author makes the following statement:
I think the Tarski reproduction of the [liar's] paradox inside TNT points the way to a ...
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Turing Machines that interact with physics [closed]
Fix a Turing-complete programming language P and character set. For sufficiently large 'n', an 'n' character program in P cannot decide the halting behavior of all programs with fewer than 2n ...
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Is Arithmetic more Extensional than Probability?
One of the views of probability is that it should be viewed as a multi-valued logic where p(A) represents the probability that a proposition A is true.
In a discussion of this, I once read that ...
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Why does division take a lot more mental effort than multiplication?
It is mentally more difficult to divide 2 numbers than it is to multiply them. If you ask me what is 3 * 27, i will immediately tell you 'a little less than 90'.
However, I really have no idea what is ...
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Are the truths of arithmetic logically necessary? [duplicate]
Are true statements of arithmetic logically necessary? That is, is "2+3=5", the commutativity of addition of natural numbers, and the infinitude of primes, among other statements, logically ...
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Can we logically derive a value for 0÷0? [closed]
I have a "proof" that 0÷0 = 2:
0÷0 = (100 - 100) ÷ (100 - 100)
= (10⋅10 - 10⋅10) ÷ (10⋅10 - 10⋅10)
= (10² - 10²) ÷ 10(10 - 10)
= (10 + 10)(10 - 10) ÷ 10(10 - 10)
= (10 + 10) ÷ 10
=...
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Robinson Arithmetic and Church-Turing Thesis
What is the connection (if any) between proving the undecidability of Robinson Arithmetic and the Church-Turing Thesis? If there is any connection to CTT, is it necessary?
user49323
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Good texts on logicism
I'm trying to learn about the logicist programme by myself so I was wondering, what are some good book/papers/articles on logicism? I'm looking for introductory to medium level texts, nothing very ...
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Can we add to PA a new predicate T such that for every sentence A of the old vocabulary the new theory proves T(Godel numeric number of A) iff A
I am new to logic but I believe this is not a difficult problem, yet I am still soo confused, and the reason for that is because there are so many gaps in my knowledge or maybe I have overlooked so ...
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Can mathematical sentences in different theories be identified?
My question motivated by a part of this page from Saul Kripke's book Naming and Necessity, which is also viewable on google books. In the middle of the page he say something, which seems unnatural to ...
- 1,143
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How should we characterize the relationship between mathematics and philosophy of mathematics?
How should we characterize the relationship between mathematics and philosophy of mathematics?
Specifically, in what ways might the study of philosophy of mathematics make a mathematician better at ...
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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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Is there any possible world in which 2+2=5?
Gödel's incompleteness theorems show that arithmetic is either inconsistent or incomplete, and that arithmetic cannot prove its own consistency. It is useful to believe that arithmetic is consistent, ...
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