Questions tagged [philosophy]
Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.
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Gödel Incompleteness theorems - gap between first order logic and arithmetic
I have a doubt concerning Gödel's incompleteness theorem which might be stupid but that makes me uneasy. If I'm not mistaken, Gödels proof is broadly undertaken using first order formulas, numbering ...
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(When) are recursive "definitions" definitions?
This is a "soft" question, but I'm greatly interested in canvassing opinions on it. I don't know whether there is anything like a consensus on the answer. Under what conditions (if any) are ...
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What are the criteria for a subject to be under the domain of mathematics [duplicate]
It is to my understanding that mathematics is in some way the domain of all logical systems. However unconventional, as long as certain criterias are met, they could be considered as part of ...
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Confused about abstract models for axiomatic systems
I am studying axiomatic systems and I have a hard time understanding how one is supposed to come up with an "abstract" model for an axiomatic system.
I will use the following example taken ...
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Proof by Contradiction: "Bad Form" or "Finest Weapon"? Reconciling Perspectives [duplicate]
G.H. Hardy famously described proof by contradiction as "one of a mathematician's finest weapons." However, I've encountered claims that some schools of thought consider proof by ...
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statements that can be accepted by finitists.
"On the finitist view, the formula $\exists n P(n)$ is meaningful only when it is used as a statement specifying how to calculate an $n$ for which $P(n)$ is true".
It is mentioned as above ...
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Why do we use real numbers for (for example) masses in physics and how do we verify product axioms? [closed]
I have studied the definition of real numbers as V.A.Zorich explains it in his first book Mathematical Analysis I. Basically, he says that any set of objects that respects a certain list of properties ...
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Why Does This Proof Hold?
I'm currently reading "Mathematics Without Numbers" by Hellman, G., and I'm on pages 26-27. It seems like Hellman is discussing opposition to viewing mathematical proofs solely through the ...
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Does it make sense to divide mathematical theorems into those susceptible to experimental conjecture and those that are not?
I read the following in a good book: ”let's start from zero", the authors are Vinicio Villani and Maurizio Berni (pisan mathematicians) but I don't know if the book is also marketed outside Italy....
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What is the formal system when we are using many different sets of axioms?
I am just starting to learn about formal systems, and have learnt that the many axiom systems in Mathematics, such as those of plane geometry, Peano's axioms, vector axioms, etc. can each be used to ...
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Why do we need a metatheory if we can include self-referencing language in the object theory?
I am wondering why we need to have a metatheory in order to talk about a theory- why can't we just add self-referencing terms to the language of the formal system on which the theory itself is based, ...
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Are quasi-sets (and therefore Schrödinger logic(s)) studied by mathematicians or are they purely in the domain of philosophers?
Context:
I'm a fan of different kinds of logic. I'm conflicted about whether different logics actually exist beyond, say, a philosophical oddity.
The Question:
Are quasi-sets (and therefore ...
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Is there a mathematical or physical, real world use for numbers passed I? Who determines what can be conceptualized or not? [closed]
I is the Square root of -1, such that I * I = -1. Through this, I can be considered like a "Half Negative."
Why hasn't this been taken further? Why don't we make a quantity such that I^...
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Definite description in homotopy type theory
I asked this question there and I have been suggested to ask it here.
In a paper by David Corfield, we have an account of definite description in homotopy type theory. The author gives the following ...
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Creating larger structures from smaller ones without an explicit construction
I'm asking this question as a replacement for my previous one, which I admit isn't clear, and which I am voting to close. Hopefully I'll be clearer now.
Admittedly, I'm not sure if this question ...
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