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Questions tagged [philosophy-of-mathematics]

Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.

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Is there a natural example of a non-self-referential semantic paradox in philosophy?

A commonly studied paradox is the liar's paradox. The liar's paradox is to determine whether "this statement is false". The usual resolution is to state this the sentence is not actually a statement ...
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Are there counter-examples to this broad characterization of mathematics?

Mathematics can be broadly characterized as the study of non-trivial apriori symbolically displayed axiomatic systems. Or more elaborately the study of non trivial apriori implicit or explicit ...
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What is the difference between depth and surface information?

I was looking for an answer to this question: Was Euclid's method of proof axiomatic? While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" ...
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Distinguishing between procedure-like and collection-like mathematical objects

Is it useful/productive to draw a distinction between "active" things with "computational force" (procedure-like) and "passive" things without such force (collection-like)? Does this distinction have ...
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Does Reflective Set Theory “RfST” fulfill the requirements of founding Category Theory and Mathematics?

On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
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Similar to Douglas Adam's HGTTG, Is there any philosophy that views human society as a computation?

In Douglas Adam's Hitchhikers guide to the Galaxy, Earth is a supercomputer that is computing the the Ultimate question, whose answer is 42. I was wondering is Douglas Adams was inspired by any ...
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102 views

Does the snake bite its own tail: “Philosophy of philosophy”

I was just philosophizing about the philosophy of mathematics. Then at one point I philosophized: is there a philosophy of philosophy? Is that meta-philosophy, or is that just philosophy again? Can ...
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129 views

Truth in Science vs. Truth in Math

Two scientists independently try to solve a problem to predict a certain phenomenon. The two scientists come up with different answers, but both of their solutions seem logical to each other. How do ...
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How can truth exist if every statement is ambiguous? [closed]

I have read online and personally believe that every statement has some degree of ambiguity to it. With this in mind, I was wondering how any propositions can be true. For example, I have heard some ...
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265 views

Mathematics and disagreements

I was just pondering as a mathematics major, is there a particular instance where a mathematician's work doe NOT require agreements among peer scholars of mathematics to determine the quality of the ...
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219 views

Are there any good philosophical arguments for or against Cantor's theorem, other than the ones that Cantor came up with?

I am looking for philosophical arguments for and against Cantor's theorem other than the ones Cantor came up with, if you know any, can you present them or a link to them? I post this in philosophy ...
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Can results be predicted?

I wanted to know that, what can we assume as the result of some experiment which we have not conducted on the basis of mathematical proofs? I mean, in general, equations are created after analyzing ...
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Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
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Is mathematics something real or just an abstraction we created?

Is mathematics something real like something so correlated in our universe which would be different in other theoretically universes or is it just an abstract universe-independent layer/framework we ...
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Do mathematicians use logic when adding things up?

I asked a similar question recently, and it was closed. So, bear with me. When two things are materially equivalent we don't add anything to work out how much we have of both together, right? If ...
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What are the philosophical implications of using inconsistent mathematics?

I have stumbled across the idea of 'inconsistent mathematics' and could not fully understand: why mathematicians would prefer at times to work with inconsistent systems (from which I assume everything ...
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1answer
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If our world is mathematical، Does not this increase the probability of being complex as well?

Tegmark's mathematical universe hypothesis, posits that reality is a mathematical structure. This mathematical nature of the universe, Tegmark argues, has important consequences for the way ...
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Is there a summary of Russell’s Principia Mathematica?

Perhaps better, is there an accessible version of the Principia? I am looking for a summary that would summarize and clarify Russell’s reasoning behind his famous conclusion that 1 + 1 = 2.
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Are there infinitely many “unique” mathematical concepts? [closed]

The difficulty in formulating my question lies in defining what I mean by "unique." What I mean by "uniqueness": For example, the concepts that 1 + 1 = 2 5 + 2 = 7 6 x 3 = 18 6 - 9 = -3 etc. only ...
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What is the empirical basis for justifying mathematics?

In the introduction of a very nice book by M. Giaquinto, called Visual Thinking in Mathematics, he investigates the conditions that give rise to mathematical knowledge - the following ideas are ...
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237 views

Can infinity be made finite in certain conditions?

In mathematics there are not only infinitely big numbers, but also infinitely small numbers. One can consider arbitrarily small numbers that can exist only in the mathematical world. For example, ten ...
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Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?

Tegmark's mathematical multiverse hypothesis assumes that all mathematical structures exist as universes But do you know whether his hypothesis also allows/accept universes described by other types ...
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Mathematical structuralism and Saussure

Is mathematical structuralism related with structuralism that arose from Saussurean linguistics?
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57 views

Is everything in the universe made of 0s and 1s? [closed]

Qubits are the quantum counterpart of the bits used in traditional computing. While traditional bits represent data as 0s or 1s, qubits are distinguished by what's known as superposition, or the ...
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Is there any correlation between numbers and sensory experience?

Numbers exist, that is clear to me, but is there any logical correlation between numbers and sensory experience? This question came while I was reading Einstein's comments on Bertrand Russell's theory ...
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Can a reason cost 5 dollars?

Imagine a school where no one can wear a red hat. John goes to school with a red hat costing 5 dollars. Someone says John's red hat "is" the reason why he can't get into the school. What is the ...
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What is the principle of underdetermination?

While studying I read about the principle of underdetermination of scientific theories. I made some researches online but I am more confused than before. I read about the Quine-Duhem holistic thesis, ...
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Mathematical Consensus

Can anyone give me a reason why mathematics may require consensus to determine the quality of knowledge from the general mathematical community? Also what would be the counter to such a claim, as in ...
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64 views

What is frequentism?

I am studying for an exam and I ran into frequentism. Honestly, I don't understand anything about that. Is frequentism related to probability only? Why are probabilities understood as frequencies? I ...
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1answer
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What are the implications of relativity of Mathematics?

I came across the idea that the same statement can be true in one model while not true in another, while both models are being consistent. An example is "Is the sum of the angles of a triangle equal ...
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Is the commutative property of multiplication intuitive to everyone at first glance? [closed]

a × b = b × a Most people speak about this as if it is common sense. For example, let's say 265 * 7948 = 7948 * 265. I can't get my head around when arbitrarily putting this adding 7948,...
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Does an infinitesimal instant of time have zero duration? [closed]

Is there a philosophical argument supporting the hypothesis that an infinitesimal instant of time has zero duration? The reference to infinitesimal includes the modern presentation of it in non-...
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5answers
224 views

Can anything be less than one?

Zero itself seems to be an absurd number because if there is really zero of something, then nobody has ever sensed it. But even with temperatures, we don’t really have negative and positive ...
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206 views

Can randomness be random?

In mathematics, a true random number generator it's impossible, because any formula defines a process that, however complex, is not random. A random event must be unrelated to any cause or condition, ...
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Why do the limits to the computation of the universe appear to us as fundamental physical constants? [closed]

According to the Estakhr's Principle of Physical Constants Physical Constants are Computational limits or vice versa. Why do the limits to the computation of the universe appear to us as fundamental ...
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Can infinity have a beginning? [closed]

I have trouble with the mathematical notion of infinity. Example: Consider all of the natural numbers. It has a beginning, therefore it is bordered, therefore it cannot be infinity.
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Anyone defined the geometric point before Aristotle?

Did Plato or anyone else discuss/define the geometric point? I know Pythagoras discussed the math point. I read that Euclid's definition (with no part) is a mistake in translation from the original ...
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How can infinity become actual? [closed]

There are two mathematical concepts of infinity, potential infinity and actual infinity. I do not understand how the latter is being used. For the simplest infinite set, the natural numbers, we get: ...
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Is a set containing itself already a paradox?

This is inspired by Russel's paradox stating there is not set of all sets. It uses the presupposition that set can contain itself. However, this already seems paradoxical. Suppose a set A = {}. Then ...
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Can any logic system provide the impossible solution to Russell's paradox in naive set theory?

In naive set theory in classical logic, we cannot describe or find a solution to Russell's set paradox (it is impossible). But is it there any logic system or any method that can provide this ...
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Understanding hypothetical reasoning and material implication

I am a little bit frustrated in how we use hypothetical reasoning in everyday life. Many times we make "if-then" statements. For example, if i get ill ,then i cant go to work and if i cant go to work ,...
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If nature is inherently imprecise, how is it so easy for us to conceptualize mathematical certainties?

In modeling any real physical system, we are required to employ inductive reasoning. We can never be completely certain about the state or properties of any system or of any future observation we will ...
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Implication vs sufficient condition vs hypothetical reasoning

I was bit confused to clarify the difference between them because "if-then" are used a lot in everyday life. So for example we have a car which is full function and someone says if i turn the key the ...
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1answer
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Is there any logical system/method where impossible/illogical/inconsistent things can exist (like a solution to Russell's paradox that makes sense)? [duplicate]

Discussing with a philosopher about impossible things existing or being allowed within a particular logic system, he told me: "This is a funny thing about logically impossible things. You can prove ...
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Understanding the simulation argument

I came across Nick Bostrom's paper called Are You Living in a Computer Simulation?. The paper argues that at least one of the following propositions is true: The human species is likely to go extinct ...
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Is psychologism still a thing? What are common rejections of psychologism?

Recently, I learnt that there exist people who go so far as to claim that "mathematics is a branch of psychology". I thought that psychologism was long outdated, in connection with mathematics at ...
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Can paraconsistent or other logics make the impossible happen?

A paraconsistent logic system it is defined as "a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that ...
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Are mathematical results influenced by the way we reason?

Intuitions of mathematicians, and the mathematics they develop, are ostensibly influenced by whether they primarily rely on visual_spatial and/or verbal_symbolic reasoning skills. Is it fair to say ...
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166 views

Is there a mathematical framework where both potential and actual infinity are used?

1) By actual infinity I mean that given X, it is inaccessible by Y, where Y is a placeholder for any possible non-finite set, such that no non-finite set is accessible to X (X is beyond the notion of ...
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Where does science end?

Being a physics student I have been behind many mysterious actions of nature, but when we remove one of these mysteries another pops up. Does science end anywhere? Or are these mysteries just ...