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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Mathematical Platonism vs Platonic Platonism

According to the summary of Platonism (ie the Forms) by Aristotles Metaphysics: Besides sensible things, and the Forms, there are mathematical objects; of the first (the sensible) they share in ...
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Is the inconsistent (or paraconsistent) line a possibility?

According to the SEP: Another place to find applications of inconsistency in analysis is topology, where one readily observes the practice of cutting and pasting spaces being described as ...
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452 views

Is mathematics as pure as originally thought?

It is said that theorems in mathematics cannot be proved or disproved by experimentation. I assert that if a statement is decidable, then it can be proved or disproved in a finite amount of time by a ...
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What is the number 2?

My friend told me that he took a course in the philosophy of mathematics and said that they defined the number 2 to be "the set of all sets with two elements." I may be remembering wrong, but this is ...
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If a cone is divided in a plane parallel to its base, are the surfaces produced by the cut the same or different in size?

Democritus of Abdera, the ancient philosopher of Greece, reasoned over two thousand years ago: If a cut were made through a cone parallel to its base, how should we conceive of the two opposing ...
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Can we add Pi to Pi [closed]

Can we say we can add Pi plus Pi? (from http://deepturtel.blogspot.in/2015/01/pi-plus-pi.html): Are the rules of addition in Maths defined for such a process? Or do we always add only approximations ...
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Mathematical versus philosophical reasoning (and the mathematics of philosophical arguments)?

What is the difference between mathematical reasoning and philosophical reasoning and why isn't philosophy just considered to be a branch of mathematics? Is any study not a branch of mathematics ...
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How historically grounded is the standard narrative of the Irrationals in Antiquity?

Its commonly said that the Pythagoreans were unbalanced by the discovery of the irrationals; since their philosophy was predicated on ratios; ratios of two finite numbers. Still, it is natural to ...
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Input/output in 'mathematical' programming languages [closed]

More than once I have observed this: A person describes a functional programming language (as opposed to a programming language that makes heavy use of interspersed states), that person will say it is ...
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Creativity in mathematics [duplicate]

Hello can anyone especially e.g. an actual mathematician, from the horses mouth, explain what role this has in mathematics, both through the whole course of learning skills and mathematics, and ...
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Is mathematical platonism compatible with Platonism?

When calling themselves "Platonists" mathematicians usually mean that they feel they discover ideal facts that eternally exist in some way. My question is if this sentiment is consistent with Plato's ...
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What does Deleuze mean by “the world can be regarded as a 'remainder'”?

Deleuze in Difference & Repetition writes in the chapter named as the Assymetrical synthesis of the sensible: It is therefore true that God makes the world by calculating, but his calculations ...
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What is the intersection of Physics & Philosophy?

(I've already asked this question on Meta, but as one answer (by Joseph Weissman) pointed out this is already a philosophical question; so I thought it worth asking here). I've asked a number of ...
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Dual of identity relation?

Does anyone have any intuitions about what the dual of the identity relation might be? I.e. is there a 'natural' concept expressed by a statement such as 'it is not the case that a is not identical to ...
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Countable additivity

Graham Oppy writes in »Philosophical Perspectives on Infinity«: Without countable additivity, it seems – for example – that we must lose the result that an arithmetic sum of an infinite series is ...
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Why does Aristotle suggest One is not a number?

Parmenides showed Nothing is not the same as Zero; the second is a number, and the first is not, in more than one sense; it also differs from the Buddhist notion of Sunyatta, which is nothing in a ...
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240 views

What is one divided by zero?

The Pythagoreans were (probably apocryphally) disturbed by the discovery of irrational magnitudes; its useful pointed out here, that irrational means, in one sense, and not now generally alluded, ...
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Mathematical reductionism: senseless

Does it make any sense to ask if logic can be reduced to math? Truth be told I have no idea what the inverse logical reduction could look like. Naturally I'm familiar with a kind of reductionism, in ...
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Should the easiness with which math is applied to the world be a surprise?

I study physics at an undergraduate level. Since early on, I've was a person who thought math was 'logical' and as such, its applications to the world aren't really a surprise since math is so ...
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What purpose do mathematics and philosophy serve epistemologically (compared to sciences)?

Kant did not consider them sciences, but meta-disciplines that study a priori conditions of doing science. Indeed, both mathematics and philosophy permeate all empirical sciences to varying degrees, ...
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Are there any naturally occuring non-embedded manifolds?

Mathematicians are always insisting that manifolds need not be embedded, and by Occams Razor, are best thought without the surrounding ambient space. For example, the surface of a table is a 2d ...
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Do mathematician always agree at the end?

I know it's a off beat question but I thought philosophical answer would be better. I've been trying to study some different sciences in my life, ranging from biology to mathematics, and if I try to ...
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321 views

Do Mobius Strips have a front and back?

Mobius strips, are generally held to have only one side - if one marks a place on the strip and on what looks like the other side then a pencil can draw a line between these two points without ever ...
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When is Mathematics not about counting?

A comment on an answer I posted asserted that "Mathematics is NOT always about counting". My thoughts were that if there's a unit (inches / milligrams / light years etc), then someting is being ...
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Where does Quine say logic should have no ontological presuppositions?

I'm sure I recall Quine saying in various places that one distinction between logic and set theory is that logic should have no ontological presuppositions (or, at most should presuppose some thing ...
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What is mathematics? [duplicate]

Is mathematical practice: an act of discovery of eternal objects and ideas independent of human existence; an intuition-free game in which symbols are manipulated according to a fixed sets of rules; ...
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What proves the law of non-contradiction true?

How has man determined that "The Law Of Non-contradiction" is true? The first time I heard it, if I understand it correctly, I proved it false. Do I understand correctly, that a matter for ...
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Jorge Luis Borges suggests that using a lottery is an “intensification of chance.” Does this make sense?

By intensification of chance, Borges adds that a lottery brings "a periodic infusion of chaos into the cosmos." To me, the idea that chance can be "intensified" seems strange. However, I'm also not ...
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Are there any other branch of mathematical philosophy?

Are there any other branch of mathematical philosophy? I am refer to the mathematical logic, are there any other branch of mathematical philosophy? For example, philosophical graph theory would be ...
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Does phenomenology determine ontology?

There were many historical instances where phenomena could be explained by seemingly incompatible theories, Copernican and Ptolemaic systems, corpuscular and wave theories of light, interpretations of ...
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Are ordinal or cardinal infinities theories for real?

There are a number of notions of infinity in mathematics that are respectable. One of the first is 'the point at infinity' to the line or plane; but one can argue that this is a spurious infinity as ...
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Does mathematics apply to physics in one way or multiple ways?

Does mathematics apply to physics in one way or multiple ways? What do Aristotle and Plato think? It would seem that Aristotle thinks mathematics can be applied to physics in one way only because, ...
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494 views

If the Platonic world exists how would we know?

If we assume existence of a non-material world of ideas that mathematics describes there are some questions that a Platonist has to address. 1) How is the ideal world related to the real one, where ...
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Are there two different mathematics in philosophy?

I was looking at arguments about mathematics being a science (or not), here for example, but it seems that these arguments are more about some metaphysical idea of mathematics rather than the subject ...
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Existence vs tertium non datur

This is my first question here, sorry if it turns out to be a duplicate. Mathematical constructivism states that contradicting the non-existence of something won't imply its existence. Does it mean ...
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Can mathematics be sublime?

The Sublime is sometime used as a synonym for subtle or sophisticated but with aesthetic overtones. In the original setting for this aesthetic notion it was a combination of Beauty & Greatness, ...
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Sources for the aesthetics of mathematics

Many mathematicians often equate mathematics to art and find a deep beauty in its method, results, and ideas. The classic example of this romanticism is captured by G.H. Hardy's A Mathematician's ...
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Is it possible to assign an objective profundity to theorems in a formal system?

To be concrete and specific, let us say we are working in Peano Arithmetic. Is it possible to assign a partial order among theorems of Peano Arithmetic that agrees with our vague intuitive notion of ...
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Formal systems and interpretations for numbers

In my book (Hodel's Intro To Mathematical Logic), we are given several examples of formalized mathematical theories such as group theory, Peano arithmetic, etc. But I've had this ongoing confusion: ...
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Can anyone explain the very beginning of The Analysis of Matter to me?

Can anyone explain the very beginning of The Analysis of Matter to me? What exactly is it that he is saying is an aesthetic choice with respect to physics? I just opened up the book and can't get ...
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What is an infintely small unit (of time)

Is there a philosophy of the infinitely small? Does anyone apply it to qualitative experience, and ask if that is divided up into instants? It seems to me that the infinitely small could not be like ...
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Why isn't Cantor's diagonal argument just a paradox?

Cantor's diagonal argument concludes the cardinality of the power set of a countably infinite set is greater than that of the countably infinite set. In other words, the infiniteness of real numbers ...
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How do we know if a mathematical proof is valid?

Georg Cantor has showed there are more real numbers than natural numbers in his diagonal argument. Assuming that two sets have the same size if we can make a pair up elements from set A with elements ...
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What makes a math problem “difficult”?

Someone shared with me a video of Fermat's last theorem: http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem Obviously it's been solved now: is the answer in an information rich vocabulary, is that ...
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Circular nature of the cosmos. (π) [closed]

I've been pondering the irrational number that is pi and how it relates to the infinity of the universe. We often see many cycles in nature, current scientific theory states that the universe began as ...
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Universal quantifier in Russell's Theory of descriptions - Who is the UNIVERSE?

In Russell's 1905 paper "on denoting" in which he introduces his theory of descriptions, he uses his method of analyzing propositions that include denoting phrases (descriptive ones), by rewriting ...
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Difference between math and physics in terms of describing the/a universe?

"The difference between math and physics is that physics describes our universe, while math describes any potential universe" This was one of my math professor's arguments in trying to convince me to ...
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Where is philosophy today [closed]

Basically I'd like to know which are the main philosophical schools today (meaning maybe the last 5-10 or even 15-20 years), where they come from and, if there is a reasonable answer, where are they ...
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Why do we have a problem about understanding the concept of the “empty set”?

   The title seems quite bit more generalized, but I'm saying about the philosophers and mathematicians in the past who discussed about the concept of nothing, or the empty set. I'm ...
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Is Mathematics considered a science?

Science, generally is analyzing information gathered from observing phenomena, and coming up with theories to try and explain the phenomena. Then, attempting to predict a new phenomenon before it ...