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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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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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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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Are the “laws” of deductive logic empirically verifiable?

"Is Logic Empirical?" strongly suggests a question that I would like very much to get a handle on. That phrase is a title of an article by Hilary Putnam, and, according to synopses/reviews, the ...
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Help wanted - need descriptor for a partcular type/form of argument

I am writing a paper on cognition, and to simplify my discussion I need an adjective or descriptor for particular category of argument as follows: I am arguing for the necessity of a construct with a ...
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can we reason about logic?

People who study mathematical logic make arguments about logic itself. So it seems that people take for granted an "intuitive logic" (otherwise, how would they form arguments?). So the observation is ...
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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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Looking for references for some remark of Quine's

I'm looking for a comment I think I remember Quine having made. He's talking about our understanding of proofs. I think he says something along the following lines... If you understand many different ...
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315 views

What is the relevance of applicability to the natural sciences in pure mathematics?

I think I am coming to a good, new understanding of the relationship of pure mathematics to the natural sciences. A major concern of mine is just how reliable is rigorous (characteristically "pure") ...
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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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what is the ontology-ideology distinction in phil of math

Quine proposed a distinction between ontology - the doctrine of what there is - and ideology - the complex terms and predicates expressible in one's theoretical language (though in his 1971 paper he ...
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120 views

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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209 views

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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Examples of theories that assume the existence of an “External Reality”?

In this paper written by physicist Max Tegmark (https://arxiv.org/pdf/0704.0646.pdf) it talks about "External Reality Hypothesis". Specifically, he says: Although many physicists subscribe to the ...
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Philosophy - Is Nietzsche's Eternal Return theory true?

Is Nietzsche's Eternal Return theory true? I am extremely worried that it is because of the very likely fact that Einstein's Block Universe theory is true, and what renders Einstein's Block Universe ...
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What questions or areas in the foundations of mathematics remain active research fields?

By foundations of mathematics I am referring to the mathematical, logical, and philosophical foundations of the subject. I'm interested in seeing which of these have active research going on within ...
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Does Tegmark's hypothesis include dynamical mathematical structures?

Tegmark's hypothesis is the idea that mathematical structures are physical and thus have physical existence (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) Zuse's thesis says that ...
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Relation of Mathematical Propositions to Natural Language

Treating Natural Language as a language game, what role does it play in our understanding of mathematics? Does natural language provide meaning to mathematics? Does a proof of a conjecture, say FLT,...
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202 views

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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Mathematical structuralism and Saussure

Is mathematical structuralism related with structuralism that arose from Saussurean linguistics?
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journal for mathematics of philosophy/mythology

I have been working on research involving the use of mathematical formulas and reasoning in order to philosophical concepts, specifically concepts concerning mythology, the Jungian model of the psyche,...
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why is ontological parsimony important for philosophy of mathematics

It appears that one important motivation for being a (Quinean) nominalist about mathematical objects is ontological parsimony: mathematical objects are ontologically extravagant; so if we can rewrite ...
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Criticisim of Hilbertian Formalism

The two main criticisms against the philosophical position on mathematics which is called game formalism (see here for details) are, The first is the question of applicability: if mathematics is ...
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Why didn't Newton pursue philosophy?

Why didn't he pursue philosophy in the same way Leibniz did, many "natural philosophers" during that time often delved into many fields since it wasn't really required to specialize yet, but it seems ...
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Philosophy and Reading: Towards Math, and Physics

I was reading a book about learning philosophy for beginners called Introduction to Philosophy Classical and Contemporary Readings Edited by John Perry, Michael Bratman, John Martin Fischer It ...
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Some questions on Graham Priest's remarks about Russell's solution of paradoxes

In his book Beyond the Limits of Thought while talking about Russell's solution of paradoxes Graham Priest writes (text made bold, footnotes and references omitted), Russell solved these problems ...
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Do (any) philosophers worry if there can be a priori truths about a changing world?

Do (any) philosophers question how there can be a priori truths about a changing world -- has anyone worried whether this is possible, or if those different modes, of timeless truth and contingent ...
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What are the differences (if any) between classical and modern predicativity

I am researching Predicativity and I've encounterd defenition for classical predicativity and for modern predicativity but I can't understand the differences between them. Thanks
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Nominalist views and contradictions

Given a flavor of nominalism which denies that simple sentences and existential quantifiers referring to mathematical objects are literally true (pretense theory, fictionalism, figuralism, etc.), ...
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How can rational choice theory be explanatory?

In his work, John Harsanyi appears to have taken issue with classical social theorists' account of social phenomena. For example, he criticized Max Weber's typological approach on the grounds, "If we ...
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Should I take Math GRE Subject Tests for applying to Philosophy Phd to study Philosophy of Math?

If I was interested in studying philosophy of another field (e.g. philosophy of math or physics), would philosophy phd programs I apply to be interested to see my scores on the gre subject test for ...
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considering the line and circle as not just a contrary, but as a extremes on a continuum

Question: In Greek philosophy, it is generally taken that the line and the circle form a contrary. For example in Aristoteles Physics generally takes that motion can be formed out of this contrary, ...
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Are numbers universal in Set Theory and nominalist in Category Theory?

The number 3, when considered as a universal, abstracts the property of 3'ness from all groups of 3 objects. One supposes that this universal, by conceptual neccessity of what is understood by the ...
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The nature of Nominalist Formalism

In this entry in the stanford encyclopedia of philosophy, it is stated that the theory of nominalist formalism deals with the metatheory problem of formalism as follows: Commendably, Goodman and ...
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What was Wittgenstein's argument against Cantor's transfinite numbers and where did he make his objection?

G. E. M. Anscombe had this to say about propositions in Wittgenstein's Tractatus: (page 137) It seems likely enough, indeed, that Wittgenstein objected to Cantor's result even at this date, and ...
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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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Is the couplet about mathematics and poetry about logocentricism and deconstructionism?

I find this couplet really interesting: Mathematics is the art of giving the same name to different things Poetry is the art of giving different names to the same thing The first one is made ...
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William James on mathematical conceptions not related to perceptions?

I'm studying William James. I'm mainly interested in his Radical Empiricism and Pluralism. I really like his views but I need some clarification on what is his position on conceptions that are not ...
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Is it 'natural' to hold that big sets and proper classes exist?

Various set\class theories present different kinds of ontology, broadly speaking there is the dichotomy of classes versus Ur-elements, and the former can be further subdivided into sets and proper ...
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240 views

Does string theory raise new philosophical questions about existence of physical objects?

If you look at the configuration space of a robot arm, it is a manifold. Does this manifold exist in the same sense as strings in string theory? Or do the strings in string theory exist in another ...
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Rethinking arithmetic operations after J.L. Austin's performativity?

According to Kant, arithmetic statements such as "7+5=12" are synthetic a priori. Could we alternatively think of this not as a statement, but as an arithmetic-logic operation to be executed (like a ...
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What consequences (types of) exist in the real world (categorical monoidal logic)?

Springer book http://www.springer.com/la/book/9783642128202 "New Structures for Physics" (which contains lot of metaphysics despite the physics in its title) elaborates categorical and monoidal ...
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Question about Imre Hermann's book Parallelismes

Apparently, in his book Parallelismes, Imre Hermann discusses Hilbert, Brouwer en Russell from the viewpoint of psycho-pathology. Does anyone know whether the entire book is about mathematicians/...
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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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Are Axiomatic systems derived from Law?

Axiomatic systems arose in Greece & India in Geometry and Language, the exemplary texts being Euclids Elements and Paninis Ashtadyayi (grammar). Now, when one considers the idea of Law: Law ...
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How much this theory fulfills of criteria for a foundational theory of mathematics?

[EDIT] The criteria for a founding theory of mathematics, especially if it uses large cardinal axioms that I want to refer to are those of Harvey Friedman's 2000 criteria given in pages 5-6 of the ...
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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 other “sciences” be applications of mathematics?

Can other "sciences" (it's in quotation marks, because the definition for a science is not necessarily exact) be applications of mathematics? If other sciences, be it philosophy or economics or ...
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230 views

What is going on with Russell's “beauty cold and austere” of mathematics?

I admit that this is an idle question, but I wondered why it is that mathematics appears "beautiful cold and austere" to those who are particularly gifted at it. The full quite from wikipedia on this ...
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Hilbert's formalism and game formalism differences and similarities

I've recently encounterd differences and Hilbert's formalism and game formalism. They seem pretty much simillar in my eyes. I wish to understand, In what way Hilbert’s formalism resembles game ...
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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 “...