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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Platonism and causality

The Stanford Encyclopedia of philosophy states that - "Because abstract objects are wholly non-spatiotemporal, it follows that they are also entirely non-physical (they do not exist in the physical ...
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67 views

Has Alexandre Grothendieck ever expounded a particular stance on metaphysics or ontology?

It seems that in Recoltes et Semailles, he does go into quite a bit of philosophizing. the only thing of relevance I've found is that he notes how Riemann "in passing" said how he thought perhaps the "...
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108 views

Using differential equation to estimate epistemological growth constant

I found some tweets (1,2) describing a philosophy paper as follows: I came across this paper from the academic journal of philosophy that tries to solve a differential equation for an ...
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141 views

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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207 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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1answer
114 views

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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76 views

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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136 views

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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1answer
103 views

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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88 views

Could the axiom of infinity be in itself inconsistent?

I've seen several threads discussing the axiom of infinity but I wasn't able to find a discussion on this particular aspect. And recent conversations with some people have led me to wonder if it is ...
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43 views

Is 'in re' structuralism a non-eliminative theory in mathematical structuralism?

As far as I understand it the definitions are: Non-eliminative structuralists believe that talk of structures is ontologically committed to the existence of abstract structures. In re structuralism ...
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69 views

Transition of Mathematical Propositions

There are axioms, and then there are well established methods of working with them. It is clear that these methods are nothing but logical operations (rules of manipulation of symbols) on previous ...
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66 views

Mathematical Universe

I have a beginner question on the type of claims this book or similar theories make. That book claims that universe is math structure. I just want to clarify if I correctly understood his goal: Does ...
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80 views

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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64 views

Mathematical structuralism and Saussure

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

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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1answer
81 views

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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149 views

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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254 views

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 just ...
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106 views

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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114 views

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 says ...
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244 views

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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53 views

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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142 views

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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100 views

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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309 views

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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83 views

Is logic part of Philosophy or Mathematics?

Is logic part of Philosophy or Mathematics? I asked this question "Does programming use logic more or mathematics more" and users on some site insisted that logic was part of mathematics, I ...
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88 views

Do all paradoxes of naive set theory have something in common?

If P(x) is the formula "x ∉ x", then ... the assumption that a set h has P(x) purity ... (i.e. the assumption that for all t, if t∈h then P(t)) ... implies that there exists a set k, where ...
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1answer
52 views

Actual and potential truth for neo-verificationists

Neo-verificationists such as Martin-Löf and Prawitz make a distinction between actual and potential truth of a proposition, roughly defined as follows: ... that a proposition A is actually true means ...
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263 views

Mathematical models of dynamic algorithmic processes

This question primarily concerns dynamical or time-dependent phenomena in philosophy and to what extent such heuristic discourse features in more precise mathematical settings. In order to model ...
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52 views

If intuitionism were true, could a mathematical system exist that is incompatible to our system?

If mathematical intuitionism were true, could there be a System that Describes reality accurately and consistently like current maths do Consists of equations that cannot be described by current ...
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2answers
280 views

How do philosophers formally characterise mathematical objects?

In the Stanford Encyclopedia of Philosophy article, 'Platonism in the Philosophy of Mathematics', the following formalisation is given for the existence of a mathematical object: Existence can be ...
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110 views

Justification for applied mathematics

I'm familiar with some philosophy of mathematics and what does mathematical knowledge mean (Plato, Kant, Frege, Brouwer etc.). And as mathematicians, we establish a set of axioms and work up from ...
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32 views

Minimalist philosophical assumptions to reason, deductively/inductively

I've been thinking a lot about foundations of science recently and I was wondering. Are there existing books/essays/works, or were there attempts that try to achieve the following: With a ...
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53 views

Is this an argument about the world or about human cognition?

This is a question about a thesis I have encountered regarding the relation of abstract mathematics ( Category Theory in particular ) with reality and the nature of human cognition. The argument goes ...
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81 views

Are the foundations of mathematics “doomed” to be set-theoretic in nature?

Let's say we want to come up with a foundational theory for all of mathematics and let's say that it is embedded in first-order logic. Note that the machinery of first-order logic is described with ...
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172 views

Are Max Tegmark's Mathematical Universe Hypothesis and Seth Lloyd's Cosmological Model compatible?

I have been interested in Seth Lloyd's cosmological model (which proposes that the universe is a some kind of quantum computer or at least similar to it: https://en.wikipedia.org/wiki/...
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79 views

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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69 views

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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54 views

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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90 views

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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115 views

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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99 views

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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249 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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95 views

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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55 views

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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163 views

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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49 views

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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44 views

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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154 views

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 ...