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 defining the concept of Probability still an open problem in the Philosophy of Science?

There exist several interpretations of the concept of Probability: https://en.wikipedia.org/wiki/Probability_interpretations Being the assumption of Repeatability an important difference between them. ...
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80 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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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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112 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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144 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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142 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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79 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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141 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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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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37 views

Summary of philosophical positions on how belief revision proceeds in mathematics?

Since mathematicians have embraced classical logic, as e.g. MacFarlane points out in his 2021 intro book to philosophical logic (§ 7.4), one needs to distinguish between [meta-]reasoning and argument/...
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73 views

Do constructivists (or intuitionists) reject real numbers, except the computable ones?

SEP has a bunch of pages on what (various flavors) of intuitionists or constructivists seem to accept as a model theory or as a set theory (they actually seem to diverge on the latter, in the sense of ...
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153 views

Does panpsychism imply mathematical entities are conscious?

Does panpsychism claim that even mathematical entities, like numbers and functions and sets, are conscious entities? Or is it restricted to physical objects?
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80 views

What's the role of logic in logical positivism?

I'm reading up on a bit of the ideas of logical positivism. It seems that the main components were the distinction of synthetic and analytic statements, and the verification principle. Without giving ...
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46 views

How would a monistic approach account for these categories of probabilities?

Donald Gillies, in his book "Philosophical Theories of Probability," draws a distinction between monistic views and dualistic views of probability, the latter of which, at least in his ...
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330 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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59 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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71 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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69 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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87 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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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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68 views

Mathematical structuralism and Saussure

Is mathematical structuralism related with structuralism that arose from Saussurean linguistics?
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195 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
111 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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151 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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276 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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108 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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116 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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255 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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58 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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328 views

Existence of mathematical objects: how?

In mathematical philosophy, one asks the question "do mathematical objects really exist"? This is then followed by "yes" or "no" answers, but does the question even make sense? Is it even meaningful ...
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147 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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112 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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320 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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178 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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106 views

Is paraconsistent logic used in other areas of mathematics other than discrete mathematics and in other areas such as physics and philosophy?

Is paraconsistent logic used in other areas of mathematics other than discrete mathematics and in other areas such as physics and philosophy? I heard that paraconsistent logic is an area of discrete ...
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88 views

What is the current status of Foundation-of-Mathematics programmes?

I have been reading 'A Very Short Introduction to Mathematics' by Timothy Gowers and at one point he mentions that most of the mathematical proofs can be finally resolved to a set of logical ...
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49 views

Is there some non-classical logic where the van der Waerden theorem does not apply?

The van der Waerden theorem is a theorem in the branch of mathematics called Ramsey theory which states that for any given positive integers r and k, there is some number N such that if the integers {...
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197 views

Do sets and the empty set exist?

The original title of this question was supposed to be "Do sets exist?", but it was too short. In philosophy of mathematics we sometimes ask whether mathematical objects exist. I think this ...
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42 views

Axioms in philosophy

In mathematics one lays an initial sets of axioms and rules of inference, and builds a theory from there: does philosophy, nowadays, proceed like this? if yes, what are other currently "...
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99 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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264 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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53 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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172 views

About Wigner's view on the relation between mathematics and physics?

Physicist Eugene Wigner argued that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it ...
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114 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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84 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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187 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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88 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 ...