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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Does panpsychism imply mathematical entities are conscious?
Does panpsychism claim or logically imply that even mathematical entities, like numbers and functions and sets, are conscious entities? Or is it restricted to physical objects?
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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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Rather than "ought to be true = is true" being impossible, might it not just be a trivial stage of moral representation?
I just finished reading Eugenia Cheng's essay on moral phraseology in mathematics, and so I want to go over something she says on pg. 20:
A recent lecturer of Part III Category Theory declared that ...
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Entry points from philosophy into mathematics at higher levels?
Everytime I look up of the link between philosophy and mathematics, I see the topics only of the most foundational levels discussed. As in logic, and stuff. When I study higher mathematics theories, ...
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Can abstract concepts be represented by types in mathematics?
I am reading about type theory along with abstraction and am wondering how they relate. Am i right in thinking that an abstract concept (from the result of abstraction) can be represented by a type in ...
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How could second-order logic satisfy (neo) Fregean's epistemic goal?
Recently I've been reading Shapiro's Higher Order Logic in The Oxford Handbook of Philosophy of Mathematics and Logic, Chapter 25. There are some paragraphs confusing me:
One traditional goal of ...
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Have the indispensability arguments been examined for probability theory?
Indispensability arguments are widely known in the philosophy of mathematics, the idea being (roughly) that we should commit to the existence of those mathematical entities that are indispensable for ...
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Are there any resources that discuss the relevance of mathematical fields/problems to philosophy?
I've been enjoying reading Scott Aaronson's paper Why Philosophers Should Care About Computational Complexity. The paper discusses how the field of computational complexity is of major relevance to ...
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What is the meaning of Principle C'' in Hartry Field's 'Science Without Numbers'?
For Field, the following is 'perfectly obvious', but I would like confirmation that I understand it completely.
Let A be a nominalistically statable assertion.
Let A* be the assertion that results by ...
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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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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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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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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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Is the classical theory of concepts compatible with logical positivism's view on analyticity of mathematics?
Doing some work on theory of mathematical concepts and need a good framework that suits my own views. Is the classical theory of concepts, which seems to no to suffer very much when considered in ...
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Turing's bridging argument of conflating mathematical logic and the philosophy of mind?
So I read this paper and I'll quote the relevant parts:
'Turing's machines are humans who calculate
On Computable Numbers' thus took on the
aspect of a hybrid paper: an attempt to integrate what ...
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Constructivism and function definition in mathematics
In this blog post, we find the following passage:
This connects with something Thomas Forster said, when he rightly highlighted the distinctively modern conception of a function as any old pairing of ...
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What is an object's properties?
What can we consider an object's properties, for example, when can we consider an object's properties as 'changing'? For example, if I move an object from my desk to my table, has it changed? If I ...
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How does aesthetic relate to structure?
If we are to take a subject say mathematics, then often mathematicians may attribute to the well defined structure and precision in describing its theories. I believe there are also other things like ...
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Are questions truth-apt; what is the use of assigning questions a truth-value?
Is John black (or white)?
Yes he is black.
No he is not (black).
I don’t see how can the question be truth-apt and what use is there in assigning (or even being able to assign) a truth-value to the ...
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What in mathematics has the property of beauty?
I might or might not be at an impasse in my writing... I have around 200 pages of notes, and I finally sat down and tried to compile some of the material, but I feel like the presentation is off ...
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Is Frege and Russell's definition of number reducible to Hilbert's?
This is my first post on this site and I hope that its length/format is not inconsistent with any moderation guidelines. My question relates to the distinction that can be drawn between the logicist ...
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Does psychology/cognition come prior to mathematics?
I am not a hundred percent sure this belongs in Philosophy SE, but I couldn't think of a better SE to ask it, so I am asking it here. I got into an argument with a friend who claimed that the science ...
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{Stipulativism vs. ostensivism} vs. {Formalism/if-then-ism vs. ante rem realism}
The SEP article on definitions includes the following two passages:
See Frege 1914 for a defense of the austere view that, in mathematics at least, only stipulative definitions should be countenanced....
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Mathematical style and ethical fictionalism
The SEP article on mathematical style got me thinking: what is the relationship between mathematical style, mathematical fictionalism, and ethical style/fictionalism? There seem to be at least three ...
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Deductive methodology in philosophy
Introduction
Mathematics uses deductive methodology to produce results called theorems that are indisputable truth by logical necessity, with respect to the axioms of the starting axioms and ...
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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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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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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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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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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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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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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 just ...
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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 says ...
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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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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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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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Are "A ∧ A" and "A ∨ A" degenerate expressions?
Although some time ago I had become somewhat familiarized with the notion of degeneracy in mathematics and physics, in my musings on the trivial/nontrivial distinction I found that both Wikipedia and ...
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Would "to avoid the class/set distinction" be, or not be, an ad hoc reason to propose a couniversal set?
Once upon a time, von Neumann proposed the axiom of limitation-of-size, which says that any class "too large to be a set" is then a "proper class," meaning that there is a ...
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Probabilities and Certainties on the Monkey Axis: Yet more about those monkey typists
I was reading with some interest the answers and comments to this question about that familiar, weird and somewhat inhumane infinite-monkey experiment which, somehow, is still generating fresh and ...
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Why not move from proof numbers to theories instead of theories to proof numbers?
In mathematics, they do this thing where they figure out what are called "proof-theoretic ordinals" (see this section of the SEP article on proof theory for background details) of theories, ...
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Language, Meaning and Cardinality?
So I have been pondering about language. By language L I just mean a series of symbols. The upper limit of this series of symbols is Aleph-zero. Yet somehow using these symbols the human is able to ...
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