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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Was mathematics invented or discovered?
What would it mean to say that mathematics was invented and how would this be different from saying mathematics was discovered?
Is this even a serious philosophical question or just a meaningless/...
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Why is there something instead of nothing?
A simple but fundamental question.
The "something" means the whole Universe (known and unknown), it could be represented as the reality version of the set of all sets, which is itself debated. It ...
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What is the difference between depth and surface information?
I was looking for an answer to this question: Was Euclid's method of proof axiomatic?
While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" ...
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What are the necessary conditions for an action to be regarded as a free choice?
A common philosophical question revolves around the existence of free will, but what I've found is that these debates seem to gloss over the concept of "free will" itself, either taking it as a given ...
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What are the historic stances on the epistemological status of mathematics?
I know that Plato and Kant thought it was synthetic a priori (although Plato would not have phrased it in that way). What other major thinkers have weighed in on this issue, on both sides of both the ...
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Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?
Tegmark's mathematical multiverse hypothesis assumes that all mathematical structures exist as universes
But do you know whether his hypothesis also allows/accept universes described by other types ...
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What is the philosophical ground for distinguishing logic and mathematics?
I was wondering why the field of mathematics and that of logic are perceived as two distinct fields. Although could be pleased with the intuition that logic is rather meta-mathematics, still would ...
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Does Quine's dissolution of the Analytic/Synthetic distinction challenge mathematical realism?
I was surprised to learn that Quine is a mathematical realist (See this interview for example). I always assumed that his "Two Dogmas of Empiricism" and specifically his dissolution of the Analytic/...
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Is Aristotle's resolution of Zeno's paradoxes vindicated by motion in the intuitionistic continuum?
In Physics VIII.8, Aristotle refers to his usual resolution of Zeno's paradox of motion:
We should make the same response to anyone who uses Zeno's argument to ask whether it is always necessary to ...
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Was there a Kantian influence on Hilbert's formalist programme?
In this paper by Cassou-Nogues which is on an aspect of the mathematical philosophy of Cavailles he quotes the mathematician Hilbert (a colloborator of Einstein in Gottingen)
...We find ourselves ...
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Is it possible to visualize higher dimensional space?
This might seem like a trivial question, but it may be more complicated than it seems. I'm wondering if it would be technically possible to visualize higher dimensional space. By that I mean seeing ...
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Have the exact sciences tried to obtain their legitimacy from "outside" the human being?
I'm not really specialized in the history of science. But it seems for me that as the time passed, the exact sciences tried to do that. For example: The second is measured in relation to the spinning ...
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What should philosophers know about math and natural sciences?
My question is whether a lack of knowledge about formal mathematics or theoretical science in general would have an impact on a philosopher's ability to think and make judgments.
Why should a ...
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Are numbers real?
I am confused as to what numbers are. Numbers are defined to be what they are, so numbers aren't real? But numbers are found in nature, right? So if we invented them, how can they be found in nature? ...
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What makes something mathematics?
Dictionary.com definition of math:
(used with a singular verb) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.
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Is the use of inconsistent definitions a logical fallacy?
I am not asking for a defense of or pro/con of the existence of an omnipotent (or multiple omni-x) being, or for the existence of square-circles or any other similar thing. These arguments are well ...
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Math Universe Hypothesis
Can someone please explain in simpler terms what does this:https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis, mean?
Does this mean tegmark says for example: humans have corresponding math ...
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Is geometry mathematical or empirical?
Is Euclidean geometry a mathematical theory, or is it a theory of empirical science?
If taking it to be a mathematical theory would it be due to having alternative geometries? If so, is it in some ...
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Is Logic Empirical?
We use the logical system that we know from observations (empirical data) holds true in the world we live in (please correct me if I am wrong). Hence the axioms of logic we choose are themselves ...
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What is mathematical existence?
When I make a claim in a proof that a mathematical entity exists, is this no more than saying that the theory I'm working within is consistent, and that all the steps upto that point in the proof are ...
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How does actual infinity (of numbers or space) work?
Is infinity just continuous generation of numbers, or can space be actually infinite? If it is finite can we see it expand if we went to the edge?
When I say "I am counting to infinity" does it mean ...
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Do numbers exist independently from observers?
Do numbers have an objective existence? If life had not evolved on planet earth would there be numbers or are numbers an invention of human minds?
Are there any relevant works that discuss this? (I ...
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Why is Aristotle's objection not considered a resolution to Zeno's paradox?
It seems to me, perhaps naïvely, that Aristotle resolved Zenos' famous paradoxes well, when he said that,
Time is not composed of indivisible nows any more than any other magnitude is composed of ...
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Is mathematics truth? As in the sense of that which is manifest or possible in reality?
In mathematics there are imaginary numbers which cannot be represented directly in reality (the physical world). For example, you can't have i apples where
i = √-1 (square root of -1)
Can we ...
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Which field is more rigorous, mathematics or philosophy?
I don't know if this question is best suited for this stack exchange, but I couldn't think of a better stack exchange. I want to know, which field of study is more rigorous, mathematics or philosophy? ...
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What are the arguments for and against "one true arithmetic"?
This question was born out of a discussion Is the real number structure unique? on Math SE, but since it is more philosophical than mathematical I decided to ask here.
From Gödel completeness and ...
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Is logic subjective?
If logic is constructed from axioms, and axioms are depended on observation which in term could be subjective, does this means that logic could be limited to our observation, and not really absolute ...
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Are mathematical statements necessary truths?
I apologize if a similar question has been asked here, but I haven't found it.
Are mathematical statements necessary truths?
By 'mathematical statements', I mean both mathematical axioms as well as ...
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What is the difference between a statement and a proposition?
I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
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What are the foundations of philosophy?
I'm a student majoring in mathematics. I've taken a course in mathematical logic and a course in set theory. My problem is basically that I'm always finding philosophical concepts, for example syntax, ...
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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 ...
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What sources discuss Russell's response to Gödel's incompleteness theorems?
In his book My Philosophical Development Russell writes,
In my introduction to the Tractatus, I suggested that, although in any given
language there are things which that language cannot express,
...
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What is the difference between logic and mathematics?
I’ve read the article in the SEP about the philosophy of mathematics. I believe I follow most of it.
However, I am a bit puzzled by something that may be due to some basic misunderstanding on my part. ...
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Is mathematics an art?
I'm thinking of art in the traditional sense as visual, musical or literary.
Mathematics certainly requires technique, and hence one can say craftmanship. But whereas the production of an art (at ...
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How does Russell's argument for identity refute that of Wittgenstein's?
In My Philosophical Development Russell wrote,
I come next to what Wittgenstein had to say about identity, which has an importance that may not be obvious at once. To explain this theory, I must ...
user13627
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Are analogies between ethics and mathematics philosophically coherent?
Analogies between ethics and mathematics are pretty common – probably because of their shared a priori nature. Philosophical laymen use them, like “Scott Alexander” (no, you don't need to know him), ...
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Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets?
Cantor defined an infinite set as a set whose subset can be placed in a one-to-one correspondence with its subset. That is, take the set of all natural numbers: {0, 1, 2, 3, 4,...}. From that set, you ...
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Can all mathematical reasoning be translated into traditional logic?
Can all mathematical reasoning be translated into traditional (Aristotelian, syllogistic) logic?
It would seem not ∵ one cannot syllogistically establish the validity of the reasoning in the ...
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Gödel’s Incompleteness Theorem: How can truth go deeper than proof?
My current understanding:
Math starts with a set of basic (purportedly self-evident) statements that are taken as a given without the need to prove them true, like e.g., a + b = b + a etc. Such ...
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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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Relationship between real quantities and numbers [closed]
Is there a definition of the relationship between real quantities and the numbers we relate to them, generally we use 'numbers' as mathematical objects with a 'proper' nouns, but we associate them ...
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Did Russell understand Gödel's incompleteness theorems?
Russell was active in philosophy (although no longer in math) for many years after the Gödel's 1931 publication. Gödel's paper were not obscure, and Russell would have been aware of their effect on ...
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Is First Order Logic (FOL) the only fundamental logic?
I'm far from being an expert in the field of mathematical logic, but I've been reading about the academic work invested in the foundations of mathematics, both in a historical and objetive sense; and ...
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What are the philosophical implications of category theory?
I have heard about topoi being the ideal entities to use for foundations of mathematics (since we are able to reasonably interpret our theories in them), so I imagine there might possibly be some ...
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Is mathematics founded on beliefs and assumptions?
Note: I originally posted the question in meta.math.stackexchange.com but I reckon this would suit a more philosophical audience so I am posting it here.
Background: I am a 28 year old ...
user1207
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Are mathematical suppositions of physical theories determined uniquely according to Aristotle and Plato?
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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What are the truth-values of intuitionistic logic?
Classical propositional logic is bivalent, that is its set of truth-values has cardinality 2 (True & False). Intuitionistic logic drops the law of the excluded middle; does it have the same set of ...
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What philosophies does Wigner's "Unreasonable Effectiveness of Mathematics" threaten?
Wigner's paper "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is a well-known paper in the community of the philosophy of mathematics.
The overbearing question in his paper ...
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What does Wittgenstein mean when he says "there are no numbers in logic"?
From the Tractatus:
5.453 All numbers in logic stand in need of justification. Or rather, it must become evident that there are no numbers in logic. There are
no pre-eminent numbers.
What does ...
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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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