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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101 views

Are there infinitely many “unique” mathematical concepts? [closed]

The difficulty in formulating my question lies in defining what I mean by "unique." What I mean by "uniqueness": For example, the concepts that 1 + 1 = 2 5 + 2 = 7 6 x 3 = 18 6 - 9 = -3 etc. only ...
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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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Mathematical structuralism and Saussure

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

Is there such a thing as provability of provability?

Gödel says that there are true statements that can't be proved, given a sound axiomatic system. Does anyone say anything about the provability of the provability of statements? Is it still an open ...
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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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Can a reason cost 5 dollars?

Imagine a school where no one can wear a red hat. John goes to school with a red hat costing 5 dollars. Someone says John's red hat "is" the reason why he can't get into the school. What is the ...
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5answers
235 views

Can anything be less than one?

Zero itself seems to be an absurd number because if there is really zero of something, then nobody has ever sensed it. But even with temperatures, we don’t really have negative and positive ...
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1answer
254 views

Cosmological truth and the theory of cosmic epochs

According to Whitehead’s theory of cosmic epochs and extensive continuum, there are material conditions that drive the more general metaphysical descriptions and principles. We only can account for ...
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If nature is inherently imprecise, how is it so easy for us to conceptualize mathematical certainties?

In modeling any real physical system, we are required to employ inductive reasoning. We can never be completely certain about the state or properties of any system or of any future observation we will ...
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What is frequentism?

I am studying for an exam and I ran into frequentism. Honestly, I don't understand anything about that. Is frequentism related to probability only? Why are probabilities understood as frequencies? I ...
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261 views

Is there an idea of non-spatial reality in philosophy?

Our world is spatial. In particular there are 3 dimensions and we can measure lengths of objects in either of them. However, when thinking about metaphysics I came to the conclusion that there might ...
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What is the principle of underdetermination?

While studying I read about the principle of underdetermination of scientific theories. I made some researches online but I am more confused than before. I read about the Quine-Duhem holistic thesis, ...
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Is time more “real” than math and, if so, why?

How is time different from math? Is time a part of math? For me time is like math rather than a "real" thing. Time is just a tool rather than a "fundamental thing". I feel confident saying that an ...
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1answer
150 views

What are the implications of relativity of Mathematics?

I came across the idea that the same statement can be true in one model while not true in another, while both models are being consistent. An example is "Is the sum of the angles of a triangle equal ...
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3answers
218 views

Does an infinitesimal instant of time have zero duration? [closed]

Is there a philosophical argument supporting the hypothesis that an infinitesimal instant of time has zero duration? The reference to infinitesimal includes the modern presentation of it in non-...
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1answer
159 views

Does the propensity interpretation of probability rely on the principle of indifference?

According to the late Popper, among others, probability is the propensity of a set of conditions to produce certain long run relative frequencies. Therefore if we say that a certain set of conditions ...
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3answers
339 views

Can randomness be random?

In mathematics, a true random number generator it's impossible, because any formula defines a process that, however complex, is not random. A random event must be unrelated to any cause or condition, ...
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Why do the limits to the computation of the universe appear to us as fundamental physical constants? [closed]

According to the Estakhr's Principle of Physical Constants Physical Constants are Computational limits or vice versa. Why do the limits to the computation of the universe appear to us as fundamental ...
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5answers
294 views

Can infinity have a beginning? [closed]

I have trouble with the mathematical notion of infinity. Example: Consider all of the natural numbers. It has a beginning, therefore it is bordered, therefore it cannot be infinity.
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533 views

What is the formal definition of mathematics? [closed]

REWRITE I am curious if mathematics could be defined as: "exact abstract descriptions of reality". I use "descriptions" in plural because there are multiple distinct mathematical views on problems ...
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1answer
55 views

Anyone defined the geometric point before Aristotle?

Did Plato or anyone else discuss/define the geometric point? I know Pythagoras discussed the math point. I read that Euclid's definition (with no part) is a mistake in translation from the original ...
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4answers
311 views

Is a distinction between actual and potential infinity philosophically significant?

I could use a little exposition on the significance of the distinction. I'm aware that potential infinities have arbitrarily large numbers, whilst actual infinities refer to the number "infinity" ...
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1answer
222 views

Is there a mathematical framework where both potential and actual infinity are used?

1) By actual infinity I mean that given X, it is inaccessible by Y, where Y is a placeholder for any possible non-finite set, such that no non-finite set is accessible to X (X is beyond the notion of ...
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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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147 views

How can infinity become actual? [closed]

There are two mathematical concepts of infinity, potential infinity and actual infinity. I do not understand how the latter is being used. For the simplest infinite set, the natural numbers, we get: ...
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121 views

Sentences and reality

Would sentences have meaning even if humans did not exist? For example, would "the earth is round" have meaning if humans did not exist? Would it be true?
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1answer
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Is Euclid's syllogistic approach to proving mathematical theorems logically insufficient?

I think that deduction used in syllogistic systems, employing axioms and hence inferential conclusions i.e. theorems is rather weak, and cannot suffice for the robustness needed for proving ...
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2answers
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Is a set containing itself already a paradox?

This is inspired by Russel's paradox stating there is not set of all sets. It uses the presupposition that set can contain itself. However, this already seems paradoxical. Suppose a set A = {}. Then ...
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558 views

Understanding hypothetical reasoning and material implication

I am a little bit frustrated in how we use hypothetical reasoning in everyday life. Many times we make "if-then" statements. For example, if i get ill ,then i cant go to work and if i cant go to work ,...
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1answer
149 views

Can any logic system provide the impossible solution to Russell's paradox in naive set theory?

In naive set theory in classical logic, we cannot describe or find a solution to Russell's set paradox (it is impossible). But is it there any logic system or any method that can provide this ...
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3answers
84 views

Implication vs sufficient condition vs hypothetical reasoning

I was bit confused to clarify the difference between them because "if-then" are used a lot in everyday life. So for example we have a car which is full function and someone says if i turn the key the ...
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4answers
159 views

Where does science end?

Being a physics student I have been behind many mysterious actions of nature, but when we remove one of these mysteries another pops up. Does science end anywhere? Or are these mysteries just ...
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1answer
111 views

Is there any logical system/method where impossible/illogical/inconsistent things can exist (like a solution to Russell's paradox that makes sense)? [duplicate]

Discussing with a philosopher about impossible things existing or being allowed within a particular logic system, he told me: "This is a funny thing about logically impossible things. You can prove ...
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956 views

Hume on matters of fact and mathematics

Hume thinks that we can have relations of ideas, but we can't have matters of fact by them. Thus we cannot relate matters of fact with the real world so certain truth cannot be found. My question is ...
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0answers
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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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Why might you not accept ¬(¬A) = A?

What motivates intuitionism's rejection of double negation: If A exists, then ¬(¬A) = A. I can't see what's wrong this statement or why someone would reject it.
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What is the philosophical status of category theory?

In the philosophy of mathematics, some attempts have been made to give it ultimately secure foundations; a notable example is the Hilbert Program. Goedel's Theorems show that it is not quite possible, ...
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5answers
373 views

Why is mathematics so fantastically successful at describing the universe?

Anyone who has studied physics will quickly see how fantastically successful mathematics is at describing the universe. The famous physicist Richard Feynman said in his book "the character of physical ...
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How do mathematicians reconcile that an infinite set does not have to be larger than its proper subset?

If we imagine an infinite number of fractions and, within them, an infinite number of integers, doesn't the former constitute a "larger" infinite set of numbers? This has always been paradoxical for ...
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If there were only one single mathematician in the world, would s/he be able to produce a mathematical proof?

If there were only one single mathematician in the world, would s/he be able to produce a mathematical proof? This question was motivated by the Math stackexchange question: Should a mathematical ...
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4answers
451 views

If the Universe(s) didn't exist, Would all maths still exist?

Many scientists say that maths transcends creation, the future, it exists for all time. For example the Mandelbrot is just an equation that can still exist when the universe goes cold. Because I don'...
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427 views

Is causality a type of necessary and sufficient condition?

Does 'A caused B' mean that A is a necessary and sufficient condition for B? Imagine that we go to a shop and buy two items with a total cost 40 dollars (30 for 1st item and 10 for the 2nd). Is the ...
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What is the relation between proof in mathematics and observation in physics?

Recently in his 2015 Hirzebruch Lecture in Bonn, Arthur Jaffe re-amplified his famous perspective that finding proof in mathematics is analogous to making experimental observation in physics. In ...
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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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Can you list examples of problems that can not be solved within a formal system but human beings have solved through construction or creativity?

This kind of problem is mentioned in a book I have read, but the book did not give a concrete example. If any such problem existed, this might help me understand human creativity. I think it would ...
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Can you divide the natural numbers in half sequentially? [closed]

My brief stint on SE has been quite interesting because it forced me to make the premises of my inquiry more explicit. I resisted this initially simply for reasons of economy, but economy proved to be ...
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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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1answer
82 views

Can we give a well-motivated distinction between finitary and non-finitary mathematics?

I'm reading up on Hilbert, and wondering if there's actually anything fundamental to his distinction between finitary and infinitary mathematics. His system seems to be an attempt to avoid too much ...
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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 ...