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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 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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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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Mathematical Consensus

Can anyone give me a reason why mathematics may require consensus to determine the quality of knowledge from the general mathematical community? Also what would be the counter to such a claim, as in ...
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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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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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Is the commutative property of multiplication intuitive to everyone at first glance? [closed]

a × b = b × a Most people speak about this as if it is common sense. For example, let's say 265 * 7948 = 7948 * 265. I can't get my head around when arbitrarily putting this adding 7948,...
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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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215 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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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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183 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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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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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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Is there any logical system that would allow us to describe/conceive really logical impossible things?

Discussing with a philosopher about this, he told me: "You seem to be assuming that paradoxes are "impossible things" and such things do not exist. I would maintain, on the contrary, that (a) ...
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Conditionals vs mathematics implication [duplicate]

What are conditionals ? Do they have a relationship like implications in mathematics ? i mean is neccesary that antecedent and consequent have a causal relationship ? for example if 2-1=1 then earth ...
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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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1answer
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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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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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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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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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1answer
84 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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4answers
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Understanding the simulation argument

I came across Nick Bostrom's paper called Are You Living in a Computer Simulation?. The paper argues that at least one of the following propositions is true: The human species is likely to go extinct ...
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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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2answers
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Can paraconsistent or other logics make the impossible happen?

A paraconsistent logic system it is defined as "a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that ...
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185 views

Are mathematical results influenced by the way we reason?

Intuitions of mathematicians, and the mathematics they develop, are ostensibly influenced by whether they primarily rely on visual_spatial and/or verbal_symbolic reasoning skills. Is it fair to say ...
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2answers
158 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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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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2answers
265 views

Is there a limit beyond which mathematics, if used correctly, cannot be applied to reality?

And if so, why, and which? Take this case: If I've two apples and I believe that with two more I'll have four apples, then I implicitly believe that summation applies to reality. Yet there are ...
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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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2answers
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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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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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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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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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Philosophy - If Space and Time are infinite and therefore infinite copies of us would end up existing, then wouldn't we still be gone after we die?

I have a question pondering in my head that if Space and Time are infinite, then does that mean that Nietzsche's Eternal Return theory is true in the way that my life would recur that when 'I' ('I' ...
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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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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 - Does Einstein's Block Universe theory prove Nietzsche's Eternal Return theory is true?

If the Past, Present, and Future all exist in exactly the same way, then every single moment would be a ‘Now’ moment for me. it would also mean that me being dead in the future is equally real in the ...
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What are the logical fallacies of this argument?

SCIENTIFIC FACT: Nothing in the universe, ceases to exist, it just appears in some other form. LOGICAL FACT: We can be absolutely sure that what we experience right now, exists. Let's mark ...
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doomsday argument — microstate-vs-macrostate objection

(Note: crossposted from https://math.stackexchange.com/questions/2856241/ where some comments suggested maybe the question isn't appropriate on math.se, although I thought the "statistical-inference" ...
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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
67 views

Is it true that modern statistics was created to prove eugenics? [closed]

Karl Pearson, Francis Galton, R.a Fisher were all prominent figures in the development of modern statistics and were all proponents of Eugenics. Is this true that it was a scientific/mathematical ...
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283 views

Badiou vs. Deleuze - Set Theory vs. Differential Calculus - Limits vs. Infinitesimals

My question is triggered by a quote from Manuel DeLanda which I find difficult to unpack as it is probably not only that they prefer different mathematical tools but that there is a profound ...
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If-then syllogisms

We have a sentence like this: If you are right above 85/100 then you can enter a university. Does this sentence presuppose that a university exists in order for it to be true?
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1answer
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Philosophical feminism and logic

Are there any resources to study about academic works on philosophical feminism and logic?
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1answer
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Correct Way of Handling A Corollary of A Corollary?

I have a conclusion S that is moderately interesting. While the corollary of S is more interesting, the corollary of the corollary of S is extremely interesting. Should I just label them corollary 1 ...
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Probabilty of a coin head on nth toss after a few coind head tosses? [closed]

Suppose, you have been flipping a fair coin and got coin head 5 times in a row. Now, what is the probability of getting 6th? On the one hand, it is said that probability is 1/2. On the other hand, ...
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Can a solid theory ever exist without any axioms?

In math, numbers and addition are logically defined by Zermelo Set Theory, a small group of axioms upon which everything else can be built. Could it be possible to have a working theory, (in any field ...
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Are propositions in mathematics synthetic or analytic?

I'm reading Kant's Critique of Pure Reason and I understand that he thought that "Mathematical Judgements are all synthetic". I would like to know where does this debate lies or if it is of interest ...