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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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Where dos the science ends?

Being a physics student I have been behind many mysterious actions of nature ,but when we move one of these another pops up. Does the science ends anywhere?or these are just actions of god?
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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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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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114 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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70 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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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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1k views

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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1answer
88 views

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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86 views

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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3answers
153 views

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
63 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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2answers
246 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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4answers
73 views

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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88 views

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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1answer
108 views

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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1answer
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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 ...
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What were the minimal conditions if any for something to be regarded as a mathematical proof during the period of Ancient Greece?

In particular, were there any methods of proof prior to Euclid's axiomatic method? Are there any examples in the literature of such non-axiomatic mathematical proofs in the period of ancient Greece?
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Can a physicalist be also realist about mathematical objects?

Is it possible to believe that mathematical objects enjoy some kind of mind-independent existence while holding physicalism? And if they are mind-dependent, should one embrace constructivism ...
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5answers
161 views

Questioning determinism (example)

Questioning the world's deterministic behaviour, I shall present an example which seems to defy any certainty about the recurrence of events and is (obviously) a result of faulty logic, but I would ...
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Theory of Chaos

One example given by my philosophy teacher in highschool to explain the chaos theory was this : Take this sequence of numbers : 1, 2, 4, 8, 6, 2, 4, 8, 6, ... Built following these rules : Take ...
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If you can “divide” anything other than numbers [closed]

I am wondering about a system with division defined for non-numbers. From what I have encountered so far, it seems division is only applied to numbers. For example: 4 * 6 = 24 You can then take the ...
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55 views

Information of a sentence

Someone rolls a six-sided die, but before he rolls it he says, "the outcome can be 1 or 2." Is he lying because he didn’t refer the other possible outcomes?
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Do morphisms and their compositions capture the essence of “having a structure”?

As you may have guessed from the title I'm talking about category theory (CT). It's a fascinating subject to me. It can beautifully describe the essence of what it means to "have a structure" and it'...
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5answers
236 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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What would happen if suddenly, 1+1=2 is disproved?

Would the universe be thrown into chaos when the most fundamental equation is proved to be wrong?
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117 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
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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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What is the intuitive notion that ZF minus Extensionality minus Regularity plus Collection capture?

In order to clarify my questions I'll here introduce the concept of intuitive completeness of an axiomatic system, an axiomatic set A of a consistent theory would be said to be intuitively complete if ...
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How does a Bayesian respond to the Grue-hypothesis?

According to Bayesian inference/confirmation theory, your confidence in a hypothesis increases as you observe more and more evidence predicted by that hypothesis (according to bayes theorem and the ...
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175 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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Why do mathematical Axioms work so well in science? [closed]

Axiom, an established rule or principle or a self-evident truth. Better yet, An Axiom is a mathematical statement that is assumed to be true Why does math apply so well to science? Why is 1 atom+1 ...
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Can any correct logical reasoning in natural language sentences be translated into a formal mathematical proof?

Since natural languages (e.g. English) are prone to ambiguities and misunderstandings due to their constant evolving nature and lack of rigorous formalization, and given an arbitrary philosopher X who ...
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Definition of “mathematics” [closed]

REVRITE as suggested by @Mark Andrews I was thinking about the meaning of the word "analogy" and I realized mathematics could be defined as: "exact abstract analogies about reality". I see it as "...
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Ontological status of Axiom of Choice

Mathematical facts are necessary truths, either in a Platonic sense or by way of axioms. In the latter sense I mean that the Peano Axioms prove that 2+3=5, for example. In other words, "PA ⊨ 2+3=5"...
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The tags for the 21st century philosophy

What are the tags, if I'd like to read something about 21st century philosophy? Where do I find the list of the greatest philosophers of the 21st century? Is it true that the pure philosophy is in ...
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Quote of Russell on Mathematics

My memory seems to be failing me at the moment, but I seem to recall Russell saying something like the following on some occasion: The consistency of mathematics does not show that it is true but ...
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960 views

Was Bishop Berkeley part of the Enlightenment and if so - how did it fit his adherence to religion?

In his The Analyst Berkeley argued, among other things, that mathematicians must not "submit to Authority, take things upon Trust" and so expressed a view of the Enlightenment. This made me think: if ...
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Gödel's incompleteness theorem and non-standard logics/foundational systems

I am amateur in the field of mathematical logic, so sorry for any confusing parts of this question. It is well known that Gödel's incompleteness theorem shows there are great limits to what first-...
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1answer
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In which publication does Bertrand Russell define “philosophy”?

I've personally read a book or an article by Bertrand Russell where he defines philosophy. The definition --- IIRC --- is that philosophy is the study of the unknown. If it becomes a matter of fact, ...
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189 views

Nature of Logic and Mathematics, and its relationship with God and materialism

I believe that logic is infallible, mathematics is true and that an entirely mathematical description of the entire universe is possible. Are these inconsistent with materialism and atheism? Can ...
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2answers
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Is anything truly continuous?

The idea that there is some space between any two spaces is somewhat related to continuity, but the mathematical term for this is "dense". The rationals are dense, as there is some rational between ...
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676 views

Will McDuck go bankrupt?

The present question is of interest because it is answered in very different ways by different groups (mathematicians, physicists, students, professionals of non-mathematical occupations). I ask here ...
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Is the couplet about mathematics and poetry about logocentricism and deconstructionism?

I find this couplet really interesting: Mathematics is the art of giving the same name to different things Poetry is the art of giving different names to the same thing The first one is made ...
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What factors could affect the resolvability of disputes over knowledge claims (within a discipline in an area of knowledge)?

I am considering the area of knowledge of History but it has so many disciplines that I don't really understand fully. As for answering the question, I already thought of one factor: the lack of data ...