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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Why is 1 considered an odd number? [closed]

Since there is no way to divide 1 by any natural numbers other than 1 itself, how can 1 be divided into pairs until either 0 or 1 units are left, letting us call it even or odd? Perhaps the ...
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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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How can teleological explanations not fit with modern science?

Source: Prof Michael Sandel, Justice: ..., Episode 09: "ARGUING AFFIRMATIVE ACTION 52:21: We grew up and and we’re talked out of this way thinking about the world. 52:30: But here's a question: ...
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Do the Existence of Mobius Strips Prove that Mathematical Platonism is True?

Consider Mobius strips (eg. strips of paper with one or more half-twists joined together at the ends--for example, a Mobius strip with one half-twist has the interesting property of having only one ...
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Implication rules problem

P -> Q is equivalent to ~P v Q, so why isn't P -> ~Q equivalent to ~P v ~Q? I can't figure out why the rule for P -> Q does not apply to P -> ~Q.
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Can zero be defined without some definition of one? Can one be defined without some definition of zero?

I would prefer to ask this in the math community, but that crowd is hostile toward anything hinting of philosophy. It is my contention that a construction of the real number system which begins with ...
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Did any philosopher make the claim that mathematics can be as illusory as visual information?

The Greeks postulated that the world we observe may be just an illusion and Kant based some of his philosophy on that very idea. From that idea, came the idea that mathematical truths are more certain ...
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Implications of finding there is order in total randomness?

With "total randomness" I mean that every number generated has exactly the same probability of appearing and there is no way to predict which number will come next in a set. With order I mean that a ...
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What does “open sentence” mean in philosophy? [closed]

I'm reading some books on theory of knowledge and philosophy of mind. In those readings, notion of "open sentences" are used for certain extension, for example by Davidson. Question: what does open ...
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What's the relationship between infinity and a dimension? [closed]

When I was reading Kant's Critique, I got the sense that he'd sort of found a formula for calling something a dimension. Space seems to arise out of an infinity of extension. Time seems to arise ...
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How much math must tenured full philosophy professors know?

I'm talking math not logic. I'm referring to full tenured Professors of Philosophy at world famous universities like Oxbridge, Ivy League, Stanford, or MIT. Please be specific and type the math course ...
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How does one go about this natural deduction proof?

From no assumptions derive the conclusion ∃x t = x (where t can be any term).
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Size of infinite sets [duplicate]

Cantor's method of comparing set size uses one to one correspondence i.e. existence of a bijection. Now, set A = (0, 1) and set B = (0, 2). Using the function x → 2 x, every element of set A can be ...
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Syntactic VS Semantic Provability

Consider a new Conjecture C. The task is to determine whether the conjecture is true or false. Now let us suppose, after working very hard, we are finally able to establish the truth or falsehood of C....
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How much platonism do I need to handle the halting property?

I always considered myself as platonist (in contrast to formalist / finitist) but recently I realized (if this is actually true) that you need a bit of platonism to even make sense of questions like '...
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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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The tags for the 21st century philosophy [closed]

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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Mathematics and logicism

If reducing mathematics to logic is the goal of logicism, what other conceptions of mathematics are there?
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Gödel's Incompleteness Theorems and Implications for Science

A few days ago, I heard a biologist mention that one implication from Gödel's Incompleteness Theorems is that an unlimited number of general statements can account for a given set of observations. ...
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What form of formalist am I? [duplicate]

I am an formalist in the sense that I think that mathematics is just manipulation of symbols. But I think that this manipulation is motivated by the phantasy of humans: mathematical objects are for me ...
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183 views

Philosophical interpretation of computability of a finite math problem

There is an interesting debate in the area of Enumerative Combinatorics, a branch of Mathematics. Several mathematician are having a somewhat tongue-in-check debate whether a certain (very large and ...
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Does Math, or analogically Language really have any impact on our “Thoughts”?

Here I see many say, language has an important impact on our thoughts. But according to this question, Foucault in the preface to The Order of Things wrote how he 'laughed out loud' when he ...
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Circular nature of the cosmos. (π) [closed]

I've been pondering the irrational number that is pi and how it relates to the infinity of the universe. We often see many cycles in nature, current scientific theory states that the universe began as ...
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What is the justification for topological arguments in philosophy? [closed]

What is the justification for topological arguments in philosophy? For instance, it is common to say that we are not the only conscious animals because there is a continuity between humans and animals ...
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Question regarding the proof 3.3 in the Principia Mathematica

As far as I can understand, the key of PM is to make sure there are no leaps and gaps when making inferences. In other words, all the premises and rules of inferences should be explicitly enumerated ...
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Does imaginary numbers correspond to a real phenomenon? [duplicate]

Note: this is not a realism-esque question on the reality of numbers. Also, to not be confused with this question, I'm not questioning the usage of these numbers. As far as I know, every numerical ...
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Mathematics vs Time

Suppose we have a person that one day states "x+3=5". The next day he again states "x+3=5". As events, we can say they are different but does the meaning of the expression has changed? It seems ...
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On reading Kripke

I've recently read that Saul Kripke has had a huge impact in philosophy over the last century, especially philosophy of language and "truth". My question is wether reading his works (or studying it ...
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Another critique of the unreasonable effectiveness of mathematics in natural sciences

It seems the majority of scientists hold for a the hyper-effectiveness of mathematics in natural sciences as a sign that nature is deeply mathematical. Although I believe that some mathematisism is ...
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Does Wittgenstein's “The limits of my language mean the limits of my world” relate ontology with language?

Since Badiou equates ontology with Mathematics, if both philosophers are to be taken verbatim, there's a triple equivalence to consider: ontology = Mathematics = language.
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Use-mention distinction

Is it 1+1 or “1+1” that is a formula of addition? To my intuition, it is the former, and the latter seems to be a name of the formula. The reason why I ask this question is that provided my intuition ...
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Did logicists use mathematical entities (in their attempt) to reduce mathematics to logic?

Two concepts F,G are equinumerous if there exists a one-to-one correspondence between the objects that fall under F and G. Equinumerosity is one the most fundamental building blocks of Gottlob ...
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Are there any systems of mathematics that permit such a wide range of ways to formulate ideas

... that there is no algorithm for determining whether or not a given sequence of symbols is a wff ("well-formed formula"), but instead non-trivial proofs are required, so that some sequence of ...
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Why is 2 + 2 = 4? [closed]

It is clear that 2 + 2 = 4. It is also clear that applying the successor function on 1 yields the next number, i.e. 2, and this operation can be repeated infinitely. This method can be used to verify ...
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Is there any physics-model version of Tegmark's hypothesis?

Tegmark's mathematical universe hypothesis is very interesting (https://en.m.wikipedia.org/wiki/Mathematical_universe_hypothesis) but it has virtually no support among physicists because it is too ...
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Mathematics and disagreements

I was just pondering as a mathematics major, is there a particular instance where a mathematician's work doe NOT require agreements among peer scholars of mathematics to determine the quality of the ...
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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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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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What does Weyl mean by this remark?

In the Philosophy of Mathematics & Physics, Weyl writes: The coordinate system is, as it were, the residue of the annhilation of the ego. What does he mean by this?
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Are mathematical spaces falsiably real?

I responded to Eugene Wigner's famous paper by taking a position that human mind matches patterns in Physics and Mathematics (treating the latter as nothing more than a formal game) - http://tech-...
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Can you imagine a completely different logical/mathematical system than that we have?

Can you imagine a different logic and mathematics? For example, with a different arithmetic, or even a universe with no logic or mathematics and contradictions? A non consistent system?...
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Is this a lucky person or an unlucky person? [closed]

Suppose a person is such that when he is presented a number of choices out of which one is 'correct' and the others give nothing, most of the time he lands on the that choice. Suppose he plays a game ...
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What is meant by the following: This law is well motivated in cases where we may be ignorant of the facts

The folllowing text is taken from a part in a book (reference below) which are about mathematical philosophy. "... the theorem of classical logic known as the law of excluded middle: for every ...
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Can we compare the believe that mathematics refers to an objective reality with the believe in god(s)?

Some people think mathematics is not an invention of man, but that mathematics exists independently of human beings, no matter what we think about it. Some people think god(s) is (are) not an ...
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What is the study of systems (like logic, maths etc) called?

Before I begin, what I mean by 'systems' is what I've dubbed 'axiomatic systems', those which act as the starting point for all knowledge, for which I know of three: Maths, Logic, and Set Theory. I'll ...
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What does “self-contradictory” mean?

In this video, the mathematician Gregory Chaitin states that "the notion of the set of all sets is self-contradictory". What does "self-contradictory" mean? Is it different from "contradictory"? There ...
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Formalism: philosophy of mathematics

Is it a contradiction, if I am a formalist but I think that mathematical objects are created by human mind ? In other words: Am I allowed to be a formalist and to believe that mathematical ...
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Jorge Luis Borges suggests that using a lottery is an “intensification of chance.” Does this make sense?

By intensification of chance, Borges adds that a lottery brings "a periodic infusion of chaos into the cosmos." To me, the idea that chance can be "intensified" seems strange. However, I'm also not ...
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Descartes' Enlargement or Limitation of Cognition?

Descartes gives the metaphysical implications of freedom of the will as it relates to the power of cognition. This involves the function of judgement in its natural character and representational ...
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Question regarding proof of ❋3.47 in Principia Mathematica by Whitehead and Russell

❋3.03 in the the last step seems unnecessary. Can someone explain to me why 3.03 is listed? The last step can be written out in full like this: ⊦: p .⊃. q ⊃ r (1) ...