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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109
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22answers
20k views

Why don't fair coin tosses “add up”? Or… is “gambler's fallacy” really valid?

I have always been perplexed by a seeming paradox in probability that I'm sure has some simple, well-known explanation. We say that a "fair coin" or whatever has "no memory." At each toss the odds ...
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15answers
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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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2answers
324 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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27answers
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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 ...
3
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2answers
231 views

What makes mathematical ideas provable but philosophical ideas unprovable?

Assuming that math is the the study of relationships between quantities and sets, why are those entities provable while more qualitative abstract ideas such as beauty or consciousness in philosophy ...
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2answers
122 views

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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3answers
162 views

Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
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0answers
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Philosophy question [closed]

Hi guys, i require help in this question where I have been stuck for days.
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1answer
70 views

Statements about real world

We make statements like "This table is composed from atoms". This statement must be true or false. But what if tomorrow the atomic theory is completely abandoned and we work with another ...
6
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3answers
161 views

Formal systems and interpretations for numbers

In my book (Hodel's Intro To Mathematical Logic), we are given several examples of formalized mathematical theories such as group theory, Peano arithmetic, etc. But I've had this ongoing confusion: ...
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0answers
85 views

Is logic part of Philosophy or Mathematics?

Is logic part of Philosophy or Mathematics? I asked this question "Does programming use logic more or mathematics more" and users on some site insisted that logic was part of mathematics, I ...
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0answers
70 views

Are axioms more important than definitions?

To prove a theorem in mathematics we usually use our axioms, definitions and other already proved theorems. Suppose we wante to prove a specific theorem and we haven't prove any other theorem and also ...
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1answer
111 views

Do mathematical objects exist after their definition? [duplicate]

Suppose we have a system with a set of axioms. Now we begined to define new terms. E.g. in maths we have a particular set of axioms and then we define what a function is. But do all the functions ...
0
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1answer
105 views

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 ...
2
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4answers
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Does truth exist without proof?

When we prove something (e.g. in maths) we show that a particular statement is true. But if we couldn't prove that statement that doesn't mean that the statement would be false right? So is proof a ...
25
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4answers
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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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4answers
842 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 can't go to work and if I can't go to ...
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1answer
54 views

Actual and potential truth for neo-verificationists

Neo-verificationists such as Martin-Löf and Prawitz make a distinction between actual and potential truth of a proposition, roughly defined as follows: ... that a proposition A is actually true means ...
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16answers
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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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3answers
383 views

How could I possibly apply rule-utilitarianism in real life?

If I believe in rule-utilitarianism as the best moral system we have to judge what actions are right and wrong, how would I go about applying this system pratically in real life decisions? For ...
2
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0answers
90 views

Could the axiom of infinity be in itself inconsistent?

I've seen several threads discussing the axiom of infinity but I wasn't able to find a discussion on this particular aspect. And recent conversations with some people have led me to wonder if it is ...
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0answers
89 views

Do all paradoxes of naive set theory have something in common?

If P(x) is the formula "x ∉ x", then ... the assumption that a set h has P(x) purity ... (i.e. the assumption that for all t, if t∈h then P(t)) ... implies that there exists a set k, where ...
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4answers
2k views

Is tautology for logic what theorems are for mathematics?

Consider the following statements. "If x is an integer then 3+2=5" and "If x is not integer then 3+2=5". Constructing truth tables for the above statements show that there is no ...
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0answers
48 views

does the addition operator of arithmetic contain meaning, or did we assign it meaning

When we see a problem containing addition, we usually visualize it using a number line or containing quantities of some sorts. Does this meaning of the addition operator as combining quantities, or ...
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2answers
94 views

Do actual and potential infinity collapse into each other?

https://plato.stanford.edu/entries/set-theory/ states outright that set theory "can be defined as the mathematical theory of the actual—as opposed to potential—infinite," and the article on ...
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1answer
50 views

Epistemological Basis of Mathematics Debate

In the following link: https://plato.stanford.edu/entries/intuitionism/ in the last paragraph in Section 1, there is mention of the "lack of epistemological and ontological basis for Mathematics.&...
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1answer
58 views

Is there a Physics-limited-mathematics?

For example,how about in this mathematics if If we calculate to the 80th power of 10 and still don't have a single counterexample, we can say that we have "proved" Goldbach's Conjecture, ...
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2answers
55 views

Do mathematicicans care about implications where the hypothesis is always false?

Suppose we want to prove the implication P implies Q. Now we can use proof by contradiction and show that there is no case were P is true and not Q is true. But this does not imply that there is a ...
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2answers
99 views

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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2answers
195 views

Platonism and causality

The Stanford Encyclopedia of philosophy states that - "Because abstract objects are wholly non-spatiotemporal, it follows that they are also entirely non-physical (they do not exist in the physical ...
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5answers
357 views

Can mathematics and physics be thought of as branches of philosophy?

I think that they can be viewed like that, with some suitable definition of philosophy. Then mathematics could be defined as one of the branches of philosophy in which theories are built on ...
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2answers
189 views

Are mathematical axioms arbitrary?

I've been thinking recently about whether or not mathematical axioms are arbitrary. I'm trying to figure out what axioms in systems are derived from and just how arbitrary they really are. My main ...
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2answers
280 views

How do philosophers formally characterise mathematical objects?

In the Stanford Encyclopedia of Philosophy article, 'Platonism in the Philosophy of Mathematics', the following formalisation is given for the existence of a mathematical object: Existence can be ...
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0answers
46 views

Validity/Soundness of an argument from R. Carrier

This is about training in argumentation. I use a text from R. Carrier: https://www.richardcarrier.info/archives/468, where he claims that from nothing everything follows. (Don't get shocked, the ...
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1answer
221 views

Is physics or pure math better at explaining reality?

I have been interested in philosophy for a while and I was just curious on what you guys thought about this question. On one hand you have a science that is able to (basically) relate all the bodies ...
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0answers
35 views

What are the differences in belief between the Mathematical Universe Hypothesis and platonism?

The beliefs are very similar in nature, but they have some different ideas. I am confused where the line of distinction is between MUH and platonism; therefore, I would like to know if anyone has ...
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1answer
222 views

Comparisons between two notions of existence

I have the following, rather naive question: To what extent can the a priori existence of mathematical objects be reasonably compared with the seemingly a posteriori existence of objects established ...
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0answers
57 views

What are the best books in defense of Platonism in Philosophy of Mathematics?

I am interested in the subject and was recently doing some research about literature to read about it, but it seems that there aren’t many books on the topic. Some suggestions for books in defense of ...
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1answer
102 views

Is pure math invented or discovered? [duplicate]

I know that many people believe that math is discovered, but here I want to know if pure mathematics, in specific, is discovered or invented and why. There are definitely many arguments to both sides. ...
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2answers
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Does Wittgensteins own solution to Russells Paradox actually work?

In the Tractatus, Wittgenstein attempts a solution of Russells paradox 3.333 A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and ...
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1answer
100 views

Mathematical Analyticity Within Context of Physical Theory [closed]

Postulate: Mathematics is constructed. We construct the syntax, grammar and assign semantics to mathematical statements artificially. Lemma: There is no constraint on what constructed mathematical ...
3
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1answer
114 views

Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
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3answers
177 views

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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7answers
3k views

Why isn't Cantor's diagonal argument just a paradox?

Cantor's diagonal argument concludes the cardinality of the power set of a countably infinite set is greater than that of the countably infinite set. In other words, the infiniteness of real numbers ...
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1answer
70 views

What is the meaning of Principle C'' in Hartry Field's 'Science Without Numbers'?

For Field, the following is 'perfectly obvious', but I would like confirmation that I understand it completely. Let A be a nominalistically statable assertion. Let A* be the assertion that results by ...
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1answer
164 views

Kant on triangles vs unicorns

In the critique of pure reason, according to my reading, Kant is positing that propositions of mathematics are true because they can be situated in space and time, i.e, they can be conceived in space ...
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2answers
106 views

Contradiction vs Impossiblity

When we do proof by contradiction we think in the following way: Suppose we know that Q is true. We assume that not P is true and through implications we conclude not Q is true. Now how we proceed ...
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0answers
165 views

Classical Semantics, Truth, and Frege's Argument

I'm trying to understand Frege's argument for the existence of mathematical objects. Specifically, I'm trying to understand the premises of classical semantics and truth. Classical Semantics. The ...
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1answer
87 views

How definition relates to abstract/concrete objects?

I am having a hard time to understand what a definition does. Is it an abbreviation we use instead of using too many words? But then why mathematicians define mathematical objects? Does it mean they "...
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1answer
201 views

Validity of physical laws and observation

I am placing this question on philosophy stack exchange because a mathematician wouldn't care, and a physicist would be extremely insulted. Consider Newton's Law F=ma. First, I am observing this as ...

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