# 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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### How can you determine if a hypothesis (mathematical logic ones) is falsifiable enough to be “good”?

We had a group discussion and the prof gave us the following question and left. The problem is that I hardly understand the question. How can you determine if a hypothesis (in particular, ...
32 views

### Reasoning for Inductive inference?

Just out of curiosity, if I should replace the deductive inference related questions to inductive inference, then which are true? Inductive inferences rearrange current knowledge in such a way that ...
39 views

### What are some key differences between an argument in logic and a theory in mathematics?

Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
213 views

### Gödel's Results and Philosophy of Mathematics [closed]

Gödel's results essentially conclude that there are True but Unprovable statements in arithmetic. My thoughts are as follows: Axioms form the foundation of mathematics -because we need to assume ...
183 views

This may be a duplicate question. What is the best way to get started with the philosophy of mathematics? Given that I know (from university) the basics that are discussed (Set theory, Russell's ...
167 views

### Infinity in modern integration theory

The Riemann integral itself doesn't work with infinity (±∞) as “endpoints”, you have to take a detour by calculating the integral for arbitrary endpoints ±z and then take the limit for z→∞, which ...
98 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 ...
146 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: ...
107 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 ...
69 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 ...
82 views

### 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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1: Why do we say that there can't be other logics/mathematics than those we have? 2: Logic and maths are independent of reality. Then, if we have invented a logic/math based on reality, would it be ...
131 views

### What was the “rigorous” definition of “number” for the Pythagoreans?

I am not sure if this is the right stackexchange for this question. However, I'm wondering about the following thing: We know n+ow that there are rational and irrational numbers. Pythagoras however, ...
142 views

### How “concrete” is mathematics, even when it's formal, rather than natural science?

How "concrete" is mathematics, even when it's formal, rather than natural science? So because it relates to natural science, then it's unreasonable to view it as "entirely abstract" or "entirely ...
28 views

### Methods for testing the posibility of some action? [closed]

Suppose a thing T needs to do an action (or change in the environment) A. Then A must be able to be composed of some posible actions A_1, A_2, ..., A_N. But I am using the definition of posible ...
79 views

### Putnam's argument against the possibility of nominalising 'distance-statements' in “Philosophy of Logic” (1972)

In chapter V, The Inadequacy of Nominalistic Language, of Philosophy of Logic (1972), Putnam argues that there can be no nominalistic "translation scheme" of sentences of the form "the distance ...
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### Foundations of logic and reasoning in natural languages

My intuition tells me that any theory, whether expressed using mathematics(and therefore more precise and structured) or argued for using natural languages have to involve blind faith in certain ...
89 views

### Can Second Order Logic (SOL) be a fundamental logic?

I was wondering, can Second Order Logic (SOL) be a fundamental logic? I am trying to gather some opinions from both sides to see what others might think.
79 views

### How is this 'explanation' of the unreasonable effectiveness of mathematics even an explanation?

In R. W Hamming's response to the "Unreasonable effectiveness of mathematics" by Eugene Wigner, he gave four 'partial explanations' as to why it may be unreasonably effective. However, I am struggling ...
190 views

### Is it appropriate to say that mathematical knowledge has intrinsic value for mathematicians?

I have been toying with the idea of value for a while and came up with this question a few days ago. I think that it is impossible to say that mathematical knowledge has intrinsic value for ...
173 views

### Alan Turing on the philosophy of mathematics [closed]

What was Alan Turings opinion on the philosophy of mathematics? Was he a platonist? A formalist? If not: what else?
277 views

### Interpreting Leibnitz's “Law Of Continuity” [closed]

For my personal reason, I have to write a blog which tries to explain about the symbols of the differential as well as the integral. In that process, I hit upon the Leipnitz's "Law Of Continuity",, ...
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### Infinity recursive simulation on a turing machine? [closed]

Do you think, that it would be possible to run a infinite and recursive simulation of the universe on an turing machine?
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### could an algorithm that writes algorithms be written? [closed]

Could an algorithm that writes algorithms be written? Wikipedia says: An algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Starting ...
206 views

### Equality Awareness (for minorities, LGBT, women, etc.)

Recently there has been a facebook campaign to raise awareness of the struggle for LGBT equality, whereby facebook users change their profile pictures to an "equal" sign. This campaign seems to be ...
248 views

### are something and nothing the same “thing”? if is something infinitely small is equivalent to nothing then what are the implications of this? [closed]

are something and nothing the same "thing"? if is something infinitely small is equivalent to nothing then what are the implications of this? in regards to the the universe v.s before big bang ...
120 views

### Cognitive science/brain sciences and their impact on philosophy of mathematics

How does/did cognitive science influence philosophy of mathematics? I saw somewhere (Wikipedia, "Cognitive science") that it helped to create new perspective on philosophy of mathematics, but it did ...
34 views

### Question on Hypothetico-Deductive Method

I had another quiz related Hypothetico-Deductive (HD) Method. I couldn't answer this because the way it was posed is so baffling to me. I am so sorry to ask all the basic questions (I think all ...
198 views

### Is it there any theory or model in theoretical physics that is akin to Tegmark's Mathematical Universe Hypothesis?

Physicist Max Tegmark proposed a hypothesis that asserts that all mathematical structures do exist as universes. (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) But this hypothesis ...
188 views

### Is it there any direct relation between Tegmark's Mathematical Universe Hypothesis and the Holographic Principle?

I would like to ask you about Tegmark's Mathematical Universe Hypothesis and its relation to the holographic principle: Could we use the holographic principle as a framework to Tegmark's MUH? I mean, ...
185 views

### How much this theory fulfills of criteria for a foundational theory of mathematics?

[EDIT] The criteria for a founding theory of mathematics, especially if it uses large cardinal axioms that I want to refer to are those of Harvey Friedman's 2000 criteria given in pages 5-6 of the ...
115 views

### Does the snake bite its own tail: “Philosophy of philosophy”

I was just philosophizing about the philosophy of mathematics. Then at one point I philosophized: is there a philosophy of philosophy? Is that meta-philosophy, or is that just philosophy again? Can ...
128 views

### Can other “sciences” be applications of mathematics?

Can other "sciences" (it's in quotation marks, because the definition for a science is not necessarily exact) be applications of mathematics? If other sciences, be it philosophy or economics or ...
188 views

### If we assume logic is correct, does it imply that our consciousness proccesses real information?

[major edits] Even if our consciousness is an illusion (even in the sense Denett suggests), the mere fact we see some information flowing across the universe means there is at least something that ...
285 views

### What is going on with Russell's “beauty cold and austere” of mathematics?

I admit that this is an idle question, but I wondered why it is that mathematics appears "beautiful cold and austere" to those who are particularly gifted at it. The full quite from wikipedia on this ...
197 views

### Hilbert's formalism and game formalism differences and similarities

I've recently encountered differences between Hilbert's formalism and game formalism. They seem pretty much similar in my eyes. I wish to understand in what way does Hilbert’s formalism resemble game ...
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### Is the inconsistent (or paraconsistent) line a possibility?

According to the SEP: Another place to find applications of inconsistency in analysis is topology, where one readily observes the practice of cutting and pasting spaces being described as “...
190 views

### Is mathematics something real or just an abstraction we created?

Is mathematics something real like something so correlated in our universe which would be different in other theoretically universes or is it just an abstract universe-independent layer/framework we ...
290 views

### Can infinity be made finite in certain conditions?

In mathematics there are not only infinitely big numbers, but also infinitely small numbers. One can consider arbitrarily small numbers that can exist only in the mathematical world. For example, ten ...
528 views

### Existence of numbers, were they invented or discovered? [duplicate]

Fire is a good example of matter that human beings discovered; Fire has been a part of nature even before human beings found it and at some points and we have used it ever since we discovered the ...
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### What does philosophy exactly do? [closed]

I need your help understanding philosophy. For some reason, I'm not understanding the objective of this subject. Frankly, I only had 1 semester of philosophy so maybe it isn't enough to really ...
174 views

### Can there be ugliness in the world of a Mathematical God? [closed]

Let us assume that Mathematics is infinite, represents the multiverse and beyond, and is the deterministic cause of everything we know to exist (the Big Bang and our universe, the formation of the ...
821 views

### What is the connection between conscious mind and Gödel's incompleteness in a mathematical universe?

Assume that our universe is a mathematical one, similar to the one that Tegmark proposed (see here). In contrast to what I read there, let's assume that the axioms upon we build the universe are such ...
112 views

### What use is model theory?

I have never been able to understand any need or even any benefit of model theory. Both Rudolf Caranp and Richard Montague showed how to encode semantics directly in the syntax. Can you help me ...
163 views

### Does a thing being subtracted from ever disappear completely?

Suppose I take any finite length and subtract half of it continuously. So the size of the remainder, after each subtraction, is equal to its original length multiplied by one half taken to the nth ...
317 views

### Contradiction, and the Being and Becoming of Mathematics [closed]

Mathematics is rife with contradictions, is shot through with them: the fault-lines lie where theories collide, fade or open up. Does this disturb the incarnation of mathematics - the Ideal ...
1k views

### Is math really the language Nature speaks?

It´s often heard among physicists: math is the universal language of Nature. But like all languages, mathematics is made by men, and made universal by man (like English is becoming the universal ...
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### Are the assertions “2 + 2 equals 4” and “2 + 2 is 4” identical [closed]

I asked the same question at math.stackexchange but I thought that the answers here could be quite different. I hope I am not breaking protocol/etiquette by doing that, if I am then I apologize. If ...