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.

Filter by
Sorted by
Tagged with
-2
votes
0answers
159 views

A question on the proposition Nature = mathematics

Some philosophers and physicists claim that nature is mathematics at its foundations. This can be considered a non-transcendental form of Platonic realism. The problem I have with this statement is ...
0
votes
0answers
42 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 ...
0
votes
0answers
34 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 ...
0
votes
0answers
49 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 ...
0
votes
1answer
96 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. ...
1
vote
1answer
41 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 ...
0
votes
1answer
211 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 ...
1
vote
1answer
95 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 ...
1
vote
2answers
73 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 ...
1
vote
1answer
162 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 ...
0
votes
0answers
162 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 ...
0
votes
2answers
103 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 ...
1
vote
1answer
60 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 "...
-1
votes
2answers
68 views

Why we don't use always inclusive or? [closed]

Consider that the following is always true. "If A then B XOR C". If we change exclusive or to inclusive or, then the following statement also holds, because every time exclusive or is true, the same ...
1
vote
3answers
169 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 ...
0
votes
2answers
83 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 ...
2
votes
4answers
270 views

Do complex quantities and irrational numbers exist in nature?

Completeness Theorems of Model Theory, a branch of Mathematical Logic. Together, these two Theorems show that: under the Field Axioms (the rules of the game for scalars) existence of rationals is ...
1
vote
1answer
136 views

What does a priori mean in a math paper?

Sometimes, in a math paper, we read something like "Although a priori this statement could be true, it is in fact false, as proven by this theorem". But aren't all mathematical statements a priori? So ...
0
votes
0answers
116 views

Is there an infinity of axioms in mathematics?

As I was trying to find a list of mathematical axioms used in modern branches of mathematics, I wondered if there's any meaning to the question of "how many mathematical axioms are there ?", and then ...
0
votes
2answers
148 views

Non-consistent mathematical axioms

It is known that axioms are the building blocks of mathematics. Differents sets of axioms different "games". What I don't understand is how do we know that we pick axioms that are consistent? . Does ...
-1
votes
1answer
200 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 ...
0
votes
0answers
21 views

Who are the philsophical successors of Sellars?

Have these philosophical successors of Sellars written books or papers presenting an overview of Sellars' work along with their latest work which built on it?
1
vote
2answers
334 views

What's more fundamental than logic and mathematics?

I just studied some basic abstract algebra, and it opened up my eyes into concepts more fundamental than found in Boolean algebra and elementary algebra, showing deeper insights about them both. Is ...
0
votes
2answers
92 views

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 ...
1
vote
4answers
141 views

What is Number again

I came here having asked on the math stack exchange site about number. There are several responses to that question or one similar that suggest that here is the best place to ask the question. On ...
1
vote
2answers
269 views

Is Quantum Bayesianism a viable solution to interpretational problems of quantum mechanics? [closed]

I noticed that Quantum Bayesianism (Qbism) seems to solve a number of issues in QM like non-locality, decoherence and the measurement problem. But I am not sure if physicists and philosophers would ...
-1
votes
1answer
320 views

Which problems do you consider as most important open problems in philosophy of mathematics?

At the "intersection" of mathematics and philosophy, or, rather, within their "union", surely some problems are still open and no general consensus is attained when those problems are discussed. ...
0
votes
0answers
71 views

Axiomatic system and symbolic, formal, mathematical language

Is there any need for axiomatic systems to be in a symbolic, formal, mathematical language? Equivalently is there any prohibition of axioms in axiomatic systems being in natural language? In other ...
-3
votes
1answer
81 views

Is the attempt to separate between Philosophy and Mathematics may be considered as some kind of Philosophy?

When deal with fundamental notions, many mathematicians and some philosophers agree that Philosophy is not an appropriate framework for mathematical frameworks' developments. Is the attempt to ...
0
votes
1answer
429 views

The notion of a point vs space as the most primitive notion?

I hear the notion of a point being the most primitive notion in geometry. But to talk about a point, one needs to think of a space of some sort. Only then, the point can be understood as a position ...
1
vote
1answer
315 views

Are there universes where rules of mathematics do not follow?

According to Max Tegmark the ultimate reality is the Mathematical world. Mathematically possibility also refers to physical possibility. Can there be such a type of universe where mathematical ...
0
votes
1answer
93 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 ...
4
votes
5answers
247 views

Do Mathematics “exist” in some sort of “Reality” that is different from our Physical Reality

I will explain why I am asking this question. Let's say, there are mathematical truths and truths about our physical reality. But, there is no way we can establish the truth of any statement about our ...
2
votes
4answers
154 views

Two positions at once is logically impossible

Assume that the position of an object is x1 and x2 at once, where x1 does not equal x2. Let's define the statements A and B as: A: The position of the object is x1. B: The position of the object ...
1
vote
3answers
179 views

When does “zero” exist? [closed]

When does zero exist? ex: if i say, "I dont have a hat" it seems more fair to say -1(hat) rather than 0(hat) ,because 0(hat)=0 would mean (hat)=0 and -1(hat)=(-hat) implying there is a hat in ...
-1
votes
1answer
387 views

Why was the zero not discovered long ago or in the beginning? [closed]

The rules governing the use of zero appeared for the first time in Brahmagupta's Brahmasputha Siddhanta (7th century). This work considers not only zero, but also negative numbers and the algebraic ...
3
votes
5answers
209 views

Human Mind vs Computer

We start from axioms, use rules of logic, and derive theorems. These theorems establish what is the case in relation to the context. In all disciplines employing mathematics, we reason by saying '...
0
votes
2answers
252 views

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 ...
0
votes
0answers
31 views

What are the possible philosophical inspirations for the philosophical concept of “antifragility” that was defined by Taleb?

It seems to me that this is just a generalization of "hormesis" by trivially abstracting some of it's aspects but I am not very well versed in philosophy.
-3
votes
2answers
240 views

Can we imagine a perfect circle?

Applied mathematicians often work with circles, but I'm guessing it's an abstraction that cannot save all the empirical data. Can we conceive of a perfect circle in our visual field -- as apparently ...
4
votes
2answers
220 views

When is it meaningful to say that an undecided conjecture is true or false?

I see that other questions have already been asked about mathematical truth but here I want to ask clarifications on a particular perspective. One can think the answer to the question could be "when ...
0
votes
2answers
172 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 ...
0
votes
0answers
216 views

(Non-)Mathematical examples - towards a philosophy of mathematics-

I need your help: I'm looking for a list of interesting examples (see below) that are of high interest to philosophy of mathematics. To specify this, I need you to consider the following: ''...
2
votes
1answer
252 views

Why does Gödel's incompleteness theorem apply to multiple formal systems?

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor ...
0
votes
0answers
67 views

Does Weyl's tile argument defeat the discrete spacetime?

Weyl shows that in a discrete spacetime Pythagoras's theorem fails to arise. Of course it may be that although Pythagoras's theorem arises naturally but actually does not model the real world. So Does ...
26
votes
10answers
6k views

Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

I've seen a few different formulations of this, but the most famous is "monkeys on a typewriter" - that if you put a team of monkeys on a typewriter, given infinite time, they will eventually produce ...
1
vote
0answers
263 views

Mathematical models of dynamic algorithmic processes

This question primarily concerns dynamical or time-dependent phenomena in philosophy and to what extent such heuristic discourse features in more precise mathematical settings. In order to model ...
7
votes
1answer
150 views

Hume on infinity

I know Hume argued against dividing finite space into infinitely many regions, but I can't seem to find anything regarding his thoughts on infinity itself. From his Enquiry you sort of get that he ...
1
vote
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 ...

1
2 3 4 5
19