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
44
votes
15answers
9k views

Is Mathematics always correct?

It seems Mathematical theories/Laws/Formulas are the least questioned in all of the sciences. Is mathematics that good at being closest to the laws of universe, or is it just a logical tool of our own ...
2
votes
3answers
246 views

Understanding the simulation argument

I came across Nick Bostrom's paper called Are You Living in a Computer Simulation?. The paper argues that at least one of the following propositions is true: The human species is likely to go extinct ...
0
votes
2answers
175 views

Existence of numbers on number line

Consider the fraction 10/3. One way to interpret this is by stating the following: in the process of long division, which is a rule, take divisor as 3, and take dividend as 10, and initiate the ...
0
votes
0answers
49 views

Solipsistic Thinking :: Is there no maximum number;

I have something(s) that causes me both trouble with (keeping emotionally connected to what I'm trying to express) Λ (expressing myself). So please be nice and ask questions :: εὐχάριστος (Grateful) ...
1
vote
0answers
142 views

Are Max Tegmark's Mathematical Universe Hypothesis and Seth Lloyd's Cosmological Model compatible?

I have been interested in Seth Lloyd's cosmological model (which proposes that the universe is a some kind of quantum computer or at least similar to it: https://en.wikipedia.org/wiki/...
3
votes
1answer
84 views

Did anyone argue against the possibility of a perfect prediction from within a system?

Did anyone offer an argument against the possibility of a perfect and complete prediction about a system from within that system along the following lines: Let's imagine a machine (like a desktop ...
2
votes
1answer
124 views

Did Whitehead express his motivation for writing with Russell the Principia Mathematica?

I imagine Bertrand Russell's motivation for participating in the project leading to the Principia Mathematica was an attempt to justify logicism and reject Kant's synthetic a priori, but what was ...
21
votes
4answers
33k views

What is the difference between a statement and a proposition?

I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
1
vote
3answers
586 views

How is Wittgenstein’s “notorious paragraph” about the Gödel's Theorem not obviously correct?

Timm Lampert quotes from Wittgenstein's "notorious paragraph" (§8 of Remarks on the Foundations of Mathematics, Appendix 3) in http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6....
6
votes
2answers
713 views

What are the philosophical implications of using inconsistent mathematics?

Why mathematicians would prefer at times to work with inconsistent systems (from which I assume everything can be proven unless changing the logic used)? In particular, how could working with an ...
4
votes
1answer
95 views

Who first studied “logical (ir)reversibility”?

Who first studied "logical (ir)reversibility" philosophically? By "logical (ir)reversibility" I mean questions like:Why is it easier to multiply large numbers than to factorize them? understand a ...
21
votes
5answers
2k views

What was Cantor's philosophical reason for accepting the infinite but rejecting the infinitesimal?

I have begun inquiring recently into mathematical aspects of Georg Cantor's theory of transfinite numbers and sets, which he developed between the years of 1874 and 1897. Throughout his theory, Cantor ...
2
votes
0answers
58 views

Transition of Mathematical Propositions

There are axioms, and then there are well established methods of working with them. It is clear that these methods are nothing but logical operations (rules of manipulation of symbols) on previous ...
0
votes
2answers
109 views

Argument against Platonism

Platonic view of mathematics states that numbers have abstract reality. One way to test what this really means is to do a thought experiment of extinction of humanity. Also suppose after all evidence ...
-1
votes
1answer
156 views

Is the claim of mathematical objects being *abstract* necessary for understanding them and their applications? [closed]

One hears a lot about mathematical entities being abstract or at least spoken about as such. Now abstract is usually presented as non spatio-temporal, for example its said that number 2 is present [in ...
8
votes
3answers
682 views

Is Aristotle's resolution of Zeno's paradoxes vindicated by motion in the intuitionistic continuum?

In Physics VIII.8, Aristotle refers to his usual resolution of Zeno's paradox of motion: We should make the same response to anyone who uses Zeno's argument to ask whether it is always necessary to ...
0
votes
0answers
193 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 ...
10
votes
4answers
1k views

How do we separate rules of logic from non-logical constraints?

I think that very often the idea of 'constraint' appears in mathematics. For example, when a triangle is considered, 3 points are constrained not to be co-linear, and then we try to discover the ...
0
votes
0answers
181 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, ...
5
votes
1answer
2k views

What are the main issues on which the schools of Intuitionism, Formalism, and Logicism disagree?

What is the difference between Intuitionism, Formalism, and Logicism? Namely - on which issues do they disagree? And what is the relation of those schools of thought to Platonism, Nominalism, and ...
1
vote
1answer
175 views

Are there recent coherence theory of truth for mathematical truths?

Are there any recent works (papers, books, etc) in philosophy of mathematics where it is given an account of mathematical truth in terms of a coherence theory of mathematical truth? I am interested ...
0
votes
1answer
103 views

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 function x -> 2x, every element of set A can be uniquely ...
4
votes
4answers
278 views

Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets?

Cantor defined an infinite set as a set whose subset can be placed in a one-to-one correspondence with its subset. That is, take the set of all natural numbers: {0, 1, 2, 3, 4,...}. From that set, you ...
1
vote
1answer
178 views

Examples of theories that assume the existence of an “External Reality”?

In this paper written by physicist Max Tegmark (https://arxiv.org/pdf/0704.0646.pdf) it talks about "External Reality Hypothesis". Specifically, he says: Although many physicists subscribe to the ...
2
votes
1answer
81 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 ...
0
votes
2answers
393 views

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 ...
2
votes
2answers
39 views

Help wanted - need descriptor for a partcular type/form of argument

I am writing a paper on cognition, and to simplify my discussion I need an adjective or descriptor for particular category of argument as follows: I am arguing for the necessity of a construct with a ...
39
votes
12answers
5k views

What should philosophers know about math and natural sciences?

My question is whether a lack of knowledge about formal mathematics or theoretical science in general would have an impact on a philosopher's ability to think and make judgments. Why should a ...
2
votes
0answers
56 views

Mathematical Universe

I have a beginner question on the type of claims this book or similar theories make. That book claims that universe is math structure. I just want to clarify if I correctly understood his goal: Does ...
1
vote
2answers
197 views

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 ...
-2
votes
1answer
70 views

Can a different universe be built with three dimensions? [closed]

Can you theoretically create a universe that will have the same dimensions but will look different? For example, a paper that has a limit, or another similar dimension can it be different?
6
votes
1answer
307 views

What's so bad about giving up the Axiom of Choice?

The Axiom of Choice (AoC) in set theory famously gives rise to controversial and counterintuitive theorems. (Examples: Banach-Tarski paradox and existence of non-measurable sets.) I'm aware of some ...
2
votes
1answer
315 views

What is the relevance of applicability to the natural sciences in pure mathematics?

I think I am coming to a good, new understanding of the relationship of pure mathematics to the natural sciences. A major concern of mine is just how reliable is rigorous (characteristically "pure") ...
2
votes
0answers
73 views

Does Tegmark's hypothesis include dynamical mathematical structures?

Tegmark's hypothesis is the idea that mathematical structures are physical and thus have physical existence (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) Zuse's thesis says that ...
2
votes
0answers
125 views

Relation of Mathematical Propositions to Natural Language

Treating Natural Language as a language game, what role does it play in our understanding of mathematics? Does natural language provide meaning to mathematics? Does a proof of a conjecture, say FLT,...
4
votes
1answer
209 views

Is there a natural example of a non-self-referential semantic paradox in philosophy?

A commonly studied paradox is the liar's paradox. The liar's paradox is to determine whether "this statement is false". The usual resolution is to state this the sentence is not actually a statement ...
0
votes
3answers
269 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 ...
2
votes
1answer
66 views

what is the ontology-ideology distinction in phil of math

Quine proposed a distinction between ontology - the doctrine of what there is - and ideology - the complex terms and predicates expressible in one's theoretical language (though in his 1971 paper he ...
-1
votes
3answers
135 views

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 ...
2
votes
3answers
129 views

Can a problem be solved if there exists no solution for it in any context?

Is finding a solution for a problem in a given context is an attempt to find a solution for the problem in another context? For example, it seems some of the hardest problems of real analysis were ...
1
vote
3answers
106 views

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 been pondering a question in my head. 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' ...
0
votes
2answers
87 views

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....
0
votes
3answers
177 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 ...
1
vote
2answers
115 views

What's the meaning of this quote of Pythagoras on the good and bad principle?

Simone de Beauvoir attributed the following quote on the good and bad principles to Pythagoras in The Second Sex, page 114 : There is a good principle that created order, light, and man and a bad ...
1
vote
1answer
88 views

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 ...
1
vote
5answers
279 views

Is getting 100 Heads in a row from a fair coin a miracle or not?

Suppose a man continues to toss a coin until he gets 100 heads in a row. Suppose the outcomes of all tosses from the 9999901th toss to the 10 millionth toss are all heads and 100 heads in a row didn't ...
2
votes
3answers
109 views

Probability calculus and Quantum Mechanics [closed]

I am not an expert and probably this question highlights this. Anyway, is the probability calculus used in Quantum Mechanics? Does the concept of probability adopted in Quantum Mechanics satisfy the ...
3
votes
1answer
99 views

Why is ZFC not as susceptible to Gödel's incompleteness as was the Principia Mathematica?

So, from what little I have read (such as this answer), it appears to be that one reason why the program of Logicism, as laid out in the Principia Mathematica, failed was that its goals (of finding a ...
0
votes
0answers
24 views

Discovery VS Invention in Mathematics [duplicate]

Asking specifically in the context of philosophy of Mathematics, on what basis do we classify or should classify a new expression as a Creation of Mind (Invention) OR a Discovery?
1
vote
4answers
517 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 ...