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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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1answer
73 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 ...
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7answers
276 views

Why does mathematics work in the physical sciences?

Why does mathematics work in the physical sciences? I looked at reddit, and they said that it's not surprising it does, just because that's what it's there for. But there's definitely a question ...
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1answer
110 views

Why is Math not Logic? [duplicate]

So I've heard, "Math is not logic," because logic has no notion of order. However, consider the following argument: There once was a man on a mountaintop. He came down, murdered a villager's cat, and ...
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3answers
608 views

Is the real number line actually real when we construct it?

Intuitionism is akin to constructivism in mathematics but not quite the same from what I can tell. In the usual treatment of the real line, the additional numbers are found between the rationals by ...
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0answers
30 views

Minimalist philosophical assumptions to reason, deductively/inductively

I've been thinking a lot about foundations of science recently and I was wondering. Are there existing books/essays/works, or were there attempts that try to achieve the following: With a ...
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4answers
166 views

Mathematical proof of a philosophical theory

Can I prove a philosophical theory mathematically? If yes? How? For example, can the theory of materialism be proved mathematically?
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3answers
192 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 ...
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1answer
107 views

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, ...
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0answers
66 views

What are numbers? [closed]

What are numbers? Does the number two exist? If so, how?
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5answers
295 views

Can a solid theory ever exist without any axioms?

In math, numbers and addition are logically defined by Zermelo Set Theory, a small group of axioms upon which everything else can be built. Could it be possible to have a working theory, (in any field ...
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2answers
80 views

Help with an existential natural deduction proof

From the assumption ∃x∃y R(x, y) I need to derive the conclusion ∃y∃x R(x, y) From the comments: I tried to use Existential Elimination but I can't figure out how to do it properly.
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5answers
604 views

Is infinite divisibility of Something the same concept as Nothing?

There must be some kind of proof for that. I have always be intrigued by the notion that if something is endlessly divisible then that would mean that it is nothing indeed. (An example? Matter which ...
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4answers
1k views

Why do we need geometry for pure math?

Karl Weierstrass had a very interesting critique of Riemann's work. Supporters of Riemann, claim that a pure logician would never have been able to see the things that the "geometric imagination" of ...
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1answer
65 views

Mechanics of Perception

How is perception formed? By perception I mean 'thought' or 'idea' of the World. What I see by itself does not contribute anything to thought. Only an acknowledgement can contribute to structuring of ...
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0answers
42 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 ...
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1answer
44 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 ...
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3answers
87 views

Does infinity imply uncertainty? (Or the other way around?)

This is a follow on question from my question here Consider the hypotenuse of a right angle triangle where the opposite and adjacent sides both have length 1. The hypotenuse has length sqrt(2)... ...
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4answers
109 views

Russel's paradoxical set from a different view

Suppose naïve set theory, let's do a tought experiment: Informally, let's define a set € such that € contains all the sets that don't contain themselves.(yes, all but not necessarily only those), ...
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2answers
45 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?
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4answers
750 views

Why is there so little discussion / research on the philosophy of precision?

I was thinking the other day about the difference between rational and irrational numbers, and wondering whether the distinction between them is created by leaving out discussion of precision. So for ...
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2answers
154 views

Did physicist Max Born think that mathematical structures are platonic entities?

It seems that prominent physicist Max Born (https://en.wikipedia.org/wiki/Max_Born) believed in some kind of Platonism. We can infer this, for example, from the book "The Innermost Kernel" (https://...
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0answers
51 views

Is this an argument about the world or about human cognition?

This is a question about a thesis I have encountered regarding the relation of abstract mathematics ( Category Theory in particular ) with reality and the nature of human cognition. The argument goes ...
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0answers
72 views

Are the foundations of mathematics “doomed” to be set-theoretic in nature?

Let's say we want to come up with a foundational theory for all of mathematics and let's say that it is embedded in first-order logic. Note that the machinery of first-order logic is described with ...
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3answers
381 views

Do Gödel's First Incompleteness Theorem imply the inconsistency of Platonic Infinity?

According to Modern Mathematics (where the majority of mathematicians agree about the notion of actual infinite sets, as established mostly by George Cantor) an inductive set (as given by ZF(C) Axiom ...
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1answer
226 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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1answer
193 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 ...
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11answers
9k views

Is Mathematics considered a science?

Science, generally is analyzing information gathered from observing phenomena, and coming up with theories to try and explain the phenomena. Then, attempting to predict a new phenomenon before it ...
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1answer
29 views

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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5answers
3k views

Was Kant incorrect to assert all maths as 'a priori'?

Preface: Kant's assertion is rebutted by Prof David Joyce who references non-Euclidean geometry and by the last sentence on Sparknotes which states that 'empirical geometry is synthetic, but it is ...
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2answers
225 views

Does mathematical formalism have an opinion on semantics?

Mathematical formalism regards mathematics as a syntactic matter, where symbols are manipulated according to rules and the symbols need not have any meaning. I am wondering though whether it has ...
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1answer
74 views

Decidability of predicate logic

In the language of predicate logic with only identity and no predicates, function symbols, or constants, is it possible to construct infinitely many non-equivalent formulas?
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4answers
2k views

How long is the standard meter?

In the Philosophical Investigations §50, Wittgenstein writes: There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the ...
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17answers
13k views

How does mathematics work?

If I am given a parking lot with ten thousand cars and I want to determine whether one of the cars is orange, the only way I can do this is go through the parking lot examining each car until I find ...
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1answer
122 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 ...
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4answers
179 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 ...
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3answers
116 views

Consistency of Axioms

In Godel's Proof by Nagel & Newmann, they write : In Riemannian geometry, for example, Euclid's parallel postulate is replaced by the assumption that through a given point outside a line no ...
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3answers
231 views

Is Mathematics the Ultimate Culmination of Analytic Philosophy?

As a novice amateur, the similarities between mathematics and analytic philosophy seem striking to me. At least in a caricature view of analytic philosophy, it is the project of establishing the ...
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2answers
240 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 ...
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3answers
156 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 ...
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1answer
120 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 the function x → 2 x, every element of set A can be ...
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1answer
132 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) ...
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1answer
105 views

How do proponents of finitism respond to the claim that their position is “dubiously coherent”?

Michael Dummett writes (page 349) Since primality is decidable, the statement that any particular natural number is prime must be determinately either true or false, since the decision procedure, ...
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3answers
263 views

Does philosophy of mathematics affect mathematical research?

I am interested in a special case of the general question about whether the philosophy of X has an effect on the research or practice of X. My special interest is in the area of mathematics. I am a ...
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0answers
103 views

Using differential equation to estimate epistemological growth constant

I found some tweets (1,2) describing a philosophy paper as follows: I came across this paper from the academic journal of philosophy that tries to solve a differential equation for an ...
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3answers
835 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....
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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 ...
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3answers
292 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 ...
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0answers
163 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/...
2
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1answer
137 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 ...
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4answers
36k 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 ...