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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Is there stance that every logical and mathematical derivation exists/is contructable but we only care about a proper subset?
I'm thinking every logical derivation as something like all the derivations in the Principle of Explosion - really everything.
It could just be a helpful interpretation, not trying to get super deep ...
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What are some examples of math that does *not* apply to the real world?
The "unreasonable effectiveness" of mathematics in describing the universe is often mentioned, but what about the sections of math that aren't applicable anywhere in physics at all? and why?
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What is an object's properties?
What can we consider an object's properties, for example, when can we consider an object's properties as 'changing'? For example, if I move an object from my desk to my table, has it changed? If I ...
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Is mathematics politically and culturally neutral?
Lately, there have been many people who say that mathematics itself is racist, that it is simply a creation of dead white Greek men. As a mathematician, I strongly disagree, and believe that ...
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Abstract objects and changing properties
I like to use This website to explain some of the simple ways of mathematical thinking, but in the linked article by Wells, he gives his ideas on how mathematical objects are inert, but in this he ...
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How do we determine if a statement can't be proved by mathematics alone?
How do we determine if a statement can't be proved by mathematics alone? It seems mathematics can only prove something that can be defined purely in mathematics terms, but can't prove simple ...
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What we can prove mathematically only applies to the system of logic used and mathematics, and not the world itself?
What we can prove mathematically only applies to the system of logic used and mathematics, and not the world itself? I am wondering if what we prove mathematically, only applies for the mathematical ...
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What do we explictly refer to in mathematical expressios
My friend has a theory about 'instantiation' of numbers, they believe that every time we think of a number we create an 'instance' of it in our own heads, it's the same idea, but each time we think, ...
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Is life experience a necessity to generate mathematical thought?
The beginning of mathematics for the Human race was motivated by Human experience. This made me wonder, suppose if there was a concious being existing in deep space devoid of any life experience, ...
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What are some fundamental differences between mathematics as a language and language spoken by humans?
What are some fundamental differences between mathematics as a language and language spoken by humans? I heard mathematics is more restricted, but aside the fact that it's restricted I can't think of ...
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Mathematical nominalists and realists on "there are at least as many possible intentional states as mathematical objects"?
I think this can be meaningfully asked. Intentional states
**Ideally I'm asking this about: mathematical nominalists, constructivists, intuitionists, and realists (and ideally I'd ask this about ...
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How does aesthetic relate to structure?
If we are to take a subject say mathematics, then often mathematicians may attribute to the well defined structure and precision in describing its theories. I believe there are also other things like ...
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What is the motivation to study Modern mathematics? [closed]
I believe in the beginning of Human race, mathematics emerged as a necessity so simplify descriptions of the things we observe in our daily life. But as of the last few centuries, it seems so ...
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Are questions truth-apt; what is the use of assigning questions a truth-value?
Is John black (or white)?
Yes he is black.
No he is not (black).
I don’t see how can the question be truth-apt and what use is there in assigning (or even being able to assign) a truth-value to the ...
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Discerning between a number 'x' as a Natural or Real number
The usual way of teaching is to explain the numbers that are element of the reals and naturals as being the same, this was a perfectly valid way of understanding for me, why do some consider '2' as an ...
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What mathematical models can we use to represent the truth value of an opinion?
What mathematical models can we use to represent the truth value of an opinion? Obviously, I don't think we can use boolean, except in cases where the opinion of a person represent a statement of fact,...
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do you know if mathematical formulas are right? [closed]
for example the formulas for some geometric figures like circles i dont remember other figures which i think the formulas are wrong for example the formula for a square it seems sound but for other it ...
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Space as being "cardinal-like"?
I was thinking about Zermelo's critique of Cantor's reasoning for the well-ordering principle, how Zermelo characterized it as an appeal to temporal intuition, whereby time itself does the well-...
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If there are theories of everything for science, are there equations of everything for math?
Some considerations:
A related question is whether math is finite, and has been asked here before. Unlike science, math does not seem to be finite. As a dear friend of mine once retorted to me, "...
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Why is math powerful?
I've been having this thought for days now, and I haven't been able to come up with a satisfactory answer.
It seems to me that one can arguably caricature mathematics as an impoverished natural ...
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If math is so deductive, why is it so hard to discover new math?
Some considerations:
The conclusions of much latter/new math may be said to be already existent within the premises of current math
The importance of deduction changes depending on if math is said ...
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What is the best argument against the Platonic idea that mathematical objects are concrete things with causal powers?
What is the best argument against the Platonic idea that mathematical objects are concrete things with causal powers?
But what is a Platonic Form or Idea? Take for example a perfect
triangle, as it ...
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Are numbers particulars?
I've often seen numbers be called 'abstract particulars' but as explored in a few of the following questions and answers that I will list, they seem to have the ability to be 'instantiated', does this ...
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If "erotetic model theory" makes sense, what is its relationship to the downward Löwenheim–Skolem theorem?
First, a point-of-departure introduction to/outline of model theory:
An interpretation of an axiomatic system is the assignment of meanings or values to a given axiomatic system such that all ...
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Does the existence of Gödel Encoding imply that any formal system is itself already included in Peano arithmetic?
The notion of Gödel Encoding is extremely important from a philosophy of mathematics standpoint, but seems to be rarely noted explicitly. Take the following claims for example (which are implied by ...
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Can the "doctrine of degrees of existence" be used to support the well-ordering lemma apart from the axiom of choice?
I was pleasantly surprised to read (in a Wikipedia article) that:
In second order logic, however, the well-ordering theorem is strictly stronger than the axiom of choice: from the well-ordering ...
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Paradox involving the principle of indifference
The principle of indifference states that:
"in the absence of any relevant evidence, agents should distribute their credence (or 'degrees of belief') equally among all the possible outcomes ...
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Can we logically derive a value for 0÷0? [closed]
I have a "proof" that 0÷0 = 2:
0÷0 = (100 - 100) ÷ (100 - 100)
= (10⋅10 - 10⋅10) ÷ (10⋅10 - 10⋅10)
= (10² - 10²) ÷ 10(10 - 10)
= (10 + 10)(10 - 10) ÷ 10(10 - 10)
= (10 + 10) ÷ 10
=...
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Multiple interpretations of the same syntax in mathematics?
Mathematics are doing a very odd usage of syntax and semantics. Let's take a wikipedia page as an example : https://en.wikipedia.org/wiki/Intuitionistic_logic
Here we have a syntax which is given, and ...
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Is applying Mathematics inevitably a form of analogical reasoning? [closed]
As mathematical models are abstractions, applying them in any context is inevitably an analogical reasoning.
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Is the fact that ZFC implies that 1+1=2 an absolute truth?
This question is somehow of a follow up to to this other one, and it's something that has bugged me for a while.
I understand the notion that there's no "absolute truth" in math, in the ...
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I thought about some reasons for why the empty set is a subset of every set?is there some validity in them?
I have some reasons for why the empty set is a subset of every set,are they correct? i think they are.correct me if I'm wrong,or tell me more
I think the empty set being a subset of every set is like ...
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Platonism in modern philosophy of physics: Stephen Wolfram and Max Tegmark ideas
Recently, Stephen Wolfram wrote an interesting article about his proposed relationship between maths and physics (https://writings.stephenwolfram.com/2022/03/the-physicalization-of-metamathematics-and-...
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Necessity of arithmetic truths into Godel sentences
My layman but hopeful to understand self is slowly trying to understand some of Godel and the philosophical implications of his work (uh oh).
Currently my understanding is that on some level:
Godel ...
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Do concepts transcend reality?
I often come to wonder about a specific, quite abstract question. Since I am not used to writing about such thing, it is very difficult for me to explain, but I will try to present my reasoning by ...
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Is there a notion of "because" in mathematics?
Sometimes, in math classes, we are asked to give justification for our mathematical assertions. We say that mathematical statement X is true because Y is true. However, I don't know if "because&...
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Unique-ness in the languages of Math and Physics?
Background
So here's something I was pondering about:
A teacher asks a student: "what is 3+1?"
The student replies "3+1"
It's not that the student's reply is wrong. But it's not an ...
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Which philosophy topics are necessary for philosophy of mathematics?
I'm currently a math major, but I'm very interested in philosophy of mathematics. I wonder if there are any prerequisites for learning philosophy of mathematics (such as studying metaphysics or ...
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is the theorem of Pythagoras right? [closed]
We don't know if the theorem of Pythagoras is right or not because we have to find a way to size things correctly, and to prove it or disprove it, and the angle too, we have to draw an right triangle ...
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Proper Philosophical Texts on the Philosophy of Science
I am a college freshman majoring in Philosophy and Physics. I am interested in the Philosophy of Physics, but before that, I would like to get an idea of general philosophical issues in the sciences. ...
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Why can't numbers be 'used up'?
I was speaking with a young student who has been learning about addition and subtraction (essentially functions, but he doesn't know that yet) with the idea of a 'number machine' and he could not ...
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Why do universities not teach constructive mathematics to CS undergraduates?
I had a conversation with a user on the Internet. And it did indeed wake my interest regarding something that I had also been asking myself long ago. Why do so many universities still teach beginners ...
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Are mathematical proofs subject to the problem of induction?
When I consider a proof, such as Euclid's proof of the infinitude of primes, it can give a sense that something necessarily true has been obtained.
I cannot remember where I got the idea, but a few ...
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Does logic give us a single definitive and universal answer for comparing the odds of unlikely events?
As an amateur who has interest in logic and mathematics I've been reading about the concept of different probability perceptions. I'd like to have your opinions over the subject below.
When it comes ...
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Is there "empirical" distance without "mathematical" distance?
Mathematicians since antiquity have been thinking about length and angle, including doing things with straight-edges, rulers, compasses, and protractors. Fast-forward to modern physics, and you'll see ...
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How could second-order logic satisfy (neo) Fregean's epistemic goal?
Recently I've been reading Shapiro's Higher Order Logic in The Oxford Handbook of Philosophy of Mathematics and Logic, Chapter 25. There are some paragraphs confusing me:
One traditional goal of ...
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Per Mathematical Structuralism, can a pure mathematical theory have semantics that is not closed on isomorphism?
This question is the philosophical side of a question that I've recently posted to MathOverflow. Here, I'm specifically asking about the output of Mathematical Structuralism on that question that I'll ...
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Do any philosophers say surreal numbers are reason to doubt platonism?
Not trying to be inflammatory at all, this is a genuine (maybe dumb) question.
Especially in regards to the genesis of the surreals, which was Conway thinking about Go endgames. They seem among the ...
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Constructing natural numbers from nothing
I found that many of us (mathematicians) try to construct natural numbers defined from the intuitive concept 'size of the set'. They take ϕ, the empty set, as the starting point, then define and ...
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Did Gödel think certain math could only be understood if platonism is correct? (and correspondence and nominalism)
I’m reading Shapiro’s Thinking About Mathematics, and there’s a quote by Godel which I would like to fully understand, both his intended meaning and how it’s viewed in the wider context of mathematics,...
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