New answers tagged philosophy-of-mathematics
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Questions about mathematical models of the real world
Mathematicians typically define as little as possible, so that their results are as generic as possible. If they found a need to have a "BankAccount" type, it would be because we needed ...
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Questions about mathematical models of the real world
Representing a brick in maths is done differently depending on which attribute of the brick you wish to build into your model that has bricks in it.
For example, if you wish to build a model which ...
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Is there a paradox in the proof of Godel's incompleteness theorem?
I'm not entirely sure that I'm justified in rejoining this question by way of a full answer, because I'm not entirely sure as to the justification of the question itself. But so I've decided to read ...
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Is there a paradox in the proof of Godel's incompleteness theorem?
Cogito ... Gödel's argument is that in a given axiomatic system capable of math, call it A, there is a statement/mathematical theorem, call it T, such that:
T is true
T is unprovable in A
A few ...
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Is there a paradox in the proof of Godel's incompleteness theorem?
In my paper, there are two core ideas that are mutually corroborating and well-documented.
I found a paradox in the proof of Gödel's Incompleteness Theorem and found the concrete form of the paradox. ...
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Is it possible to do physics without mathematics?
A fundamental question in the philosophy of physics is whether physics can stand independently of mathematics. If we were to take remove the support of mathematics from physics, what will remain?
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what's means scope of further modal operators?
sry
I understand now, □◇∃a∀x(x in a iff {Fx}_1) is Fx within □ but not within ◇ because □ occurs at first and {Fx}_1 say Fx falling within the scope of the first 1 modal operator which Fx occurs in ...
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Why is the gambler's fallacy a fallacy?
It’s quite simple mathematics and would fit there better than under “philosophy”. But basically, you are misunderstanding what the statements mean.
Assuming that every coin throw has a probability of ...
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Is Intuition Indispensable in Mathematics?
You may be confusing the concepts of Intuitionism and metalanguage. It is the latter that - implicitly or explicitly - underpins all work in mathematics and of course especially in logic. The ...
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Is Intuition Indispensable in Mathematics?
If we're using something like one of the normal(?) variants of an indispensability argument via ontological commitment-mongering, wouldn't the form of the reasoning look something like:
Our best ...
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Is Intuition Indispensable in Mathematics?
No. Nearly all mathematicIANS rely on intuition, however; despite the stereotype of the pure mathematician being entirely dissociated from reality, nearly all "realized mathematics" is ...
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Is Intuition Indispensable in Mathematics?
You ask:
Is Intuitionism Indispensable in Mathematics?
No. Mathematics existed and functioned very well before Brouwer introduced intuitionism in mathematics (SEP) and Dummett went after classical ...
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If mathematics isn't fundamental to the universe, will we need to develop a new, non-mathematical approach to physics?
OP: “Physics, as a discipline, aims to understand reality at its most basic level, and mathematics is deeply ingrained in modern physics. However, if reality doesn't truly conform to laws expressible ...
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Can there be mathematical facts of the matter without mathematical realism?
Yes. If mathematics is more like a structured language imposed upon the universe by minds, rather than an external truth being discovered by minds, then the truth of the statements are true if the ...
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Can there be mathematical facts of the matter without mathematical realism?
Linnebo[10] pertains to truth-value realism (see also this section of the SEP entry on mathematical Platonism). But so the most convenient way I have found in the literature, to think of the ...
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Is it possible to do physics without mathematics?
IMHO, it is possible to do physics without any underlying mathematics, but you will not go very far. The main goal of physics is to build a model that is able to reproduce what is observable in the ...
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Is it possible to do physics without mathematics?
I am not a philosopher but an ex-physicist. I also taught physics.
The clear answer is no.
There is no need to look for contrived reasons - whatever you do in physics is measured, and you need to have ...
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Is it possible to do physics without mathematics?
At least since the 17th century, physical knowledge and mathemathical methology are inextrictably linked. The revolution which exchanged the Aristotelian way to see the world with a scientific ...
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If mathematics isn't fundamental to the universe, will we need to develop a new, non-mathematical approach to physics?
If mathematics isn't fundamental to the universe, will we need to develop a new, non-mathematical approach to physics?
Mathematics isn't fundamental to the universe. Mathematics is a set of theorems ...
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Is it possible to do physics without mathematics?
Take the scientific method, which lies at the heart of physics. We make an observation, formulate a theory, which provides us with a hypothesis about nautre. By conducting an experiment, we can ...
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Is it possible to do physics without mathematics?
Understanding physics as purely descriptive, yes you can but that statement doesn't apply to all of the physics you can do with mathematics. For example you can make the observation that objects with ...
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Is it possible to do physics without mathematics?
It depends a bit on what you consider "math". When one thinks about math in physics, one imagines differential equations, tensors, linear equation systems and the like.
But would you also ...
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Is it possible to do physics without mathematics?
Absolutely possible.
If you devote some time in reading the beautiful works of Michael Faraday, you would be convinced that physics (study of nature) is a subject in its own right which requires no ...
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Is it possible to do physics without mathematics?
Yes.
Put simply, physics is the study of the physical universe, which answers the question of what does it mean to "do physics". It means you are studying the physical universe.
You cannot ...
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Is it possible to do physics without mathematics?
Yes. Sort of. It is called Naïve physics
Naïve physics or folk physics is the untrained human perception of basic physical phenomena. In the field of artificial intelligence the study of naïve ...
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If mathematics isn't fundamental to the universe, will we need to develop a new, non-mathematical approach to physics?
The map not being the territory has no impact whatsoever on its utility for mapping the territory.
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Is it possible to do physics without mathematics?
This question seems to me to confuse a number of things that don't seem well supported:
Having component elements does not have to make an object reducible to only that element.
Having a well ...
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Is it possible to do physics without mathematics?
About your last question (invented vs. discovered):
In my view, we shouldn't make too much (philosophically) out of the "unreasonable effectiveness of mathematics in physics" as it is ...
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If physics can be reduced to mathematics (and thus to logic), does this mean that (physical) causation is ultimately reducible to implication?
The simplest law of quantum physics ( Heisenberg's uncertainty principle ) states that you cannot accurately know the position and velocity of elementary particles. Therefore, by definition the future ...
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Is category theory as philosophically intuitive as basic logic?
Surprisingly, category theory corresponds to formal logic, so the answer is necessarily yes and the fusion of techniques is known as categorical logic (WP, nLab). In the next two paragraphs, I'll crib ...
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Is it possible to do physics without mathematics?
The way mathematics is done in theoretical physics is different from the mathematics done in mathematics and mathematical physics. Many physicists don't know logic and those who know a lot of ...
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Is it possible to do physics without mathematics?
No
Take one of the absolutely simplest physical problems imaginable: "How long does it take for a mass m to fall a distance d?" How can you possibly begin to answer this question without ...
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Is it possible to do physics without mathematics?
Physics is the study of the relationships between measurements. Mathematics is the study of relationships in the abstract, especially the relationships between quantities and sets.
You cannot study ...
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Is it possible to do physics without mathematics?
It depends on what you mean by 'do' physics. You can certainly get a grasp of key ideas of physics, such as relativity and electromagnetism, without resorting to mathematics, but real physics, of the ...
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Is it possible to do physics without mathematics?
At about 1600 CE Galilei made his famous statement that the book of
nature is written in the language of mathematics. At least since
this time it was beyond doubt that progress in astronomy and ...
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If physics can be reduced to mathematics (and thus to logic), does this mean that (physical) causation is ultimately reducible to implication?
If physics can be reduced to mathematics (and thus to logic), does this mean that (physical) causation is ultimately reducible to implication?
The idea of reducing mathematics (or anything else) to ...
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If physics can be reduced to mathematics (and thus to logic), does this mean that (physical) causation is ultimately reducible to implication?
Bumble's answer is spot on, but I thought I'd show you the fallacy of your reasoning a little more concisely.
You are engaging a fallacy called reification. From WP:
Reification (also known as ...
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Accepted
If physics can be reduced to mathematics (and thus to logic), does this mean that (physical) causation is ultimately reducible to implication?
Physics, or indeed any other science, does not reduce to mathematics. Rather, physical relationships are expressible in the language of mathematics. If you wish to state Coulomb's Law, you can use a ...
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If physics can be reduced to mathematics (and thus to logic), does this mean that (physical) causation is ultimately reducible to implication?
A simple model of a universe is Conway's game of life. The universe in Conway's game of life is an infinite 2d grid of "live" (black) and "dead" (white) cells that change in ...
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What do all branches of Mathematics have in common to be considered "Mathematics", or parts of the same field?
Classical logic. Make definitions ("this is a Line."), make relations between these definitions ("These two lines compare equal.").
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What do all branches of Mathematics have in common to be considered "Mathematics", or parts of the same field?
I've been reading Mathematical Models: A Sketch for the Philosophy of Mathematics by Saunders Mac Lane, and I think he has something useful to say.
Mac Lane talks about the origin of various sorts of ...
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Why do constructivists accept the countable choice?
edit: changed notation after I realised philosophy stackexchange does not render mathjax.
I have not done any formal logic, but from an analyst's perspective the difference between countable choice ...
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What are the philosophical implications of Gödel's First Incompleteness Theorem?
What Gödel showed: In any mathematical system T that is strong enough, you can make a statement S which can in layman’s terms be interpreted as “in the mathematical system T there is no proof for the ...
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Can Balaguer’s argument we don’t, and couldn’t, have any good argument for Platonism or ficitonalism in math extend to realism/antirealism in general?
I see no issue in extending Herr Balaguer's argument beyond mathematics, to other/the whole ontological domain(s). His condition for existence is clear-cut: For x to exist, it has to be consistent (x ...
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What do all branches of Mathematics have in common to be considered "Mathematics", or parts of the same field?
"Mathematics" is a topic which does not have well defined edges. It is generally accepted that it operates on rather abstract concepts, such as using the number 5 rather than physical ...
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What do all branches of Mathematics have in common to be considered "Mathematics", or parts of the same field?
Mathematics concerns itself about idealized objects, their asserted properties (axioms) and the resulting deduced properties of such objects (lemmas and theorems). Deduced proprties can found - ...
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What are the philosophical implications of Gödel's First Incompleteness Theorem?
The original question concerns the first incompleteness theorem, but some of the answers, including the highly upvoted answer https://philosophy.stackexchange.com/a/2645, delve into the second ...
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What do all branches of Mathematics have in common to be considered "Mathematics", or parts of the same field?
To recall some branches of mathematics: Set theory, algebra,
topology were the first books of Bourbaki in the middle of the 20th
century, for more information see
Bourbaki.
Later category theory ...
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What do all branches of Mathematics have in common to be considered "Mathematics", or parts of the same field?
Mathematical formalism gives an easy definition of the field. For example, Haskell Curry defined mathematics as the "science of formal systems". From this perspective, it's easy to test if a ...
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Is there any mathematically valid statement that defies logic?
What are these rules of logic you are referencing?
Most of standard mathematics is embedded inside some kind of First Order Logic.
And so, is all coherent with first order logic.
There are higher ...
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