19
votes
How many Platonic ideals are there?
Although Plato's Theory of Forms presents as a consistent, "scientific" system of metaphysics, it doesn't really hold up under scrutiny, and there's a strong tradition of thought that it was ...
- 30.7k
15
votes
How do mathematical realists explain the applicability and effectiveness of mathematics in physics?
Physics doesn't follow any rules. Physics just is. If physics stops following our rules, we don't say physics is wrong. We have to adapt our rules.
Many of the rules and patterns we discover in ...
- 2,243
12
votes
Accepted
Mathematical Platonism. Are numbers real?
By "real" here I assume, by your example, that you're talking about "physically real". And in that case real=experimentally_measurable. And that, in turn, means units. Even your ...
- 585
12
votes
How do mathematical realists explain the applicability and effectiveness of mathematics in physics?
why does the physical universe adhere to mathematical principles?
It might not. The adherence is generally understood to be the other way around. We have proposed mathematical models that adhere to ...
- 5,460
10
votes
Plato and the knowledge of the forms
I'm not sure Plato directly answers this question, but the dialogs clearly suggest the answer is yes. Plato frequently uses the metaphor of traveling closer or further away from the divine, immortal ...
- 30.7k
10
votes
Mathematical Platonism. Are numbers real?
Asking whether a number, such as four, is real is like asking whether a word such as 'big' is real. The qualities which we think of as big are real. When we say a football stadium, for example, is big,...
- 26.3k
8
votes
Mathematical Platonism. Are numbers real?
Mathematicians, specifically set theorists, have so little faith in the existence of numbers that they must posit an axiom for something even as fundamentally obvious as the existence of an empty set.
...
- 197
6
votes
In what realm do mathematics objects exist according to Platonists?
Interpretation of the Platonic forms is a big wrangle and may be undertaken in many ways. But the simplest answer to your question "in what realm" might just be to say everywhere or in every ...
- 13.7k
6
votes
Did God "design" logic?
He could have made it so that 2 + 2 = 5, without modifying the meaning of "2" or "+" or "=" or "4" or "5" (i.e. keeping all of that exactly the same).
...
- 18.9k
6
votes
How do we justify the Power Set Axiom?
The motivation, according to the iterative conception of sets - see also Von Neumann universe - is that sets "come into being" at stages.
There is an initial collection of individuals: ...
- 41.1k
5
votes
Accepted
Does the Platonic triad originate with Plato?
No. Nor does it originate with other venerable authors commonly implicated, Plotinus, Aquinas, Ficino, etc. Plato's "triad", as read into Philebus, was supposedly Truth, Beauty and ...
- 44.2k
5
votes
Accepted
Can set theory be non-extensional?
For sets, extensionality is defined as follows.
∀S∀T(S=T ↔ ∀x(x ∈ S ↔ x ∈ T))
All modern set theories have this as an axiom or theorem, so they are all extensional.
Russel did not reject ...
- 13.1k
5
votes
Mathematical Platonism. Are numbers real?
An interesting number like e, Euler's number, a 'constant of nature', as real as could be. It is known inexhaustively by many representations. Many discoveries and many perspectives, but never the ...
- 7,650
5
votes
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 ...
- 4,015
5
votes
If mathematical platonism is true, how do biological brains governed by physical laws access eternal platonic mathematical truths?
We learn mathematics at school. Learning the concepts, the
mathematical operations and some algorithms, e.g. how to multiply or
how to divide in written form.
The question, how we learn, is better ...
- 42.3k
5
votes
Formalist or Platonist--does it make any difference in mathematical practice?
To pick up on user Bumble's comment on infinitesimals, I would point out that there would indeed be practical differences between a Formalist and a Platonist, as determined by their respective ...
- 4,015
5
votes
How do we justify the Power Set Axiom?
Welcome to the brave new world of Constructivism (Errett Bishop) and Predicativism (Hermann Weyl, Solomon Feferman, ...). These schools indeed reject the generalized application of the power set ...
- 4,015
4
votes
Did Plato not believe in institution of marriage?
Conifold provides the reference, Republic, III.423e-424a. The rationale of Plato's proposals regarding marriage and the family is set out briefly by Julia Annas :
Plato is not interested in
the ...
- 36.1k
4
votes
Plato and the knowledge of the forms
When the Soul wants to experience something she throws out an image in front of her and then steps into it.
Meister Eckhart
There's an issue with your question.
You say "his soul" ie "Plato's soul"....
- 5,394
4
votes
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 ...
- 885
4
votes
Is mind-body dualism necessary for mathematical Platonism?
You ask:
Is mathematical Platonism possible without mind-body dualism?
Yes. I've never seen anyone claim that Platonic thinking requires mind-body dualism, and I don't believe any compelling ...
- 35.5k
4
votes
Is mind-body dualism necessary for mathematical Platonism?
I would say that there is dualism, but it is not necessarily mind-body-dualism or at least mind-body is not the most accurate label.
I believe a better label for the fundamental dualism would be ...
- 3,860
4
votes
Is mind-body dualism necessary for mathematical Platonism?
Synthesizing an answer from a bunch of Conifold comments on (P/p)latonism from
here (an old one)
here (this question)
here (from a few days ago)
with some suitable rephrasing and reordering and (...
- 5,394
4
votes
How do we justify the Power Set Axiom?
The Power Set Axiom is the set theoretic Analogue To Exponentiation.
The same way the Union and Pairing Axioms allows us to have a successor of a set.
The Power Set let's us have exponentiation of ...
- 472
4
votes
Accepted
What is the ontological difference between platonism and non platonism?
Translated to mundane speech Platonism means that certain concepts like mathematical objects exists independently from human thinking. These concepts can be discovered by humans, but they are not ...
- 42.3k
4
votes
How do mathematical realists explain the applicability and effectiveness of mathematics in physics?
I think that there is an underlying assumption that we "found" mathematics and that it just "happens to" align with physical reality, but there is no reason to believe that this is ...
- 321
3
votes
Accepted
Was the idea of different physical realms advanced by other philosophers?
If you're specifically interested in other physical realms that aren't part of the same space that we inhabit (i.e. you couldn't get there by traveling some distance in space), this article talks ...
- 2,867
3
votes
Plato and the knowledge of the forms
Some priests and priestesses who have thought a great deal about explaining their concerns, say that our souls are immortal. A soul will come to an end which is called dying, but at another time be ...
- 1,300
3
votes
Accepted
What evidence is there that Gödel believed the mind to be non-physical?
SEP itself refers to Platonism and Mathematical Intuition in Kurt Gödel's Thought by Parsons and On the Philosophical Development of Kurt Gödel by van Atten and Kennedy as the sources for this ...
- 44.2k
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