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 ...
- 565
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 ...
- 25.8k
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,...
- 9,459
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 ...
- 13.3k
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 ...
- 6,931
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 ...
- 4,955
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 ...
- 35.3k
4
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 ...
- 42.3k
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"....
- 1,402
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 ...
- 2,837
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 ...
- 1,230
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 ...
- 42.3k
3
votes
Why are abstract realms/the abstract realm thought of as being so orderly/restricted?
Note in advance: I am assuming that the abstract realm you're referring to is something along the lines of the "third realm" that Frege posited (alongside physical and mental domains).
...
- 10.3k
2
votes
How is that any non-causal explanation of reliability is incompatible with the language- and mind-independence of mathematical objects
See Hartry Field's Realism, Mathematics, and Modality, Blackwell (1989), page 230:
a realist view of mathematics involves the postulation of a large variety of aphysical entities - entities that ...
- 35.9k
2
votes
Is there any physics-model version of Tegmark's hypothesis?
Max Tegmark answers the question Is the physical world isomorphic to some mathematical structure? with the claim that "The physical world is completely mathematical" and "Everything that exists ...
- 19.2k
2
votes
Nominalistically Finding Radioactive Half-Life?
One way to express the concept of half-life without math is to fill a see-through container with pennies, marking their volume on the side with a horizontal line. Shake the container and then spread ...
- 2,342
2
votes
How much platonism do I need to handle the halting property?
Any absolute statement about the future is subject to change. Will it snow where I am on February 19, 2020? That's impossible to say as of February 19, 2019. Will we find a contradiction in ZFC? ...
- 1,134
2
votes
Accepted
How much platonism do I need to handle the halting property?
This is more a finitist vs non-finitist issue than it is about Platonism or formalism: Admitting that For no integer P(x) holds is sensible statement for a decidable property P is compatible with ...
- 936
2
votes
Platonism and causality
The relationship between abstract objects and platonic forms is obviously difficult, as is the relationship between modern (specifically mathematical) platonists and adherents of Plato's philosophy of ...
- 116
2
votes
Did physicist Max Born think that mathematical structures are platonic entities?
The answers to both "some kind of platonism" and "infinitely many universes instantiating mathematical structures" is no. Born is closer to Hegel than to Plato, and even further from Tegmark than ...
- 42.3k
2
votes
Plato and the knowledge of the forms
No, Plato did not learn anything new about forms during his life on earth.
According to Plato, he learned everything about forms when dwelling in a pre-existent form in the realm of forms. Moving ...
- 20.8k
2
votes
If mathematical platonism is true, is mathematics then a discovery?
We could go through the permutations of Platonism, nominalism, intuitionism, empiricism, and fictionalism. The guts of the question is whether, if Platonism is true, we can and do discover ...
- 35.3k
2
votes
Why do mathematical platonists believe in the abstract when math clearly comes from FOL, a non-abstract?
You are correct that formal logic provides a link between mathematics, and tangible things we can operate on mechanically (formal proofs).
The concept of a "formal proof" is an abstract, ...
- 10.8k
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