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 ...
- 27k
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
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,...
- 13.1k
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.
...
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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 ...
- 5,198
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).
...
- 12.3k
3
votes
Are MUH and IIT compatible
IIT is essentially a flavor of physical monism. It presupposes that what we typically think of as the mental--consciousness--is a manifestation of a physical state. That, in itself, is not unusual. It'...
- 27k
2
votes
Did Gödel think certain math could only be understood if platonism is correct? (and correspondence and nominalism)
We do not have a definition for existence.
Take a naïve (read best possible) notion of existence:
x is perceivable -> x exists (fails because of hallucinations)
x exists -> x is perceivable (...
- 3,196
2
votes
An argument against neural reductionism based on the necessity of abstract ideas
And I think it's those commonplace instances of the use of inference that can't be explained in terms of neuroscientific analysis, because they are dependent on the intellectual act of abstraction. ...
- 11.1k
1
vote
Accepted
An argument against neural reductionism based on the necessity of abstract ideas
I think a more robust defense of non-reductionism can be made in terms of the mechanisms of meaning.
I'd agree with that assessment. Various computational models of vision grow more and more ...
- 22.7k
1
vote
Are MUH and IIT compatible
MUH states that the ontological representation of reality IS mathematics. IIT on the other hand accepts the traditional view that consciousness is grounded on physical matter, but instead of trying to ...
- 1,561
1
vote
Are Bourbaki and Deligne Mathematical Realists?
Bourbaki have insisted that they are interested in the way
mathematicians do their work rather than in foundations, and there are
indications that their philosophy of mathematics is not carefully
...
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1
vote
Are Bourbaki and Deligne Mathematical Realists?
Concerning your first question see Nicolaus Bourbaki The
architecture of mathematics. The paper is a self-presentation of Bourbaki from 1950, on request I can send a copy.
Reading the paper confirms @...
- 24k
1
vote
What are some points to refute the Mathematical universe hypothesis?
My suggestion is don't call it a category error, or problematize his math. He can easily find refuge within the mysteries and idiosyncratic views of consciousness. Most arguments against MUH attack ...
- 2,385
1
vote
Accepted
How do modern platonists explain the objective, specific connections between the physical and abstract?
The usual way of this involves possible worlds as abstract objects (or, then, possible objects as abstract, for that matter). Since every permutation of possible properties is encoded by abstract ...
- 12.3k
1
vote
Accepted
Can someone explain the terms "virtual cause" and "eminent cause"?
These are terms used by medieval philosophers, and also by Descartes and some others. Today, only a few scholars in the Aristotelian or Thomistic tradition continue to use them.
The idea is to ...
- 22.8k
1
vote
An argument against neural reductionism based on the necessity of abstract ideas
And abstractions are only perceptible by a mind, as a matter of definition. They're not physical things.
What should we make of the case of numbers? They don't seem to be physical things, so maybe we ...
- 2,402
1
vote
Mathematical Platonism. Are numbers real?
I would actually like to echo @JiK a bit, especially since I am a physicist.
One of my first lessons in physics was on the fundamental concept of measure and measurement. We we tasked with defining ...
- 136
1
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Mathematical Platonism. Are numbers real?
This is an ill-formed question because you don't explain what you mean by "real." And I'm not even sure you have a good idea of what you mean by "numbers" (though that may not be ...
- 129
1
vote
Mathematical Platonism. Are numbers real?
The underlying question is - can the components of mathematics (like numbers) be separated from the processes of computation?
Take pi. Pi is a number, pure and simple. If pi can not considered to be a ...
- 11
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Mathematical Platonism. Are numbers real?
This is my first post here. I cannot comment yet.
In the movie matrix the character morpheus asked "How would you define reality? Is it what your senses feel?" or something like that.
I ...
1
vote
Mathematical Platonism. Are numbers real?
The question assumes multiple facts that are not, the language is imprecise, and some elements are incorrect. This is moreover a long comment.
Real in this context refers to the counterpart of ...
- 6,830
1
vote
Accepted
What do contemporary philosophers mean when they say abstract objects exist (or realism of abstract objects)?
I don't think that Putnam or Quine (or for that matter Plato) were all that concerned about the exact nature of these 'abstract objects'. The point is that they felt certain other philosophical ...
- 18.5k
1
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Did Gödel think certain math could only be understood if platonism is correct? (and correspondence and nominalism)
The passage from Shapiro does not mention nominalism at all, whereas four out of your five conclusions deal with nominalism. One wonders how they are derived from Shapiro's passage.
As far as Gödel ...
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