Platonism is demonstrably false. For it to be true it would mean there would have to be a Platonic form for every wrong idea as well as every true one, or it couldn't be conceived. So there is a Platonic form for Unicorns? Or the Hindu Gods Shiva or Ganesha? Or the mistaken Ptolemaic geocentric Universe? Or the ether? Why didn't Newton discover Einstein's Theories instead of the ones he did formulate? If mathematics were pure discovery rather than formulation then no one could ever get it wrong.
He believed that what makes mathematics true is that it's descriptive -- not of empirical reality, of course, but of an abstract reality.
I don't care if it is Gödel an 'abstract reality' is a contradiction in terms. An 'abstract' by definition is a concept that subsumes a number of concretes (real things = reality) or a number of other abstracts. An abstract has no other reality than as a concept. Period.
Mathematical intuition is something analogous to a kind of sense perception.
Another sentence that has very little meaning. It is just a pile of words.
Gödel wrote that we're not seeing things that just happen to be true, we're seeing things that must be true. The world of abstract entities is a necessary world -- that's why we can deduce our descriptions of it through pure reason.
Same thing applies here, “abstract entities” in the sense that they have a reality separate from the fact they are concepts is a contradiction in terms. These are assertions that aren't founded on anything other that opinion. To say they must be true is to Beg the Question that they are, not proof. The ability of the mind to formulate ever higher level abstractions doesn't mean they have actual existence. This is reminiscent of the theory of the 'ether' that Michelson & Morley finally put to rest. What medium do these 'abstract entities' exist in? Unprovable, by definition.
things are not true because they are logical, but logical because they are true; our ability to use logic and math to describe the world is because they derive from something higher and eternal (more on which below).
The part in blue presents a false dichotomy and reaches a false conclusion thereby and the part in red is an Assertion Without Proof. It shows a very poor understanding of what logic actually is and, in fact, Reifies logic. How does someone determine if something is true or not without using logic? Thus the first part of the blue sentence is demonstrably false. Logic can be used to create valid syllogisms that are constructed with false premises so that Assertion is false. Logic is a mental process, not a thing.
Since the physical world exists prior to our exploration of it, so do the higher worlds. This is easy to prove to anyone who goes there. But for those who wish they were mere animals no proof is enough to convince them otherwise.
A human being is not a mere animal so this assertion is without meaning. If higher worlds exist then they should be provable. If they are dependent upon the 'belief' of the individual then they are not provable, by definition. Another Straw Man constructed to knock down an argument not made.
.....our access to the realm of beauty is a key that unlocks many cosmic mysteries.
That is an opinion, not fact. You write as if beauty were an objective fact. Beauty is in the eye of the beholder. My father lived in Fiji for a while. He told me a story of how he was fishing with a bunch of Fijians at sunset and there was this incredible sunset. My dad said, “Wow! Look at that!” The Fijians all turned and said, “What? What?” My father said, “The sunset, it is so beautiful.” The Fijians all shrugged and went back to fishing. They couldn't see it, couldn't see what he was talking about.
"....How stupid would I have to be to think any of my answers to questions asked by ignorant flat-landers --(who limit their thinking to the horizontal world)-- would make any sense at all to them?
Careful there, your arrogance is showing.
"the properties we ascribe to our object of interest and the questions we ask about it reinforce the original metaphorical image and we miss aspects of the system that do not fit the metaphorical approximation."
Agreed, see how it applies to you?
. . . have the capacity to understand any of the answers I would give to their "questions".
As I said, your arrogance is showing.
LogicWings: "Another sentence that has very little meaning. It is just a pile of words. "
Really?
ON KURT GÖDEL'S PHILOSOPHY OF MATHEMATICS
by MK Solomon
"... in Gödel's well-known analogy of mathematical intuition to sense perception (see the .... kind of perception, i.e., in mathematical intuition
ABSTRACT
".... We compare Gödel's philosophy of mathematics to Steiner's "epistemological structuralism."
§1. Introduction
"We show that Gödel's philosophy of mathematics, as presented in his published works, with possible clarification and support provided by his posthumously published drafts, can be considered as being formulated by Gödel as an optimistic neo-Kantian epistemology (obtained from Kant's epistemology regarding the physical world in terms of sensory appearances as distinct from things in themselves, not obtained from Kant's epistemology of mathematics as being synthetic a priori knowledge) superimposed on a platonic metaphysics. By Platonic metaphysics, we of course mean that abstract objects have an objective existence. By neo-Kantian we mean obtained from the Kantian epistemology with one important modification, namely, removing the doctrine of the unknowability of things in themselves.
"Indeed, we will see in section 2.2 that Gödel thought that abstract things in themselves may be progressively knowable. Furthermore, it is pointed out in section 2.4 that he explicitly indicated that the knowability of physical things in themselves is possible through the progressive advancement of modern science. ...."
<><><><><><><><><>
"I’ll begin by reminding the reader that I am a mathematician. The way that mathematicians use logic is different from the way that it is often used in philosophy. Some people distinguish between the two by using the expression “philosophic logic” to refer to the use of logic within traditional philosophy. The reader should be warned that my view of the limitations of logic is colored by my background as a mathematician. .....
"...most mathematicians see logic as a branch of mathematics. Many, self included, see logic as a relatively minor branch of mathematics. I don’t think this is just a territorial dispute (as in “who owns the territory of logic”). The way we mathematicians use logic is different from the way that philosophers use it. Once we have an axiom system, we use logic to explore the consequences of those axioms. But coming up with axioms systems is itself an important part of mathematics, but seems to be outside the scope of logic. ...."
Here:
LogicWings: "A human being is not a mere animal ..."
How do you know this?
M-PI: ".....our access to the realm of beauty is a key that unlocks many cosmic mysteries."
LogicWings: "That is an opinion, not fact. You write as if beauty were an objective fact. Beauty is in the eye of the beholder..
"Without a doubt, the ultimate Black Swan is whatever it was that permitted merely genetic human beings to emerge into full humanness just yesterday (cosmically speaking), some 50,000 years ago. .....
"....once man consciously enters the sensorium of time and space, he is implicitly aware of both Absolute and Infinite, and therefore Love, Truth, Justice, Beauty, Virtue, and Eternity. These are the things that define man, not his genome. ....."