This statement negates itself. You cannot know that you are conceiving of things "not of this world" (and I prefer Universe) because you cannot verify the existence of anything outside of this time/space, by definition. Your whole conception takes place within this Universe, and may not represent anything outside it. And you simply cannot know otherwise.
Fantasy doesn't mean that the "fantasy" is not of this world. It is very much of this world, just as lies are, but none and neither are true.
the representation that makes the object possible rather than the object that makes the representation possible.
Precisely the flaw. For it truly to be an "object" it must exist prior to the perception, or it is mere illusion. (Also precisely the argument made by another here that is entirely self contradictory, "Everything is an illusion." (So is the illusion that everything is an illusion.)
This introduced the human mind as an active originator of experience rather than just a passive recipient of perception.
This statement is without meaning. To say the mind is "an active originator of experience" is to Beg the Question that it "originates" anything. There very thing that cannot be shown because you cannot stand outside your own mind to verify the "origination." It is simply an opinion with no epistemological basis.
To simplify the above, Kant's contribution is that he essentially argues that "experience only gets you so far."
Yes, K.I.S.S.
His argument is purely theoretical and without any possibility of proof. There is no way of knowing there is any "knowledge" that stands outside of experience, because no one has ever existed outside of experience to be able to separate the two. It simply isn't possible. It is theory without any referent in reality. Like if I said Martians are why the stock market went down today. Prove me wrong.
You have to make rational sense out of what you experience and that reasoning faculty is not borne of experience.
And how do you know that it isn't "borne of experience?" Any "evidence" theoretical or otherwise that you provide is entirely garnered within the realm of experience. This statement cannot be proven without resorting to "experience" in the attempt to justify it.
Therefore it negates itself. Stolen Concept Fallacy.
Again, you are correct that one cannot have an idea of what life would be like outside of one's experience of life.
Enough said.
But, if I may quote Shakespeare, "there are more things in heaven and earth than are dreamt of in your worldly philosophy."
Prose only occasionally makes good philosophy. "Worldly philosophy" is Begging the Question.
Here I definitely disagree. And the question I offer in contrast is "why does 1 + 1 = 2"?
Because somebody stuck fingers in your face 4 thousand times and said, "This is one - this is two - and one plus one equals two." This is precisely where the reification and mystification of abstracts enters the picture.
Is it because of the ways in which we define the numbers "1" and "2" or is there some underlying objective reality that is reflected in mathematics?
It is because your "experience" taught you how to define those concepts, not because there is some "underlying objective reality that is reflected in mathematics" which is proven by the fact you can only understand as much of these concepts that you reflect, study and think upon. If they had an independent existence that all you had to do was tap into, nobody would ever need to invent them, teach them and study them. Everyone would just know and nobody would ever make any mistakes.
This last is crucial. If there were an "underlying objective reality" (which to be "objective" would have to exist in this reality, not outside it - another contradiction) then all the wrong concepts that were ever held would also have to "exist" in the non-reality other as errors and mistakes. The erroneous idea that tomatoes were poisonous would have to exist along the corrrect idea that they help prevent prostate cancer. That's a lot to ask of the nether world.
I say there is too much in mathematics to reduce it to such nominal terms.
"Say" whatever you want, you cannot demonstrate otherwise. That is the whole point. Numbers, geometrical objects, algebra and such are abstracts. The heirarchy of abstracts is simply too complex for you to follow. Ok. That's fine.
All theories about what lies outside experience are metaphysical, but are supported by some pretty impressive argumentation at times, Albert Einstein, e.g.
This assertion Begs the Question that such arguments address what "lies outside experience" - which is contradicted by the fact that all Einstein's theories concerned and defined what lies within this space/time continuum or "experience."
This is just the kind of leap of faulty logic that I object to. You arrive at a conclusion that is totally unwarranted by the given evidence. Nothing Einstein said supports your position.
Which leads me to your quote of my statement: ". . . And, by definition, they are incapable of definition." And you wrote,
I believe you will find that this last statement is either a Tautology or begs the question (Petitio Principii).
In this you reveal you don't understand what I am saying. Yes, it is a Tautology, but not mine. I am using the definition of the words in question to demonstrate that by the very definition of the words, they CANNOT BE VERIFIED, they are a Tautology. This is the nature of asserting that the "Platonic Philosophical Realism" exists or that there are things, "outside this world" that 'exist," a Question Begging Tautology. Don't criticize me with what you cannot defend.
Suppose I try to sell you a fertilizer that is better than any other, because it is Unicorn manure.
Doesn't this Beg the Question of the existence of Unicorns?
Now apply this to your same argument:
is there some underlying objective reality that is reflected in mathematics?
BY DEFINITION don't you Beg the Question that "there some underlying objective reality that is reflected in mathematics?
What is this "underlying objective reality?" How do you know it exists? Upon what criteria? What evidence do you have? Who verified it? How did you arrive at this "definition?" What do these words really mean?
Answer me without referring to "experience" or abstract concepts not rooted in reality.
Then I will get back to you.