The Lesser of Three Evils - Intuition, Induction, and Transcendental Idealism

[I and I]

So, I'm writing a paper mainly about intuition but as you can see, it has spun off into Induction and Kant's Theory of Transcendental Idealism as well.
I am not finished with it yet but I was wondering if all of you could take a look at it. It is mostly the induction part and that I have so far that I fear may not make logical sense. Anyway, here it is:

Intuition is the “mental states or events in which a proposition seems true in the manner of these propositions” (The Stanford Encyclopedia of Philosophy). Steven Hales writes, “Our intuition is rational, not empirical; it is the pure light of reason that shines upon necessary propositions.” This intuition does not include knowledge based on memories nor does it include predictions of future events based upon knowledge from similar past experiences. Here is an example of intuition: Sally believes that there is a God - an all powerful being unable to known by our senses, because when she considers this notion, it intellectual seems the her that it is necessary for God to exist (NOI).
Intuition is the root of the majority of philosophy though it may not be recognized due to “a fairly vigorous institution of professional repression” (POI 135). Intuition is typically a starting point of strong rationalists - those who do not derive their basis of knowledge experience from our five senses but instead from pure internal thought. Gottfied Leibniz believed that the mind inherently held but could not attain all the knowledge of the universe. Leibniz would view the type of knowledge derived from complete intuition, as necessary truth because it cannot be contradicted (TPB 137).
Many of the great philosophers throughout history have used intuition to make ambitious strides for the advancement of philosophy (POI 137). Some intuitions have even been supported many years later by physics. Parmenides, for example believed through intellectual reasoning alone that “everything that is real must be eternal and unchanging.” Twenty-five hundred years later, this intuition was supported by quantum physics (41 TPB). Intuition, however, can lead to false beliefs debunked by science like Miletus’ theory that everything is made of water, or it can lead to the ultimate truth unattainable by empirical reasoning (TPB 23).
One major problem with intuition is that when it justifies itself, it becomes a circular fallacy - an argument where the conclusion is found in the reason for the conclusion. Here is an example: God exists because the Bible is true. The Bible is true because God exists (Oxford dictionary). For intuition, a simpler example would be that God exists because God exists. One could say, however, that there are instances when intuitions can justify themselves though there is a circular fallacy (POI 138). But this poses another problem when two people have different intuitions that contradict each other and claim that only their intuition is justifiable (POI 138).
Because of these problems with intuition, one may say that they are not a source a evidence in itself and only empirical evidence can be used as a source of evidence. David Hume thought that intuitive statements were meaningless, because they were not demonstrative - a statement in which rejecting the statement leads to a contradiction (i.e. 2 + 2 = 4), or probable - a statement that can be traced back to an experience. One may say that science is a way of justifying evidence because something like physics create statements that are probable because they can be trace back to the experience of cause and effect. Cause and effect, however, is not something that one can actually experience. It is merely based on environmental conditioning and therefore is irrational according to Hume. Consequently, there is a problem with induction - the same thing may not happen again if under the same conditions or, put another way, what has happened in the past will not necessarily happen again in the future. To claim that inductive reasoning will have to suffice as the basis of knowledge until there is a better systematic approach to discovering knowledge is to fall into the same vicious circle fallacy as intuition.

I do not agree with Kant nor do I agree with your notions of idealism, which from the part you posted seem to center around Kant.

Are you asking for a critique of kant?