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But separating knowledge into these two types, which is mirrored in using the terms intuition (deduction) and experience (induction), implies that one has taken a perspective that knowledge must be defined in terms of whether it relates to the material world or not

From the first breath you take you literally live in the world of "experience." You know no other. You cannot conceive of what it would be like to live in a world of "no experience" or prior to "experience."

This is the whole flaw in this whole argument, whether it is Kantian "Synthetics" and "Analytics" or not. There is no way anyone can have any idea what life would be like without "experience." A person garners more experience before he or she develops enough consciousness and conceptual ability to understand what that experience is than can be measured or understood. All thoughts and concepts are inherently rooted in and dependent upon "experience." All theories about what lies outside "experience" are just that, unsupported theories. And, by definition, they are incapable of definition.

faith is an act of the will and the will, not reason, is "faith" has a meaning that is separate from "reason" means that the A is A relationship between the meaning of the word faith in contrast to the word reason means that "reason" is primary to faith for either word to have any "objective" meaning. And if they have no "objective" meaning, then they mean nothing.

"From the first breath you take you literally live in the world of 'experience.' You know no other. You cannot conceive of what it would be like to live in a world of 'no experience' or prior to 'experience.'

The above part is hard to argue with in so far as it relates to the way one conceives of the world. But it is possible to conceive of things that are not "of the world," otherwise we would not be discussing it, which is a central flaw in arguing that all knowledge comes from experience.

". . . This is the whole flaw in this whole argument, whether it is Kantian 'Synthetics' and 'Analytics' or not. . . ."

There are problems in Kant, but I think most give him credit for handling the role of the rational, thinking mind better than you do.

The following is from an analysis of Kant's epistemology:

Kant's most original contribution to philosophy is his "Copernican Revolution," that, as he puts it, it is the representation that makes the object possible rather than the object that makes the representation possible. This introduced the human mind as an active originator of experience rather than just a passive recipient of perception. Something like this now seems obvious: the mind could be a tabula rasa, a "blank tablet," no more than a bathtub full of silicon chips could be a digital computer. Perceptual input must be processed, i.e. recognized, or it would just be noise -- "less even than a dream" or "nothing to us," as Kant alternatively puts it.

To simplify the above, Kant's contribution is that he essentially argues that "experience only gets you so far." You have to make rational sense out of what you experience and that reasoning faculty is not borne of experience.

". . . There is no way anyone can have any idea what life would be like without 'experience.' A person garners more experience before he or she develops enough consciousness and conceptual ability to understand what that experience is than can be measured or understood. . . ."

Again, you are correct that one cannot have an idea of what life would be like outside of one's experience of life. But, if I may quote Shakespeare, "there are more things in heaven and earth than are dreamt of in your worldly philosophy."

". . . All thoughts and concepts are inherently rooted in and dependent upon 'experience.'. . ."

Here I definitely disagree. And the question I offer in contrast is "why does 1 + 1 = 2"? 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? If everything comes from experience the truth of the equation is derived from our definitions of "1" and "2." I say there is too much in mathematics to reduce it to such nominal terms.

". . . All theories about what lies outside "experience" are just that, unsupported theories. . . ."

All theories about what lies outside experience are metaphysical, but are supported by some pretty impressive argumentation at times, Albert Einstein, e.g.

". . . And, by definition, they are incapable of definition."

I believe you will find that this last statement is either a Tautology or begs the question (Petitio Principii).

Interesting discussion though.