## Kant & a priori knowledge

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### Kant & a priori knowledge

I've been somewhat fixated on and very confused by Kant's suggestion that mathematics (or at least certain aspects of it) can be known independent of experience. For example, he makes reference to three straight lines and asks us to consider the straight lines and the number three to construct a figure (a triangle): something that could not be done with merely two lines (as two lines can't enclose a space). However, when he begins to break down how we know this, he claims that it is through intuition. He seems to be suggesting that because space is something we just know, we can move the lines in our minds construct the triangle from the lines a priori.

My issue is that we only know what a triangle is through experience and definition: manipulating three straight lines to form a triangle could never be done without knowing what a triangle's properties are in the first place -- which is something you're not born with knowledge of. So how can he claim that the formation of the triangle is intuitive and not rooted in experience? I assume I'm missing some steps in his thought process. Another example could perhaps be found in algebra, but I suppose sticking with geometry is sufficient for my question. Any advice?
Avant Garde Jazz

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### Re: Kant & a priori knowledge

Avant Garde Jazz wrote:I've been somewhat fixated on and very confused by Kant's suggestion that mathematics (or at least certain aspects of it) can be known independent of experience.
...
I assume I'm missing some steps in his thought process. Another example could perhaps be found in algebra, but I suppose sticking with geometry is sufficient for my question. Any advice?
The central theme of Kant lays out two contrasting elements, i.e.
1. Reason-based
2. Empirically-based

Empirically-based is sub-divided into two, i.e.
1. Sense-based - a posteriori
2. Intuition-based and non-sensual - a priori.

In 2. Intuition-based and non-sensual - a priori - this is still based on 'experience' i.e. it is based on the past collective experience embedded in the DNA [Kant did not explain it this way, but that is the principle]. Kant relate such past embedded collective experiences to the Categories and intuitions, i.e. Space and Time.

Mathematics is independent of post experience i.e. a posteriori but interdependent with a priori experiences, i.e. past collective experiences embedded in the DNA and psyche. This is based on the collective experiences with the use of our fingers which has evolved over millions of years.

It is the same with a 'triangle' a shape which is observable in nature [empirically based] and has been encoded from past collective experiences and embedded in the DNA in principles. With this past collective experience humans use their reason to abstract theories of what is a triangle [3 lines, angles, etc.], thus the actualization of the empirical-rational reality.

Based on the above arguments Kant assert Mathematics, Geometry, and Science is possible BUT...

the idea-of-God via Metaphysics is an impossibility because the idea of God is merely based on reason [purely] that is very crude, thus Kant's Critique of Pure Reason.
The idea of God do not have any empirically elements especially a priori ones and thus is an impossibility within empirical-rational reality.
I am a progressive human being, a World Citizen, NOT-a-theist and not religious.
Prismatic567
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