Kant: How is pure natural science possible? Section18

"Empirical Judgements, so far as they have objective validity, are judgements of experience, but those which are only subjectively valid I name mere judgements of perception"

kant is aying that Judgements come from proof of observations are judgements of experience because these judgements are something you have experienced and are proved to be right. Judgement that are of perception are something that just exist in your mind. It is an assumption and something you have not experienced. It is a judgement you believe that is right.

Kant: How is Pure Natural science Possible? section 16

"The word nature assumes yet another meaning, which determines the object, whereas in the former sense it only denotes the conformity to law of the determinations of the existence of things generally"

I think kant is saying that nature serves as a symbol of agreement to the law of determining the existence of things. Nature determines what exist and what doesn't exist

KANT How is Pure Natural Sciece Possible? Section 14

"For if experience is to teach us laws to which the existence of things is subject, these laws, if they refer to things in themselves, would have to refer to them of necessity even outside our experience. But experience teaches us what exists and how it exists but never that it must necessarily exist so and not otherwise. Experience therefore can never teach us the nature of things in themselves"

This quote is very confusing. I don't really get what Kant is saying. At he says experience teaches us laws about the existence of things and these laws refer to the needs outside of our experience. But experience teaches us what exist but it doesnt teach us that it must neccessarily exist? How can experience teach us what exists but that the things that exist don't really exist?

kant section 13 how is pure math possible

"What can be more similar in every resoect and in every part more alike to my hand and to my ear than their images in a mirror? And yet I cannot put such a hand as is seen in the mirror in the place of its original, for if this is a right hand, that in the mirror is a left one, and the image or reflection of the right ear is a left one, which never can serve as a substitute for the other. There are in this case no internal differences which our understanding could determine by thinking alone. yet the differences are internal as the senese teach, for, notwithstanding their complete equality and similarity the left hand cannot be enclosed in the same bounds as the right one'

I think Kant is saying how there are internal difference between things that can be the same. These things may seem to be equal but they are not because of their internal differences.

KANT SECTION 10 HOW IS PURE MATH POSSIBLE

"Accordingly it is only the form of sensuous intuition by which we can intuit things a prori, but by which we can know objects only as they appear to us(to our senses), not as they are in themselves"


I think here Kant is saying how we assume things without examining the situation. We feel as if we are just right about certain things without even finding proof that our assumptions are true.

KANT: HOW IS PURE MATHEMATICS? SECTION 7

"All mathematical cognition has this peculiarity: it must first exhibit its concept in intuition, and do so a priori, in an intution that it is not empirical but pure. Without this mathematics cannot take a single step, hence its judgements are always intuitive; whereas philosophy must be satisfied with discursive judgements from mere concepts, and though it may illustrate its apodeictic doctrines through intuitions, can never derive them from it"

I think that here Kant is saying that math shows it concepts as an instinct and something that you should already know. It is not something that can be proven it is something that is pure and comes naturally. He also compares philosophy to math saying that philosophy has many ideas and proceeds to a conclusion through reason instead of intuition.

I don't understand because math really doesn't come naturally unless you learn it. For example, when you learn 2+2=4. You may know this now and when someone asks you this the answer comes naturally to know because you know it but at first you did not know it and someone had to teach it to you so it really isn't natural.

Kant: HOW IS METAPHYSICS IN GENERAL POSSIBLE?

"Without solving this problem reason never is justified." (section 40)

Here Kant is talking about how problems within the metaphysics will never be reasoned as true if they are not solved. This applies to everything in life. Nothing is proven true unless it is solved. To figure out that 2+2=4 one must solve the problem 2+2 to know that it equals 4.