How do synthetic apriori judgements differ from analytic and synthetic aposteriori judgements? give examples?

Question

This is in the book "prolegomena to any future metaphysics" by Immanuel Kant

Answer 1

A priori: Concluded from existing knowledge. (rational thinking)
A posteriori: Concluded from observation (Empirical)
Analytic: Deducted from a larger unit of information.
Synthetic: Deducted by adding together smaller pieces of information.

Synthetic a priori are the ones that cause a problem for Kant. It means you're accumulating new knowledge, from things you do not observe. He concluded the human mind was naturally made in a certain way as that certain knowledge could be acquired this way. He believed, for example, that mathematics was based on an innate understanding of time. (Because the basis of mathematics is counting, and counting is based on a succession: 1,2,3...)
Analytic a posteriori judgments are bits of information taken from existing knowledge based on empirical observation. I see a dog outside my house. I know that dogs have four legs. Therefore, there are four legs outside my house.
Synthetic a posteriori judgments are based on empirical observation also, but add to knowledge. There is an animal outside my house. It barks. Dogs bark. Therefore, the animal is a dog.
The difference is that I could not make that second judgment until I heard the sound of barking (an empirical observation) - In the first case, I observed the dog, and then deducted it had paws.
Wouldn't it had been nice if Kant had taken a writing class at some point in his life?

Answer 2

A synthetic proposition is a non-tautological proposition. An analytical proposition is tautological. An apriori proposition is reached prior to experience. An aposteriori proposition is reached after experience. Kant attempted to answer whether there existed any apriori synthetic propositions, ie whether knowledge was possible. He answered this question in the affirmative. Some of his examples involved the concepts of space and time. You can read all about this in his "Critique of Pure Reason."