I am going to walk through my thoughts to see if I understand this. If I make a mistake feel free to comment, criticize, or accost.
An a priori analytic judgment is made when concept A is logically deducible from concept B. A is contained within the definition of B: All bodies are extended.
An a postriori synthetic judgment is made when one joins concept A with concept B, while A is particular and contingent to B: (I'm not sure if these judgments are expressed in universal terms or not but I am doing so) walls are dusty. Nothing within the the concept of "wall" could lead one to the concept of "dusty". I have done this through experience.
An a priori synthetic judgment is made when one joins concept A with concept B, while A is not found within B, yet "necessity and strict universality are sure criteria of a priori knowledge" (B4). I give two examples from Kant: 5+7=12, and "in all changes of the material world the quantity of matter remains unchanged". The first example is a priori synthetic because one cannot get the concept of 12 from "5", "7", "+", or the whole mathematical proposition. Although this is true, the answer 12 is necessary and universal so it is an a priori synthetic judgment. In the second example the concept of quantify preservation is not found within the concept of mass, yet this principle is universally true.
Here is my first question: To verify an a priori synthetic judgment mustn't one consult experience? If one is consulting experience, says the skeptic, then how can one make such universal claims? Kant addresses this: "Now the proper problem of pure reason is contained in the question: How are synthetic judgments possible?" (B19).
Kant's solution seems to be that instead of looking for cause and effect, or space and time in the outside world, we need to realize that these are not real objects. They are the condition for the possibility for encountering objects. Presumably, instead of storing a collection of observed facts in our memory, we can by access our pure reason and discover the conditions for the possibility of experiences.
If this is true don't we still have to have experience to ever "use" the categories in our mind? If this is the case, then do we consult experience in forming a priori synthetic judgments? This last question is premature but are we now able to get around the skeptic when forming these a priori synthetic judgments? In other words how are able to attach new concepts to our original a priori concepts (using a priori synthetic judgments) that are ensured to be universal? Can the skeptic still doubt the necessity of a claim like all bodies are heavy?
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I'm not sure, but it seems like Kant has no problem if in one's experience of contingent objects, one is forced to reflect on the necessity of some law governing experience that cannot itself be experienced. The occasion may well be a dusty wall, but the experiential law (it would be impossible for this matter to be what it is and yet simply disappear, leaving nothing where there was something) concerns something that is neither conceptually contained nor empirically contingent.
ReplyDeleteIn other words, it doesn't matter if you are watching a billiards game when you realize causality is necessary for apprehending this particular and all possible billiards games,
What you realize is not there on the billiard table, though it was sparked by it - that doesn't matter. You don't have to be meditating in order to access the pure understanding. You just have to see no way around the necessity of a law for the possibility of a kind experience at all.
BUt that is all a long way from demonstrating the necessity of the 1st law of thermodynamics. That is done, however, by scientific experiment aiding pure intuition. So Kant is only defending the possibility of synthetic a prioris not giving full demonstrations of their individual validity. If newtonian physics is true, then its laws are synthetic aprioris. If quantum physics reveals a new state of affairs, we may have to rethink the synthetic a priori. This would mean revoking necessity already granted, or at least, shifting the terms of it. Which is worrisome.
ReplyDeleteI don't know how to say anything with regard to synthetic a priori judgments about the physical world (Newton's Law), but I think the transcendental aesthetic shows how synthetic a priori judgements regarding math are possible.
ReplyDeleteTo add 5 and 7 together, for example, we can imagine a group of five points in imaginary space and a group of seven other points somewhere nearby in imaginary space. The intuition of space allows us to "see" the group of 7 and the group of 5, and furthermore to see what happens when we group the 7 and 5 together. All of a sudden, we see 12 points now. It has to be that way, because of the way space is.
Kant doesn't really talk about arithmetic so much, but, at least historically, geometry preceded arithmetic, and arithmetic was always presented in terms of geometric units.
I'd imagine physical laws, since they involve numbers, would have to be defended somewhat similarly. Once we comprehend what "force" is, and the units that make it up, as well as the properties of space, the effect that forces will have upon one another in space are necessary. The truth follows upon the definitions of mass (kg), space (m), and time (s^2), the way these concepts are constituted in force (kg*m/s^2), and the X that allows us to make this judgment is not experience but the a priori character of our subjective intuition.
These are all just guesses though, and as far as I know not supported in any way by what I've read so far.
Dr. Davis: You are correct. I believe this comes down to the point which has been brought up in class twice now: "Though all our knowledge begins with experience, it does not follow that it all arises out of experience."
ReplyDeleteMr. Lefavor: I think your math point is correct, but I am not sure about the physics example. Is it true that all of physics can be represented with math equations through synthetic a priori judgments? This seems to make sense. Kant says his project validates empirical reality and keeps sciene in tact. For some reason it seems odd to say that he can do this, but I think I am just missing something...