Wednesday, April 14, 2010
question about a priori knowledge
Kant sets forth the category of a priori knowledge as that knowledge which is independent of experience. He cites mathematics as an example. In today's world technology has progressed far beyond what Kant was familiar with. I am specifically referring to the realm of computers. Everything done with the computer is a series of complex mathematical equations--graphics being created through the use of geometry. Do computer graphics and virtual worlds give us the means of experiencing mathematics?
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Maybe these graphics give us the means to experience the result of applied mathematics, but I think the same analogy could be used in real life (especially if you're a Pythagorean). With the graphics, we do not see the geometry, we see the graphic. If geometry can be applied to real objects and calculus to real movement, I am not sure how our experience or mathematical explanation of the graphics differs.
ReplyDeleteI second Bethany. We are not immediately aware of the logical functions that govern computer graphics, just as we are not immediately aware of the functions that govern physics--if physical functions exist.
ReplyDeleteAt any rate, I think computer mathematics isn't, strictly speaking, a priori. In the first place, in order for us to trust the results of a computer program, we need to perform a strict a priori mathematical proof of correctness on the program, which is different from the actual math going on inside the computer.
Second, when computer scientists do such proofs, they do so assuming it will run on an idealized "Platonic Form of a computer," one that does not possess wires and transistors and, in general, physical parts, which go wrong. So in effect, these proofs just tell us a priori that, if nothing goes wrong, then the output of the computer program is correct. And we can never have absolute Cartesian certainty that nothing is going wrong inside any actual computer.
The probability of a computer result being wrong for that reason and us not noticing is astronomically low. Even still, mathematicians tend to strongly dislike using computers for this very reason.
I agree with Ms. Somma. In a case such as this I feel Kant would make the distinction between pure mathematics and applied mathematics, your example of the graphic being the latter. While we use geometry and mathematical equations to create the graphic within the computer's programming, we gain no further understanding of the equations or geometry itself. We are merely utilizing information we have already discovered a priori through pure mathematics, which can only be discovered when we step beyond the bounds of experience.
ReplyDelete"First of all, it has to be noted that mathematical propositions, strictly called, are always judgments a priori, which cannot be derived from experience..."
ReplyDeleteHe goes on to say that this is basically 'by definition.'
The question, "could a computer make an a priori judgment?" (though I am not sure how to phrase it more precisely) seems like it could be further developed and become something interesting.
Here's a good book from a Heideggerian perspective on AI- http://www.amazon.com/What-Computers-Still-Cant-Artificial/dp/0262540673