Mathematics is easy to imagine satisfying D’s worries about doubt and (eventually) firmness of foundation, but his appeal to self-evidence is noteworthy. One might expect (especially since I went on about innateness in an earlier post) that mathematical foundations would be settled because of some innate installation of mathematical propositions, or perhaps through an (innate) ability to grasp geometric relations—something of the sort Kant later urged. But D here appeals to self-evidence, which is really a claim about the nature of the demonstration rather than the nature of that which is demonstrated. It’s a claim about proof rather than mind. I think that suggests a way that logical problems of mental architecture start to pull away from psychological problems. They are starting to insist on some badly needed attention.
On the contrast of mathematics with the virtues, D complains that though the ancients extol the virtues, they fail to tell us how to recognize them. Frankly I was surprised that this was his complaint, since he is clearly worried about foundational problems (“magnificent palaces built only on sand and mud”). Hmm.
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Timothy Chow on the NF consistency proof and Lean
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He also talks about math in part 4 of the discourse as well. In part 4 I think he uses geometry to explain that people make mistakes so you cant always believe what you see because errors are easily made.
I agree with how you said "Mathematics is easy to imagine satisfying D’s worries about doubt...." To Descarte mathematics is something that no matter what you do the solution will always be the truth. There will always be only one answer. This reassures Descarte that math unlike other subjects he can believe in because there will always be proof. In other subjects there are always other ways to answer questions and you are allowed to have different views, but not math.
I agree with Candice. I was going to say the exact same thing. Mathematics always has a formula and a strategy to find its one and only reolution that never changes. All other subjects of life are questionable because they are based upon one experience, or one theory that may have worked out to be credible. Meanwhile there could be a number of other theories that have not even been thought about that could bring upon almost the same conclusion.
I agree with what all of you are saying that there is no doubt when it comes to mathematics. You have formulas and theorums and whatever else. You have 3 oranges and you add one and theres 4, but I think we mentioned in class what is 3? what is 4? It is easy to see how many of something there is but how can u explain it? You can keep asking why, but you'll never really know. Its just another thing were programmed to just understand.
He talks about simplifying everything to its simplest form. Math only has one answer, one solution. In English you can have many answers but math only has one true and final answer.
I have to say I agree with Descartes whole logic on mathematics, and who wouldnt, it seems to make perfect sense...or does it? Well, for example, two plus two will ALWAYS be four, theres no doubt about that...but what is four? that's a good question but in our world, as we know it, that is how we were educated to read numbers, with formulas - addition, subtraction, multiplication, division, etc, etc. no matter what type of mathematics there is always a formula, a specific way to solve something and in the end there is always a solution. The solution may not always be an easy one to get to, it may take a lot of effort and it can be time consuming but in the end, you will succeed, I think that's what Descartes is getting at with all of this Mathematics talk...pretty much that in life, Mathematics was the only thing he was completly certain of and it still remains true today.
I also agree with what you say about Descartes in this part of the discourse. He loves to use mathematics to solve the problems about doubt. He brings up mathmatics agian in the sixth chapter of the Meditations. He uses it to talk about the existence of material objects and the difference between mental images and understanding by using the idea of a triangle.
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