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Lecture 4

Lecture 4 on Knowledge of Mathematics, & Objections to Descartes' Views

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York University
HUMA 1160
Stanley Tweyman

Sept.30 , 2013 HUMA 1160 st Test #1: October.21 , 2013 (20% of Final Grade) Course Kit: pgs.4-5 Problems in Reading Descartes: Certainty of Mathematics a. Mathematics is indubitable b. Mathematics is certain Regulae: Why mathematics is certain? 1) Faculty of Reasons a. Never faulty b. Errors in reasoning are never due to the mind c. Errors in reasoning are due to premises that are put forward which are false d. Errors in reasoning are also due to inattention 2) Object of study in mathematics is pure and uncomplicated a. Pure: No empirical content, Not empirical objects, They are known simply thru the mind b. Uncomplicated: When you imagine a mathematical object, such as an isosceles triangle, if you are doing it correctly, you have the complete thought – You never have to worry about completeness – Whereas, if you were looking at your kitchen for example, you might be leaving out your chair Therefore, Descartes says math is indubitable and cannot be doubted. In the Regulae, mathematics is never ever questioned. The certainty of mathematics is never questioned in the Regulae ever. In other works, math can be doubted. In Other Places: Math is dubitable Pg.48 – Meditations Pg.59-60 – Meditations Pg.220 – Cours Kit – principle 5 3 Reasons for Doubting Mathematics: Principle 5, Pg.220 in Course Kit 1) 7+5+2=14, 7+5+2=15 a. Why are you certain that it is 14? Why are you certain that it is 15? b. “I have a feeling that I got the correct answer” c. The feeling of confidence is the same whether you get the right answer or the wrong answer d. The feeling that is associated with the confidence in mathematic answers is unreliable and untrustworthy 2) Right now, we have no knowledge of God a. If there is a God and if God had created us, it may be the case that God is a deceiver b. If the God is a deceiver, he could cause us to believe that things are certain and true when in fact, they are false c. He could force us to believe things and we would never know it d. Therefore, before we can know about the certainty of mathematics, we must know two things: i. That there is a God ii. God is not a deceiver *Important Passage pg.60 in Meditations 3) Even if you are an Atheist or non-believers, there is still a problem with mathematics a. If you believe that God is your creator, you therefore must believe that God is Omnipotent b. Given that God is powerful, if he doesn’t want you to be deceived in mathematics, you won’t be deceived c. Therefore if you are an Atheist, whatever you believe that you came about (how you were created – cause of your existence), you must believe that the cause of your existence has limited power d. If you believe that there is no God, then you must also believe that your existence has finite power e. Analogy: An automobile manufacturer wants to build a perfect car. The perfect car would have a perfect breaking system. The intention of the automobile manufacturer is correct because it will save lives. In the mail and on television, you hear of a recall of the breaking system of these cars. The manufacturer says there has been a mistake, so you should take it to your manufacturer. Any living thing, which has limited power, cannot always carry out what they want to carry out. They don’t always succeed in what they want to do. f. If you are an Atheist, the cause of your existence, whatever it is, has limited power g. Whatever caused you to exist, had an intention to make no errors in mathematics but the reality is however, that a finite creator cannot guarantee that the creation will always follow the plan h. Therefore even if the creator had an intention to create you to make no mistakes, in reality, you can make mistakes The only way to achieve certainty in mathematics is to prove that God, who is all- powerful, created you. Furthermore, his intention in creating you is not to be deceived. Therefore, the upshot of all of this is that Descartes believes that the certainty of mathematics hinges on the existence of god. 2 Problem: Pgs210, 211 in Course Kit (Principles of Philosophy) Plato and Descartes both believed that you need to be a certain age before studying philosophy (pgs.45-46 in Medidations) Order of Study: 1) Code of ethics 2) Logic of discovery a. NOT the logic of the schools (logic of the school was Aristotelian
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