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Lecture 3

Lecture 3 on Descartes' View of Knowledge, Moralities, and Certainty of Mathematics

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York University
HUMA 1160
Stanley Tweyman

Sept. 23 , 2013 HUMA 1160 Test: Monday. October. 21 , 2013  If you miss the test, you need a valid doctor’s note  No substitutions for a test  Duration of test (8:30 to 10:20)  Next week: Details about the test Descartes’ View of Knowledge (Based on mathematical knowledge) How does Descartes think that knowledge should be expressed? o Believes there are two forms of expression o 2 types of statements o If there is knowledge, it has to be expressed in these two types 1) My shirt is white 2) 1+1=2 I. Verification (to show something is true/false) II. Modality (how the subject and predicate can be connected) III. Temporality (how long is it true – time) IV. Origin or Connection? 1) My shirt is white  Verification: Senses (empirical) o Even though the shirt is white, it can be altered o Any empirical sentence can be falsified if circumstances justify 2) 1+1=2  Verification: Triggered by empirical o Connection between subject and predicate cannot be altered ever o If the sentence is true, it’s true always and if it’s not true, it can never be true o For mathematical sentences, there is no empirical verification possible Four kinds of Modalities (only one modality can fit a sentence) 1) Modality of possibility a. What MAY be the case 2) Modality of actuality a. What IS the case 3) Modality of necessity a. What MUST be the case 4) Modality of impossibility a. What CANNOT be the case My shirt is white  Modality: Possibility, or Actuality - If modality is necessity, it is impossible (logically, or physically) to separate the subject from the predicate - The subject is necessary and therefore, the subject and predicate are inseparable - In cases like “my shirt is white,” the temporality of empirical sentences are temporary because it will be false when the shirt is not white anymore - On the other hand, in the case of mathematical sentences such as 1+1=2, the temporality will be true forever - Therefore, these sentences are called eternal truths - In the case of shirts, the origin or connection is the external world WHITE SHIRT - Connection between subject and predicate is contingent - The predicate can be changed from the subject - Contingent: It is the case, but it doesn’t have to be the case Case of a mathematical sentence: 1+1=2 - Modality of this sentence is necessity - Therefore, 1+1 must be 2 - Given that the modality is necessity, we now come to understand something that we didn’t before - Anything that you learn through observation (senses), and anything that has the modality of actuality, is subject to change - You can alter the object which means altering the truth of the claim - Connection here is not contingent - Impossible to alter the claim Descartes Problem - We are looking for certainty in knowledge - He argues that there can be no certainty in empirical knowledge - Therefore, the model of paradime of the type of knowledge that we’re seeking is typified in mathematics because mathematical knowledge cannot be altered by anyone - Therefore, he argues that this is the type of knowledge that we are seeking - We want to mathematize learning and this is the type of knowledge that we want - Knowledge that is eternal truth Origin of Connection: Empirical sentences – no problem in a connection Mathematics – what Descartes wants to say is the origin of the connection is not empirical; Furthermore, the connection is eternal (true before we became alive, and true even after we die) – Descartes says that in the case of mathematics, the truths are eternal, and what we now need to raise is if a truth is eternal, does it have a creator? “If a truth is eternal, does it have a creator?” Origin? (What we will be studying – Meditations) Rule 2: (Pg.3 in Course Kit) - States that what we are seeking is certainty - If he wants certainty, and since it is not attainable through senses, then whatever he wants must be non empirical - He claims that mathematical knowledge is not only certain, it is also indubitable (cannot be doubted) - Therefore, dubitability is a good enough reason to reject a
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