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Week Two.pdf

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Nicholas M Ray

Week T wo Week Two Aristotle's Logic: - Syllogism --> Premise 1, Premise 2, then Conclusion (structure). - All men are mortal (P1) - Socrates is a man (P2) - Therefore Socrates is mortal (Conclusion) -- Truth preserving or deductively validruth of the premises leads to the validity of the conclusion -- Deductively invalid argument: - (P1) If I go to the store then I will have cigarettes - (P2) I have cigarettes - (C) I went to the store - if you find the conclusion to be false then the argument is deductively invalid. (P1) Nancy is taller than Scott (P2) Scott is taller than Mohammed (C) Nancy is taller than Mohammed ---> Aristotelian logic is limited to categories but not relations such as these. --> you need a new logic to account for this type of inference (relations) The New Logic: - Frege: Predicate logic (second order predicate logic) - Russell & Whitehead --> definitive and used in mathematics - numbers are logical objects where you find in sets - Logisism: logical development in order to figure how mathematics works (which is a form of logic) "Pegasus is a winged-horse" -- pegasus does not exist - Plato's Beard: every word in every sentence has to refer 2 to something if that sentence is meaningful - Pegasus subsists and does not exist (not spacio- temporal) Russell's Old Theory of Denoting The denoting concept pulls the thing being denoted into the proposition. Problematic if you want to talk about denoting objects as they are (absent) Frege: Sense of a proper name = sense Sense of a sentence = thought - we can associate different senses for a proper name. - a sense is a descriptive phrase - NAPOLEON (linguistic item) --Sense: ... subjective conceptions (how you connect linguistics to referent... INDIRECT) 3 --Referent: Napoleon (spacio temporal object) --Meaning: sense and reference --> Sense: not a mental object, objective, public whereas ideas/mental objects are subjective, particular and private. Senses can be universally grasped whereas ideas cannot. ---> Sense of a sentence (thought) - has truth value ---> Ideas do not have truth value? Sentences without sense. ---> Ideas are subjective so cannot be true or false because they are private. Logic: - Truth - True propositions (thoughts) - Senses/Reference - does not care about how people make inferences - they only care about the logic behind the inferences. -
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