lecture19

lecture19 - Announcement Tuesday111.SouthHall5717...

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    Announcement I will have extra office hours this week:  Tuesday 11-1. South Hall 5717.
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    Categorical Logic Recall the distinction between  categorical logic  and  statement logic . 1) All A are B 1) if P then Q 2) No B are C 2) if Q then R 3) No A are C 3) if P then R In  categorical   logic  we use letters to stand for terms; the  logical   vocabulary  is ‘all’, ‘no’, ‘some’, ‘not’. In  statement   logic  we use letters to stand for statements;  the  logical   vocabulary  is ‘not’, ‘and’, ‘or’, ‘if…then’, ‘if and  only if’.
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    Categorical Logic Not all valid arguments can be represented as valid in statement  logic: (1) All dogs are mammals (2) No mammals are reptiles So,  (3) No dogs are reptiles In L: (1) P (2) Q  So, (3) R The symbolization in L is an invalid form, but the original  argument is clearly valid. The problem is that L does not reveal  the  structure  of  atomic statements . Categorical logic will help  here.
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    Categorical logic Categorical  logic deals with the logic of  categorical statements . Ex. All dogs are mammals Some politicians are liars Categorical statements relate two classes   or categories  of things.
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    The 4 standard forms of  categorical statements A : All S are P E No S are P I Some S are P O : Some S are not P These are the four basic types of categorical statements. Each  has: a subject term: S   a predicate term: P a copula: are a quantifier: All, No, Some
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    The terms, and copula The predicate and subject terms refer to  classes : ‘dogs’ 
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lecture19 - Announcement Tuesday111.SouthHall5717...

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