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Lecture 3

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PHIL 120
Leslie Burkholder

Week 3: PHIL 120 / Chapter 9 Section 1,2,3 (AND, NOT, XOR, IF) Google: syllogistic 1) Simple and Complex Propositions logic. Lotsa stuffs! - A form of sentence can be presented in other similar forms (example pg 203) - 2 kinds of propositions: conditional and conjunction - Complex Propositions: combine simple propositions with connectives - Simple Propositions: - Negations: a proposition that denies another proposition  Possible form of negations: original case is ‘g’. Negations are as follow: ~g / g is not the case / Not g  Other forms of words that represent negation: no, never, can’t, nothing, nowhere, un- - Double Negations: can be equivalently presented as X = ~~X or X = Not Not X. Double negations act to make the sentence positive. - Conjunctions: read pg 206 - Do exercise pg 206: 1-a)d), 2-b)f) Try to 2) understand Disjunctions and Conditionals (or) - the Exclusive Disjunctions: when statements of both X and Y can’t significance be both true which means, you can have either one but not both. *I difference think this is represented by XOR whereas it the option between either..or is made explicit and YOU CAN’T HAVE BOTH Exclusive and - Inclusive Conditionals (If X, then Y): the other forms that exist; X  Y, if X, then Y.  Have to be careful with some statements as the antecedents could be combined.  E.g: If (X & Y), then Z  See example pg 210 and read the notes in the block - Do exercise pg 211: 1- a)d)g), 2—b)f)i)l) 3) Translation (10 Rules to Obey) #1 Use lowercase letters to represent simple propositions - Let the simple proposition appears as a POSITIVE statement #2 Use brackets to avoid ambiguity - Example: If a, then b or c.  this can be interpreted as follow: if a, then (b or c) / (if a, then b) or c. Both imply different meanings. #3 Do not confuse indicator words with connectives - Words like because and therefore are logical indicators that are used to identify argument and premises - So, they can’t be represented with symbols << can only be used by connectives #4 Distinguish ‘if’ and ‘only if’ - The phrase that follow ‘if’ is called antecedent. E.g: If [the t-shirt is blue] - The phrase that follow ‘only if’ is the consequent. Only if [you’re done with your homework] - ‘only if’ also denotes that the condition is necessary but not sufficient for the premise. Meaning, there could be additional premises exist. #5 Treat biconditionals as conjunctios with conditional conjuncts - Ordinary condition: the implication goes one way; the antecedent implies the consequent - Biconditional condition: the implication goes 2 ways; the antecedent implies the consequent and the consequent implies the antecedent - The case where ‘if and only if’ applies – order doesn’t matter #6 Treat ‘unless’ statements as conditionals #7 Translate sentences that express the same proposition in the same way #8 Translate logical connectors literally if you can #9 Ignore variations that do not affect the validity of an argument #10 Check your translation by translating back to ordinary English - Do exercise pg 216. 1—e)i)j)l)q), 2—a)b)e)f), 3—f), 4—e)g) Supervised Lab 3 - Lots about deductively valid arguments – read / figuring out how to know when does th
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