Lecture #8 - ' Branden Fitelson Philosophy 12A Notes 1...

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Philosophy 12A Notes 1 ' $ % Leonard Cohen Administrative Stuf – HW #2 1st-submissions are due Today (4pm, drop box). Note: This involves problems ±rom chapters 2 and 3. Consult the HW Tips Handout ±or help±ul tips on HW #2. Homework formatting. Please put the following information: Name, GSI, section time, and date. on all assignments and exams (upper-right corner of Frst page). Chapter 3 — Truth-Functional Semantics ±or LSL The truth-±unctions and the LSL connectives Truth-Tables — a tool ±or “seeing” LSL’s “logically possible worlds” Formal explications o± Logical truth, validity, etc. — in LSL UCB Philosophy Chapter 3 , Intro. 02/11/10 Branden Fitelson Philosophy 12A Notes 2 Abstract Argument Logical Form LSL / LMPL / LFOL Symbolization English Argument Valid Form? Deciding Formal Validity Chapters 3 Valid English Argument? Valid Abstract Argument? Articulation of Thought in English UCB Philosophy Chapter 3 , Intro. 02/11/10 Branden Fitelson Philosophy 12A Notes 3 Chapter 3 — Semantics of LSL: Truth ±unctions I The semantics o± LSL is truth-functional — the truth value o± a compound statement is a ±unction o± the truth values o± its parts. Truth-conditions ±or each o± the ²ve LSL statement ±orms are given by truth tables , which show how the truth value o± each type o± complex sentence depends on the truth values o± its constituent parts. Truth-tables provide a very precise way o± thinking about logical possibility . Each row o± a truth-table can be thought o± as a way the world might be . The actual world ±alls into exactly one o± these rows. In this sense, truth-tables provide a way to “see” “logical space.” Truth-tables will also provide us with a rigorous way to establish whether an argument ±orm in LSL is valid ( i.e. , sentential validity). We just look ±or rows o± a salient truth-table in which all the premises are true and the conclusion is ±alse. That’s where we’re headed. UCB Philosophy Chapter 3 , Intro. 02/11/10 Branden Fitelson Philosophy 12A Notes 4 Chapter 3 — Semantics of LSL: Truth ±unctions II We begin with negations, which have the simplest truth ±unctions. The truth table ±or negation is as ±ollows (we use and ±or true and ±alse): p p In words, this table says that i± p is true than p is ±alse, and i± p is ±alse, then p is true. This is quite intuitive, and corresponds well to the English meaning o± ‘not’. Thus, LSL negation is like English negation. Examples: It is not the case that Wagner wrote operas. ( W ) It is not the case that Picasso wrote operas. ( P ) W ’ is ±alse, since ‘ W ’ is true, and ‘ P ’ is true, since ‘ P ’ is ±alse (like English). UCB Philosophy
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Lecture #8 - ' Branden Fitelson Philosophy 12A Notes 1...

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