This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 ' & $ % Announcements and Such • Today’s Music: Michael Hedges • HW #4 is due today @ 4pm, usual drill (chapter 4 — proofs). • I’ve posted HW #5, which is due next Thursday @ 4pm. – A few LMPL symbolization problems (chapter 5). – Mostly, working with LMPL Interpretations (chapter 6). + I’ve posted a new handout entitled “Working with LMPL Interpretations”, which I will be going over in class very soon. • Today: Chapter 5 (rather quickly), and then Chapter 6 (Intro.) – Finishing-up our discussion of symbolizations into LMPL. – Introduction to LMPL Semantics (working with LMPL interpretations). UCB Philosophy Chapter 5 & Chapter 6 Intro. 06/17/10 Branden Fitelson Philosophy 12A Notes 2 ' & New Elements of LMPL • Now, upper-case letters can be used as LSL sentences or predicates . – E.g. , the predicate ‘is tall’ can be symbolized using ‘ T ’. • Lower-case letters ‘ a ’–‘ s ’ will be used as individual constants ( names ). • This yields new atomic sentences with subject-predicate structure : – E.g. , ‘Branden is tall’ , ‘ Tb ’. • We also have two quantifier phrases : all ( ∀ ) and some ( ∃ ). • Lower-case letters ‘ t ’–‘ z ’ will be used as variables . • We use variables + quantifiers to symbolize general claims . – E.g. , ‘Someone is wise’ , ‘There exists an x such that x is wise.’ , ‘ ( ∃ x)Wx ’ • Each general claim quantifies over a domain/universe of discourse . UCB Philosophy Chapter 5 & Chapter 6 Intro. 06/17/10 Branden Fitelson Philosophy 12A Notes 3 ' & $ % Symbolization in LMPL VI: More Examples with ∃ • Let’s symbolize the following sentences. Whenever we symbolize in LMPL, we must state our dictionary of monadic predicates, and we must also say what the domain of discourse is over which we are quantifying. 1. No smoggy city is unpolluted. 2. Vampires do not exist. 3. If ghosts and vampires do not exist, then nothing can be a ghost without being a vampire. • If the dictionary is (where the domain is people in this classroom now): S __ : __ is standing up at the podium. W __ : __ is wealthy. b : Branden then what do the following two LMPL sentences assert (in English)? ∼ ( ∃ x)(Sx & Wx) ∼ Wb UCB Philosophy Chapter 5 & Chapter 6 Intro. 06/17/10 Branden Fitelson Philosophy 12A Notes 4 ' & Symbolization in LMPL VII: Back to and • Now, we are in a position to symbolize in LMPL the argument that we saw at the beginning of this lecture: LMPL Ws ∴ ( ∃ x)Wx • Since there are only finitely many people, we can see why this argument is valid, by representing its conclusion as a long (but finite!) disjunction, in which its only premise is a disjunct: Ws ∴ Wa ∨ ··· ∨ Ws ∨ ··· • We can use a similar trick for argument . In that case, it’s premise [‘ ( ∀ x)Hx ’] entails a conjunction [‘ Ha & ··· & Hp & ··· ’], and its conclusion [‘ Hp ’] is one of the conjuncts of that conjunction.’] is one of the conjuncts of that conjunction....
View Full Document
This note was uploaded on 11/26/2011 for the course PHILOSOPHY 101 taught by Professor Buechner during the Fall '06 term at Rutgers.
- Fall '06