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[PHILOS 31] - Final Exam Guide - Comprehensive Notes fot the exam (33 pages long!)


Department
Philosophy
Course Code
PHILOS 31
Professor
Levy Steven
Study Guide
Final

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UCLA
PHILOS 31
FINAL EXAM
STUDY GUIDE

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1- Our logical language
Argument- a set of sentences, one of which is designated as the conclusion (other
sentences are premises)
Keywords to look for a conclusion- therefore, so, it follows that, my conclusion is,
this shows that, hence, accordingly, ergo, thus, accordingly, consequently
Keywords to look for premises- since, for, given, because, in view of, whereas, this is
implied by
Validity- an argument if it impossible for the premises all to be true and the
conclusion false
- In other words, if the premises are all true, then the conclusion must be true
Soundness- an argument is sound if it is valid and all of its premises are true
Example: if we raise corporate taxes, then consumer prices will rise
If we do not raise corporate taxes, then the income gap between rich and poor will
increase
If consumer prices do not rise, then the income gap between rich and poor will not
increase.
Consumer prices will rise. -VALID
Implication- a set of sentences implies a given sentence if and only if the truth of the
given sentence is guaranteed by the truth of all the members of the set (sentence A
implies another sentence B if and only if A’s truth guarantees B’s
Example: Peter likes pizza and Patsy likes pasta.
Peter likes pasta.
The first sentence implies the second.
Logical equivalence- sentence A is equivalent to sentence B if and only if A and B
always agree in truth value
Example: No dogs are cats. No cats are dogs. (Equivalent)
Either Peter likes pizza or Patsy likes pasta. Peter likes pizza. (not equivalent)
First we must extract the logical structure from each sentence (look at them
syntactically), then we analyze the logical structure of the argument
Vocabulary:
- Sentence letters: P-Z (P,Q,R,S,T,U,V,W,X,Y,Z) with or without subscripts
- Sentential connectives- and (^), or (v), if… then (→), if and only if (↔), it is not
the case that (~)
- Punctuation- ( , )
Connectives
- Atomic- one clause without a connective, cannot be broken down
- Compound/Molecular- connected with a connective, mmade of 2 atomic
Truth functional connectives- a connective is truth functional if and only if the truth
values of the component sentences the connective joins always completely determine the
truth value of the compound sentence. (and, or)
- Uniary truth functional connective- it is not the case that
Grammar
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- Language- words to refer to something in the world
- Metalanguage- the words use to talk about language
1. A sentence letter is a symbolic sentence (P)
2. A symbolic sentence preceded by a ~ is a symbolic sentence (~P)
3. If a binary connective is placed between two symbolic sentences and the entire
expression is enclosed in parentheses, the result is a symbolic sentence (P^Q)
Terminology
- Atomic sentence- a symbolic sentence containing no conneectives
- Molecular sentence- a symbolic sentence that contains one or more connectives
- Negation: a sentence of the form ~P
- Conditional: a sentence in the form (P→Q)
o Antecedent: P
o Consequent: Q
- Conjunction: a sentence of the form (P^Q); left and right conjunct
- Disjunction: a sentence of the form (PvQ); left and right disjunct
- Biconditional: a sentence of the form (P↔Q); left and right component
Scope of the connective- the scope of a connective occurrence in a formula is the
connective occurrence itself, together with the components (and any grouping indicators)
it links together in the formula
Main connective- the connective occurrence in the formula with the largest scope, always
ranges over the entire formula
Informal conventions
1. Outermost parentheses may be omitted
2. Conditionals and biconditionals will be assumed to mark a greater break than
conjunctions and disjunctions, thus parenthesis around conjunctions and disjunctions
may be omitted when no ambiguity results
3. Allow brackets [ ] and braces { } on paper only
4. Restore parentheses to the left (main connective on the right)
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