PHIL 210 Study Guide - Midterm Guide: Disjunction Elimination, Disjunction Introduction, Conjunction Elimination
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Section 2.1 – Valid and Sound Arguments
Logical Consequence – when a statement follows validly from given premises, it
is also a logical consequence of the premises
Section 2.2 – Methods of Proof
Identity Elimination – given b=c, anything that holds true of b also holds true of c
Identity Introduction – a=a can always be inferred from any set of premises,
even no premises
Identity Symmetry – given a = b, b = a
*Transitivity of Identity – if a = b, and b = c, then a = c
Chapter 4 – The Logic of Boolean Connectives
Truth-functional – describes connectives, which, when used in a complex
sentence, allows one to know the truth value of the complex sentence simply by
looking at the truth values of the sentence's immediate constituents.
Examples include ^, v, and the negation connective.
Section 4.1 – Tautologies and Logical Truth
Logical necessity – sentences that cannot be false, no matter the premises. Such
a sentence is true in every logically possible circumstance.
Ex. a = a
Three forms of derivation:
2) Truth tables
3) If one can prove a sentence using no premises whatsoever
Logical possibility – a sentence that could be (or could have been) true, at least
on logical grounds
Ex. Going faster than the speed of light.
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Tautology – a simple kind of logical necessity; it is any sentence whose truth table
has only T's in the column under its main connective.
All tautologies are logically necessary; their truth is guaranteed by the structure
and meaning of the truth-functional connectives, independent of the truth values of
its constituent sentences.
However, not all logically necessary claims are tautologies.
Ex. a = a
Section 4.2 – Logical and Tautological Equivalence
Logical Equivalence – sentences that have the same truth values in every
possible circumstance; having the same truth conditions
Tautological Equivalence – sentences that can be seen to be equivalent simply in
virtue of the meanings of the truth-functional connectives.
All tautologically equivalent sentences are logically equivalent, but the reverse is
usually not true.
1) The negation of a conjunction is logically equivalent to the disjunction of the
negations of the original conjuncts.
2) The negation of a disjunction is equivalent to the conjunction of the negations
of the original disjuncts
Section 4.3 – Logical and Tautological Consequence
Logical Consequence – sentence S is a logical consequence of set of premises
P1... Pn, if it is impossible for the premises all to be true while the conclusion S is
Logical truths are sentences that are a logical consequence of a set of
Logically equivalent sentences are sentences that are a logical consequence of
Tautological consequence – a strict form of logical consequence; P is a
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