# PHIL 210 Study Guide - Midterm Guide: Disjunction Elimination, Disjunction Introduction, Conjunction Elimination

by OC14207

This

**preview**shows pages 1-2. to view the full**7 pages of the document.**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:

1) TW

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.

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

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.

DeMorgan's Laws

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

false

Logical truths are sentences that are a logical consequence of a set of

premises.

Logically equivalent sentences are sentences that are a logical consequence of

each other.

Tautological consequence – a strict form of logical consequence; P is a

###### You're Reading a Preview

Unlock to view full version