Logic – Chapter 2 (Sentential Logic)

Takeaways

learning to paraphrase into an argument

to convert into sentential logic

Summary

Represent an atomic sentence with a capital letter.

non functional truth connectives – a connective is used truth functionally when the truth value of the compound only depends on the truth functional value of the sentences used to generate it.

p is weaker than q if truth of q guarantees the truth of p but not vice versa

safest way to frame non truth functional compounds is to frame them as simple sentences

mentioned vs used – ‘A’ vs A

Language SL – vocabulary and grammar

Sentences – A, B, C … A_1, B_1,…. A_2….

Operations

  1. conjunction – and &
  2. disjunction – or V
  3. negation – not ~
  4. belongs to – horseshoe
  5. equivalent – triple =

( ) – Punctuation marks

Material conditional – if A then B statements which can be written as ~B || A. (>) horseshoe

material biconditional – if and only if.

because is non-truth functional – two trues can be false

  1. If P is of form Q, it doesn’t have any connectives and no immediate sentential components.
  2. If P is of form ~Q, ~ is the main connective and Q is the immediate sentential component.
  3. If P is of form Q&R, &(or whatever in between) is the main connective and Q, R are the sentential components
  4. atomic component is a sentential component which is an atomic sentence.
  5. Sentential components include the sentence itself, its immediate sentential components and the sentential components of the immediate sentential components.

Definitions and terms

sentential connectives

simple and compound sentences

truth functional value – the truth value of a sentence

subjunctive conditionals – something which might have happened

indicative conditional – something which definitely happen?

meta variables – when you talk about a sentence or expression generically (~P is negation of P)

Truth functional use of a connective – When the truth functional value of a compound sentence generated depends solely on the truth value of the sentences used to generate it.