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Logic - Paul Tomassi

The book is an introductory textbook on logic. It gets the student up to date with most modern advancements in Logic. The chapters are as follows.

  • How to think logically
  • How to prove that you can argue logically #1
  • How to prove that you can argue logically #2
  • Formal logic and formal semantics
  • Intro to first order predicate logic
  • How to argue logically in QL
  • Formal logic and formal semantics

Chapter 1: How to think logically

This chapter is a brief introduction in to the importance of being able to think logically and how that will often play out. It gives some examples of valid and invalid arguments, soundness of arguments. Deduction and induction. Formal logic. Aswell as a brief note on the history of formal logic. The brief history is good in showing where aristotelian logic had gotten formal logic and then the makes illusions to the significant contributions of gottlob frege to formal logic.

Chapter 2 : How to prove that you can argue logically #1 A formal language for formal logic

Formal logic is not english but is its own formal language.

Sentential constants are represented by capital letters P, Q, R

sentential variables are represented by lower case letters. p, q, r

The expression of a formal language sentence refers to itself it is an autonym

A formal language sentence is bets broken up in to atomic units

Each premise can be represented as its own capital letter P Q etc

The connection of formal sentences can be done with logical connectives

Propositional logic contains 5.

We can translate a regular language like english in to formal logic with the use of a key

Either I’ll stay in my bed and read my book or i’ll have a shower

I’ll stay in bed and either I’ll read my book or I’ll have a shower

1)I’ll stay in my bed P

  1. I’ll read my book. Q

  2. I’ll have a shower. R

When we are looking at complex sentences we use brackets for connectives

(P&Q)

When we need to use connectives it is called a well formed formula

Each individual sentence is known as an Atomic formula

A well formed formula using sentence letters and connectives is a compound formula

We can break a sentence down by its conjuncts

conjucts can themsleves be compounds and. have their own conjuncts

Either I’ll stay in my bed and read my book or i’ll have a shower

(P & Q) v R

I’ll stay in bed and either I’ll read my book or I’ll have a shower

P & (Q v R)

What the connective is reaching is called its scope

The scope that conects the entire sentence is called the main connective