Logic & Propositions

Kareem KhalifaDepartment of Philosophy

Middlebury College

Overview

• What is Logic?• Propositions

What is Logic?

• Logic: the study of the methods and principles used to distinguish good from bad reasoning

• Synonyms for reasons: “backing up,” support, arguments, evidence, justification– Distinguished from rhetoric and

persuasion

Propositions

• Proposition: an abstract entity that asserts something is the case. – Synonyms: statement, claim– Is the kind of thing that is either true or

false

Propositions ≠ sentences

• A sentence is a linguistic entity, i.e., it is made up of sounds or images;

• Declarative sentences express propositions, which are abstract entities.– Ex. “It’s raining” and “Il pleut” are two

sentences, but they express the same proposition, i.e., it’s raining.

Testing for proposition-hood

• Take a sentence. Attach “It’s true that” or “It’s false that” to it.

• If the resulting sentence is grammatical, then it’s a proposition.

• Ex. it’s raining.

• Ex. Khalifa is evil.It’s true thatIt’s true that

It’s false thatIt’s false that

Both sentences express

propositions!

But one might be

misleading!

Sentences that do not express propositions

• Questions– Ex. What time is it?

• Imperatives– Ex. Do your

homework.

• Exclamations– Ex. Holy crap!

It’s false that

This doesn’t make sense!

It’s true that

It’s true that

Holy crap! This is

nonsense too!

How can imperatives be turned into propositions?

• Do your homework.– You should do your homework.– Doing your homework is good.– Your homework is worth doing.

Can you think of examples of questions or exclamations that express propositions?

Compound propositions

• Compound proposition: proposition composed of other propositions.

• Conjunctions (P and Q)– Khalifa is smart and Khalifa is handsome.

• Disjunctions (P or Q)– Either you do your homework or you go to the

concert.• Conditionals (If P then Q)

– If you do your homework, then you will pass.• Under what conditions are these

statements false?

Recap• Logic studies the methods and

principles used to distinguish good from bad reasoning

• Propositions are the basic building blocks of reasoning

• Propositions are the kinds of things that can be true or false, and reasoning aims to ascertain what is true and what is false.