Logic Propositions Kareem Khalifa Department of Philosophy Middlebury

Logic & Propositions Kareem Khalifa Department 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 true that it’s raining. • Ex. It’s false that Khalifa is evil. Both sentences express propositions! But one might be misleading!

Sentences that do not express propositions This doesn’t make sense! • Questions – Ex. It’s false that What time is it? • Imperatives – Ex. It’s true that Do your homework. • Exclamations – Ex. 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.