1. Logic & Propositions Kareem Khalifa Department of Philosophy Middlebury College

2. Overview What is Logic? Propositions

3. 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

4. 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

5. 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.

6. 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 that It’s false that Both sentences express propositions! But one might be misleading!

7. 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 Holy crap! This is nonsense too!

8. 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?

9. 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?

10. 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.