Propositions & Arguments Kareem Khalifa Department of Philosophy Middlebury College

Overview What is Logic? Propositions Arguments Exercises Bonus: Why Are Philosophy Majors So Successful?

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

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

Arguments Argument: a set of propositions such that one member of that set, the conclusion, can be affirmed on the basis of the others, the premises. Inference: the process of affirming the conclusion on the basis of the premises.

The canonical example of an argument If it’s raining, then the streets are wet. It’s raining. So the streets are wet. PREMISES CONCLUSION

What is Logic? (Redux) Ideally, we reason well with true beliefs. Logic is concerned with good and bad forms of reasoning. “Forms of reasoning” = “types of arguments” Good reasoning ≠ true beliefs Bad Luck: We can reason well but have false beliefs Good Luck: We can reason poorly and have true beliefs Ideally, we reason well with true beliefs.

Bad Luck: Good reasoning, false beliefs Example: A If C is longer than A, then C is not the shortest line. C is longer than A. Therefore C is not the shortest line. B C

Good Luck: Bad reasoning, true beliefs If it’s raining, the streets are wet. The streets are wet. So it’s raining.

By themselves, conditionals are NOT arguments! If you study hard, then you will pass the course. Because you study hard, you will pass the course. This statement asserts neither that you study hard nor that you pass the course. This one asserts both.

However, conditionals can be parts of arguments If you study hard, then you will pass the course. You study hard. So you’ll pass the course. In this case, the conditional is a premise If you study hard, then you’ll do well on the tests. If you do well on the tests, then you’ll pass the course. So if you study hard, then you’ll pass the course. Here, the first two conditionals are premises; the last is a conclusion.

Exercise #3 Aquinas argued that human intelligence is a gift from God and therefore “to apply human intelligence to understand the world is not an affront to God, but is pleasing to him.” Premise Conclusion

#5) (1) Standardized tests have a disparate racial and ethnic impact; (2) white and Asian students score, on average, markedly higher than their black and Hispanic peers. (3) [These disparities appear in] fourth-grade tests, college entrance exams, and every other assessment on the books. (4) If a racial gap is evidence of discrimination, then all tests discriminate.

Exercise #9 Houses are built to live in, not to look on; therefore, use [should] be preferred before uniformity.

Exercise #14 Omniscience and omnipotence are mutually incompatible. If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means he can’t change his mind about his intervention, which means he is not omnipotent. 1) If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. 2) If God already knows how he will intervene, then God cannot change his mind. 3) If God cannot change his mind, then he is not omnipotent.

Exercise #15 Reason is the greatest enemy that faith has; (1) it never comes to the aid of spiritual things, but more frequently than not (2) [reason] struggles against the divine Word, treating with contempt all that emanates from God.

Why Are Philosophy Majors So Successful?