Logic is the study of reasoning and involves deducing new facts from known facts through valid arguments. Formal sentential logic examines arguments expressed in sentences without context. An argument is reasoning meant to convince someone of a conclusion and involves premises, a conclusion, and an inferential structure connecting the premises to the conclusion. Deductive arguments provide infallible proof while inductive arguments are very likely but not certain. For an argument to be good, it must be both valid, meaning the conclusion follows logically from the premises, and sound, meaning the premises are actually true.

1. Introduction – What is logic? Logic 101 – Lecture 1

2. The study of reasoning The process by which one passes from certain known (or unquestioned) facts to new facts The study of good or correct reasoning Formal sentential logic What is Logic?

3. Formal = without context If it was raining today, my friend would have an umbrella in her hand. She does not have an umbrella. Therefore, it is not raining today. If that object was metallic, it would have been pulled out of your hand when I activated the electromagnet. It’s still sitting there, therefore it is not made of metal. If there was nothing in solar system beyond Neptune, then Neptune’s orbit would be regular. Neptune’s orbit is irregular, so there must be something else there. Formal Sentential Logic

4. Formal = without context If X were true, Y would be true. But Y is not true. Therefore, X is not true. If X, then Y. Not Y. Therefore X. Sentential = within a sentence But not just any kind of sentence! ...but more on that later. Formal Sentential Logic

5. Reasoning meant to convince someone of something …which is not necessarily angry, impassioned, or loud What is an argument?

6. J.T.: I could have totally been a college football player! Ryan: Not without going to a college with a football team. If you attend a college with a football team, you could have been on a college football team. You do not attend a college with a football team. You could not have been on a college football team. What is an argument?

7. F = J.T. could be on a football team C = Your college has a football team If F, then C Not C. Therefore, not F. Breaking it down a little more… F  C ~ C ∴ ~F What is an argument?

8. First: What we agree on If your college has a football team, you could have played college football Second: The point I’m making You could not have played college football Third: This is why it’s a good point Your college does not have a football team What is an argument?

9. First: Premises If your college has a football team, you could have played college football. Second: Conclusion You could not have played college football Third: Inferential structure (reasoning) Your college does not have a football team What is an argument?

10. Deduction Completely infallible proof Either Obama or McCain is president. McCain is not president. Therefore, Obama is president. Induction Very veryvery likely to be true, but not necessarily true Either Obama or McCain will be president. Obama holds a 53% majority with 85% of precincts reporting Therefore, Obama will be president. Types of Logic

11. Validity A deductive argument is valid if (and only if) the following is true: If the premises of the argument are true, the conclusion must be true This doesn’t care about whether or not they are ACTUALLY true …and it’s not just dependent on everything being true What makes an argument good?

12. Soundness An argument is sound if (and only if) the following is true: The argument is valid and the argument has all true premises. Since a valid argument’s conclusion must be true given true premises, true premises guarantee a true conclusion What makes an argument good?