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Logic 101 lecture 1

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Logic 101 lecture 1

1. 1. Introduction – What is logic?<br />Logic 101 – Lecture 1<br />
2. 2. The study of reasoning<br />The process by which one passes from certain known (or unquestioned) facts to new facts<br />The study of good or correct reasoning<br />Formal sentential logic<br />What is Logic?<br />
3. 3. Formal = without context<br />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.<br />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.<br />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.<br />Formal Sentential Logic<br />
4. 4. Formal = without context<br />If X were true, Y would be true. But Y is not true. Therefore, X is not true.<br />If X, then Y. Not Y. Therefore X.<br />Sentential = within a sentence<br />But not just any kind of sentence!<br />...but more on that later.<br />Formal Sentential Logic<br />
5. 5. Reasoning meant to convince someone of something<br />…which is not necessarily angry, impassioned, or loud<br />What is an argument?<br />
6. 6. J.T.: I could have totally been a college football player!<br />Ryan: Not without going to a college with a football team.<br />If you attend a college with a football team, you could have been on a college football team.<br />You do not attend a college with a football team.<br />You could not have been on a college football team.<br />What is an argument?<br />
7. 7. F = J.T. could be on a football team<br />C = Your college has a football team<br />If F, then C<br />Not C.<br />Therefore, not F.<br />Breaking it down a little more…<br />F  C<br />~ C<br />∴ ~F<br />What is an argument?<br />
8. 8. First: What we agree on<br />If your college has a football team, you could have played college football<br />Second: The point I’m making<br />You could not have played college football<br />Third: This is why it’s a good point<br />Your college does not have a football team<br />What is an argument?<br />
9. 9. First: Premises<br />If your college has a football team, you could have played college football.<br />Second: Conclusion<br />You could not have played college football<br />Third: Inferential structure (reasoning)<br />Your college does not have a football team<br />What is an argument?<br />
10. 10. Deduction<br />Completely infallible proof<br />Either Obama or McCain is president.<br />McCain is not president.<br />Therefore, Obama is president.<br />Induction<br />Very veryvery likely to be true, but not necessarily true<br />Either Obama or McCain will be president.<br />Obama holds a 53% majority with 85% of precincts reporting<br />Therefore, Obama will be president.<br />Types of Logic<br />
11. 11. Validity<br />A deductive argument is valid if (and only if) the following is true:<br />If the premises of the argument are true, the conclusion must be true<br />This doesn’t care about whether or not they are ACTUALLY true<br />…and it’s not just dependent on everything being true<br />What makes an argument good?<br />
12. 12. Soundness<br />An argument is sound if (and only if) the following is true:<br />The argument is valid and the argument has all true premises.<br />Since a valid argument’s conclusion must be true given true premises, true premises guarantee a true conclusion <br />What makes an argument good?<br />