Logic 101 lecture 1

Introduction – What is logic?

Logic 101 – Lecture 1

The study of reasoningThe 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?

Formal = without contextIf 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

Formal = without contextIf 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 sentenceBut not just any kind of sentence!...but more on that later.

Formal Sentential Logic

Reasoning meant to convince someone of something…which is not necessarily angry, impassioned, or loud

What is an argument?

J.T.: I could have totally been a college football player!

Ryan: Not without going to a college with a football team.1. If you attend a college with a football team,

you could have been on a college football team.

2. You do not attend a college with a football team.

3. You could not have been on a college football team.


F = J.T. could be on a football teamC = Your college has a football team

1. If F, then C2. Not C.3. Therefore, not F.

Breaking it down a little more…1. F C2. ~ C3. ∴ ~F


First: What we agree onIf your college has a football team, you could

have played college football

Second: The point I’m makingYou could not have played college football

Third: This is why it’s a good pointYour college does not have a football team


First: PremisesIf your college has a football team, you could

have played college football.

Second: ConclusionYou could not have played college football

Third: Inferential structure (reasoning)Your college does not have a football team


DeductionCompletely infallible proof

Either Obama or McCain is president.McCain is not president.Therefore, Obama is president.

InductionVery very very likely to be true, but not

necessarily trueEither Obama or McCain will be president.Obama holds a 53% majority with 85% of precincts

reportingTherefore, Obama will be president.

Types of Logic

ValidityA deductive argument is valid if

(and only if) the following is true:If the premises of the argument are

true, the conclusion must be trueThis 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?

SoundnessAn 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?

Logic 101 lecture 1

Education

Transcript of Logic 101 lecture 1