logic 101 lecture 1
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UofR's Logic 101 Lecture 1!TRANSCRIPT
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.
What is an argument?
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
What is an argument?
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
What is an argument?
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
What is an argument?
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?