Elementary Logic
PHIL 105-302Intersession 2013MTWHF 10:00 – 12:00ASA0118CSteven A. MillerDay 1
Syllabus Highlights
Instructor: Steven A. MillerOffice hours: MW – 12:30-2:00Faner3026Contact info: [email protected]
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Texts:Schaum’sOutline of Logic, 2nded.Priest’sLogic: A Very Short IntroductionWestin’sA Rulebook for Arguments, 4thed.All three texts are “required.”
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Policies:1) Attendance is optional.2) Electronic devices should not distract.3) Conversational abuse and distractions are also unwelcome.4) Papers must conform to formatting standards.5) Academic dishonesty will result in harsh penalties, likely involving failure.
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Grading:Thursday quizzes (4, 50 points each) – 25%Friday exams (4, 100 points each) – 50%Short papers (2, 100 points each) – 25%All points are equally weighted. Except with prior arrangement, late work will not be accepted. There will be no curving or extra credit.There is no homework.
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Schedule:Week 1 – basics, truth table / tree proofsWeek 2 – propositional calculusWeek 3 – categorical and predicate logicWeek 4 – informal logic / rhetoric
“Elementary Logic”
“Elementary”– basic, straightforward, obvious– e.g. “Elementary, my dear Watson.”“Logic”– unemotional, cool, detached– commonsensical beliefs– reasoning
What is logic?
“Being reasonable”Logic, then, is reasoningwell.It is not necessarily an account of how wedoreason but rather an account of how weshould do so.
Should!?
Oneshouldreason this way because…1) It’s truth-preserving.2) It’s convincing.3) It’s fair.
Arguments
Theargumentis this course’s prime focus.So, what’s an argument?Definition: “An argument is a sequence of statements of which one is intended as a conclusion and the others, the premises, are intended to prove or at least provide some evidence for the conclusion” (S, p. 1).
Words, words, words.
“Anargumentis a sequence ofstatementsof which one is intended as aconclusionand the others, thepremises, are intended toproveor at least provide someevidencefor theconclusion.”
Statement
A sentence, usually in the declarative mood, thathasorcould havea truth-value.Truth-value: A sentence’s being either true or false.
Statement
True– the statement is the case“All squares are rectangles.”“Barack Obama is the president.”“I am called ‘Steven’.”False– the statement is not the case“All dogs are reptiles.”“No one here is older than 5.”
Are thesestatements?
“Carbondale is south of Chicago.”“The fire-truck is red.”“Grapes are orange.”“My father is an electrician.”“What’s your favorite food?”“Stop it!”
INTERMISSION(Try our fresh-popped popcorn and refreshing soda!)
Argumentdefinition
“Anargumentis a sequence ofstatementsof which one is intended as aconclusionand the others, thepremises, are intended toproveor at least provide someevidencefor theconclusion.”
Conclusion
A statement that one istryingto show is true, through support ofpremises.For our purposes,allarguments haveonly oneconclusion. (They may, however, have multiple “sub-conclusions.”)
Conclusion “signaling” words
thus therefore henceconsequently as a result soaccordingly clearly must be thatshows that conclude that follows thatfor this reason
Premises
A statement that is offered asevidencefor the conclusion.For our purposes,allarguments haveat least onepremise.
Premise “signaling” words
because given that furthermoresince for moreoveras indicated due to besidesfor example owing to in additionfor the reason what’s more after allin fact this can be seen from
Sample argument
1) All cats are fluffy.2)BabyFritzis a cat.3) Therefore,BabyFritzis fluffy.Which line(s) is / are the conclusion?Which line(s) is / are the premise(s)?
Sample argument
1)BabyFritzis fluffy.2) All cats are fluffy.3)BabyFritzis a cat.The conclusion may appearanywherein the argument.The conclusion won’t always be signaled.
Sample argument
1) All cats are fluffy.2) All fluffy things are soft.3)BabyFritzis a cat.4) So,BabyFritzis fluffy.5) Therefore,BabyFritzis soft.Line 4appearsas a conclusion, but its function in the argument is as a further premise. We call these premises “sub-conclusions.”
Argumentdefinition
“Anargumentis a sequence ofstatementsof which one is intended as aconclusionand the others, thepremises, are intended toproveor at least provide someevidencefor theconclusion.”
Is it an argument?
All men are mortal.Socrates is a man.Therefore, Socrates is mortal.
Is it an argument?
All men are mortal.Socrates is a man.The Cardinals are the worst team.Therefore, Socrates is mortal.
Is it an argument?
91% of Polish people are Catholic.Pitoris a Polish person.We can conclude thatPitoris likely Catholic.
Is it an argument?
You are mean to me.We fight too much.Therefore, why don’t we break up?
Is it an argument?
2x + 1 = 52x = 4Therefore, x = 2.
Is it an argument?
All Quakers are pirates.The Cardinals are the best team.Grass is painted nightly by gnomes.Therefore, blackboards are black.
Argument recap(itulation)
1) At least two statements.2) One (and only one) of which is the conclusion.3) Some sort of relationship of support intended between the conclusion and the other statement(s).
Diagramming
Schaumpages 7-20.A numerical / graphical strategy for understanding the relationships between statements.If you’re having trouble finding conclusion / seeingimplications, try it out.
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