Elementary Logic

Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 1

Syllabus Highlights Instructor: Steven A. Miller Office hours: MW – 12:30-2:00 Faner 3026 Contact info: mllrstvn@siu.edu 847-312-2737

Syllabus Highlights, cont. Texts: Schaum’s Outline of Logic, 2nd ed. Priest’s Logic: A Very Short Introduction Westin’s A Rulebook for Arguments, 4th ed. All three texts are “required.”

Syllabus Highlights, cont., cont. 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.

Syllabus Highlights, cont., cont., cont. 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.

Syllabus Highlights, cont., cont., etc. Schedule: Week 1 – basics, truth table / tree proofs Week 2 – propositional calculus Week 3 – categorical and predicate logic Week 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 reasoning well. It is not necessarily an account of how we do reason but rather an account of how we should do so.

Should!? One should reason this way because… 1) It’s truth-preserving. 2) It’s convincing. 3) It’s fair.

Arguments The argument is 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. “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.”

Statement A sentence, usually in the declarative mood, that has or could have a 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 these statements? “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!)

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.”

Conclusion A statement that one is trying to show is true, through support of premises. For our purposes, all arguments have only one conclusion. (They may, however, have multiple “sub-conclusions.”)

Conclusion “signaling” words thus therefore hence consequently as a result so accordingly clearly must be that shows that conclude that follows that for this reason

Premises A statement that is offered as evidence for the conclusion. For our purposes, all arguments have at least one premise.

Premise “signaling” words because given that furthermore since for moreover as indicated due to besides for example owing to in addition for the reason what’s more after all in fact this can be seen from

Sample argument 1) All cats are fluffy. 2) BabyFritz is a cat. 3) Therefore, BabyFritz is fluffy. Which line(s) is / are the conclusion? Which line(s) is / are the premise(s)?

Sample argument 1) BabyFritz is fluffy. 2) All cats are fluffy. 3) BabyFritz is a cat. The conclusion may appear anywhere in the argument. The conclusion won’t always be signaled.

Sample argument 1) All cats are fluffy. 2) All fluffy things are soft. 3) BabyFritz is a cat. 4) So, BabyFritz is fluffy. 5) Therefore, BabyFritz is soft. Line 4 appears as a conclusion, but its function in the argument is as a further premise. We call these premises “sub-conclusions.”

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.”

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. Pitor is a Polish person. We can conclude that Pitor is 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 = 5 2x = 4 Therefore, 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 Schaum pages 7-20. A numerical / graphical strategy for understanding the relationships between statements. If you’re having trouble finding conclusion / seeing implications, try it out.

Elementary Logic