# Elementary Logic - Southern Illinois University Carbondale

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:[email protected] 847-312-2737 Syllabus Highlights, cont. Texts: Schaums Outline of Logic, 2

nd ed. Priests Logic: A Very Short Introduction Westins 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 Week

Week Week 1 2 3 4

basics, truth table / tree proofs propositional calculus categorical and predicate logic 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) Its truth-preserving. 2) Its convincing. 3) Its fair. Arguments The argument is this courses prime focus. So, whats 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 truthvalue. Truth-value: A sentences 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. Whats 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 subconclusions.)

Conclusion signaling words thus therefore hence consequently as a result

accordingly clearly so 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 thatfurthermore since for

moreover as indicateddue to besides for example owing to in addition for the reason whats 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 wont always be signaled. Sample argument 1) 2)

3) 4) 5) All cats are fluffy. All fluffy things are soft. BabyFritz is a cat. So, BabyFritz is fluffy. 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 dont 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 youre having trouble finding conclusion / seeing implications, try it out.

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