Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Introduction to Logic IDr. Bob HamiltonUniversity of South CarolinaDepartment of PhilosophyFall 2013All documents for this course (syllabus, schedule, lecture notes, powerpoints, answer keys, etc.) will be posted on our Blackboard course website, under ‘Course Documents’.If you don’t yet know how to access Blackboard, you need to learn how asap!The syllabus . . .The semester schedule . . .You need to get up and running with the software . . .Install the CD or download from internetMake use of the Introduction in the textbook as well as the software user manualRegister with GradeGrinder (“You Try It” section on pp. 8-10 of textbook)Don’t forget there’s a pdf version of the textFirst software program we’ll use: Tarski’s WorldFirst part of your assigned reading for next class, pp. 1-11, gives an overview of what logic is and why it’s important . . .Logic provides the standards of rationality assumed by every field of inquiry and science.what counts as a good argumentwhat you can conclude from given informationwhat is convincing and what is notwhat is valid reasoning and what is not.Deductive inference: Drawing certain (i.e., guaranteed) conclusions from a set of known or assumed facts. That is, starting with a set of premises, what conclusion follows from the premises—what can be validly inferred from the premises?A famous syllogism:Socrates is a man (premise)All men are mortal (premise)Socrates is mortal (conclusion)Is the above argument airtight?Is the conclusion certain?Socrates is a man (premise)All men are mortal (premise)Socrates is mortal (conclusion)Yes.If the premises are true, then the conclusion necessarily follows—it is necessarily true as well.Logicians have found it useful to formalize the process and work with artificial languages . . .Sample argument expressed in the language of First-Order Logic (FOL):1. ∀x (Cube(x) ᴠ Tet(x) ᴠ Dodec(x))2. ¬Ǝx (Cube(x) ᴠ Dodec(x))3. ∀x Tet(x)1. Every object (in some particular world) is either a cube or a tetrahedron or a dodecahedron. (premise)2. There are no cubes or dodecahedrons. (premise)3. Therefore, every object is a tetrahedron. (conclusion)Logical consequence:“one claim is a logical consequence of another if there is no way the latter could be true without the former also being true” (p. 4)Logical consequence is the basis for deductive inference; it’s what makes a good deductive argument ‘work’. In this course you’ll learn how to recognize it, how to prove it, and lots more.Assignments for next class (this info is given in the semester “Schedule” posted on Blackboard):Sections of Textbook covered: Constants (1.1) / Predicate Symbols (1.2) / Atomic Sentences (1.3) / General first-order languages (1.4)Read pp. 1-11, 19-29Homework exercises: 1.1-1.10 (this includes the “You Try It” exercise that registers you with GradeGrinder). Note that I will post on Blackboard an answer key to the handwritten exercises 1.7, 1.8, and 1.10Website address for LPL (on p. 16): http://lpl.stanford.eduAlso be sure to carefully read through the Syllabus and look over the Schedule, and come to the next class prepared to ask any questions you have.Our first quiz will be this Friday (class meeting #3) and will cover the material from today’s and Wednesday’s lessons.Finally, I will hold office hours this Friday only if there is interest, if you notify me beforehand. My first regular office hours will be next Friday
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