notes_2_2x2 - Branden Fitelson Philosophy 12A Notes 1...

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Branden Fitelson Philosophy 12A Notes 1 Announcements and Such Today’s Music: Janelle Monáe — The ArchAndroid Last time we talked about administrative stuff. If you need a syllabus, pick one up from us today. Then: study the website, and ask your me or your GSI any questions you have. Sections will meet Monday & Friday (starting this Friday). Bledin: 1–3:30 MF. Students AHN – LIN. Room: 213 Wheeler. Lawrence: 1–3:30 MF. Students LIU – ZHANG. Room: 130 Wheeler. HW #1 has been posted (it will be done as a “quiz” in section Friday). I’ve also posted a handout on validity and soundness , and a handout on tips & guidelines for homeworks . You should download & study these. HW #2 will be posted tomorrow (it will be due next Thursday). Today: Intro. & Chapter 1, continued. Then, Chapter 2: Our first formal logical theory/framework — the L anguage of S entential L ogic ( LSL ). UCB Philosophy Introduction (Cont’d) & Chapter 2 05/26/10 Branden Fitelson Philosophy 12A Notes 2 Informal (“Absolute”) Validity — Our Fundamental Concept An argument is a collection of propositions , one of which (the conclusion ) is meant to follow-from the others (the premises ). From a logical point of view, an argument A is “good” just in case its conclusion does follow-from its premises — that is, if A is valid . Our (informal) definition of validity is as follows: Definition . A is valid iff it is ( logically !) impossible for both of the following to be true simultaneously ( i.e. , in the same situation): (1) All of A ’s premises are true. (2) A ’s conclusion is false. A more operational way of understanding the definition is as follows. Suppose that all of A ’s premises are true. Then, try to imagine a situation (or possible world) like that in which A ’s conclusion is false. If that is conceivable, then A is in valid (otherwise, A ’s valid). UCB Philosophy Introduction (Cont’d) & Chapter 2 05/26/10 Branden Fitelson Philosophy 12A Notes 3 Validity, Soundness, and “ All-Things-Considered Good” Arguments A “good” argument is one in which the conclusion follows from the premises. But, intuitively, there is more to a “good” argument (all things considered) than mere validity. [But, after chapter 1, we won’t care.] Ideally, arguments should also have (actually) true premises . If the premises of an argument are (actually) false, then (intuitively) the argument isn’t very “good” (or actually useful) — even if it is valid. Definition . An argument A is sound if and only if both : ( i ) A is valid, and ( ii ) all of A ’s premises are (actually) true. So, there are two components or aspects of “good” arguments: Logical Component: Is the argument valid? Non-Logical Component: Are the premises (actually) true?
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