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notes_10_2x2 - Branden Fitelson Philosophy 12A Notes 1&...

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Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 ' & $ % Announcements & Such • Shuggie Otis : Freedom Flight • Administrative Stuff – HW #2 is due (first submission) Today @ 4pm @ the 12A Drop Box. ∗ See my “HW Tips & Guidelines” Handout, pertaining to HW #2. ∗ We’re a little behind where the HW is. We’ll catch-up soon. • Chapter 2 (LSL) — Finalé – Symbolizing entire English arguments into LSL. ∗ Symbolizing sentences in the context of an argument . ∗ Here, we have a principle of charity for argument symbolization. • Next: Chapter 3 Introduction — LSL Semantics – Truth-Functional Semantics for LSL Connectives – Our “Fundamental Idealization” — T-F semantics and → UCB Philosophy Chapter 2 Finalé & Chapter 3 Intro. 09/19/08 Branden Fitelson Philosophy 12A Notes 2 ' & Symbolizing Arguments: Example #4 • Step 2: Symbolize the premises (here, there are as many as five): (1) Suppose no two contestants enter; then there will be no contest. ∗ “Logish”: Suppose that not T ; then it is not the case that C . ∗ LSL: ‘ ∼ T → ∼ C ’. (2) No contest means no winner. ∗ “Logish”: Not C means not W . [ i.e. , not C implies not W .] ∗ LSL: ‘ ∼ C → ∼ W ’. (3) Suppose all contestants perform equally well. Still no winner. ∗ “Logish”: Suppose E . Still not W . [ i.e. , E also implies not W .] ∗ LSL: ‘ E → ∼ W ’. (4) There won’t be a winner unless there’s a loser. And conversely. ∗ “Logish”: Not W unless L , and conversely . ∗ LSL: ‘ ( ∼ L → ∼ W ) & ( ∼ W → ∼ L) ’. [ i.e. , not W iff not L .] • The final product is the following valid sentential form: ∼ T → ∼ C . ∼ C → ∼ W . E → ∼ W . ∼ L ↔ ∼ W . Therefore, L → (T & ∼ E) . UCB Philosophy Chapter 2 Finalé & Chapter 3 Intro. 09/19/08 Branden Fitelson Philosophy 12A Notes 3 ' & $ % A Few Final Remarks on Symbolizing Arguments • We saw the following premise our last argument: ‘There won’t be a winner unless there’s a loser. And conversely.’ I symbolized it as: – “Logish”: If not L , then not W , and conversely . [ i.e. , not L iff not W .] – LSL: ‘ ∼ L ↔ ∼ W ’, equivalently : ‘ ( ∼ L → ∼ W ) & ( ∼ W → ∼ L) ’. • One might wonder why I didn’t interpret the “and conversely” to be operating on the unless operator itself, rather than the conditional operator. This would yield the following different symbolization: – “Logish”: not W unless L , and L unless not W . – LSL: ‘ ( ∼ L → ∼ W ) & ( ∼∼ W → L) ’, equivalently : ‘ ( ∼ L → ∼ W ) & (W → L) ’. • Answer: This is a redundant symbolization in LSL, since ‘ ∼ L → ∼ W ’ is equivalent to ‘ W → L ’. Moreover, the resulting argument isn’t valid....
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notes_10_2x2 - Branden Fitelson Philosophy 12A Notes 1&...

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