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## MATHEMATICAL LOGIC

by: Cleve Schinner

30

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3

# MATHEMATICAL LOGIC PHIL 505

Cleve Schinner
Rice University
GPA 3.93

Richard Grandy

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COURSE
PROF.
Richard Grandy
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

## Popular in PHIL-Philosophy

This 3 page Class Notes was uploaded by Cleve Schinner on Monday October 19, 2015. The Class Notes belongs to PHIL 505 at Rice University taught by Richard Grandy in Fall. Since its upload, it has received 30 views. For similar materials see /class/225044/phil-505-rice-university in PHIL-Philosophy at Rice University.

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Date Created: 10/19/15
Phil 505 R E Grandy 2005 An argument for the equivalence of 3 and if then Since we know that ADB is equivalent to AvB we will proceed to give an argument that If A then B follows from AvB and conversely and thus they are equivalent 1 If A then B Assumption 2 AvB Assumption for reductio 3 AampB DeMorgan principle on 2 4 A Simplification on 3 5 B Simplification on 3 6 A Double Negation Elimination on 4 7 B Modus ponens 16 8 B amp B Conjunction 57 9 AvB Reductio 2 through 8 Thus from the assumption 1 we have deduced 9 AvB B If B then ifA then AampB If A then AampB If AampB then B If A then B A If A then if B then A ampB 9 If B then AampB 10 If AampB then A ll lfB then A 12 If A then B 13 If A then B poaownhwwe Assumption Assumption for disjunctive syllogism amp Intro Modus ponens 23 amp elimination Transitivity of If then Assumption for disjunctive syllogism amp Intro Modus ponens 7 9 amp Elimination Transitivity of if then Contraposition Disjunctive syllogism l26 7l2 A shorter argument for the second half 1 A V B Assumption 2 A Assumption 3 B Disjunctive syllogism 12 4 If A then B Conditional proof If you believe that the English ifthen and the material conditional diverge then you must decide which of the principles used above is incorrect and argue for that claim Examples to show that 39if then39 is not well represented by 3 Failure of transitivity ADB BDC ADC If Queen Elizabeth dies next week there will be a large state funeral in the UK If a comet strikes the earth and annihilates all humans next week Queen Elizabeth will die next week Therefore If a comet strikes the earth and annihilates all humans next week there will be a large state funeral in the UK Failure of Addition ADB AampC 3B If I hold a lit match to this book it will ignite Therefore if I soak this book thoroughly in water and I hold a lit match to this book it will ignite Failure of contraposition ADB B D A If George is not living in Boston he is living somewhere in New England Therefore If George is not living somewhere in New England he is living in Boston Failure of modus ponens due to Van McGee A D B A B Before the 1980 election it Ronald Reagan a Republican seemed very likely to beat the Democrat Jimmy Carter John Anderson another Republican appeared likely to get less than 1 of the vote So it seemed true that If a Republican wins if Reagan doesn t win Anderson will win A Republican will win Therefore If Reagan doesn t win Anderson will win

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