The disparity between Elementary Logic and Methods of Logic: Philosophy Forums

The disparity between Elementary Logic and Methods of Logic

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Nozickean

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Posted 06/10/05 - 07:30 AM: Subject: The disparity between Elementary Logic and Methods of Logic	#1
I purchased "Elementary Logic" and "Methods of Logic" by W.V.O. Quine. I initially began reading the former text, but was immediately puzzled because Quine chooses to express the conditional as ~(p~q) - using only conjunction and denial - and expresses the disjunction as ~(~p~q), again using only conjunction and denial. As I proceeded, somewhat confused over his choice, it became increasingly complicated to use these manners of expression in the exercises. During a break, I took a cursory glance at "Methods of Logic" only to notice that Quine adopted the conventional (or modern?) symbols of '->' for conjunctions and the 'down arrow' for disjunctions. ' What is the reason for this discrepancy? Do I benefit by skipping 'Elementary Logic' altogether and working on 'Methods of Logic'? I have already taken an introductory course to logic, so I am familiar with the basics.
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Nozickean

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Posted 06/10/05 - 07:32 AM:	#2
Sorry, Quine adopts the modern symbol of -> for conditionals, not conjunctions.
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Posted 06/10/05 - 10:45 PM:	#3
It is easier to start with a smaller language and then define the other operators in terms of other ones (by equivalences). Also your eye will get used to seeing ~(p & ~q) as p -> q and likewise for disjunction. If you are doing exercises yourself, just use the notation you feel most comfortable with--it doesn't matter. Just be glad he isn't solely using the Scheffer stroke.

sweetiepie
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Posted 06/25/05 - 12:27 AM:	#4
regarding anything academic, the more you can skip, the more you should skip. If i were you, i would just check to make sure your books eventually get to Godel's incompleteness theorem, since, imo, that's the best part.

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1 of 1 people found this post helpful Posted 06/25/05 - 03:19 AM:	#5
sweetiepie wrote: regarding anything academic, the more you can skip, the more you should skip. If i were you, i would just check to make sure your books eventually get to Godel's incompleteness theorem, since, imo, that's the best part. What?! That advice is on a par with telling someone to go play in traffic. Don't skip anything, if you have the time, because you'll pick up stuff you either missed in another presentation of the material or it might be a different approach to said material. Also, Godel's theorems can be proved in numerous ways and if you learn one way, you have not learned them all. It's interesting to see the various different but equivalent proofs. (E.g. Kripke gives a proof using algebraic techniques and something like game-theoretical semantics which is presented by Putnam in a Notre Dame Journal of Formal LOgic article here http://projecteuclid.org/Dienst/UI/1.0/Summarize/...) It's also a good refresher especially since you're not an expert in the field. (Even experts cite introductory texts, and often.)

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