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Lecture 9

PHIL 2110 Lecture Notes - Lecture 9: Disjunctive Syllogism, Syllogism, Thanetian


Department
Philosophy
Course Code
PHIL 2110
Professor
Yussif Yakubu
Lecture
9

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PHIL2110 – Elementary Symbolic Logic
2016/02/11
Lecture –Disjunction continued
Disjunction (Disj): From any statement, infer the disjunction with another statement (can
add whatever statement you want to help you solve the problem)
oIn symbols: from p (stated alone), infer p V q. From q (stated alone), infer p V q
oValidity: one cannot assert p to be true and at the same time deny that either p or q is
true; similarly, one cannot assert q to be true and at the same time deny that either p
or q is true
oP V q is a weaker statement than p so we wouldn’t normally infer it. But we need the
rule for our formal proofs – so to reason from p V q to p or q is invalid!
oExample:
1. E
2. (EvF)→¬G
3. HG
4. E v F: 1 Disj
5. ¬G: 2,4 MP
6. ¬H: 3,5 MT
E&¬H: 1,6 Conj
Disjunctive syllogism involves v and ¬ so it is analogous to conjunctive syllogism which
involves & and ¬
oDS says: either one or the other, not one, therefore the other
oCS says: not both, one, therefore not the other
oDisjunction is the counterpart of conjunction. But remember you only need one of the
disjuncts to apply Disj!
oThere is no counterpart for simplification
2016/02/23
Lecture – Disjunction part 3
De Morgan’s Laws (DM):
o‘not either’ is equivalent to ‘neither
o‘not both’ is equivalent to ‘either one or not the other’
oIn symbols: from ¬(pvq) infer ¬p & ¬q (and vice versa); from ¬(p&q) infer ¬p v¬q
(and vice versa)
oProof of formal validity will come later
oP V q is a weaker statement than p so we would not normally infer it, but we need it
for our formal proofs
Example:
o1. (A v B) C Prem
o2. ¬C v D Prem
o3. ¬D Prem
o4. ¬C 2,3 DS
o5. ¬(A v B) 1,4 MT
o6. ¬A & ¬B 5 DM
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