This document discusses different types of reasoning including logical arguments using premises and conclusions, Boolean operators, and truth tables. It also covers modern logic using quantifiers and examining statements about mothers. Additionally, it addresses language and logic through examples of implicature and presupposition. Finally, it touches on plausible reasoning using inductive inference, probabilities, and Bayes' theorem.

1. REASONING
Chapter Six

2. methods of reasoning
 argument: premise -> conclusion
logical if the premise cannot be true without the
conclusion also being true
 Boolean operators (“and”, “or”, etc.)
 contradiction: p&p, tautology: (p&p)
 truth-tables p q p->q
T T T
T F F
F T T
F F T

3. modern logic
 everyone has a mother, so there is someone
who is everyone’s mother
 subject-predicate information, quantifiers
(y) (x) xMy (x) (y) xMy
“there is nobody who is the mother of everybody”
“x is the mother of y”
existential quantifier: “someone is the mother of y”
universal quantifier: “everyone has a mother”

4. language and logic
“Tom was polite even though he smoked”
truth-condition implicature
 presupposition, terminology, word order
“Have you stopped beating your wife?”
“Is your brother still in the hospital?”

5. plausible reasoning
 most possibilities lead to the conclusion
being true
 inductive inference
 probabilities of the real world?
 no logical argument for the uniformity of nature
 Bayes’s theorem
Prob (h/e) = Prob (h) x Prob (e/h)
Prob (e)
the prior probability of the evidence
the probability of e, given h
the prior probability of the hypothesis
the probability
of h, given e

6. (The end)