This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Branden Fitelson Philosophy 290 Notes 1 Conditionals Seminar: Day 3 Administrative: Ive added a link to Hajeks SEP entry (good background on probability) The lecture notes for my PHIL 148 class may also be useful on this score Oct. 5 : Alan Hajek will present most of the Chapter 5related material Ill present this week and next week (ch. 4 and intro to Ch. 5). Then, well move on to student presentations. Volunteers for Chapter 6 / 7 (in 2 weeks)? More Background: A Brief (Classical) Probability Calculus Primer Back to Bennett: Chapter 2 WrapUp, and then Chapters 3 & 4 Ramsey and Grice (or, more accurately, Ramsey and Bennetts Grice) Jackson on Conventional Implicature, the Ramsey Test, , and The ortoif inference [one more time] Next: Chapter 4 Leadup to The Equation, and Lewisian attacks on it UCB Philosophy C 2 & 3 ( ) & 4 ( ) B 09 / 14 / 04 Branden Fitelson Philosophy 290 Notes 2 A Brief (Classical) Probability Calculus Primer 1: Small Boolean Algebras For present purposes, it su ffi ces to think of the probability calculus as a (very simple) quantiative augmentation of classical, Boolean logic (or algebra). In fact, we wont even need to worry about algebras with more than three atomic propositions! Two representations of a 3atom Boolean algebra: X Y Z States T T T s 1 T T F s 2 T F T s 3 T F F s 4 F T T s 5 F T F s 6 F F T s 7 F F F s 8 X Y Z s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 In a 3atom algebra, there are 2 3 8 states . Each proposition in an algebra can be expressed as a disjunction of states . From here, probability is easy . UCB Philosophy C 2 & 3 ( ) & 4 ( ) B 09 / 14 / 04 Branden Fitelson Philosophy 290 Notes 3 A Brief (Classical) Probability Calculus Primer 2: Probability Models 1 A probability function Pr pq on a Boolean algebra B is just a function that maps each state s i of B to a real number on the unit interval r , 1 s such that the sum of all the Pr p s i q is equal to one. Example of a 2atom B plus a Pr: X Y States Pr p s i q T T s 1 1 6 T F s 2 1 4 F T s 3 1 8 F F s 4 11 24 X Y s 1 s 2 s 3 s 4 The area of the box is 1, since Pr( T ) = 1. On the left, we have a stochastic truthtable representation of x B , Pr y , and on the right we have a Venn Diagram representation in which the area of the regions is proportional to the probability of the corresponding propositions. A pair x B , Pr y consisting of a Boolean algebra of propositions B and a probability function Pr over B is called a (classical) probability model ....
View
Full
Document
This note was uploaded on 08/01/2008 for the course PHIL 290 taught by Professor Fitelson during the Fall '06 term at University of California, Berkeley.
 Fall '06
 FITELSON
 Philosophy

Click to edit the document details