This is an introductory textbook on probability and induction written by one of the world's foremost philosophers of science. The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementar
An Introduction to Probability and Inductive Logic
✍ Scribed by Ian Hacking
- Publisher
- Cambridge University Press
- Year
- 2001
- Tongue
- English
- Leaves
- 322
- Category
- Library
No coin nor oath required. For personal study only.
✦ Synopsis
This is an introductory textbook on probability and induction written by one of the world's foremost philosophers of science. The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic. It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction. The key features of the book are: * A lively and vigorous prose style Lucid and systematic organization and presentation of the ideas Many practical applications A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science Numerous brief historical accounts of how fundamental ideas of probability and induction developed.* A full bibliography of further reading Although designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction. Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance).
✦ Table of Contents
Cover
Half Title
Title Page
Copyright
Dedication
Contents
A Note on the Cover Illustration
Foreword
Odd Questions
Logic
1. Logic
Arguments
Going Wrong
Two Ways to Criticize
Validity
True Versus Valid
Metaphors
Sound
Like Building a House
Validity Is Not Truth!
Invalidity Is Not Falsehood!
Two Ways to Criticize a Deduction
2. What Is Inductive Logic?
Oranges
Samples and Populations
Proportions
Probability
Deducing Probabilities
Another Kind of Risky Argument
Inference to the Best Explanation
“Abduction”
Testimony
Rough Definition of Inductive Logic
Decision Theory
Rough Definition of Decision Theory
How to Calculate Probabilities
3. The Gambler’s Fallacy
Roulette
Fair
Biased
Independence
Two Ways to be Unfair
Unbiased and Independent
Biased Bones, Independent Outcomes
Unbiased Draws, Dependent Outcomes
Bias and Dependence
The Gambler’s Fallacy
Impossibility of a Successful Gambling System
Compound Outcomes
Odd Question 3
Odd Question 7
The Alert Learner
Risky Airplanes
Models
Two Ways to Go Wrong with a Model
4. Elementary Probability Ideas
What Has a Probability?
Propositions and Events
Why Learn Two Languages When One Will Do?
Notation: Logic
Notation: Sets
Notation: Probability
Two Conventions
Mutually Exclusive
Adding Probabilities
Independence
Multiplying
Sixes and Sevens: Odd Question 4
Compounding
A Trick Question
Understanding the Trick Question
Laplace
5. Conditional Probability
Categorical and Conditional
Notation
Bingo
Parking Tickets
Definition of Conditional Probability
Conditional Dice
Overlaps
Well-shuffled Cards
URNS
Drawing the Calculation to Check It
Models
Shock Absorbers
Drawing to Check
Weightlifters
Two in a Row: With Replacement
The Gambler’s Fallacy Once Again
Two Weightlifters: Without Replacement
6. The Basic Rules of Probability
Assumptions
Normality
Certainty
Additivity
Overlap
Conditional Probability
Multiplication
Total Probability
Logical Consequence
Statistical Independence
Proof of the Rule for Overlap
Conditionalizing the Rules
Statistical Independence Again
Multiple Independence
Venn Diagrams
Odd Question 2
Are People Stupid?
Axioms: Huygens
Axioms: Kolmogorov
7. Bayes’ Rule
Proof of Bayes’ Rule
Generalization
URNS
Spiders
Taxicabs: Odd Question 5
Base Rates
Reliability
False Positives
Probability of a False Positive
Strep Throat: Odd Question 6
Sheer Ignorance
Rev. Thomas Bayes
How to Combine Probabilities and Utilities
8. Expected Value
Acts
Notation
Just Two Possible Consequences
A Free Ride
Fair’s Fair
Fair Price Argument 1
Fair Price Argument 2
Generalizing
Two Tickets
A Raffle
Street Life
I Self-employed
IIEmployed, Honest Boss
Expected Time of Travel
Roulette
Lotto
Expected Value of Lotto 6/49
Actual Probabilities
Actual Winnings
Incredible Odds: Only 5,500 Tickets Can Be Sold!
Which Lottery Would You Prefer?
Cheap Thrills
Martingales
The St. PetersburgGame
Strange Expectations
Paradox
Solution 1: Any Finite Pricea Bargain!
Solution 2:The Game Is Impossible
Solution 3: No Expected Value Is Defined
Solution 4: Diminishing Marginal Utility
Solution 5: Low Chances
Daniel Bernoulli
Logic, or the Art of Thinking
9. Maximizing Expected Value
Risky Decisions
Decision Theory
Reservations
Utiles
Saving the Rule?
Volatility
Insurance
Actuarial Insurance
Extraordinary Insurance
Parking
What to Do?
Party Talk
Risk Aversion
Ideal Models
Disagreements
The Probabilities
The Consequences
The Danger
The Allais Paradox
Allais’ First Gamble
Allais’ Second Gamble
Applying the Rule
Risk Aversion?
L. J. Savage and Maurice Allais
Savage’s Reaction
10. Decision Under Uncertainty
Dominance
Three Rules
Pascal’s Wager
A Psychological Theory
Live Possibilities
A Partition
Decision Problems
Pascal’s Partition
First Utility Assignment
First Decision Table
First Wager: Dominance
The Dominance Rule
Second Utility Assignment
Second Wager: Use a Probability
Third Wager: Use a Range of Probabilities
Dominating Expected Value Rule
Criticisms
Recombinant Dna
Blaise Pascal
Kinds of Probability
11. What Do You Mean?
A Biased Coin
The Extinct Dinosaurs
Dinosaurs and Probability
On Not Mentioning Evidence
Interpersonal/evidential
Subjective/objective—Not
Personal Degree of Belief
Time to Think About Yourself
Belief-Type
Frequency-Type
Other Names
Shocks
Strep Throat
Stating That, and Reasons For
The Single Case
Switching Back and Forth
The Frequency Principle
Relevant Subsets
Probabilities of Probabilities
12. Theories About Probability
Frequency Dogmatists
Belief Dogmatists
Our Eclectic Approach
The Weather
Four Theories About Probability
Personal Probability
Logical Probability
The Principle of Insufficient Reason
Too Easy by Half
Bayesians
Keynes and Ramsey
De Finetti and Savage
Limiting Frequency
Propensity
Expected Values
The Old Coke Machine
Why Do We Have Different Kinds of Probability?
Modeling
Meanings
The Last Word
Probability as a Measure of Belief
13. Personal Probabilities
The Program
Thought Experiments
First Thought Experiment: Gifts
Risk-FreeGambles
Events and Propositions
Reality Check: Settle Soon
Reality Check: Unrelated Prizes
Second Thought Experiment: Use Fair Coins
Representing, Not Measuring
Betting
Betting Rates
Payoff
Third Thought Experiment
Fair Betting Rates
Not Real-life Betting
Fair Means No Edge
Odds
Conditional Bets
Conditional Betting Rates
The Conditional Payoff Matrix
The Argument
14. Coherence
Fourth Thought Experiment: Sets of Betting Rates
Fifth Thought Experiment: Simple Inconsistency
Sure-LossContracts
A Three-StepArgument
Normality
Certainty
Additivity
Conditional Sure-LossContracts
Conditional Coherence
Frank Ramsey and Bruno De Finetti
15. Learning from Experience
Bayes’ Rule
Hypotheses
New Evidence
The Bayesian Idea
Prior Probability
Example: Shock Absorbers (1)
Likelihood
Shock Absorbers (2)
Posterior Probability
Shock Absorbers (3)
Summary Form of Bayes’ Rule
Repeated Application of Bayes’ Rule
Shock Absorbers (4)
Shock Absorbers (5)
Reversing the Order
Example: Appendicitis
Summing Up the Available Information
Using Bayes’ Rule to Stage 4
Using Bayes’ Rule to Stage 5
Do Not Stop Thinking!
Likelihood Ratios
A Model of Learning?
Jeffrey’s Rule
Logic-bayesians
The Requirement of Total Evidence
Logic Versus Opinion
L. J. Savage
Probability as Frequency
16. Stability
The Program
Belief and Frequency Compared
New Wine in Old Bottles
Statistical Stability
An Experiment
Sample Mean
Sample Standard Deviation
Odd Question 1
Bernoulli Trials
Limits
An Urn Model
Repeated Draws
Most Probable Number
Most Probable Relative Frequency
Expected Number of Green Balls to Be Drawn inn Draws
Expected Relative Frequency of Green Balls in nDraws
Convergence and Stability
Margin of Error and Accuracy Probability
Bernoulli’s Theorem
Jacques Bernoulli
17. Normal Approximations
Experimental Bell-shaped Curves
An Ideal Bell-ShapedCurve
Meaning of the Curve
Application: Normal Fact I
Application: Normal FactII
How Good an Approximation?
How Fast Does Relative Frequency Converge on Probability?
Normal FactIII
Laws of Large Numbers
Light Bulbs
A Bored Prisoner
One-Half is theWorst-Case Scenario
Abraham De Moivre
18. Significance and Power
Astrology
Alert Learner
Statistical Hypotheses: Roulette
Statistical Hypotheses: Visioperfect
Is the Hypothesis True?
Two Frequency-TypeIdeas
Bad Lights
Funny Coins
Significance
Experimental Farms
Experimental Design
Example: Pesticide
Regions of Significance
Test Design
The Inductive Logic of Significance Tests
At Home with Farmers
Medicine
Experimental Psychology
Social Sciences
Statistical Packages
Fat and Beans
Causes
Common Cause
Standards
Rival Hypotheses
Acceptance and Rejection
The Neyman–PearsonFramework
Two Types of Error
Power
Utilities
R. A. Fisher
19. Confidence and Inductive Behavior
Samples and Populations
Opinion Polls
Worry 1:The Model
Worry 2:The Data
What Inductive Logic Is Not About
Estimation
Reliability
Point Estimates
Interval Estimates
Smoke
What the Report Does Not Say
Bernoulli Trials
Deduction
The Worst-case Scenario
The Confidence Idea
Confidence Intervals
Exact Intervals
More Smoke
The Three Percent Solution
More Confidence, More Error
Not Always Tidy: More Fat
What These Statements Mean
An Idealized Picture
Stratified Sampling
Technicalities
Confidence Intervals and Neyman–PearsonTests
Researchers at War over Child Deaths
Against Inference
Inductive Behavior
Significance Tests
Neyman’s Foes
For Inductive Inference
Jerzy Neyman
Probability Applied to Philosophy
20. The
David Hume
Skepticism
Philosophical Skepticism
A Skeptical Problem
Past and Future
Cause
Experience
Not Probability
A Famous Circle
Custom
Was Hume Really a Philosophical Skeptic?
Probability Evasions
An Anti-inductive Evasion
David Hume
Karl Popper
21. Learning from Experience as an Evasion of the Problem of Induction
Convergence
What Are Conditional Betting Rates?
Objection
Undogmatic Response
22. Inductive Behavior as an Evasion of the Problem of Induction
Inductive Behavior
The Evasion
The Modeling Objection
Response
The Single-case Objection
Three Logical Sentiments
Charles Sanders Peirce
Answers to the Exercises
Further Reading
Index
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📜 SIMILAR VOLUMES
This book clearly explains ideas in logic and in statistics/probability courses I have taken, and includes several insights new to me. It contains several real world exercises and answers. For me it's hard to put down. Every minute spent going through it has been very much worth it.
<p><em>A Logical Introduction to Probability and Induction</em> is a textbook on the mathematics of the probability calculus and its applications in philosophy.</p><p>On the mathematical side, the textbook introduces these parts of logic and set theory that are needed for a precise formulation of th
Two new philosophical problems surrounding the gradation of certainty began to emerge in the 17th century and are still very much alive today. One is concerned with the evaluation of inductive reasoning, whether in science, jurisprudence, or elsewhere; the other with the interpretation of the mathem