Book contents
- Frontmatter
- Contents
- Editor's foreword
- Preface
- Part I Principles and elementary applications
- 1 Plausible reasoning
- 2 The quantitative rules
- 3 Elementary sampling theory
- 4 Elementary hypothesis testing
- 5 Queer uses for probability theory
- 6 Elementary parameter estimation
- 7 The central, Gaussian or normal distribution
- 8 Sufficiency, ancillarity, and all that
- 9 Repetitive experiments: probability and frequency
- 10 Physics of ‘random experiments’
- Part II Advanced applications
- Appendix A Other approaches to probability theory
- Appendix B Mathematical formalities and style
- Appendix C Convolutions and cumulants
- References
- Bibliography
- Author index
- Subject index
1 - Plausible reasoning
from Part I - Principles and elementary applications
Published online by Cambridge University Press: 05 September 2012
- Frontmatter
- Contents
- Editor's foreword
- Preface
- Part I Principles and elementary applications
- 1 Plausible reasoning
- 2 The quantitative rules
- 3 Elementary sampling theory
- 4 Elementary hypothesis testing
- 5 Queer uses for probability theory
- 6 Elementary parameter estimation
- 7 The central, Gaussian or normal distribution
- 8 Sufficiency, ancillarity, and all that
- 9 Repetitive experiments: probability and frequency
- 10 Physics of ‘random experiments’
- Part II Advanced applications
- Appendix A Other approaches to probability theory
- Appendix B Mathematical formalities and style
- Appendix C Convolutions and cumulants
- References
- Bibliography
- Author index
- Subject index
Summary
The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man's mind.
James Clerk Maxwell (1850)Suppose some dark night a policeman walks down a street, apparently deserted. Suddenly he hears a burglar alarm, looks across the street, and sees a jewelry store with a broken window. Then a gentleman wearing a mask comes crawling out through the broken window, carrying a bag which turns out to be full of expensive jewelry. The policeman doesn't hesitate at all in deciding that this gentleman is dishonest. But by what reasoning process does he arrive at this conclusion? Let us first take a leisurely look at the general nature of such problems.
Deductive and plausible reasoning
A moment's thought makes it clear that our policeman's conclusion was not a logical deduction from the evidence; for there may have been a perfectly innocent explanation for everything. It might be, for example, that this gentleman was the owner of the jewelry store and he was coming home from a masquerade party, and didn't have the key with him. However, just as he walked by his store, a passing truck threw a stone through the window, and he was only protecting his own property.
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- Information
- Probability TheoryThe Logic of Science, pp. 3 - 23Publisher: Cambridge University PressPrint publication year: 2003