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Full Idea
Propositions that are individually highly probable can have an immediate implication that is not. The fact that one can assign a high probability to P and also to 'if P then Q' is not sufficient reason to assign high probability to Q.
Gist of Idea
High probability premises need not imply high probability conclusions
Source
Gilbert Harman (Change in View: Principles of Reasoning [1986], 3)
Book Ref
Harman,Gilbert: 'Change in View: Principles of Reasoning' [MIP 1986], p.23
A Reaction
He cites Kyburg's Lottery Paradox. It is probable that there is a winning ticket, and that this ticket is not it. Thus it is NOT probable that I will win.
Related Idea
Idea 6368 If my ticket won't win the lottery (and it won't), no other tickets will either [Kyburg, by Pollock/Cruz]
| 19304 | The rules of reasoning are not the rules of logic [Harman] |
| 19303 | Implication just accumulates conclusions, but inference may also revise our views [Harman] |
| 19305 | The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman] |
| 19308 | We strongly desire to believe what is true, even though logic does not require it [Harman] |
| 19307 | If there is a great cost to avoiding inconsistency, we learn to reason our way around it [Harman] |
| 19309 | Logic has little relevance to reasoning, except when logical conclusions are immediate [Harman] |
| 19306 | It is a principle of reasoning not to clutter your mind with trivialities [Harman] |
| 19310 | High probability premises need not imply high probability conclusions [Harman] |
| 19311 | In revision of belief, we need to keep track of justifications for foundations, but not for coherence [Harman] |
| 19312 | Coherence is intelligible connections, especially one element explaining another [Harman] |