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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]
| 2216 | We transfer the frequency of past observations to our future predictions [Hume] |
| 19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
| 19305 | The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman] |
| 19310 | High probability premises need not imply high probability conclusions [Harman] |
| 7448 | Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking] |
| 7447 | Probability was fully explained between 1654 and 1812 [Hacking] |
| 7449 | Epistemological probability based either on logical implications or coherent judgments [Hacking] |
| 14281 | A thing works like formal probability if all the options sum to 100% [Edgington] |
| 14284 | Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington] |
| 13857 | Truth-functional possibilities include the irrelevant, which is a mistake [Edgington] |
| 6796 | Subjective probability measures personal beliefs; objective probability measures the chance of an event happening [Bird] |
| 6797 | Objective probability of tails measures the bias of the coin, not our beliefs about it [Bird] |
| 14903 | Quantum mechanics seems to imply single-case probabilities [Ladyman/Ross] |
| 14923 | In quantum statistics, two separate classical states of affairs are treated as one [Ladyman/Ross] |
| 24054 | Everything has a probability, something will happen, and probabilities add up [PG] |