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10. Modality / B. Possibility / 6. Probability

[asserting the degree of likelihood of a fact]

14 ideas
We transfer the frequency of past observations to our future predictions [Hume]
     Full Idea: Where different effects have been found to follow from causes, which are to appearance exactly similar, all these various effects must occur to the mind in the same proportion in transferring the past to the future.
     From: David Hume (Enquiry Conc Human Understanding [1748], VI.47)
Probability can be constrained by axioms, but that leaves open its truth nature [Davidson]
     Full Idea: Kolmogorov's axiomatisation of probability puts clear constraints on the concept of probability, but leaves open whether probability is further characterised as relative frequency, degree of belief, or something else.
     From: Donald Davidson (Truth and Predication [2005], 2)
     A reaction: Davidson cites this to show the limitations of axiomatic approaches to any topic (e.g. sets, truth, arithmetic). The item in question must be treated as a 'primitive'. This always has the feeling of second-best.
The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman]
     Full Idea: The Gambler's Fallacy says if black has come up ten times in a row, red must be highly probable next time. It overlooks how the impact of an initial run of one color can become more and more insignificant as the sequence gets longer.
     From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 1)
     A reaction: At what point do you decide that the roulette wheel is fixed, rather than that you have fallen for the Gambler's Fallacy? Interestingly, standard induction points to the opposite conclusion. But then you have prior knowledge of the wheel.
High probability premises need not imply high probability conclusions [Harman]
     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.
     From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 3)
     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.
Probability was fully explained between 1654 and 1812 [Hacking]
     Full Idea: There is hardly any history of probability to record before Pascal (1654), and the whole subject is very well understood after Laplace (1812).
     From: Ian Hacking (The Emergence of Probability [1975], Ch.1)
     A reaction: An interesting little pointer on the question of whether the human race is close to exhausting all the available intellectual problems. What then?
Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking]
     Full Idea: Probability has two aspects: the degree of belief warranted by evidence, and the tendency displayed by some chance device to produce stable relative frequencies. These are the epistemological and statistical aspects of the subject.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.1)
     A reaction: The most basic distinction in the subject. Later (p.124) he suggests that the statistical form (known as 'aleatory' probability) is de re, and the other is de dicto.
Epistemological probability based either on logical implications or coherent judgments [Hacking]
     Full Idea: Epistemological probability is torn between Keynes etc saying it depends on the strength of logical implication, and Ramsey etc saying it is personal judgement which is subject to strong rules of internal coherence.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.2)
     A reaction: See Idea 7449 for epistemological probability. My immediate intuition is that the Ramsey approach sounds much more plausible. In real life there are too many fine-grained particulars involved for straight implication to settle a probability.
A thing works like formal probability if all the options sum to 100% [Edgington]
     Full Idea: One's degrees of belief in the members of an idealised partition should sum to 100%. That is all there is to the claim that degrees of belief should have the structure of probabilities.
     From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.1)
Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington]
     Full Idea: If (and only if) an argument is valid, then in no probability distribution does the improbability of its conclusion exceed the sum of the improbabilities of its premises. We can call this the Probability Preservation Principle.
     From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.2)
     A reaction: [Ernest Adams is credited with this] This means that classical logic is in some way probability-preserving as well as truth-preserving.
Truth-functional possibilities include the irrelevant, which is a mistake [Edgington]
     Full Idea: How likely is a fair die landing on an even number to land six? My approach is, assume an even number, so three possibilities, one a six, so 'one third'; the truth-functional approach is it's true if it is not-even or six, so 'two-thirds'.
     From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 3)
     A reaction: The point is that in the truth-functional approach, if the die lands not-even, then the conditional comes out as true, when she says it should be irrelevant. She seems to be right about this.
Subjective probability measures personal beliefs; objective probability measures the chance of an event happening [Bird]
     Full Idea: Subjective probability measures a person's strength of belief in the truth of a proposition; objective probability concerns the chance a certain sort of event has of happening, independently of whether anyone thinks it is likely to occur or not.
     From: Alexander Bird (Philosophy of Science [1998], Ch.6)
     A reaction: The challenge to the second one is that God would know for certain whether a meteor will hit the Earth next week. The impact looks like 'bad luck' to us, but necessary to one who really knows.
Objective probability of tails measures the bias of the coin, not our beliefs about it [Bird]
     Full Idea: In tossing a coin, the objective probability of tails is a measure of the bias of the coin; the bias and the probability are objective features of the coin, like its mass and shape; these properties have nothing to do with our beliefs about the coin.
     From: Alexander Bird (Philosophy of Science [1998], Ch.6)
     A reaction: Despite my reservation that God would not seem to be very interested in the probabilities of coin-tossing, since he knows each outcome with certaintly, this is fairly convincing. God might say that the coin has a 'three-to-two bias'.
Quantum mechanics seems to imply single-case probabilities [Ladyman/Ross]
     Full Idea: Quantum mechanics seems to imply single-case probabilities.
     From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3)
     A reaction: I know they keep telling us about such things, but I remain cautious. I think all the physicists have done is delved a bit deeper into something they don't understand.
In quantum statistics, two separate classical states of affairs are treated as one [Ladyman/Ross]
     Full Idea: In quantum statistics, what would be regarded as two possible states of affairs classically is treated as one possible state of affairs.
     From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.1)