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Single Idea 19142

[filed under theme 10. Modality / B. Possibility / 6. Probability ]

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.

Gist of Idea

Probability can be constrained by axioms, but that leaves open its truth nature

Source

Donald Davidson (Truth and Predication [2005], 2)

Book Ref

Davidson,Donald: 'Truth and Predication' [Belknap Harvard 2005], p.32

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 15 ideas with the same theme [asserting the degree of likelihood of a fact]:

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]