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Single Idea 7448
[filed under theme 10. Modality / B. Possibility / 6. Probability
]
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.
Gist of Idea
Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence)
Source
Ian Hacking (The Emergence of Probability [1975], Ch.1)
Book Ref
Hacking,Ian: 'The Emergence of Probability' [CUP 1975], p.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.
The
19 ideas
from Ian Hacking
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7447
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Probability was fully explained between 1654 and 1812
[Hacking]
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7448
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Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence)
[Hacking]
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7459
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Follow maths for necessary truths, and jurisprudence for contingent truths
[Hacking]
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7449
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Epistemological probability based either on logical implications or coherent judgments
[Hacking]
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7450
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In the medieval view, only deduction counted as true evidence
[Hacking]
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7451
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Formerly evidence came from people; the new idea was that things provided evidence
[Hacking]
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7452
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An experiment is a test, or an adventure, or a diagnosis, or a dissection
[Hacking, by PG]
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7454
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Gassendi is the first great empiricist philosopher
[Hacking]
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13833
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'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction
[Hacking]
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13834
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Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C'
[Hacking]
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13835
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Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with
[Hacking]
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13837
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With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically
[Hacking]
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13838
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A decent modern definition should always imply a semantics
[Hacking]
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13839
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Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers
[Hacking]
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13843
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If it is a logic, the Löwenheim-Skolem theorem holds for it
[Hacking]
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13840
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First-order logic is the strongest complete compact theory with Löwenheim-Skolem
[Hacking]
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13844
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A limitation of first-order logic is that it cannot handle branching quantifiers
[Hacking]
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13842
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Second-order completeness seems to need intensional entities and possible worlds
[Hacking]
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13845
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The various logics are abstractions made from terms like 'if...then' in English
[Hacking]
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