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Single Idea 7459
[filed under theme 14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
]
Full Idea
Mathematics is the model for reasoning about necessary truths, but jurisprudence must be our model when we deliberate about contingencies.
Clarification
'Jurisprudence' studies the relationship between law and morality
Gist of Idea
Follow maths for necessary truths, and jurisprudence for contingent truths
Source
Ian Hacking (The Emergence of Probability [1975], Ch.10)
Book Ref
Hacking,Ian: 'The Emergence of Probability' [CUP 1975], p.86
A Reaction
Interesting. Certainly huge thinking, especially since the Romans, has gone into the law, and creating rules of evidence. Maybe all philosophers should study law and mathematics?
The
19 ideas
from Ian Hacking
7448
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Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence)
[Hacking]
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7447
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Probability was fully explained between 1654 and 1812
[Hacking]
|
7459
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Follow maths for necessary truths, and jurisprudence for contingent truths
[Hacking]
|
7449
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Epistemological probability based either on logical implications or coherent judgments
[Hacking]
|
7450
|
In the medieval view, only deduction counted as true evidence
[Hacking]
|
7451
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Formerly evidence came from people; the new idea was that things provided evidence
[Hacking]
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7452
|
An experiment is a test, or an adventure, or a diagnosis, or a dissection
[Hacking, by PG]
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7454
|
Gassendi is the first great empiricist philosopher
[Hacking]
|
13833
|
'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]
|
13835
|
Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with
[Hacking]
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13837
|
With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically
[Hacking]
|
13838
|
A decent modern definition should always imply a semantics
[Hacking]
|
13839
|
Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers
[Hacking]
|
13843
|
If it is a logic, the Löwenheim-Skolem theorem holds for it
[Hacking]
|
13842
|
Second-order completeness seems to need intensional entities and possible worlds
[Hacking]
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13840
|
First-order logic is the strongest complete compact theory with Löwenheim-Skolem
[Hacking]
|
13844
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A limitation of first-order logic is that it cannot handle branching quantifiers
[Hacking]
|
13845
|
The various logics are abstractions made from terms like 'if...then' in English
[Hacking]
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