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Single Idea 13838
[filed under theme 2. Reason / D. Definition / 3. Types of Definition
]
Full Idea
Today we expect that anything worth calling a definition should imply a semantics.
Gist of Idea
A decent modern definition should always imply a semantics
Source
Ian Hacking (What is Logic? [1979], §10)
Book Ref
'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.239
A Reaction
He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives.
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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