more on this theme
|
more from this text
Single Idea 13837
[filed under theme 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
]
Full Idea
My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties.
Gist of Idea
With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically
Source
Ian Hacking (What is Logic? [1979], §09)
Book Ref
'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.238
A Reaction
He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth.
The
19 ideas
from Ian Hacking
7447
|
Probability was fully explained between 1654 and 1812
[Hacking]
|
7448
|
Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence)
[Hacking]
|
7459
|
Follow maths for necessary truths, and jurisprudence for contingent truths
[Hacking]
|
7449
|
Epistemological probability based either on logical implications or coherent judgments
[Hacking]
|
7450
|
In the medieval view, only deduction counted as true evidence
[Hacking]
|
7451
|
Formerly evidence came from people; the new idea was that things provided evidence
[Hacking]
|
7452
|
An experiment is a test, or an adventure, or a diagnosis, or a dissection
[Hacking, by PG]
|
7454
|
Gassendi is the first great empiricist philosopher
[Hacking]
|
13833
|
'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction
[Hacking]
|
13834
|
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]
|
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]
|
13840
|
First-order logic is the strongest complete compact theory with Löwenheim-Skolem
[Hacking]
|
13844
|
A limitation of first-order logic is that it cannot handle branching quantifiers
[Hacking]
|
13842
|
Second-order completeness seems to need intensional entities and possible worlds
[Hacking]
|
13845
|
The various logics are abstractions made from terms like 'if...then' in English
[Hacking]
|