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Single Idea 13839

[filed under theme 5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic ]

Full Idea

For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier.

Gist of Idea

Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers

Source

Ian Hacking (What is Logic? [1979], §11)

Book Ref

'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.242

A Reaction

I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea...

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]