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Single Idea 10282

[filed under theme 5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic ]

Full Idea

A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument.

Gist of Idea

Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former)

Source

Wilfrid Hodges (First-Order Logic [2001], 1.1)

Book Ref

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.9

A Reaction

[Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming.

Related Idea

Idea 13232 Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]

The 16 ideas from Wilfrid Hodges

10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]