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Full Idea
To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables.
Gist of Idea
A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables
Source
Wilfrid Hodges (First-Order Logic [2001], 1.3)
Book Ref
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.13
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [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] |
| 10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [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] |