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Full Idea
A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts.
Gist of Idea
Models are sets with functions and relations, and truth built up from the components
Source
Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.18
A Reaction
See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea.
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |