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| 5750 | Consistency is modal, saying propositions are consistent if they could be true together |
| 5737 | Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets |
| 5744 | First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) |
| 5740 | Second-order logic needs second-order variables and quantification into predicate position |
| 5741 | If every model that makes premises true also makes conclusion true, the argument is valid |
| 5736 | No sort of plain language or levels of logic can express modal facts properly |
| 5735 | Maybe names and predicates can capture any fact |
| 5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities |
| 5738 | We may be sure that P is necessary, but is it necessarily necessary? |
| 5732 | 'De re' modality is about things themselves, 'de dicto' modality is about propositions |
| 5739 | Sometimes we want to specify in what ways a thing is possible |
| 5734 | Possible worlds make it possible to define necessity and counterfactuals without new primitives |
| 5742 | In possible worlds semantics the modal operators are treated as quantifiers |
| 5743 | If possible worlds semantics is not realist about possible worlds, logic becomes merely formal |
| 5749 | Possible worlds could be real as mathematics, propositions, properties, or like books |
| 5751 | The truth of propositions at possible worlds are implied by the world, just as in books |
| 5748 | We accept unverifiable propositions because of simplicity, utility, explanation and plausibility |