Ideas from 'Modality' by Joseph Melia [2003], by Theme Structure

[found in 'Modality' by Melia,Joseph [Acumen 2003,1-902683-48-x]].

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2. Reason / A. Nature of Reason / 1. On Reason
Consistency is modal, saying propositions are consistent if they could be true together
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism
First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious)
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Second-order logic needs second-order variables and quantification into predicate position
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
If every model that makes premises true also makes conclusion true, the argument is valid
7. Existence / D. Theories of Reality / 7. Facts / a. Facts
Maybe names and predicates can capture any fact
No sort of plain language or levels of logic can express modal facts properly
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities
10. Modality / A. Necessity / 2. Nature of Necessity
We may be sure that P is necessary, but is it necessarily necessary?
10. Modality / A. Necessity / 4. De re / De dicto modality
'De re' modality is about things themselves, 'de dicto' modality is about propositions
10. Modality / B. Possibility / 1. Possibility
Sometimes we want to specify in what ways a thing is possible
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Possible worlds make it possible to define necessity and counterfactuals without new primitives
In possible worlds semantics the modal operators are treated as quantifiers
If possible worlds semantics is not realist about possible worlds, logic becomes merely formal
Possible worlds could be real as mathematics, propositions, properties, or like books
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
The truth of propositions at possible worlds are implied by the world, just as in books
19. Language / B. Meaning / 3. Meaning as Verification
We accept unverifiable propositions because of simplicity, utility, explanation and plausibility