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Single Idea 5750
[filed under theme 2. Reason / A. Nature of Reason / 1. On Reason
]
Full Idea
Consistency is a modal notion: a set of propositions is consistent iff all the members of the set could be true together.
Clarification
'Could' is a modal notion, depending on possibility rather than actuality
Gist of Idea
Consistency is modal, saying propositions are consistent if they could be true together
Source
Joseph Melia (Modality [2003], Ch.6)
Book Ref
Melia,Joseph: 'Modality' [Acumen 2003], p.129
A Reaction
This shows why Kantian ethics, for example, needs a metaphysical underpinning. Maybe Kant should have believed in the reality of Leibnizian possible worlds? An account of reason requires an account of necessity and possibility.
The
17 ideas
from Joseph Melia
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5732
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'De re' modality is about things themselves, 'de dicto' modality is about propositions
[Melia]
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5734
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Possible worlds make it possible to define necessity and counterfactuals without new primitives
[Melia]
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5742
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In possible worlds semantics the modal operators are treated as quantifiers
[Melia]
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5743
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If possible worlds semantics is not realist about possible worlds, logic becomes merely formal
[Melia]
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5738
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We may be sure that P is necessary, but is it necessarily necessary?
[Melia]
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5739
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Sometimes we want to specify in what ways a thing is possible
[Melia]
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5737
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Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets
[Melia]
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5740
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Second-order logic needs second-order variables and quantification into predicate position
[Melia]
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5741
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If every model that makes premises true also makes conclusion true, the argument is valid
[Melia]
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5736
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No sort of plain language or levels of logic can express modal facts properly
[Melia]
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5735
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Maybe names and predicates can capture any fact
[Melia]
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5744
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First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious)
[Melia]
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5746
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The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities
[Melia]
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5748
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We accept unverifiable propositions because of simplicity, utility, explanation and plausibility
[Melia]
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5749
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Possible worlds could be real as mathematics, propositions, properties, or like books
[Melia]
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5750
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Consistency is modal, saying propositions are consistent if they could be true together
[Melia]
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5751
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The truth of propositions at possible worlds are implied by the world, just as in books
[Melia]
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