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Single Idea 19287
[filed under theme 10. Modality / A. Necessity / 6. Logical Necessity
]
Full Idea
We can distinguish between narrower and broader kinds of logical necessity. There are, for example, the logical necessities of propostional logic, those of first-order logic, and so on. Maybe they are necessities expressed using logical vocabulary.
Gist of Idea
Maybe each type of logic has its own necessity, gradually becoming broader
Source
Bob Hale (Necessary Beings [2013], 04.5)
Book Ref
Hale,Bob: 'Necessary Beings' [OUP 2013], p.114
A Reaction
Hale goes on to prefer a view that embraces conceptual necessities. I think in philosophy we should designate the necessities according to their sources. This might clarify a currently rather confused situation. First-order includes propositional logic.
The
60 ideas
from Bob Hale
8261
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Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute
[Hale]
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15080
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'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true)
[Hale]
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15081
|
A strong necessity entails a weaker one, but not conversely; possibilities go the other way
[Hale]
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15082
|
Metaphysical necessity says there is no possibility of falsehood
[Hale]
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15085
|
'Broadly' logical necessities are derived (in a structure) entirely from the concepts
[Hale]
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15086
|
Absolute necessity might be achievable either logically or metaphysically
[Hale]
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15088
|
Logical necessities are true in virtue of the nature of all logical concepts
[Hale]
|
15087
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Conceptual necessities are made true by all concepts
[Hale]
|
10308
|
Questions about objects are questions about certain non-vacuous singular terms
[Hale]
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10307
|
The modern Fregean use of the term 'object' is much broader than the ordinary usage
[Hale]
|
10310
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Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated
[Hale]
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10312
|
Often the same singular term does not ensure reliable inference
[Hale]
|
10313
|
Plenty of clear examples have singular terms with no ontological commitment
[Hale]
|
10318
|
Realists take universals to be the referrents of both adjectives and of nouns
[Hale]
|
10314
|
An expression is a genuine singular term if it resists elimination by paraphrase
[Hale]
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10316
|
We should decide whether singular terms are genuine by their usage
[Hale]
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10315
|
We can't believe in a 'whereabouts' because we ask 'what kind of object is it?'
[Hale]
|
10321
|
We sometimes apply identity without having a real criterion
[Hale]
|
10322
|
If singular terms can't be language-neutral, then we face a relativity about their objects
[Hale]
|
10511
|
It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns
[Hale]
|
10513
|
Many abstract objects, such as chess, seem non-spatial, but are not atemporal
[Hale]
|
10514
|
If the mental is non-spatial but temporal, then it must be classified as abstract
[Hale]
|
10512
|
The abstract/concrete distinction is based on what is perceivable, causal and located
[Hale]
|
10517
|
Colours and points seem to be both concrete and abstract
[Hale]
|
10518
|
Shapes and directions are of something, but games and musical compositions are not
[Hale]
|
10521
|
If F can't have location, there is no problem of things having F in different locations
[Hale]
|
10520
|
Token-letters and token-words are concrete objects, type-letters and type-words abstract
[Hale]
|
10519
|
The abstract/concrete distinction is in the relations in the identity-criteria of object-names
[Hale]
|
10524
|
There is a hierarchy of abstraction, based on steps taken by equivalence relations
[Hale]
|
10523
|
Being abstract is based on a relation between things which are spatially separated
[Hale]
|
10522
|
The relations featured in criteria of identity are always equivalence relations
[Hale]
|
19275
|
You cannot understand what exists without understanding possibility and necessity
[Hale]
|
19276
|
The big challenge for essentialist views of modality is things having necessary existence
[Hale]
|
19278
|
There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p
[Hale]
|
19279
|
What are these worlds, that being true in all of them makes something necessary?
[Hale]
|
19281
|
Interesting supervenience must characterise the base quite differently from what supervenes on it
[Hale]
|
19282
|
It seems that we cannot show that modal facts depend on non-modal facts
[Hale]
|
19285
|
Logical necessity is something which is true, no matter what else is the case
[Hale]
|
19286
|
'Absolute necessity' is when there is no restriction on the things which necessitate p
[Hale]
|
19288
|
Logical and metaphysical necessities differ in their vocabulary, and their underlying entities
[Hale]
|
19287
|
Maybe each type of logic has its own necessity, gradually becoming broader
[Hale]
|
19289
|
Maybe conventionalism applies to meaning, but not to the truth of propositions expressed
[Hale]
|
19290
|
Absolute necessities are necessarily necessary
[Hale]
|
19291
|
A canonical defintion specifies the type of thing, and what distinguish this specimen
[Hale]
|
19293
|
Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures
[Hale]
|
19294
|
If necessity derives from essences, how do we explain the necessary existence of essences?
[Hale]
|
19295
|
Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers
[Hale]
|
19296
|
If second-order variables range over sets, those are just objects; properties and relations aren't sets
[Hale]
|
19297
|
The two Barcan principles are easily proved in fairly basic modal logic
[Hale]
|
19298
|
Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems
[Hale]
|
19299
|
Possible worlds make every proposition true or false, which endorses classical logic
[Hale]
|
19300
|
The molecules may explain the water, but they are not what 'water' means
[Hale]
|
19301
|
With a negative free logic, we can dispense with the Barcan formulae
[Hale]
|
19302
|
If a chair could be made of slightly different material, that could lead to big changes
[Hale]
|
10632
|
The real numbers may be introduced by abstraction as ratios of quantities
[Hale, by Hale/Wright]
|
12432
|
Explanation of necessity must rest on something necessary or something contingent
[Hale]
|
12433
|
If necessity rests on linguistic conventions, those are contingent, so there is no necessity
[Hale]
|
12434
|
Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary?
[Hale]
|
12435
|
The explanation of a necessity can be by a truth (which may only happen to be a necessary truth)
[Hale]
|
12436
|
Concept-identities explain how we know necessities, not why they are necessary
[Hale]
|