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Single Idea 11016
[filed under theme 7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
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Full Idea
We must ask whether a language without vagueness would be usable at all.
Gist of Idea
Would a language without vagueness be usable at all?
Source
Stephen Read (Thinking About Logic [1995], Ch.7)
Book Ref
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.178
A Reaction
Popper makes a similar remark somewhere, with which I heartily agreed. This is the idea of 'spreading the word' over the world, which seems the right way of understanding it.
The
42 ideas
from 'Thinking About Logic'
10966
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A proposition objectifies what a sentence says, as indicative, with secure references
[Read]
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10983
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Knowledge of possible worlds is not causal, but is an ontology entailed by semantics
[Read]
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10982
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How can modal Platonists know the truth of a modal proposition?
[Read]
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10987
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Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism'
[Read]
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10985
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We should exclude second-order logic, precisely because it captures arithmetic
[Read]
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10970
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A theory of logical consequence is a conceptual analysis, and a set of validity techniques
[Read]
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10984
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Logical consequence isn't just a matter of form; it depends on connections like round-square
[Read]
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10973
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A theory is logically closed, which means infinite premisses
[Read]
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10978
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In second-order logic the higher-order variables range over all the properties of the objects
[Read]
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10971
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A logical truth is the conclusion of a valid inference with no premisses
[Read]
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10988
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Any first-order theory of sets is inadequate
[Read]
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10974
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Compactness is when any consequence of infinite propositions is the consequence of a finite subset
[Read]
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10975
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Compactness does not deny that an inference can have infinitely many premisses
[Read]
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10977
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Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite)
[Read]
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10976
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Compactness makes consequence manageable, but restricts expressive power
[Read]
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10972
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The non-emptiness of the domain is characteristic of classical logic
[Read]
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10986
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Not all validity is captured in first-order logic
[Read]
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10979
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Although second-order arithmetic is incomplete, it can fully model normal arithmetic
[Read]
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10980
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Second-order arithmetic covers all properties, ensuring categoricity
[Read]
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10981
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A possible world is a determination of the truth-values of all propositions of a domain
[Read]
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10989
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The standard view of conditionals is that they are truth-functional
[Read]
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10992
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The point of conditionals is to show that one will accept modus ponens
[Read]
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10997
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Von Neumann numbers are helpful, but don't correctly describe numbers
[Read]
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11001
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Equating necessity with truth in every possible world is the S5 conception of necessity
[Read]
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11000
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If worlds are concrete, objects can't be present in more than one, and can only have counterparts
[Read]
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10998
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The mind abstracts ways things might be, which are nonetheless real
[Read]
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11004
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Necessity is provability in S4, and true in all worlds in S5
[Read]
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10996
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Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions)
[Read]
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10995
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A haecceity is a set of individual properties, essential to each thing
[Read]
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11011
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Same say there are positive, negative and neuter free logics
[Read]
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11007
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Quantifiers are second-order predicates
[Read]
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11005
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Negative existentials with compositionality make the whole sentence meaningless
[Read]
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11012
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A 'supervaluation' gives a proposition consistent truth-value for classical assignments
[Read]
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11013
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Identities and the Indiscernibility of Identicals don't work with supervaluations
[Read]
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11014
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Self-reference paradoxes seem to arise only when falsity is involved
[Read]
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11018
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There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers
[Read]
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11016
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Would a language without vagueness be usable at all?
[Read]
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11019
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Supervaluations say there is a cut-off somewhere, but at no particular place
[Read]
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11017
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Some people even claim that conditionals do not express propositions
[Read]
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11025
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Infinite cuts and successors seems to suggest an actual infinity there waiting for us
[Read]
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11020
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Realisms like the full Comprehension Principle, that all good concepts determine sets
[Read]
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11024
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Semantics must precede proof in higher-order logics, since they are incomplete
[Read]
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