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Single Idea 11018
[filed under theme 4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
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Full Idea
In fuzzy logic, besides fuzzy predicates, which define fuzzy sets, there are also fuzzy quantifiers (such as 'most' and 'few') and fuzzy modifiers (such as 'usually').
Gist of Idea
There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers
Source
Stephen Read (Thinking About Logic [1995], Ch.7)
Book Ref
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.189
The
49 ideas
from Stephen Read
14187
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If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter
[Read]
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14188
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Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible
[Read]
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14182
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If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence
[Read]
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14184
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In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway
[Read]
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14186
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Logical connectives contain no information, but just record combination relations between facts
[Read]
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14185
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Conditionals are just a shorthand for some proof, leaving out the details
[Read]
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14183
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Maybe arguments are only valid when suppressed premises are all stated - but why?
[Read]
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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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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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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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10986
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Not all validity is captured in first-order logic
[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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10985
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We should exclude second-order logic, precisely because it captures arithmetic
[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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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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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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10992
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The point of conditionals is to show that one will accept modus ponens
[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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10995
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A haecceity is a set of individual properties, essential to each thing
[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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10996
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Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions)
[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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10997
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Von Neumann numbers are helpful, but don't correctly describe numbers
[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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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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11013
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Identities and the Indiscernibility of Identicals don't work with supervaluations
[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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11005
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Negative existentials with compositionality make the whole sentence meaningless
[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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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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11018
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There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers
[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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11020
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Realisms like the full Comprehension Principle, that all good concepts determine sets
[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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11024
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Semantics must precede proof in higher-order logics, since they are incomplete
[Read]
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