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Single Idea 16475
[filed under theme 5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
]
Full Idea
A predicate is 'heterological' when it cannot be predicated of itself; thus 'long' is heterological because it is not a long word, but 'short' is homological. So is 'heterological' heterological? Either answer leads to a contradiction.
Gist of Idea
A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no!
Source
Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5)
Book Ref
Russell,Bertrand: 'An Inquiry into Meaning and Truth' [Penguin 1967], p.75
A Reaction
[Grelling's Paradox] Yes: 'heterological' is heterological because it isn't heterological; No: it isn't, because it is. Russell says we therefore need a hierarchy of languages (types), and the word 'word' is outside the system.
The
15 ideas
from 'An Inquiry into Meaning and Truth'
16477
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Asserting not-p is saying p is false
[Russell]
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16484
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There are four experiences that lead us to talk of 'some' things
[Russell]
|
16486
|
The physical world doesn't need logic, but the mental world does
[Russell]
|
16483
|
Disjunction may also arise in practice if there is imperfect memory.
[Russell]
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16480
|
A disjunction expresses indecision
[Russell]
|
16479
|
'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs
[Russell]
|
16481
|
'Or' expresses a mental state, not something about the world
[Russell]
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16487
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Maybe the 'or' used to describe mental states is not the 'or' of logic
[Russell]
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16475
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A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no!
[Russell]
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16482
|
All our knowledge (if verbal) is general, because all sentences contain general words
[Russell]
|
16476
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For simple words, a single experience can show that they are true
[Russell]
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16485
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Perception can't prove universal generalisations, so abandon them, or abandon empiricism?
[Russell]
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16478
|
A mother cat is paralysed if equidistant between two needy kittens
[Russell]
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2947
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Questions wouldn't lead anywhere without the law of excluded middle
[Russell]
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4758
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Naïve realism leads to physics, but physics then shows that naïve realism is false
[Russell]
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