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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 Asserting not-p is saying p is false [Russell]
16484 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]
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]
16487 Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell]
16475 A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell]
16482 All our knowledge (if verbal) is general, because all sentences contain general words [Russell]
16476 For simple words, a single experience can show that they are true [Russell]
16485 Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell]
16478 A mother cat is paralysed if equidistant between two needy kittens [Russell]
2947 Questions wouldn't lead anywhere without the law of excluded middle [Russell]
4758 Naïve realism leads to physics, but physics then shows that naïve realism is false [Russell]