Combining Texts

All the ideas for 'Mind and Its Place in Nature', 'Quine on Quantifying In' and 'Intros to Russell's 'Essays in Analysis''

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5 ideas

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

12220	Is it the sentence-token or the sentence-type that has a logical form? [Fine,K]
	Full Idea: Do we attribute a logical form to a sentence token because it is a token of a type with that form, or do we attribute a logical form to a sentence type because it is a type of a token with that form?
	From: Kit Fine (Quine on Quantifying In [1990], p.110)
	A reaction: Since I believe in propositions (as the unambiguous thought that lies behind a sentence), I take it that logical form concerns propositions, though strict logicians don't like this, for fear that logic spills into psychology.

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

12222	Substitutional quantification is referential quantification over expressions [Fine,K]
	Full Idea: Substitutional quantification may be regarded as referential quantification over expressions.
	From: Kit Fine (Quine on Quantifying In [1990], p.124)
	A reaction: This is an illuminating gloss. Does such quantification involve some ontological commitment to expressions? I feel an infinite regress looming.

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox

21554	Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
	Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom.

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox

21553	It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
	Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: Formulated by Burali-Forti in 1897.

12. Knowledge Sources / B. Perception / 6. Inference in Perception

7628	Broad rejects the inferential component of the representative theory [Broad, by Maund]
	Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory.
	From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1
	A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises.