Combining Texts

All the ideas for 'Through the Looking Glass', 'On the Frame of Reference' and 'Counting and the Natural Numbers'

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5 ideas

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

10009	Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin]
	Full Idea: In a famous paper, Wallace argued that all interpretations of quantifiers (including the substitutional interpretation) are, in the end, variants of that proposed by Tarski (in 1936).
	From: report of Wallace, J (On the Frame of Reference [1970]) by Thomas Baldwin - Interpretations of Quantifiers
	A reaction: A significant-looking pointer. We must look elsewhere for Tarski's account, which will presumably subsume the objectual interpretation as well. The ontology of Tarski's account of truth is an enduring controversy.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

17423	The essence of natural numbers must reflect all the functions they perform [Sicha]
	Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform.
	From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
	A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'.

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17425	To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
	Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed.
	From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3)

17424	Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
	Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities.
	From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)

7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing

21982	I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
	Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
	From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
	A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.