Combining Texts

Ideas for 'Mahaprajnaparamitashastra', 'Presidential Address of Am. Math. Soc' and 'Plurals and Complexes'

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6 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

10247	We have no adequate logic at the moment, so mathematicians must create one [Veblen]
	Full Idea: Formal logic has to be taken over by mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so.
	From: Oswald Veblen (Presidential Address of Am. Math. Soc [1924], 141), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: This remark was made well after Frege, but before the advent of Gödel and Tarski. That implies that he was really thinking of meta-logic.

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions

10671	Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
	Full Idea: If we extend the power of language with plural definite descriptions, these would pick out the largest class of things that fit the description.
	From: Keith Hossack (Plurals and Complexes [2000], 3)

5. Theory of Logic / G. Quantification / 6. Plural Quantification

10666	Plural reference will refer to complex facts without postulating complex things [Hossack]
	Full Idea: It may be that plural reference gives atomism the resources to state complex facts without needing to refer to complex things.
	From: Keith Hossack (Plurals and Complexes [2000], 1)
	A reaction: This seems the most interesting metaphysical implication of the possibility of plural quantification.

10675	A plural comprehension principle says there are some things one of which meets some condition [Hossack]
	Full Idea: Singular comprehension principles have a bad reputation, but the plural comprehension principle says that given a condition on individuals, there are some things such that something is one of them iff it meets the condition.
	From: Keith Hossack (Plurals and Complexes [2000], 4)

10669	Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
	Full Idea: If all properties are distributive, plural reference is just a handy abbreviation to avoid repetition (as in 'A and B are hungry', to avoid 'A is hungry and B is hungry'), but not all properties are distributive (as in 'some people surround a table').
	From: Keith Hossack (Plurals and Complexes [2000], 2)
	A reaction: The characteristic examples to support plural quantification involve collective activity and relations, which might be weeded out of our basic ontology, thus leaving singular quantification as sufficient.

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox

10673	Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
	Full Idea: In a plural language we can discuss without fear of inconsistency the things that are not members of themselves.
	From: Keith Hossack (Plurals and Complexes [2000], 4)
	A reaction: [see Hossack for details]