Combining Texts

Ideas for 'fragments/reports', 'On the Syllogism IV' and 'On What There Is'

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4 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

1613	Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
	Full Idea: The logicism of Frege, Russell, Whitehead, Church and Carnap condones the use of bound variables or reference to abstract entities known and unknown, specifiable and unspecifiable, indiscriminately.
	From: Willard Quine (On What There Is [1948], p.14)

6. Mathematics / C. Sources of Mathematics / 7. Formalism

1616	Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
	Full Idea: The formalism of Hilbert keeps classical maths as a play of insignificant notations. Agreement is found among the rules which, unlike the notations, are quite significant and intelligible.
	From: Willard Quine (On What There Is [1948], p.15)

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism

1615	Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
	Full Idea: The intuitionism of Poincaré, Brouwer, Weyl and others holds that classes are invented, and accepts reference to abstract entities only if they are constructed from pre-specified ingredients.
	From: Willard Quine (On What There Is [1948], p.14)

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism

1614	Conceptualism holds that there are universals but they are mind-made [Quine]
	Full Idea: Conceptualism holds that there are universals but they are mind-made.
	From: Willard Quine (On What There Is [1948], p.14)