more on this theme     |     more from this thinker

Single Idea 1613

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique ]

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.

Gist of Idea

Logicists cheerfully accept reference to bound variables and all sorts of abstract entities

Source

Willard Quine (On What There Is [1948], p.14)

Book Ref

Quine,Willard: 'From a Logical Point of View' [Harper and Row 1963], p.14

The 29 ideas from 'On What There Is'

8455 Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
8456 Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
10241 For Quine, there is only one way to exist [Quine, by Shapiro]
4064 The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane]
19277 Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale]
12210 Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine]
8459 Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein]
16261 If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine]
4443 Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong]
1619 There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine]
19159 Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson]
8856 Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo]
7698 If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine]
15402 There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine]
1609 I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine]
1617 The word 'meaning' is only useful when talking about significance or about synonymy [Quine]
1611 Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
1610 To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine]
1612 Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine]
1613 Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
1615 Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
1614 Conceptualism holds that there are universals but they are mind-made [Quine]
1616 Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
1618 We study bound variables not to know reality, but to know what reality language asserts [Quine]
8496 What actually exists does not, of course, depend on language [Quine]
8497 An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine]
8498 Treating scattered sensations as single objects simplifies our understanding of experience [Quine]
18209 We can never translate our whole language of objects into phenomenalism [Quine]
12443 Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine]