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Single Idea 9884

[filed under theme 7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete ]

Full Idea

The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions.

Gist of Idea

The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy

Source

Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)

Book Ref

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.239

A Reaction

This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't.

Related Idea

Idea 9918 Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen]

The 27 ideas from 'Frege philosophy of mathematics'

9848 Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
9993 There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
18257 Why should the limit of measurement be points, not intervals? [Dummett]
18255 Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
9896 A prime number is one which is measured by a unit alone [Dummett]
9895 A number is a multitude composed of units [Dummett]
9820 In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
9829 The identity of a number may be fixed by something outside structure - by counting [Dummett]
9828 Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
9833 To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
9836 Fregean semantics assumes a domain articulated into individual objects [Dummett]
9842 Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
9847 A contextual definition permits the elimination of the expression by a substitution [Dummett]
9852 We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
9849 Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
9850 An argument for conceptual priority is greater simplicity in explanation [Dummett]
9857 We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
9869 Realism is just the application of two-valued semantics to sentences [Dummett]
9858 Abstract objects nowadays are those which are objective but not actual [Dummett]
9859 It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
9860 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9872 Abstract objects need the context principle, since they can't be encountered directly [Dummett]
9873 Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
9876 Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
9884 The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
9880 Nominalism assumes unmediated mental contact with objects [Dummett]
9885 The existence of abstract objects is a pseudo-problem [Dummett]