Ideas from 'Frege Philosophy of Language (2nd ed)' by Michael Dummett [1973], by Theme Structure
[found in 'Frege Philosophy of Language' by Dummett,Michael [Duckworth 1981,0-7156-1649-8]].
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2. Reason / A. Nature of Reason / 5. Objectivity
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17621
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What matters in mathematics is its objectivity, not the existence of the objects
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
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10537
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The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}}
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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10542
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To associate a cardinal with each set, we need the Axiom of Choice to find a representative
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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10554
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Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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10552
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Intuitionism says that totality of numbers is only potential, but is still determinate
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7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
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10540
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We can't say that light is concrete but radio waves abstract
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10515
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Ostension is possible for concreta; abstracta can only be referred to via other objects [Hale]
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10544
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The concrete/abstract distinction seems crude: in which category is the Mistral?
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10546
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We don't need a sharp concrete/abstract distinction
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7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
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10548
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The context principle for names rules out a special philosophical sense for 'existence'
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10281
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The objects we recognise the world as containing depends on the structure of our language
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8. Modes of Existence / D. Universals / 1. Universals
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10532
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We can understand universals by studying predication
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8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
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10534
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'Nominalism' used to mean denial of universals, but now means denial of abstract objects
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9. Objects / A. Existence of Objects / 1. Physical Objects
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10541
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Concrete objects such as sounds and smells may not be possible objects of ostension
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9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
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10545
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Abstract objects may not cause changes, but they can be the subject of change
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9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
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10555
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If we can intuitively apprehend abstract objects, this makes them observable and causally active
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9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
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10543
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Abstract objects must have names that fall within the range of some functional expression
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9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
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10320
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If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Hale]
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10547
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Abstract objects can never be confronted, and need verbal phrases for reference
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9. Objects / A. Existence of Objects / 3. Objects in Thought
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10531
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There is a modern philosophical notion of 'object', first introduced by Frege
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18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
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19168
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Concepts only have a 'functional character', because they map to truth values, not objects [Davidson]
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18. Thought / E. Abstraction / 7. Abstracta by Equivalence
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10549
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Since abstract objects cannot be picked out, we must rely on identity statements
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19. Language / B. Reference / 3. Direct Reference / b. Causal reference
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10516
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A realistic view of reference is possible for concrete objects, but not for abstract objects [Hale]
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