### Ideas from 'Frege philosophy of mathematics' by Michael Dummett [1991], by Theme Structure

#### [found in 'Frege: philosophy of mathematics' by Dummett,Michael [Duckworth 1991,0-7156-2660-4]].

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###### 2. Reason / D. Definition / 7. Contextual Definition
 9847 A contextual definition permits the elimination of the expression by a substitution
###### 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
 9820 In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical
###### 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
 9896 A prime number is one which is measured by a unit alone
###### 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
 18255 Addition of quantities is prior to ordering, as shown in cyclic domains like angles
###### 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
 9895 A number is a multitude composed of units
###### 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
 9852 We understand 'there are as many nuts as apples' as easily by pairing them as by counting them
###### 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
 9829 The identity of a number may be fixed by something outside structure - by counting
 9828 Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1
###### 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
 9876 Set theory isn't part of logic, and why reduce to something more complex?
###### 7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
 9884 The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy
###### 7. Existence / D. Theories of Reality / 1. Realism
 9869 Realism is just the application of two-valued semantics to sentences
###### 8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
 9880 Nominalism assumes unmediated mental contact with objects
###### 9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
 9885 The existence of abstract objects is a pseudo-problem
###### 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
 9858 Abstract objects nowadays are those which are objective but not actual
 9859 It is absurd to deny the Equator, on the grounds that it lacks causal powers
 9860 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object
###### 9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
 9872 Abstract objects need the context principle, since they can't be encountered directly
###### 9. Objects / F. Identity among Objects / 2. Defining Identity
 9848 Content is replaceable if identical, so replaceability can't define identity [Dummett]
 9842 Frege introduced criteria for identity, but thought defining identity was circular
###### 18. Thought / D. Concepts / 4. Structure of Concepts / h. Conceptual priority
 9850 An argument for conceptual priority is greater simplicity in explanation
 9849 Maybe a concept is 'prior' to another if it can be defined without the second concept
###### 18. Thought / E. Abstraction / 1. Abstract Thought
 9873 Abstract terms are acceptable as long as we know how they function linguistically
###### 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
 9993 There is no reason why abstraction by equivalence classes should be called 'logical' [Tait]
 9857 We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus'
###### 18. Thought / E. Abstraction / 8. Abstractionism Critique
 9833 To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too
###### 19. Language / C. Assigning Meanings / 5. Fregean Semantics
 9836 Fregean semantics assumes a domain articulated into individual objects
###### 27. Natural Reality / C. Space-Time / 1. Space / c. Points in space
 18257 Why should the limit of measurement be points, not intervals?