Ideas from 'Frege philosophy of mathematics' by Michael Dummett [1991], by Theme Structure
[found in 'Frege: philosophy of mathematics' by Dummett,Michael [Duckworth 1991,0715626604]].
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1. Philosophy / F. Analytic Philosophy / 1. Analysis
9841

Frege was the first to give linguistic answers to nonlinguistic questions

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 higherorder logics they are purely logical

6. Mathematics / A. Nature of Mathematics / 3. 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. 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 / 3. Numbers / o. Units
9895

A number is a multitude composed of units

6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
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 / 6. 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?

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
9875

Frege was completing Bolzano's work, of expelling intuition from number theory and analysis

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
9884

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

7. Existence / D. Theories of Reality / 1. Realism
9869

Realism is just the application of twovalued 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 pseudoproblem

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 truthconditions, 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

9842

Frege introduced criteria for identity, but thought defining identity was circular

18. Thought / D. Concepts / 3. 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 / D. Concepts / 6. Abstract Concepts / a. Abstract concepts
9873

Abstract terms are acceptable as long as we know how they function linguistically

18. Thought / D. Concepts / 6. Abstract Concepts / g. Abstracta by equivalence
9857

We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus'

18. Thought / D. Concepts / 6. Abstract Concepts / h. Abstractionism critique
9833

To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too

19. Language / C. Semantics / 2. Fregean Semantics
9836

Fregean semantics assumes a domain articulated into individual objects

26. Natural Theory / B. Concepts of Nature / 3. Space / b. Points in space
18257

Why should the limit of measurement be points, not intervals?
