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]].

green numbers give full details    |     back to texts     |     expand these ideas

---

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 / 2. 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 / i. Conceptual priority

9849	Maybe a concept is 'prior' to another if it can be defined without the second concept

9850	An argument for conceptual priority is greater simplicity in explanation

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 / 3. Points in Space

18257

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