Combining Texts

All the ideas for 'The Problem of Empty Names', 'Plato on Parts and Wholes' and 'On the Infinite'

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18 ideas

2. Reason / F. Fallacies / 7. Ad Hominem
15842 An ad hominem refutation is reasonable, if it uses the opponent's assumptions [Harte,V]
4. Formal Logic / G. Formal Mereology / 1. Mereology
15841 Mereology began as a nominalist revolt against the commitments of set theory [Harte,V]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
18946 Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12456 I aim to establish certainty for mathematical methods [Hilbert]
12461 We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
12462 Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
12455 The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457 There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
7. Existence / B. Change in Existence / 1. Nature of Change
15858 Traditionally, the four elements are just what persists through change [Harte,V]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
15848 Mereology treats constitution as a criterion of identity, as shown in the axiom of extensionality [Harte,V]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
15837 What exactly is a 'sum', and what exactly is 'composition'? [Harte,V]
15839 If something is 'more than' the sum of its parts, is the extra thing another part, or not? [Harte,V]
15838 The problem with the term 'sum' is that it is singular [Harte,V]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636 My theory aims at the certitude of mathematical methods [Hilbert]