Combining Texts

All the ideas for 'Defending the Axioms', 'Truth-makers and dependence' and 'Plato on Parts and Wholes'

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23 ideas

2. Reason / F. Fallacies / 7. Ad Hominem
15842 An ad hominem refutation is reasonable, if it uses the opponent's assumptions [Harte,V]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
17325 Truth-maker theory can't cope with non-causal dependence [Liggins]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
17318 Truthmakers for existence is fine; otherwise maybe restrict it to synthetic truths? [Liggins]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
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 / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / A. Nature of Existence / 5. Reason for Existence
17320 Either p is true or not-p is true, so something is true, so something exists [Liggins]
7. Existence / B. Change in Existence / 1. Nature of Change
15858 Traditionally, the four elements are just what persists through change [Harte,V]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17326 The dependence of {Socrates} on Socrates involves a set and a philosopher, not facts [Liggins]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
17327 Non-causal dependence is at present only dimly understood [Liggins]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
17322 Necessities supervene on everything, but don't depend on everything [Liggins]
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]
14. Science / D. Explanation / 1. Explanation / a. Explanation
17324 'Because' can signal an inference rather than an explanation [Liggins]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17321 Value, constitution and realisation are non-causal dependences that explain [Liggins]
17323 If explanations track dependence, then 'determinative' explanations seem to exist [Liggins]