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All the ideas for '', 'Philosophy of Mathematics' and 'Persistence, Change and Explanation'

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16 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
5. Theory of Logic / L. Paradox / 2. Aporiai
By using aporiai as his start, Aristotle can defer to the wise, as well as to the many [Haslanger]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / D. Theories of Reality / 1. Ontologies
Ontology disputes rest on more basic explanation disputes [Haslanger]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
The persistence of objects seems to be needed if the past is to explain the present [Haslanger]
Persistence makes change and its products intelligible [Haslanger]
9. Objects / E. Objects over Time / 5. Temporal Parts
We must explain change amongst 'momentary entities', or else the world is inexplicable [Haslanger]
If the things which exist prior to now are totally distinct, they need not have existed [Haslanger]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Natural explanations give the causal interconnections [Haslanger]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Best explanations, especially natural ones, need grounding, notably by persistent objects [Haslanger]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]