Combining Texts

All the ideas for 'The Lagoon: how Aristotle invented science', 'Philosophy of Mathematics' and 'The Very Idea of a Conceptual Scheme'

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13 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
The Pre-Socratics are not simple naturalists, because they do not always 'leave the gods out' [Leroi]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Saying truths fit experience adds nothing to truth; nothing makes sentences true [Davidson]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Without the dualism of scheme and content, not much is left of empiricism [Davidson]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Different points of view make sense, but they must be plotted on a common background [Davidson]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
Criteria of translation give us the identity of conceptual schemes [Davidson]