Combining Texts

All the ideas for 'Formal and Transcendental Logic', 'What Numbers Are' and 'Mathematics and the Metaphysicians'

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9 ideas

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
21223 Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol]
21222 Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
7557 To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10059 In mathematic we are ignorant of both subject-matter and truth [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
7556 A collection is infinite if you can remove some terms without diminishing its number [Russell]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
21224 Pure mathematics is the relations between all possible objects, and is thus formal ontology [Husserl, by Velarde-Mayol]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
7554 Self-evidence is often a mere will-o'-the-wisp [Russell]