Combining Texts

All the ideas for 'fragments/reports', 'Mathematics without Foundations' and 'Ontological Relativity'

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15 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
If quantification is all substitutional, there is no ontology [Quine]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Absolute ontological questions are meaningless, because the answers are circular definitions [Quine]
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
Ontology is relative to both a background theory and a translation manual [Quine]
9. Objects / F. Identity among Objects / 1. Concept of Identity
We know what things are by distinguishing them, so identity is part of ontology [Quine]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
Two things are relative - the background theory, and translating the object theory into the background theory [Quine]
19. Language / B. Reference / 1. Reference theories
Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]