Combining Texts

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

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16 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
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 / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
An existing thing is even greater if its non-existence is inconceivable [Anselm]
Conceiving a greater being than God leads to absurdity [Anselm]
Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm]
If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm]
A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm]
The word 'God' can be denied, but understanding shows God must exist [Anselm]
Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm]
Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm]