Combining Texts

All the ideas for 'Believing the Axioms I', 'Theology and Verification' and 'On Nature Itself (De Ipsa Natura)'

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13013 The Axiom of Extensionality seems to be analytic [Maddy]
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
12756 Substance is a force for acting and being acted upon [Leibniz]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
12755 Final causes can help with explanations in physics [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
12760 Something rather like souls (though not intelligent) could be found everywhere [Leibniz]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
12759 There are atoms of substance, but no atoms of bulk or extension [Leibniz]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
12718 Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
11854 If there is some trace of God in things, that would explain their natural force [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
12758 It is plausible to think substances contain the same immanent force seen in our free will [Leibniz]
28. God / C. Attitudes to God / 2. Pantheism
19408 To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz]
29. Religion / D. Religious Issues / 1. Religious Commitment / c. Religious Verification
1470 Belief in an afterlife may be unverifiable in this life, but it will be verifiable after death [Hick, by PG]
1471 It may be hard to verify that we have become immortal, but we could still then verify religious claims [Hick, by PG]
29. Religion / D. Religious Issues / 1. Religious Commitment / d. Religious Falsification
1469 Some things (e.g. a section of the expansion of PI) can be verified but not falsified [Hick, by PG]