Combining Texts

All the ideas for 'Believing the Axioms I', 'Why coherence is not enough' and 'Intro to 'Philosophical Essays''

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15 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy

9786	Philosophers working like teams of scientists is absurd, yet isolation is hard [Cartwright,R]

2. Reason / A. Nature of Reason / 6. Coherence

9784	A false proposition isn't truer because it is part of a coherent system [Cartwright,R]

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]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma

8840	There are five possible responses to the problem of infinite regress in justification [Cleve]

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism

8841	Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve]