Combining Texts

All the ideas for 'The Architecture of Theories', 'Believing the Axioms I' and 'How to Make our Ideas Clear'

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18 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
7661 Truth is the opinion fated to be ultimately agreed by all investigators [Peirce]
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]
11. Knowledge Aims / A. Knowledge / 2. Understanding
19089 Our whole conception of an object is its possible practical consequences [Peirce]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
7660 We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
14802 Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
14906 Non-positivist verificationism says only take a hypothesis seriously if it is scientifically based and testable [Ladyman/Ross on Peirce]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
14800 The world is full of variety, but laws seem to produce uniformity [Peirce]
27. Natural Reality / G. Biology / 3. Evolution
14801 Darwinian evolution is chance, with the destruction of bad results [Peirce]