Combining Texts

All the ideas for 'Externalism', 'Mathematics, Science and Language' and 'Believing the Axioms I'

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29 ideas

1. Philosophy / H. Continental Philosophy / 4. Linguistic Structuralism
6161 Structuralism is neo-Kantian idealism, with language playing the role of categories of understanding [Rowlands]
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]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
6163 If bivalence is rejected, then excluded middle must also be rejected [Rowlands]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
6155 Supervenience is a one-way relation of dependence or determination between properties [Rowlands]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
6154 It is argued that wholes possess modal and counterfactual properties that parts lack [Rowlands]
9. Objects / F. Identity among Objects / 4. Type Identity
6157 Tokens are dated, concrete particulars; types are their general properties or kinds [Rowlands]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
6159 Strong idealism is the sort of mess produced by a Cartesian separation of mind and world [Rowlands]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
6152 Minds are rational, conscious, subjective, self-knowing, free, meaningful and self-aware [Rowlands]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
6173 Content externalism implies that we do not have privileged access to our own minds [Rowlands]
6174 If someone is secretly transported to Twin Earth, others know their thoughts better than they do [Rowlands]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
6158 Supervenience of mental and physical properties often comes with token-identity of mental and physical particulars [Rowlands]
18. Thought / C. Content / 1. Content
6168 The content of a thought is just the meaning of a sentence [Rowlands]
20. Action / A. Definition of Action / 4. Action as Movement
6167 Action is bodily movement caused by intentional states [Rowlands]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
6177 Moral intuition seems unevenly distributed between people [Rowlands]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
6156 The 17th century reintroduced atoms as mathematical modes of Euclidean space [Rowlands]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
6170 Natural kinds are defined by their real essence, as in gold having atomic number 79 [Rowlands]
27. Natural Reality / G. Biology / 4. Ecology
6178 It is common to see the value of nature in one feature, such as life, diversity, or integrity [Rowlands]