Combining Texts

All the ideas for 'Abstract of 'The Fourfold Root'', 'The Limits of Contingency' and 'Logicism in the 21st Century'

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22 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
4187 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
18851 Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8784 Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787 The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8788 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
9. Objects / A. Existence of Objects / 4. Impossible objects
18852 A Meinongian principle might say that there is an object for any modest class of properties [Rosen]
10. Modality / A. Necessity / 5. Metaphysical Necessity
18850 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen]
18849 Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen]
18857 Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen]
18858 Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen]
18856 Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen]
10. Modality / A. Necessity / 6. Logical Necessity
18848 Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen]
10. Modality / B. Possibility / 3. Combinatorial possibility
18855 Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
4192 All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
18853 A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen]
11. Knowledge Aims / A. Knowledge / 2. Understanding
4190 All understanding is an immediate apprehension of the causal relation [Schopenhauer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
4191 What we know in ourselves is not a knower but a will [Schopenhauer]
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
21368 The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
8786 One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
18854 The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
4189 Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer]