Combining Texts

All the ideas for 'The Roots of Reference', 'What is Justified Belief?' and 'On the Infinite'

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15 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
I aim to establish certainty for mathematical methods [Hilbert]
We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Only the finite can bring certainty to the infinite [Hilbert]
No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
A belief can be justified when the person has forgotten the evidence for it [Goldman]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman]
16. Persons / C. Self-Awareness / 1. Introspection
Introspection is really retrospection; my pain is justified by a brief causal history [Goldman]