Combining Texts

All the ideas for 'The Gettier Problem', 'On the Infinite' and 'Nihilism without Self-Contradiction'

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14 ideas

2. Reason / F. Fallacies / 7. Ad Hominem
We should always apply someone's theory of meaning to their own utterances [Liggins]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
We normally formalise 'There are Fs' with singular quantification and predication, but this may be wrong [Liggins]
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
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]
Only the finite can bring certainty to the infinite [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]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Nihilists needn't deny parts - they can just say that some of the xs are among the ys [Liggins]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]