Combining Texts

All the ideas for 'Letters to Jourdain', 'On the Infinite' and 'Reply to First Objections'

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17 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Any object can have many different names, each with a distinct sense [Frege]
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]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
I can't be unaware of anything which is in me [Descartes]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
We understand new propositions by constructing their sense from the words [Frege]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
Senses can't be subjective, because propositions would be private, and disagreement impossible [Frege]
23. Ethics / F. Existentialism / 5. Existence-Essence
Essence must be known before we discuss existence [Descartes]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
We can't prove a first cause from our inability to grasp infinity [Descartes]