Combining Texts

All the ideas for 'Philosophical Remarks', 'Letters to Queen Charlotte' and 'Mathematics, Science and Language'

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10 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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
Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]
9. Objects / A. Existence of Objects / 3. Objects in Thought
An 'object' is just what can be referred to without possible non-existence [Wittgenstein]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
Intelligible truth is independent of any external things or experiences [Leibniz]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Language pictures the essence of the world [Wittgenstein]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
You can't believe it if you can't imagine a verification for it [Wittgenstein]