Ideas from 'Scientific Attitude and Fallibilism' by Charles Sanders Peirce [1899], by Theme Structure

[found in 'Philosophical Writings of Peirce' by Peirce,Charles Sanders (ed/tr Buchler,Justus) [Dover 1940,0-486-20217-8]].

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6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Numbers are just names devised for counting
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
That two two-eyed people must have four eyes is a statement about numbers, not a fact
11. Knowledge Aims / B. Certain Knowledge / 4. Fallibilism
Reasoning is based on statistical induction, so it can't achieve certainty or precision
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
Innate truths are very uncertain and full of error, so they certainly have exceptions
12. Knowledge Sources / E. Direct Knowledge / 2. Inspiration
Only reason can establish where some deliverance of revelation really is inspired
If we decide an idea is inspired, we still can't be sure we have got the idea right
A truth is hard for us to understand if it rests on nothing but inspiration
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
Only imagination can connect phenomena together in a rational way