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 1940,0486202178]].
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6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
14775

Numbers are just names devised for counting

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
14776

That two twoeyed people must have four eyes is a statement about numbers, not a fact

11. Knowledge Aims / B. Certain Knowledge / 4. Fallibilism
14770

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
14774

Innate truths are very uncertain and full of error, so they certainly have exceptions

12. Knowledge Sources / E. Direct Knowledge / 2. Inspiration
14771

Only reason can establish where some deliverance of revelation really is inspired

14773

A truth is hard for us to understand if it rests on nothing but inspiration

14772

If we decide an idea is inspired, we still can't be sure we have got the idea right

15. Nature of Minds / C. Capacities of Minds / 2. Imagination
14769

Only imagination can connect phenomena together in a rational way
