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 / 4. Using Numbers / c. Counting procedure
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Numbers are just names devised for counting

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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That two twoeyed people must have four eyes is a statement about numbers, not a fact

11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
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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
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Innate truths are very uncertain and full of error, so they certainly have exceptions

12. Knowledge Sources / E. Direct Knowledge / 3. Inspiration
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A truth is hard for us to understand if it rests on nothing but inspiration

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

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

15. Nature of Minds / C. Capacities of Minds / 2. Imagination
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Only imagination can connect phenomena together in a rational way
