Combining Texts

All the ideas for 'Two Problems of Epistemology', 'works' and 'Evidentialism'

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8 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

11022

Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11065

The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]

11023

The logical connectives are 'defined' by their introduction rules [Gentzen]

11213

Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10067

Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]

11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs

19525

If the only aim is to believe truths, that justifies recklessly believing what is unsupported (if it is right) [Conee/Feldman]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure

19524

We don't have the capacity to know all the logical consequences of our beliefs [Conee/Feldman]

14. Science / A. Basis of Science / 6. Falsification

18284

Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]