Combining Philosophers

All the ideas for William S. Jevons, Gerhard Gentzen and Roy Sorensen

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27 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9136 The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen]
2. Reason / B. Laws of Thought / 1. Laws of Thought
9131 Two long understandable sentences can have an unintelligible conjunction [Sorensen]
3. Truth / B. Truthmakers / 6. Making Negative Truths
9139 If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
9140 Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen]
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 / D. Assumptions for Logic / 1. Bivalence
9119 No attempt to deny bivalence has ever been accepted [Sorensen]
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]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
9135 We now see that generalizations use variables rather than abstract entities [Sorensen]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13832 Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
5. Theory of Logic / L. Paradox / 3. Antinomies
9125 Denying problems, or being romantically defeated by them, won't make them go away [Sorensen]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
9137 Banning self-reference would outlaw 'This very sentence is in English' [Sorensen]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8628 I hold that algebra and number are developments of logic [Jevons]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
9116 Vague words have hidden boundaries [Sorensen]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9132 An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
9128 It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen]
9130 Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
9118 The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen]
12. Knowledge Sources / B. Perception / 5. Interpretation
9124 We are unable to perceive a nose (on the back of a mask) as concave [Sorensen]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
9126 Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
9121 Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
9134 The negation of a meaningful sentence must itself be meaningful [Sorensen]
19. Language / D. Propositions / 4. Mental Propositions
9133 Propositions are what settle problems of ambiguity in sentences [Sorensen]
25. Social Practice / A. Freedoms / 4. Free market
9129 I can buy any litre of water, but not every litre of water [Sorensen]
28. God / A. Divine Nature / 4. Divine Contradictions
9122 God cannot experience unwanted pain, so God cannot understand human beings [Sorensen]