Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Charles Parsons and Niccolo Machiavelli

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27 ideas

4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9470 Modal logic is not an extensional language [Parsons,C]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
12452 Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13418 The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9469 Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
9468 On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18247 Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
12451 Scientific laws largely rest on the results of counting and measuring [Brouwer]
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
13419 If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
12454 Intuitionists only accept denumerable sets [Brouwer]
12453 Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
8728 Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10117 Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
7127 If men are good you should keep promises, but they aren't, so you needn't [Machiavelli]
24. Political Theory / B. Nature of a State / 3. Constitutions
6309 The principle foundations of all states are good laws and good armies [Machiavelli]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
6306 People are vengeful, so be generous to them, or destroy them [Machiavelli]
6305 To retain a conquered state, wipe out the ruling family, and preserve everything else [Machiavelli]
6308 A sensible conqueror does all his harmful deeds immediately, because people soon forget [Machiavelli]
25. Social Practice / E. Policies / 1. War / a. Just wars
6307 A desire to conquer, and men who do it, are always praised, or not blamed [Machiavelli]
25. Social Practice / E. Policies / 2. Religion in Society
7486 Machiavelli emancipated politics from religion [Machiavelli, by Watson]
19813 All legislators invoke God in support of extraordinary laws, because their justification is not obvious [Machiavelli]
7126 Rulers should preserve the foundations of religion, to ensure good behaviour and unity [Machiavelli]