Combining Texts

All the ideas for 'works', 'Intuitionism and Formalism' and 'The Nature of Mathematics'

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14 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
14782 Philosophy is an experimental science, resting on common experience [Peirce]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
14787 Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
12452 Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
14783 Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
14788 Mathematics is close to logic, but is even more abstract [Peirce]
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]
10. Modality / B. Possibility / 1. Possibility
14786 Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
14789 Experience is indeed our only source of knowledge, provided we include inner experience [Peirce]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
14785 The world is one of experience, but experiences are always located among our ideas [Peirce]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
6587 It is always wrong to believe things on insufficient evidence [Clifford]
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]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
14784 Ethics is the science of aims [Peirce]