Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Geoffrey Gorham and Harold Hodes

expand these ideas     |    start again     |     specify just one area for these philosophers

29 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
10017 Truth in a model is more tractable than the general notion of truth [Hodes]
10018 Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes]
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 / A. Overview of Logic / 7. Second-Order Logic
10015 Higher-order logic may be unintelligible, but it isn't set theory [Hodes]
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15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]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 / D. Assumptions for Logic / 4. Identity in Logic
10011 Identity is a level one relation with a second-order definition [Hodes]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10016 When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
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 / a. Numbers
10027 Mathematics is higher-order modal logic [Hodes]
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 / f. Arithmetic
10026 Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
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 / 1. Mathematical Platonism / a. For mathematical platonism
10021 It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
10022 Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
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 / 7. Fictionalism
10023 Talk of mirror images is 'encoded fictions' about real facts [Hodes]
14. Science / A. Basis of Science / 6. Falsification
22189 Why abandon a theory if you don't have a better one? [Gorham]
22190 If a theory is more informative it is less probable [Gorham]
14. Science / B. Scientific Theories / 1. Scientific Theory
22192 Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham]
22194 Structural Realism says mathematical structures persist after theory rejection [Gorham]
22195 Structural Realists must show the mathematics is both crucial and separate [Gorham]
14. Science / B. Scientific Theories / 3. Instrumentalism
22196 For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham]
22197 Theories aren't just for organising present experience if they concern the past or future [Gorham]
14. Science / D. Explanation / 2. Types of Explanation / d. Consilience
22193 Consilience makes the component sciences more likely [Gorham]
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]
26. Natural Theory / A. Speculations on Nature / 1. Nature
22198 Aristotelian physics has circular celestial motion and linear earthly motion [Gorham]