Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, Demetris Portides and Paul Thagard

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30 ideas

2. Reason / A. Nature of Reason / 6. Coherence
Coherence problems have positive and negative restraints; solutions maximise constraint satisfaction [Thagard]
Coherence is explanatory, deductive, conceptual, analogical, perceptual, and deliberative [Thagard]
Explanatory coherence needs symmetry,explanation,analogy,data priority, contradiction,competition,acceptance [Thagard]
3. Truth / A. Truth Problems / 6. Verisimilitude
Verisimilitude comes from including more phenomena, and revealing what underlies [Thagard]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
For intuitionists excluded middle is an outdated historical convention [Brouwer]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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
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 / g. Applying mathematics
Scientific laws largely rest on the results of counting and measuring [Brouwer]
Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionists only accept denumerable sets [Brouwer]
Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
14. Science / B. Scientific Theories / 1. Scientific Theory
Neither a priori rationalism nor sense data empiricism account for scientific knowledge [Thagard]
14. Science / B. Scientific Theories / 7. Scientific Models
Theoretical models can represent, by mapping onto the data-models [Portides]
In the 'received view' models are formal; the 'semantic view' emphasises representation [Portides, by PG]
Representational success in models depends on success of their explanations [Portides]
The best model of the atomic nucleus is the one which explains the most results [Portides]
'Model' belongs in a family of concepts, with representation, idealisation and abstraction [Portides]
Models are theory-driven, or phenomenological (more empirical and specific) [Portides]
14. Science / C. Induction / 6. Bayes's Theorem
Bayesian inference is forced to rely on approximations [Thagard]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
1: Coherence is a symmetrical relation between two propositions [Thagard, by Smart]
2: An explanation must wholly cohere internally, and with the new fact [Thagard, by Smart]
3: If an analogous pair explain another analogous pair, then they all cohere [Thagard, by Smart]
4: For coherence, observation reports have a degree of intrinsic acceptability [Thagard, by Smart]
5: Contradictory propositions incohere [Thagard, by Smart]
6: A proposition's acceptability depends on its coherence with a system [Thagard, by Smart]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
General theories may be too abstract to actually explain the mechanisms [Portides]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
The best theory has the highest subjective (Bayesian) probability? [Thagard]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]