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All the ideas for 'The philosophical basis of intuitionist logic', 'Natural Kinds' and 'The Nature of Mathematics'

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32 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy is continuous with science, and has no external vantage point [Quine]
Philosophy is an experimental science, resting on common experience [Peirce]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
5. Theory of Logic / G. Quantification / 1. Quantification
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Klein summarised geometry as grouped together by transformations [Quine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Mathematics is close to logic, but is even more abstract [Peirce]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
Mass terms just concern spread, but other terms involve both spread and individuation [Quine]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Once we know the mechanism of a disposition, we can eliminate 'similarity' [Quine]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
We judge things to be soluble if they are the same kind as, or similar to, things that do dissolve [Quine]
10. Modality / B. Possibility / 1. Possibility
Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Experience is indeed our only source of knowledge, provided we include inner experience [Peirce]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The world is one of experience, but experiences are always located among our ideas [Peirce]
14. Science / A. Basis of Science / 3. Experiment
Science is common sense, with a sophisticated method [Quine]
14. Science / C. Induction / 1. Induction
Induction is just more of the same: animal expectations [Quine]
Induction relies on similar effects following from each cause [Quine]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
Grue is a puzzle because the notions of similarity and kind are dubious in science [Quine]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
General terms depend on similarities among things [Quine]
To learn yellow by observation, must we be told to look at the colour? [Quine]
Standards of similarity are innate, and the spacing of qualities such as colours can be mapped [Quine]
Similarity is just interchangeability in the cosmic machine [Quine]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
19. Language / A. Nature of Meaning / 6. Meaning as Use
Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]
19. Language / C. Assigning Meanings / 3. Predicates
Projectible predicates can be universalised about the kind to which they refer [Quine]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
Ethics is the science of aims [Peirce]
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
Quine probably regrets natural kinds now being treated as essences [Quine, by Dennett]
If similarity has no degrees, kinds cannot be contained within one another [Quine]
Comparative similarity allows the kind 'colored' to contain the kind 'red' [Quine]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
You can't base kinds just on resemblance, because chains of resemblance are a muddle [Quine]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
It is hard to see how regularities could be explained [Quine]