Combining Texts

All the ideas for 'A Slim Book about Narrow Content', 'Brains and Behaviour' and 'Elements of Geometry'

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31 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
Science is in the business of carving nature at the joints [Segal]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
Psychology studies the way rationality links desires and beliefs to causality [Segal]
2. Reason / E. Argument / 6. Conclusive Proof
Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
A unit is that according to which each existing thing is said to be one [Euclid]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Is 'Hesperus = Phosphorus' metaphysically necessary, but not logically or epistemologically necessary? [Segal]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
If claims of metaphysical necessity are based on conceivability, we should be cautious [Segal]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
The success and virtue of an explanation do not guarantee its truth [Segal]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
Superactors and superspartans count against behaviourism [Putnam, by Searle]
18. Thought / A. Modes of Thought / 4. Folk Psychology
Folk psychology is ridiculously dualist in its assumptions [Segal]
18. Thought / C. Content / 5. Twin Earth
If 'water' has narrow content, it refers to both H2O and XYZ [Segal]
Humans are made of H2O, so 'twins' aren't actually feasible [Segal]
Externalists can't assume old words refer to modern natural kinds [Segal]
18. Thought / C. Content / 6. Broad Content
If content is external, so are beliefs and desires [Segal]
Maybe experts fix content, not ordinary users [Segal]
Must we relate to some diamonds to understand them? [Segal]
Externalism can't explain concepts that have no reference [Segal]
Concepts can survive a big change in extension [Segal]
Maybe content involves relations to a language community [Segal]
18. Thought / C. Content / 7. Narrow Content
If content is narrow, my perfect twin shares my concepts [Segal]
18. Thought / C. Content / 10. Causal Semantics
If thoughts ARE causal, we can't explain how they cause things [Segal]
Even 'mass' cannot be defined in causal terms [Segal]