Combining Texts

All the ideas for 'The Essential Child', 'Maths as a Science of Patterns' and 'Letters to Coste'

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42 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
The universe is infinitely varied, so the Buridan's Ass dilemma could never happen [Leibniz]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
There are too many mathematical objects for them all to be mental or physical [Resnik]
Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
7. Existence / E. Categories / 2. Categorisation
Even fairly simple animals make judgements based on categories [Gelman]
Children accept real stable categories, with nonobvious potential that gives causal explanations [Gelman]
9. Objects / D. Essence of Objects / 1. Essences of Objects
In India, upper-castes essentialize caste more than lower-castes do [Gelman]
Essentialism is either natural to us, or an accident of our culture, or a necessary result of language [Gelman]
Children's concepts include nonobvious features, like internal parts, functions and causes [Gelman]
9. Objects / D. Essence of Objects / 2. Types of Essence
Essentialism: real or representational? sortal, causal or ideal? real particulars, or placeholders? [Gelman]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Essentialism says categories have a true hidden nature which gives an object its identity [Gelman]
Sortals are needed for determining essence - the thing must be categorised first [Gelman]
Kind (unlike individual) essentialism assumes preexisting natural categories [Gelman]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
Kinship is essence that comes in degrees, and age groups are essences that change over time [Gelman]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
Essentialism comes from the cognitive need to categorise [Gelman]
We found no evidence that mothers teach essentialism to their children [Gelman]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is useful for predictions, but it is not the actual structure of reality [Gelman]
9. Objects / E. Objects over Time / 12. Origin as Essential
Peope favor historical paths over outward properties when determining what something is [Gelman]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
There may be a world where dogs smell their game at a thousand leagues [Leibniz]
11. Knowledge Aims / A. Knowledge / 2. Understanding
There is intentional, mechanical, teleological, essentialist, vitalist and deontological understanding [Gelman]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Memories often conform to a theory, rather than being neutral [Gelman]
14. Science / C. Induction / 1. Induction
Inductive success is rewarded with more induction [Gelman]
14. Science / C. Induction / 3. Limits of Induction
Children overestimate the power of a single example [Gelman]
Children make errors in induction by focusing too much on categories [Gelman]
14. Science / D. Explanation / 1. Explanation / a. Explanation
People tend to be satisfied with shallow explanations [Gelman]
18. Thought / A. Modes of Thought / 4. Folk Psychology
Folk essentialism rests on belief in natural kinds, in hidden properties, and on words indicating structures [Gelman]
18. Thought / D. Concepts / 3. Ontology of Concepts / a. Concepts as representations
Labels may indicate categories which embody an essence [Gelman]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Causal properties are seen as more central to category concepts [Gelman]
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
Categories are characterized by distance from a prototype [Gelman]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
Theory-based concepts use rich models to show which similarities really matter [Gelman]
18. Thought / D. Concepts / 5. Concepts and Language / c. Concepts without language
Prelinguistic infants acquire and use many categories [Gelman]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
One sample of gold is enough, but one tree doesn't give the height of trees [Gelman]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
Nouns seem to invoke stable kinds more than predicates do [Gelman]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Essentialism encourages us to think about the world scientifically [Gelman]
Essentialism doesn't mean we know the essences [Gelman]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
Essentialism starts from richly structured categories, leading to a search for underlying properties [Gelman]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
A major objection to real essences is the essentialising of social categories like race, caste and occupation [Gelman]