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All the ideas for 'Stipulation, Meaning and Apriority', 'On Platonism in Mathematics' and 'The Essential Child'

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42 ideas

2. Reason / D. Definition / 13. Against Definition
How do we determine which of the sentences containing a term comprise its definition? [Horwich]
     Full Idea: How are we to determine which of the sentences containing a term comprise its definition?
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2)
     A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't?
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Very few things in set theory remain valid in intuitionist mathematics [Bernays]
     Full Idea: Very few things in set theory remain valid in intuitionist mathematics.
     From: Paul Bernays (On Platonism in Mathematics [1934])
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
     Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought.
     From: Paul Bernays (On Platonism in Mathematics [1934], p.261)
     A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Mathematical abstraction just goes in a different direction from logic [Bernays]
     Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction.
     From: Paul Bernays (On Platonism in Mathematics [1934], p.268)
     A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic.
7. Existence / E. Categories / 2. Categorisation
Even fairly simple animals make judgements based on categories [Gelman]
     Full Idea: All organisms form categories: even mealworms have category-based preferences, and higher-order animals such as pigeons or octopi can display quite sophisticated categorical judgements.
     From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims')
     A reaction: [She cites some 1980 research to support this] This comes as no surprise, as I take categorisation as almost definitive of what a mind is. My surmise is that some sort of 'labelling' system is at the heart of it (like Googlemail labels!).
Children accept real stable categories, with nonobvious potential that gives causal explanations [Gelman]
     Full Idea: By five children assume that a variety of categories have rich inductive potential, are stable over outward transformations, include crucial nonobvious properties, have innate potential, privilege causal features, can be explained causally, and are real.
     From: Susan A. Gelman (The Essential Child [2003], 06 'Intro')
     A reaction: This is Gelman's helpful summary of the findings of research on childhood essentialising, and says the case for this phenomenon is 'compelling'.
9. Objects / D. Essence of Objects / 1. Essences of Objects
In India, upper-castes essentialize caste more than lower-castes do [Gelman]
     Full Idea: The notion of caste in India is more essentialized among upper-caste than lower-caste individuals.
     From: Susan A. Gelman (The Essential Child [2003], 08 'Intro')
     A reaction: In a book defending fairly innate essentialism in the human race, Gelman offers this point as a warning that large cultural ingredients can be involved. Racism is the classic difficulty with essentialism.
Essentialism is either natural to us, or an accident of our culture, or a necessary result of language [Gelman]
     Full Idea: The two views contrasting with essentialism naturally emerging in childhood are the claim that essentialism is a historical accident emerging from Western philosophy, and that essentialism is an inherent consequence of naming things.
     From: Susan A. Gelman (The Essential Child [2003], 01 'Background')
     A reaction: Helpful. I take Idea 15682 to rule out the idea that it is just a feature of western culture. I can't conceive of early man surviving without essentialism. I don't think it rules out the naming view. Animals may do what emerges in us as full 'naming'.
Children's concepts include nonobvious features, like internal parts, functions and causes [Gelman]
     Full Idea: Children incorporate a variety of nonobvious features into their concepts, including internal parts, functions, causes, and ontological distinctions.
     From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims')
     A reaction: This remark sums up the general thesis of her book, which she supports with a wealth of first-hand evidence. It supports my view, that the desire and need for explanation is at the root of essentialist concepts. It's hard wired in us.
9. Objects / D. Essence of Objects / 2. Types of Essence
Essentialism: real or representational? sortal, causal or ideal? real particulars, or placeholders? [Gelman]
     Full Idea: We map types of essentialism by asking is it in the world or in our representations, is it sortal or causal or ideal, and is it specific particulars or placeholders for the unknown?
     From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims')
     A reaction: I am struck by the way that this practising experimental psychologist gets to ask questions and make distinctions much more extensively than most armchair philosophers on the subject. She focuses on the representational, causal, placeholder view.
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]
     Full Idea: Essentialism is the view that categories have an underlying reality or true nature that one cannot observe directly but that gives an object its identity.
     From: Susan A. Gelman (The Essential Child [2003], 01 'Intro')
     A reaction: I think the introduction of categories here is a misunderstanding. Does an uncategorisable thing therefore have no identity (even though it has properties)? If categories give objects their identity, what gives categories their identity?
Sortals are needed for determining essence - the thing must be categorised first [Gelman]
     Full Idea: I suggest that sortals are likewise required for determining essence. One cannot answer the question 'What is the essence of this?' without supplying the sortal - of this 'what'.
     From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims')
     A reaction: I remain baffled by this view. I take the category to be an inductive generalisation from other similar individuals. It can't get off the ground if you don't start with the individuals. Sortals are just a shorthand.
Kind (unlike individual) essentialism assumes preexisting natural categories [Gelman]
     Full Idea: With kind essentialism the person assumes that the world is divided up into preexisting natural categories. Individual essentialism seems not to require any such commitment to kind realism.
     From: Susan A. Gelman (The Essential Child [2003], 06 'Essentialism')
     A reaction: This pinpoints my difficulty: how do we decide whether some category or attributed essence is part of a preexisting natural kind? Some natural kinds are self-evident, like water (roughly), but others need subtle teasing out. How is the teasing done?
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]
     Full Idea: Kinship is essentialized, but admits of degrees, ...and people can be essentialist even about categories they do not view as fixed over time, such as age groupings.
     From: Susan A. Gelman (The Essential Child [2003], 03 'Summary')
     A reaction: Given my notion of essence are necessarily explanatory, I embrace both of these points. Being very athletic comes in degrees, and changes over times.
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
Essentialism comes from the cognitive need to categorise [Gelman]
     Full Idea: Essentialism has its source in the cognitive requirement of categorization in certain domains - particularly as they affect the young learner.
     From: Susan A. Gelman (The Essential Child [2003], 01 'Essentialist')
     A reaction: I think the phenomenon is better understood as part of the cognitive requirement to understand and explain. Categorisation is just one way to aid explanation. Children try to understand (essentially) a new animal without categorisation.
We found no evidence that mothers teach essentialism to their children [Gelman]
     Full Idea: We found no evidence that mothers teach essentialism to their children. ...Mothers teach children about kinds, not about essences, and mothers help children identify which categories are richly structured.
     From: Susan A. Gelman (The Essential Child [2003], 07 'Conclusions')
     A reaction: This is a psychologist who specialises in this topic. If you think essentialism is inculcated by a our culture, you will have to blame the fathers.
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is useful for predictions, but it is not the actual structure of reality [Gelman]
     Full Idea: Essentialism is a reasoning heuristic that allows us to make fairly good predictions much of the time, but it should not be confused with the structure of reality.
     From: Susan A. Gelman (The Essential Child [2003], 11 'Discussion')
     A reaction: She particularly cites biology as the area where it might be inaccurate. I'm beginning to think that the operations of induction are the place to look for an good understanding of essentialism.
9. Objects / E. Objects over Time / 12. Origin as Essential
Peope favor historical paths over outward properties when determining what something is [Gelman]
     Full Idea: People favor historical paths over outward properties when determining what something is. ...An object looking like a knife is less likely to be called 'a knife' if it is described as having been created by accident.
     From: Susan A. Gelman (The Essential Child [2003], 06 'Essentialism')
     A reaction: I like this because it talks, suggestively, of 'historical paths' rather than of 'origin'. Thus we might judge a person's identity by their traumatic experience rather than by their birth. This doesn't challenge necessity of origin, but affects labels.
11. Knowledge Aims / A. Knowledge / 2. Understanding
There is intentional, mechanical, teleological, essentialist, vitalist and deontological understanding [Gelman]
     Full Idea: The modes of understanding (or modes of construal) which have been proposed are intentional, mechanical, teleological, essentialist, vitalist (perhaps), and deontological.
     From: Susan A. Gelman (The Essential Child [2003], 11 'Broadening')
     A reaction: She cites psychological research to support this, and calls it 'a relatively small number' of modes. Compare Aristotle's four modes of cause/explanation.
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich]
     Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8)
     A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified.
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
Understanding needs a priori commitment [Horwich]
     Full Idea: Understanding is itself based on a priori commitment.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12)
     A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional.
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
Meaning is generated by a priori commitment to truth, not the other way around [Horwich]
     Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8)
     A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it.
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich]
     Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12)
     A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge.
If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich]
     Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9)
     A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate.
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich]
     Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic.
     From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11)
     A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away.
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Memories often conform to a theory, rather than being neutral [Gelman]
     Full Idea: Memory is notorious for conforming to theory (rather than memory being a neutral source of information).
     From: Susan A. Gelman (The Essential Child [2003], 09 'Theory')
     A reaction: This observation by a psychologist is music to sceptics about objectivity. Memory is so fundamental to our basic epistemology that it could even be the nature of thought itself.
14. Science / C. Induction / 1. Induction
Inductive success is rewarded with more induction [Gelman]
     Full Idea: Inductive success is rewarded with more induction.
     From: Susan A. Gelman (The Essential Child [2003], 11 'Broadening')
     A reaction: I love this one. Neat, accurate, and central to how we understand the world. I take inductive success to be stored as labels, concepts, categories, words and general truths, which are then our resource for further attempts.
14. Science / C. Induction / 3. Limits of Induction
Children overestimate the power of a single example [Gelman]
     Full Idea: We suggest that children overestimate the power of a single example.
     From: Susan A. Gelman (The Essential Child [2003], 06 'The role')
     A reaction: This conclusion arises from extensive psychological research. 'My grandma smoked, and she lived to be 97' - adults do this too. Wittgenstein says assuming other minds because of your own is induction from one example!
Children make errors in induction by focusing too much on categories [Gelman]
     Full Idea: Because of their narrow focus, children's sensitivity to categories as the basis of induction is a reasoning bias that, though useful much of the time, results in systematic errors.
     From: Susan A. Gelman (The Essential Child [2003], 06 'The role')
     A reaction: This is the bad sense of 'essentialism' which worries its opponents. Presumably, though, my favoured scientific essentialism will be 'scientific', and avoid this problem. The relation between categories and induction needs to be clear.
14. Science / D. Explanation / 1. Explanation / a. Explanation
People tend to be satisfied with shallow explanations [Gelman]
     Full Idea: People tend to be satisfied with rather shallow explanations.
     From: Susan A. Gelman (The Essential Child [2003], 06 'Is essentialism')
     A reaction: She cites some psychological research to support this. Pretty obvious really. I take the so-called 'scientific method' to be nothing more than ceasing to be satisfied with such shallowness.
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]
     Full Idea: The three components of essentialism as a folk belief are the idea that certain categories are natural kinds, the idea that some unobservable property causes the way things are, and the idea that words reflect real structures.
     From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims')
18. Thought / D. Concepts / 3. Ontology of Concepts / a. Concepts as representations
Labels may indicate categories which embody an essence [Gelman]
     Full Idea: Labels may signal categories that are believed to embody an essence.
     From: Susan A. Gelman (The Essential Child [2003], 02 'Privileged')
     A reaction: This is quoted by her, as a summary of a substantial body of research which she endorses. I cite it because it pinpoints my own view. I take 'labels' to be basic to minds, as organisers of thought, and this ties essences to labels. Satisfying picture.
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Causal properties are seen as more central to category concepts [Gelman]
     Full Idea: Properties that enter into causally meaningful links are better remembered and are treated as more central to the category than properties that are not causally meaningful.
     From: Susan A. Gelman (The Essential Child [2003], 05 'Causation2')
     A reaction: This is a summary of considerable psychological research. This account not only sounds plausible, but would fit better withy why we form concepts and categories in the first place. We are trying to relate to the causations of nature.
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
Categories are characterized by distance from a prototype [Gelman]
     Full Idea: On prototype views, categories are characterized by distance from a prototype.
     From: Susan A. Gelman (The Essential Child [2003], 05 'Causation')
     A reaction: Gelman observes that this view makes no reference to any causal features of things. This cuts them off from using underlying essences in the process of categorisation and concept-formation. How do you spot a prototype, with no category?
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]
     Full Idea: Theory-based approaches to categories are a response to the limitations of mere similarities holding the category together, and require knowledge-rich explanatory models to say which features are more central to a concept.
     From: Susan A. Gelman (The Essential Child [2003], 05 'Causation1')
     A reaction: I see a promising account in linking theory theory to essentialism. For a physical object (or even for a process) infer a structure, and then identify what is most important in that structure. That gives you your stable, agreed concept.
18. Thought / D. Concepts / 5. Concepts and Language / c. Concepts without language
Prelinguistic infants acquire and use many categories [Gelman]
     Full Idea: Language does not appear to be necessary for forming categories, since prelinguistic infants acquire many categories, and even use categories to form inferences about unknown properties.
     From: Susan A. Gelman (The Essential Child [2003], 08 'Intro')
     A reaction: She cites lots of research in support of this claim. The idea may come as a surprise to some people, but not to me. I take it that categorisation is what a brain is for, including animal brains.
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]
     Full Idea: We can confidently determine the chemical composition of gold from just a single sample, but we cannot determine the height of trees from just a single tree.
     From: Susan A. Gelman (The Essential Child [2003], 06 'The role')
     A reaction: The tricky word here is 'confidently'. If you meet one Latvian who is nice, do you assume they are all nice? At what point do you decide gold etc. really are natural kinds, where one sample tells all? Evolution of species...
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
Nouns seem to invoke stable kinds more than predicates do [Gelman]
     Full Idea: Children judged personal characteristics as more stable when they were referred to by a noun ('She is a carrot eater') than by a verbal predicate ('She eats carrots whenever she can')
     From: Susan A. Gelman (The Essential Child [2003], 08 'Naming')
     A reaction: This fits with my feeling that 'labels' are the basis of how the mind works. The noun invokes a genuine category of thing, where a predicate attaches to some preselected category ('she'). Gelman says names encourage inductions.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Essentialism encourages us to think about the world scientifically [Gelman]
     Full Idea: Essentialism encourages a 'scientific' mindset in thinking about the natural world, a belief that intensive study of a natural domain will yield ever more underlying properties.
     From: Susan A. Gelman (The Essential Child [2003], 11 'Intro')
     A reaction: Maybe scientists must be committed to essences, the way mathematicians must be committed to numbers? This idea spendidly opposes the doubts expressed by Popper.
Essentialism doesn't mean we know the essences [Gelman]
     Full Idea: Essentialism does not entail that people know what the essence is.
     From: Susan A. Gelman (The Essential Child [2003], 09 'Theory')
     A reaction: This is a fundamental and (I would say) fairly obvious point, but it needs to be made to the more passionate opponents of essentialism.
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]
     Full Idea: If my speculations are correct, then essentialism starts out strictly as a belief that many categories are richly structured kinds, then additionally becomes a search for underlying inherent properties.
     From: Susan A. Gelman (The Essential Child [2003], 10 'Figuring')
     A reaction: This is her summary of extensive essentialist research among children. She favours the priority of kinds and categories. We actually change taxonomies on the basis of revisions in our accounts of essence. Science negotiates.
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]
     Full Idea: One major argument against the view that essences are real is the rampant essentializing of categories that are socially constructed (such as race, caste and occupation).
     From: Susan A. Gelman (The Essential Child [2003], 11 'Is essentialism')
     A reaction: You can't argue with that. It raises the question of whether the approach of scientific essentialism has any value in the social, rather than physical, sciences. We jokingly essentialise groups of people such as referees or Oxonians.