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All the ideas for 'General Draft', 'Scientific Essentialism' and 'Cardinality, Counting and Equinumerosity'

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48 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy is homesickness - the urge to be at home everywhere [Novalis]
     Full Idea: Philosophy is actually homesickness - the urge to be everywhere at home.
     From: Novalis (General Draft [1799], 45)
     A reaction: The idea of home [heimat] is powerful in German culture. The point of romanticism was seen as largely concerning restless souls like Byron and his heroes, who do not feel at home. Hence ironic detachment.
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Ontology should give insight into or an explanation of the world revealed by science [Ellis]
     Full Idea: A good ontology should provide insight into, or offer some kind of explanation of, the salient general features of the world that has been revealed to us by science.
     From: Brian Ellis (Scientific Essentialism [2001], Intro)
     A reaction: I think I agree with this. The difficulty is that the most fundamental level revealed by science is a quantum one, so if you take a reductionist view then your ontology is both crazy, and resting on things which are not understood.
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis]
     Full Idea: The logic of real possibilities and necessities is just S5. This is because the accessibility relation for real possibilities links possible worlds of the same natural kind, which is an equivalence class.
     From: Brian Ellis (Scientific Essentialism [2001], 7.06)
     A reaction: Most people, except Nathan Salmon, agree with this. With full accessibility, you seem to take epistemological problems out of the system, and just focus on reality.
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Humean conceptions of reality drive the adoption of extensional logic [Ellis]
     Full Idea: A Humean conception of reality lies behind, and motivates, the development of extensional logics with extensional semantics.
     From: Brian Ellis (Scientific Essentialism [2001], 8.04)
     A reaction: His proposal seems to be that it rests on the vision of a domain of separated objects. The alternative view seems to be that it is mathematics, with its absolute equality between 'objects', which drives extensionalism.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
The meaning of a number isn't just the numerals leading up to it [Heck]
     Full Idea: My knowing what the number '33' denotes cannot consist in my knowing that it denotes the number of decimal numbers between '1' and '33', because I would know that even if it were in hexadecimal (which I don't know well).
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5)
     A reaction: Obviously you wouldn't understand '33' if you didn't understand what '33 things' meant.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
     Full Idea: An appreciation of the connection between sameness of number and equinumerosity that it reports is essential to even the most primitive grasp of the concept of cardinal number.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
     Full Idea: One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3)
     A reaction: He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals.
Is counting basically mindless, and independent of the cardinality involved? [Heck]
     Full Idea: I am not denying that counting can be done mindlessly, without making judgments of cardinality along the way. ...But the question is whether counting is, as it were, fundamentally a mindless exercise.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5)
     A reaction: He says no. It seems to me like going on a journey, where you can forget where you are going and where you have got to so far, but those underlying facts are always there. If you just tag things with unknown foreign numbers, you aren't really counting.
Counting is the assignment of successively larger cardinal numbers to collections [Heck]
     Full Idea: Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5)
     A reaction: That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality?
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
     Full Idea: It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4)
     A reaction: The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel.
We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
     Full Idea: 'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4)
     A reaction: [compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
     Full Idea: The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6)
     A reaction: He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Children can use numbers, without a concept of them as countable objects [Heck]
     Full Idea: For a long time my daughter had no understanding of the question of how many numerals or numbers there are between 'one' and 'five'. I think she lacked the concept of numerals as objects which can themselves be counted.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5)
     A reaction: I can't make any sense of numbers actually being objects, though clearly treating all sorts of things as objects helps thinking (as in 'the victory is all that matters').
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Equinumerosity is not the same concept as one-one correspondence [Heck]
     Full Idea: Equinumerosity is not the same concept as being in one-one correspondence with.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6)
     A reaction: He says this is the case, even if they are coextensive, like renate and cordate. You can see that five loaves are equinumerous with five fishes, without doing a one-one matchup.
We can understand cardinality without the idea of one-one correspondence [Heck]
     Full Idea: One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence.
     From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3)
     A reaction: This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups.
8. Modes of Existence / B. Properties / 1. Nature of Properties
The extension of a property is a contingent fact, so cannot be the essence of the property [Ellis]
     Full Idea: The extension of a property in any given world is just a contingent fact about that world; its extension is not the essence of the property.
     From: Brian Ellis (Scientific Essentialism [2001], 2.07)
     A reaction: The Quinean idea, common among logicians, that a predicate is just a set defined for some model, may be useful in the logic, but is preposterous as an account of what a property actually is in nature, even if the set covers possible worlds.
8. Modes of Existence / B. Properties / 5. Natural Properties
There is no property of 'fragility', as things are each fragile in a distinctive way [Ellis]
     Full Idea: There is no natural property of 'fragility'; glasses, parchments, ecosystems and spiders' webs are fragile in their own ways, but they have nothing intrinsic or structural in common.
     From: Brian Ellis (Scientific Essentialism [2001], 3.06)
     A reaction: This is important (and, I think, correct) because we are inclined to say that something is 'intrinsically' fragile, but that still isn't enough to identify a true property. Ellis wants universals to be involved, and even a nominalist must sort-of agree.
8. Modes of Existence / B. Properties / 6. Categorical Properties
Typical 'categorical' properties are spatio-temporal, such as shape [Ellis]
     Full Idea: The paradigmatically 'categorical' properties are spatio-temporal, depending on how things are distributed in space and time. Shape is the obvious example. ...Other examples are number, size and configuration.
     From: Brian Ellis (Scientific Essentialism [2001], 1.09)
     A reaction: I'm finding it very frustrating that this concept is much discussed in current philosophy of science (e.g. by Bird), but it is exceedingly hard to pin down any exact account of these 'categorical' properties, or even why they are so-called.
The property of 'being an electron' is not of anything, and only electrons could have it [Ellis]
     Full Idea: There is no property of being an electron. It could only be instantiated by electrons, so it does not seem genuine. And what is the thing that supposedly instantiates the property of being an electron?
     From: Brian Ellis (Scientific Essentialism [2001], 75,92), quoted by Stephen Mumford - Laws in Nature 7.3
     A reaction: I agree entirely. Bird launches an excellent attack on categorial properties.
8. Modes of Existence / B. Properties / 10. Properties as Predicates
'Being a methane molecule' is not a property - it is just a predicate [Ellis]
     Full Idea: In my view 'being a methane molecule' is not a property name, but a predicate that is constructed out of a natural kind name, and so pretends to name a property.
     From: Brian Ellis (Scientific Essentialism [2001], 2.03)
     A reaction: I can't tell you how strongly I agree with this. How long have you got? This is so incredibly right that... You get the idea. He observes that such properties cannot be instantiated 'in' anything.
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Causal powers must necessarily act the way they do [Ellis]
     Full Idea: There can be no question of a causal power's acting one way in one world and another way in a different world.
     From: Brian Ellis (Scientific Essentialism [2001], 1.12)
     A reaction: Perhaps the very core idea of scientific essentialism. It doesn't feel quite right that when you ask for the source of this necessity, you are only told that it is necessary for the very identity of a power. The truth is that it is a primitive of nature.
Causal powers are often directional (e.g. centripetal, centrifugal, circulatory) [Ellis]
     Full Idea: Causal powers are often directional. For example, they may be centripetal, centrifugal, or circulatory.
     From: Brian Ellis (Scientific Essentialism [2001], 3.11)
     A reaction: The examples all seem to raise a few questions, about whether the directionality arises from the context, rather than from the intrinsic power.
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Basic powers may not be explained by structure, if at the bottom level there is no structure [Ellis]
     Full Idea: It may be that the most fundamental things have no structure, and therefore no structure in virtue of which they have the powers they have.
     From: Brian Ellis (Scientific Essentialism [2001], Intro)
     A reaction: Maybe the world has inexplicable powers, so there is a God? It seems obvious that there will be no explanation of the 'lowest level' of reality, and also obvious (to me and Leibniz, anyway) that this lowest level has to be active.
Maybe dispositions can be explained by intrinsic properties or structures [Ellis]
     Full Idea: One view is that there must be an intrinsic property or structure in virtue of which a given thing has the behavioural disposition in question.
     From: Brian Ellis (Scientific Essentialism [2001], 3.06)
     A reaction: [He cites Prior, Pargetter,Jackson 1982] A key question in the metaphysics of nature - whether dispositions should be taken as primitive, or whether we should try to explain them in other terms. I take powers and dispositions to be prior to properties.
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
The most fundamental properties of nature (mass, charge, spin ...) all seem to be dispositions [Ellis]
     Full Idea: The properties of the most fundamental things in nature, including mass, charge, spin, and the like, would all appear to be dispositional.
     From: Brian Ellis (Scientific Essentialism [2001], 3.05)
     A reaction: This goes with the Leibnizian claim that the most fundamental features of nature must be active in character.
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
A causal power is a disposition to produce forces [Ellis]
     Full Idea: A causal power is a disposition of something to produce forces of a certain kind.
     From: Brian Ellis (Scientific Essentialism [2001], 3.09)
     A reaction: Hence when Leibniz was putting all his emphasis on the origin of the forces in nature, he was referring to exactly what we mean by 'powers'. From Ellis's formulation, I take powers to be more basic than dispositions. Does he realise this?
Powers are dispositions of the essences of kinds that involve them in causation [Ellis]
     Full Idea: The causal powers of an object are the dispositional properties of that object that are the real essences of the natural kinds of processes that involve that object in the role of cause.
     From: Brian Ellis (Scientific Essentialism [2001], 3.11)
     A reaction: This is Ellis's formal definition at the end of his discussion of causal powers. He only seems to allow powers to the kind rather than to the individual. How do we account for the causal powers of unique genius? I say the powers are the essences.
8. Modes of Existence / D. Universals / 1. Universals
There are 'substantive' (objects of some kind), 'dynamic' (events of some kind) and 'property' universals [Ellis]
     Full Idea: Three categories of universals: 'substantive' universals have instances that are members of natural kinds of objects or substances; 'dynamic' universals are kinds of events or processes; 'property' universals are tropes of real properties or relations.
     From: Brian Ellis (Scientific Essentialism [2001], 1.01)
     A reaction: I would want to distinguish real properties from relations. It is important to remember that an object can traditionally instantiate a universal, and that they aren't just properties.
Universals are all types of natural kind [Ellis]
     Full Idea: The various kinds of universals are all natural kinds of one sort or another.
     From: Brian Ellis (Scientific Essentialism [2001], 1.01)
     A reaction: This doesn't sound right. What about the universals of mathematics, or universals which are a matter of social or linguistic convention? I think Ellis is trying to hijack the word 'universal' in response to Armstrong's more idealistic account.
9. Objects / D. Essence of Objects / 3. Individual Essences
Scientific essentialism doesn't really need Kripkean individual essences [Ellis]
     Full Idea: My current view is that individual essences (about which Kripke's essentialism has a lot to say) do not matter much from the point of view of a scientific essentialist.
     From: Brian Ellis (Scientific Essentialism [2001], Intro)
     A reaction: [Kripke parenthesis on p.54] Presumably this is because science is only committed to dealing in generalities, and so natural kinds are needed for such things. I'm inclined to regard individual essences as prior in the pure ontology of the thing.
9. Objects / D. Essence of Objects / 15. Against Essentialism
The old idea that identity depends on essence and behaviour is rejected by the empiricists [Ellis]
     Full Idea: The old Aristotelian idea that the identity of a thing might depend on its essential nature, which would dispose it to behave in certain ways, is firmly rejected by empiricists.
     From: Brian Ellis (Scientific Essentialism [2001], 1.10)
     A reaction: Ellis is accusing empiricists of having a falsely passive concept of objects. This dispute is best captured in the disagreement between Locke and Leibniz on the subject.
10. Modality / A. Necessity / 3. Types of Necessity
Necessities are distinguished by their grounds, not their different modalities [Ellis]
     Full Idea: Strictly speaking, the distinction between two brands of necessity is one of grounds, rather than modality.
     From: Brian Ellis (Scientific Essentialism [2001], 1.06)
     A reaction: This idea I associate with Kit Fine. I like it, because it allows 'necessity' to be a univocal concept, which seems right to me. The types of necessity arise from types of things which already occur in our ontology.
10. Modality / C. Sources of Modality / 6. Necessity from Essence
Individual essences necessitate that individual; natural kind essences necessitate kind membership [Ellis]
     Full Idea: There are necessities grounded in the individual real essences of things, and necessities grounded in the natural kind essences of things. In the first case, without the property it isn't that individual, and in the second it isn't a member of that kind.
     From: Brian Ellis (Scientific Essentialism [2001], Intro)
     A reaction: This is the distinction we must hang onto to avoid a huge amount of confusion in this territory. I just say that ceasing to be that individual will presumably entail ceasing to be that kind, but not necessarily vice versa, so individual essences rule.
14. Science / C. Induction / 3. Limits of Induction
If events are unconnected, then induction cannot be solved [Ellis]
     Full Idea: If one believes, as Hume did, that all events are loose and separate, then the problem of induction is probably insoluble.
     From: Brian Ellis (Scientific Essentialism [2001], 8.09)
     A reaction: This points to the essentialist solution of induction - that we can genuinely derive inductive truths if we can inductively identify the essences which give rise to the necessities of further cases. I take that to be a correct account.
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
Good explanations unify [Ellis]
     Full Idea: An acceptable explanation must have some unifying power.
     From: Brian Ellis (Scientific Essentialism [2001], 3.11)
     A reaction: There is a tension here, between the particular and the general. If I say 'why did the building collapse' and you say 'gravity', you have certainly got a unifying explanation, but we want something narrower.
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Explanations of particular events are not essentialist, as they don't reveal essential structures [Ellis]
     Full Idea: Explanations of particular events in history, geology, or evolution, are causal explanations, requiring belief in some causal mechanisms. But they are not essentialist explanations because they do not seek to lay bare the essential structure of anything.
     From: Brian Ellis (Scientific Essentialism [2001], 4.05)
     A reaction: The explanation might be two-stage, as when we explain an earthquake by a plate boundary rupture, which is in turn explained by a theory of plate techtonics. The relationship between mechanistic and essentialist explanation needs study.
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
To give essentialist explanations there have to be natural kinds [Ellis]
     Full Idea: There can be no essentialist explanations constructed in any field where the subject matter is not naturally divided into kinds.
     From: Brian Ellis (Scientific Essentialism [2001], Intro)
     A reaction: A crux. I like individual essences, such as the character of a particular person. However, Ellis may be right, since while we may identify an individual essence as the source of a behaviour, we may not then be able to give any 'explanation'.
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Desire for perfection is an illness, if it turns against what is imperfect [Novalis]
     Full Idea: An absolute drive toward perfection and completeness is an illness, as soon as it shows itself to be destructive and averse toward the imperfect, the incomplete.
     From: Novalis (General Draft [1799], 33)
     A reaction: Deep and true! Novalis seems to be a particularist - hanging on to the fine detail of life, rather than being immersed in the theory. These are the philosophers who also turn to literature.
The point of models in theories is not to idealise, but to focus on what is essential [Ellis]
     Full Idea: Most model theories abstract from reality in order to focus on the essential nature of some kind of process or system of relations. ... The point of idealizing in this case is not to simplify, but to eliminate what is not essential.
     From: Brian Ellis (Scientific Essentialism [2001], 4.03)
     A reaction: I like this idea a lot. It is where scientific essentialism cashes out in actual scientific practice. Ellis's example is the idealised Carnot heat engine, which never can exist, but which captures what is essential about the process.
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
There might be uninstantiated natural kinds, such as transuranic elements which have never occurred [Ellis]
     Full Idea: There are reasons to believe that there are natural kinds that might never be instantiated, such as a transuranic element, capable of existing for some fraction of a second, but which has never actually existed anywhere.
     From: Brian Ellis (Scientific Essentialism [2001], 2.05)
     A reaction: He cautiously claims that kinds are ontologically prior to their individual members. I would say that there is no natural kind of the type that he describes. He says you have at least some grounds for predicting what kinds are possible.
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
Natural kinds are distinguished by resting on essences [Ellis]
     Full Idea: Natural kinds are distinguished from other sorts of things by their associations with essential properties and real essences.
     From: Brian Ellis (Scientific Essentialism [2001], 1.02)
     A reaction: I don't think I agree with this. I rest my notion of natural kind on the elementary realising that to know all about this kind you only have to examine one sample of it, as in the Upanishads. The source of such a phenomenon is an open question.
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
If there are borderline cases between natural kinds, that makes them superficial [Ellis]
     Full Idea: There cannot be any borderline cases between the real essences of different natural kinds because, if there were, the distinctions between the kinds would be superficial, like the blue/green distinction.
     From: Brian Ellis (Scientific Essentialism [2001], 1.05)
     A reaction: His particular target here is biological natural kinds, in which he doesn't believe, because they blur across time, in the evolutionary process. Personally I am inclined to relax the notion of a natural kind, otherwise they are too basic to explain.
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Laws don't exist in the world; they are true of the world [Ellis]
     Full Idea: Laws are not things that exist in the world; they are things that are true of the world.
     From: Brian Ellis (Scientific Essentialism [2001], 3.09)
     A reaction: I'm happy with this formulation. The one to get rid of is the idea of laws which could precede creation of the universe, and survive its demise. That might be possible, but we have absolutely no grounds for the claim. Humeans ought to agree.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
A proton must have its causal role, because without it it wouldn't be a proton [Ellis]
     Full Idea: I assume it is metaphysically impossible for a proton to have a different causal role, ...which is plausible because a proton would appear to have no identity at all apart from its role in causal processes.
     From: Brian Ellis (Scientific Essentialism [2001], Intro)
     A reaction: This seems to be a key idea in scientific essentialism, which links essentialism of identity with essentialism in the laws of nature. Could a proton become not-quite-a-proton?
What is most distinctive of scientific essentialism is regarding processes as natural kinds [Ellis]
     Full Idea: What is most distinctive of the scientific version of essentialism is that scientific essentialists are realists about natural kinds of processes, as well as natural kinds of objects and substances.
     From: Brian Ellis (Scientific Essentialism [2001], 1.11)
     A reaction: I'm not sure whether other scientific essentialists would agree with this, but I am happy to go along with it. A process like melting or sublimation seems to be a standard widespread phenomenon which is always intrinsically the same, as kinds must be.
Scientific essentialism is more concerned with explanation than with identity (Locke, not Kripke) [Ellis]
     Full Idea: Scientific essentialism is less concerned with questions of identity, and more with questions of explanation, than is the essentialism of Aristotle or of Kripke. It is closest to the kind of essentialism described by Locke.
     From: Brian Ellis (Scientific Essentialism [2001], 1.12)
     A reaction: Locke is popularly held to be anti-essentialist, but that is only because of his epistemological problems. I think Ellis is here misreading Aristotle, and I would ally Aristotle, Locke (cautiously), Leibniz, Ellis and Fine against Kripkeans on this one.
The ontological fundamentals are dispositions, and also categorical (spatio-temporal and structural) properties [Ellis]
     Full Idea: We do not claim, as some do, that fundamental dispositional properties are the ontological basis of all properties. On the contrary, there are equally fundamental categorical properties - for example, spatio-temporal relations and structures.
     From: Brian Ellis (Scientific Essentialism [2001], 3.09)
     A reaction: The source of disagreement between Bird and Ellis. Bird denies the existence of 'categorical properties'. I think I am with Bird. Space and time are as much part of the given as the elements, and then categorical properties result from dispositions.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
A primary aim of science is to show the limits of the possible [Ellis]
     Full Idea: Scientific essentialists hold that one of the primary aims of science is to define the limits of the possible.
     From: Brian Ellis (Scientific Essentialism [2001], 7.06)
     A reaction: I like this. It breaks down into the study of modal profiles, and it can work for abstracta as well as for the physical world. It even covers the study of character, and you could say that it is the subject matter of Jane Austen.