| 12966 | Objects of ideas can be divided into abstract and concrete, and then further subdivided [Leibniz] |
| Full Idea: Divide terms, objects of ideas, into abstract and concrete, then the abstract into absolute and relational, the absolute into attributes and modifications, and those two into simple and composite; the concrete are substances and their substantial things. | |
| From: Gottfried Leibniz (New Essays on Human Understanding [1704], 2.22) | |
| A reaction: Make your tree from this: ABSTRACT{absolute[attributes(simple)(composite)][modifications(simple)(composite)],relations}CONCRETE{[substance][substantial form]} |
| 10539 | Frege refers to 'concrete' objects, but they are no different in principle from abstract ones [Frege, by Dummett] |
| Full Idea: Frege employs the notion of 'concrete' (wirklich, literally 'actual') objects, in arguing that not every object is concrete, but it does not work; abstract objects are just as much objects as concrete ones. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §26,85) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: See Idea 10516 for why Dummett is keen on the distinction. Frege strikes me as being wildly irresponsible about ontology. |
| 11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
| Full Idea: 'Red' is surely not going to be opposed to 'Cayster' [name of a river], as abstract to concrete, merely because of discontinuity in geometrical shape? | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
| A reaction: I've been slow to grasp the truth of this. However, Quine assumes that 'red' is concrete because 'Cayster' is, but it is perfectly arguable that 'Cayster' is an abstraction, despite all that water. |
| 1630 | We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine] |
| Full Idea: We are prone to talk about physical and abstract objects. It is hard to know how else to talk, because we are bound to adapt any alien pattern to our own in the very process of understanding or translating the alien sentences. | |
| From: Willard Quine (Speaking of Objects [1960], pt.I,p.1) |
| 10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
| Full Idea: If abstractions were defined by whether they could affect human sense-organs, light-waves would be concrete but radio waves abstract. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is a pretty good baseline example. No account should draw an abstract/concrete line through the electromagnetic spectrum. |
| 10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
| Full Idea: Dummett distinguishes, roughly, between those concrete objects which can be possible objects of ostension, and abstract objects which can only be referred to by functional expressions whose argument is some other object. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
| A reaction: At least someone has proposed a theory! Hale gives a nice critical discussion of the proposal. It is a moot point whether in the second case, when you pick out the 'other object', you are thereby able to refer to some new abstract object. |
| 10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
| Full Idea: The dichotomy between concrete and abstract objects comes to seem far too crude: to which of the two categories should we assign the Mistral, for instance? | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He has previously given colours and points as difficult borderline cases. We can generalise this particular problem case as the question of whether a potentiality or possibility is abstract or concrete. |
| 10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
| Full Idea: There is no reason for wanting a sharp distinction between concrete and abstract objects. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This rather depends on your ontology. If you are happy for reality to be full of weird non-physical entities, then the blurring won't bother you. If the boundary is blurred but still real, it is a very interesting one. |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 9210 | Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible [Fine,K] |
| Full Idea: If it is in the nature of a possible object to be abstract, this is presumably a property it has in any possible circumstance in which it is actual. If it is actual it is also concrete. So the property of being abstract and concrete are not incompatible. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p.14) | |
| A reaction: A rather startling and powerful idea. What of the definition of an abstract object as one which is not in space-time, and lacks causal powers? Could it be that abstraction is a projection of our minds, onto concepts or objects? |
| 10227 | The abstract/concrete boundary now seems blurred, and would need a defence [Shapiro] |
| Full Idea: The epistemic proposals of ontological realists in mathematics (such as Maddy and Resnik) has resulted in the blurring of the abstract/concrete boundary. ...Perhaps the burden is now on defenders of the boundary. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.1) | |
| A reaction: As Shapiro says, 'a vague boundary is still a boundary', so we need not be mesmerised by borderline cases. I would defend the boundary, with the concrete just being physical. A chair is physical, but our concept of a chair may already be abstract. |
| 10226 | Mathematicians regard arithmetic as concrete, and group theory as abstract [Shapiro] |
| Full Idea: Mathematicians use the 'abstract/concrete' label differently, with arithmetic being 'concrete' because it is a single structure (up to isomorphism), while group theory is considered more 'abstract'. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 4.1 n1) | |
| A reaction: I would say that it is the normal distinction, but they have moved the significant boundary up several levels in the hierarchy of abstraction. |
| 9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
| Full Idea: The distinction of abstract and concrete is one of kind and not degree. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.1.a) | |
| A reaction: I think I must agree with this. If there is a borderline, it would be in particulars that seem to have an abstract aspect to them. A horse involves the abstraction of being a horse, and it involves be one horse. |
| 9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
| Full Idea: Much of what science says about concrete entities is 'abstraction-laden'. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], III.A.1.d) | |
| A reaction: Not just science. In ordinary conversation we continually refer to particulars using so-called 'universal' predicates and object-terms, which are presumably abstractions. 'I've just seen an elephant'. |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| Full Idea: David's painting of Napoleon (on a white horse) is a 'picture' of Napoleon, and a 'symbol' of leadership, courage, adventure. It manages to be about something concrete and something abstract. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 3) | |
| A reaction: This strikes me as the germ of an extremely important idea - that abstraction is involved in our perception of the concrete, so that they are not two entirely separate realms. Seeing 'as' involves abstraction. |
| 10512 | The abstract/concrete distinction is based on what is perceivable, causal and located [Hale] |
| Full Idea: The 'concrete/abstract' distinction has a strong intuitive feel, and can seem to be drawable by familiar contrasts, between what can/cannot be perceived, what can/cannot be involved in causal interactions, and is/is not located in space and time. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.I) | |
| A reaction: Problems arise, needless to say. The idea of an abstraction can be causal, and abstractions seem to change. If universals are abstract, we seem to perceive some of them. They can hardly be non-spatial if they have a temporal beginning and end. |
| 10517 | Colours and points seem to be both concrete and abstract [Hale] |
| Full Idea: It might seem that colours would qualify both as concrete and as abstract objects. ...and geometrical points also seem to be borderline. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.II) | |
| A reaction: The theory of tropes exploits this uncertainty. Dummett (1973:ch.14) notes that we can point to colours, but also slip from an adjectival to a noun usage of colour-terms. He concludes that colours are concrete. I think I agree. |
| 10520 | Token-letters and token-words are concrete objects, type-letters and type-words abstract [Hale] |
| Full Idea: In familiar, though doubtless not wholly problematic jargon, token-letters and token-words are concrete objects, type-letters and type-words abstract. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: This is indeed problematic. The marks may be tokens, but the preliminary to identifying the type is to see that the marks are in fact words. To grasp the concrete, grasp the abstraction. An excellent example of the blurring of the distinction. |
| 10519 | The abstract/concrete distinction is in the relations in the identity-criteria of object-names [Hale] |
| Full Idea: Noonan suggests that the distinction between abstract and concrete objects should be seen as derivative from a difference between the relations centrally involved in criteria of identity associated with names of objects. | |
| From: Bob Hale (Abstract Objects [1987], Ch.3.III) | |
| A reaction: [He cites Noonan 1976, but I've lost it] I don't understand this, but collect it as a lead to something that might be interesting. A careful reading of Hale might reveal what Noonan meant. |
| 8953 | Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó] |
| Full Idea: It is better not to include in the definition of abstract entities that they ontologically depend on their concrete correlates. Note: ..but they may depend on the totality of concreta; maybe 'the supervenience of the abstract' is part of ordinary thought. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: [the quoted phrase is from Gideon Rosen] It certainly seems unlikely that the concept of the perfect hexagon depends on a perfect hexagon having existed. Human minds have intervened between the concrete and the abstract. |
| 22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
| Full Idea: The word 'concrete' is often used as the negative of 'abstract', with the slightly odd consequence that desires and hallucinations are thereby classified as concrete. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Numb') | |
| A reaction: There is also the even more baffling usage of 'abstract' for the most highly generalised mathematics, leaving lower levels as 'concrete'. I favour the use of 'generalised' wherever possible, rather than 'abstract'. |
| 13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
| Full Idea: My preferred view is that there is only one fundamental entity - the whole concrete cosmos - from which all else exists by abstraction. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: This looks to me like weak anti-realism - that there are no natural 'joints' in nature - but I don't think Schaffer intends that. I take the joints to be fundamentals, which necessitates that the cosmos has parts. His 'abstraction' is clearly a process. |
| 10493 | If concrete is spatio-temporal and causal, and abstract isn't, the distinction doesn't suit physics [Ladyman/Ross] |
| Full Idea: It is said that concrete objects have causal powers while abstract ones do not, or that concrete objects exist in space and time while abstract ones do not, but these categories seem crude and inappropriate for modern physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.6) | |
| A reaction: I don't find this convincing. He gives example of peculiar causation, but I don't believe modern physics proposes any entities which are totally acausal and non-spatiotemporal. Maybe the distinction needs a defence. |
| 14934 | Concrete and abstract are too crude for modern physics [Ladyman/Ross] |
| Full Idea: The categories of concrete and abstract seem crude and inappropriate for modern physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.6) | |
| A reaction: They don't persuade me of this idea. At some point physicists need to decide the ontological status of the basic stuffs they are investigating. I'll give them a thousand years, and then I want an answer. Do they only deal in 'ideal' entities? |