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Definitions wanted: Abstract and Concrete

  1. Dec 30, 2004 #1

    honestrosewater

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    Pretty straightforward, right? I want some definitions for "abstract" and "concrete".

    If anyone is interested in doing some reading, here are some links: 1, 2, 3, 4, 5(PDF), 5(HTML). I see a connection to consciousness and qualia, but don't ask me to explain it. :yuck:
     
  2. jcsd
  3. Dec 30, 2004 #2

    loseyourname

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    A proposition form is "abstract." An instance of this form is "concrete." A definition would be "abstract," but I gave you a concrete example of these terms in context, hoping that would help instead. An abstraction is basically the most universally applicable generalization of a concept you could make, whereas a specific instance of the concept would be concrete.
     
  4. Dec 30, 2004 #3

    honestrosewater

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    What are the natures of forms and instances? Are you meaning "form" to be a facet of an entity? How do forms and instances relate to spacetime and causality, if at all?
     
  5. Dec 31, 2004 #4
    Hi,

    To me abstract is divorced from data. Concrete is based on data.

    juju
     
  6. Dec 31, 2004 #5

    loseyourname

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    "If x, then y" is a proposition form.

    "If I throw a rock at my window, then it will break" is an instance of that form.

    One is abstract, the other is concrete.
     
  7. Jan 1, 2005 #6

    honestrosewater

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    But can you class the elements of the atomic sentences as abstract or concrete? Do abstractness and concreteness apply only to propositions?
     
  8. Jan 1, 2005 #7

    loseyourname

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    What's an "atomic sentence?" Abstractness and concreteness don't apply only to propositions. I'm just giving an example of the terms in context. That is the way we learn language, after all.
     
  9. Jan 1, 2005 #8

    honestrosewater

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    I'll be completely shocked if you aren't already familiar with what I am talking about- perhaps you call it something else. It's just the simplest declarative sentence, containing names and predicates but no logical operators. In your example, "x" and "y" would be the atomic sentences, and "If x, then y" is a compound sentence. I guess it's possible that I'm confusing something, but I can't imagine what.
    Okay. Can you extend the definitions to all cases, to apply to all objects or entities?

    I'm trying to come up with some thoughts of my own to offer, but I can't do much more than blather. I'll just rattle off some of my assumptions and such. I'm interested in the ontological aspects of the abstract v. concrete distinction. I assume every object can be classed as either abstract (B) or concrete (C) but not both. So B and C are properties of objects. B is the negation of C and vice versa. Intuitively, C is pretty easy to define, while positively defining B is much harder; Any definition of B would be just "not C". I wonder what is the significance, if any, of the difficulty in positively defining B. I could define C quite easily without reference to B, as "an object is C if I can sense it or it takes up space...", and I think I can complete the definition of C without any reference to B. I would probably end up with what is a common definition of C, something like, "An object is concrete if it is spatiotemporal and/or causally efficacious." Immediately, I'm not sure if it should be "and" or "or (inclusive)" or "xor (exclusive)", keeping in mind what it would mean for B, C's negation. Sadly, that's about as far as I've gotten.
     
  10. Jan 1, 2005 #9
    A concept is abstract if it doesn't have a specific instance. For example, the concept of fruit and shape are abstract. An apple is a fruit. A triangle is a shape. However, there is nothing that encapsulates the idea of fruit or shape alone. In other words, an apple is a fruit but fruit is not an apple. It's a subtle distinction.

    Abstract concepts exist only as constructs of the mind. It's impossible to instantiate an abstract concept, so you can't classify an object as entirely abstract. Secondly, I don't think you can disassociate the two with objects. Consider the example above. An apple is a concrete instance but it is also a fruit. Every object that I can think of is both concrete and abstract, but not purely abstract or purely concrete.
     
  11. Jan 1, 2005 #10

    loseyourname

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    Oh, you mean a basic or simple proposition. Well, "x" is abstract. "Adam is 24 years old" is concrete.

    I already did:

    I'm not so sure about that. You cannot sense a proposition instance, nor does it take up space, but it is still concrete. In fact, if we look to math, any expression containing only variables is abstract, whereas an expression containing numbers that are instances of those variables is concrete. But no mathematical expression has a material existence.

    I suppose you can refine what I said to something like:

    An object is abstract if it is at least partially uninstantiated and can be specified. An object is completely abstract if it cannot be generalized any further whatsoever.

    An object is concrete if it is completely instantiated and cannot be specified any further.

    I'm actually not even certain if that is really entirely accurate. Take the expression "x+1." "x" in this case is abstract, but "1" is concrete. So what would we call the expression itself? It really depends on the context. It is more abstract than the expression "1+1" but less abstract than the expression "x+x." Perhaps the concepts are not dichotomous at all, but rather only relative.
     
  12. Jan 3, 2005 #11

    honestrosewater

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    I was using "object" in the most general sense. I may eventually need to distinguish "object" from "property", but I think "property" would just be a special kind of "object".
    I think abstract/concrete is more general than physical/nonphysical (or material/nonmaterial); I think all abstract objects and some concrete objects are nonphysical.
    Yes, the set of apples is a proper subset of the set of fruits. The relation between fruit and apple is antireflexive, antisymmetric, and transitive (right? :redface: ). But what about the relation between an abstract concept of "apple" and a concrete instance of "apple"? If the concept of "apple" were a set, it could contain more than one element; apples can be different colors, shapes, sizes, etc. If an instance of "apple" were a set, it could contain only one element (not counting empty sets for now). But is an instance of "apple" a subset of the set of the concept "apple"? (Oy, sorry, I am transitioning between terms.)
    So constructs of the mind cannot be instantiated? Do you make any distinction between instantiation and representation?
    The distinction involves sets and elements. I (try to) explain it below.
    Right, but the idea of fundamental, indivisible, irreducible, "atomic" objects is what I am getting at. "Adam is 24 years old" is atomic relative to propositions, but it is not atomic relative to terms; It contains several terms: "Adam", "is", "24", "years", and "old". Those terms are not atomic relative to letters; "Adam" contains several letters: "A", "d", "a", and "m". I am assuming propositions, terms, and letters are all objects. And I need to find some way of meaningfully classifying them.
    I think this is why a distinction between instance and representation is needed. The concept of representation makes explicit the distinction between object and medium. The concept of instantiation seems to imply some medium in which an object is instantiated. When an object is represented in some medium, the nature of the object and the nature of the medium are not the same. But it seems when an object is instantiated in some medium, the nature of the object and the nature of the medium are the same. It would seem to follow that an object can be instantiated in, at most, one medium and represented in any number of mediums. I'm less sure about the case that all objects can be instantiated and represented in at least one medium.
    It is usually agreed that all mathematical objects are abstract (acc. to what I've read- I listed some links in my first post). I'm undecided.

    I am sorely lacking some structure so I'll start to build one by borrowing the concepts of urelements and proper classes from some versions of set theory. I would loosely associate concrete objects with urelements and abstract objects with sets (or set classes) and proper classes. Since I'm not secure in my knowledge of set theory, I can't yet be more precise about those associations. Those associations do raise several questions, but two of them especially stand out.
    1) Assuming that all physical objects are concrete, I'm not sure how urelements can accommodate a hierarchical structure of physical systems, emergent properties, and such. That is, I'm not sure how urelements can be structured without using sets or how I would account for emergent properties in that structure. These may not actually be problems, as the structure and such may not actually be concrete objects, or my assumption may be false.
    2) I'm not sure that no abstract objects are urelements.
    Perhaps this structure cannot give me the two disjoint and mutually comprehensive sets I want. I may need to make some further distinctions and adjustments. For instance, that concrete objects are urelements that are elements of only the set of concrete objects and the universal class. But some abstract objects are abstracted from concrete objects (these would be the properties- like whiteness, smoothness, i.e. qualia) which I may not be able to reconcile with concrete objects being urelements (i.e. atomic). Sorry, that isn't the greatest foundation. :rolleyes: I'm just not sure how to attack the abstract/concrete distinction yet. I need to do more reading so I can consolidate everything.
    I imagine this is something like proper classes.
    And this something like urelements.
    And this something like sets (sets being different from urelements and proper classes).
    And this is where the relativity of atomic objects would come in.
    I'm not saying my explanation is better. I still have a lot of work to do. I am not yet convinced the concepts are not dichotomous. I think they may just involve a very complex structure. And I think (if it exists) the dichotomy's meaning is unique (it isn't just physical/nonphysical or mental/nonmental or anything else). Of course, I may be wrong on all accounts.
     
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