Thursday, May 20, 2004

Identity, Properties & Reduction

It seems intuitive that identical objects must share all the same properties. Right? Since if they have different properties then they clearly aren't strictly identical.

It seems similarly intuitive that any object is identical to the totality of that which it is reducible to. We want our 'reduced' description to match the original object, not some different object. For example, a table is identical to the totality S = {its four legs, the tabletop, and all the relations / inter-connections between these parts}.

But these two principles can't both be true. Why not? Because any 'reduced version' of an object necessarily has some different properties from the original X - for example, the property of 'being a reduced version of X'. So either (1) reduced-X is not identical to X, or (2) identical properties are not necessary for metaphysical identity.

Initially, (1) may seem the more appealing response. It seems reasonable to say "the whole is more than the sum of its parts". Indeed, if "parts" is understood only to mean the material component parts (excluding the relations between them), then this famous phrase is most certainly true. But here we are including the relations between the separate parts, so they are no longer separated at all. Rather, we are considering their interconnected totality. The gestalt motto now seems far less plausible (to me, at least).

What could a table possibly have that the set S does not? There are some different properties, as identified above, but these are far from obvious. It strikes me as very strange indeed that an object could be fundamentally different from its reduced counterpart, merely by virtue of its being unreduced. Where do these differences come from? Imagine reducing an object down to the atoms which make it up (and all their relevant relations / connections to each other, of course). If there is a difference, then the object must consist of some non-physical component parts. Well, I guess that's exactly what 'properties' are?

Hmmm. I did intend to go on and argue that we're better off with response (2), but I'm tired and confused - hopefully I'll be able to make more sense of this another day.

Update: Okay, now that I've actually learnt some metaphysics, I realise that we don't want to go with response (2) either, for that is to deny the widely-accepted indiscernibility of identicals principle.

Instead, we can either:
3) Deny that 'is a reduced version of X' is a property
or 4) Deny that reduced objects actually possess this property.

Now, (3) is rather ad hoc, so probably isn't the most convincing move. (It does have precedent though, since realists have to claim 'exemplifies' isn't a proper relation in order to avoid various paradoxes).

How about (4)? I think that's probably the right one, strange though it may at first seem. This works, I think, because a reduced object isn't actually a different object from the original at all, it's just a different way of describing it. So this special property doesn't belong to the 'reduced object' at all, it just belongs to the description.

In support of this idea, consider Superman, who is Clark Kent in disguise. However, we surely don't think that the person denoted by 'Superman' has the property of 'being Clark Kent in disguise', because that very same person is Clark Kent, and he's not always disguised. It's the name/persona/description 'Superman' which is the disguise. The person himself stays the same throughout.


  1. This is Greg, obviously. I just can't be bothered making an account (I like the Haloscan comments more, actually).

    I was thinking about our talk and the idea of red not being real, whereas the idea of a table was. Specifically what you said about the table being made up of things that aren't real, wouldn't that require that the table also not be real?

    I think I've more clearly clarified my thinking here, but it's probably not consistent. I'm not great at this sort of thing, so if you can see a flaw, feel free to point it out :)

    Anyway, suppose we have Red, which is not a real concept, in that it has no other properties, and when you think of the concept 'red' you likely think of an item that has its colour property = red. There is no concrete 'red' itself, only some kind of representation of it - a red ball, or a graph of the wavelengths of light with one section circled. I'm not entirely sure if this makes sense, when compared to the concept of table. Are you actually imaging the real concept 'table', or are you simply imagining a specific example of table? The latter would seem just to be the same as your imagining of red, really, yet I'm calling red 'non-existent' and table 'existent'.

    Anyway, I'll go on from that shakey basis:

    Red is not real, but a rainbow is. A rainbow consists of roughly 7 colours, which don't exist. So you would think that anything that consists entirely of things that don't exist, must also not exist. Which is where I throw in the idea of aggregation. Anything that is an aggregation of properties, is real, whereas anything that isn't, is not real. So red does not have any properties other than it itself being a property. But a rainbow would have the properties of having 7 colours, which is an aggregation, so it would be a real concept.

    The more I think about this, the more I think that this arguement is horribly flawed and silly, but oh well, interesting to consider, at least, I think.

  2. Yeah, that is an interesting idea. I disagree with it - but it is interesting :)
    I don't see any logical inconsistencies in it. It's just a bit odd to say that an aggregation of non-existent properties could be any more real than the parts from which it is made.

    There's also the problem that your assertion that "Red has no properties" is - technically - false. For example, it has the properties of 'being a property', 'being non-corporeal', 'being non-existant' (according to you ;)), and infinitely many others can be constructed along the lines of 'being zero or not-zero', etc.

    But I think I get the idea of what you mean, it's just difficult to express it precisely (in such a way as to avoid trivial objections such as the previous paragraph). Correct me if I'm wrong, but I think what you mean is that a concept is real if it is appropriately constructed out of other, more basic, concepts (which may or may not be real). [Thus you could say that 'red' is not real, because it isn't "appropriately constructed" out of the trivial properties I mentioned above.]

    This produces a new problem, in that you seem to be forced into asserting that unicorns are more real than colours. After all, the concept of 'unicorn' is appropriately constructed out of other concepts (i.e. horses and horns), in exactly the same way that the concept 'table' is constructed from more basic parts. So you might want to add in an extra condition to the effect that a 'real' concept must have at least one real-life instance/exemplar.

    So, with a bit of work, I think your theory could be made reasonable. But I'm not really too sure whether it's worth it. That is, I'm not convinced that we should want to say that complex concepts (eg 'table') are any more real than basic concepts (eg 'red'). I just don't see what the motivation for such a distinction would be.

    For myself, I'd probably prefer one of the following two extremes:

    1) Full-blown Platonism: Every possible universal concept necessarily exists (outside of space & time), from 'red' to 'table' to 'unicorn'.

    2) Austere Nominalism: No universals exist, only particular objects exist. When we say two objects are both 'tables', all we really mean is that they have a relevant similarity that makes it worthwhile for us to group them together. They don't actually share any metaphysical 'essence' though.

    There is a nice compromise called 'trope theory', which I might blog about some time soon though (I think our metaphysics lecture on Monday will be about that).

  3. I disagree with it needing a real example in order for it to be a real concept.

    Books and literature have unicorns in them, and when someone says "unicorn" you get a fairly certain picture of what they mean, just like when someone says "table". It doesn't need to exist in the world to be a real concept.

  4. Fair enough (I would tend to agree, actually, since I think if you accept any universals you should really accept them all).

    But why deny the reality of redness? Surely we can picture redness, at least as well as we picture unicorns. We can also talk about it as an abstract noun, e.g. "Red is my favourite colour". And it really doesn't seem plausible that, when pointing to a red table, saying "this object is a table" is relevantly different from saying "this object is red". (Red may be more 'basic', as previously discussed, but I'm not sure why that is a relevant difference here?)

    So why are you wanting to say that redness is not a real property? (I don't mean to be 'attacking' here, I'm genuinely curious about what reasons you have for making this distinction.)

  5. Because red is never anything more than some other object's colour property, it can't exist on its own without other objects/concepts existing for it to be applied to.

    So it's sort of a parasite, rather than a stand-alone entity.

    Maybe it still is a 'real concept', but just a different sort of 'concept'? As I said the first time, a table is a real concept because it has all sorts of intrinsic properties and actions directly associated with it; 4 legs, a table-top, and people like to have them in their houses and put objects on them. Whereas red doesn't have any of this, other than just existing. It may be someone's favorite colour, but that doesn't affect red itself, merely that person's conception of red.

  6. Is a 'reduced version' of an object simply a description of an object in terms of the totality of its parts and inter-relations among its parts?

    If so, then why would we attribute to that object (i.e., the object picked out by the description that refers to the totality of the objects' parts/inter-relations among its parts) any properties that we would not attribute to the original object?

    It doesn't seem to me, for example, that "being a reduced version of" is a property of the object picked out by the longer description at all. We are not talking about a different object, but simply a different description of the same object, or so it seems to me.

  7. Right, that's the same conclusion I come to at the end of the post.


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