Is Christmas cake homeomerous?

If Christmas cake is homeomerous, then any part, or area, of a quantity of Christmas cake is itself a quantity of Christmas cake. The grain of Christmas cake—the fact that Christmas cake stuff is lumpy—has lead many thinkers to deny that it is a homeomerous stuff. For, they argue, some sufficiently small areas of Christmas cake contain, not Christmas cake, but rather, for example, contain only sultana.

Now it’s clearly true that there are bounded areas of Christmas cake that contain sultanas without containing other cake stuff. It’s also true that no sultana is, per se, a quantity of Christmas cake. However, it would follow that Christmas cake is not homeomerous only if it were also true that no sultana constitutes a quantity of Christmas cake. That is, the failure of homeomerousness would depend on the claim that areas of Christmas cake stuff whose boundaries coincide with the boundaries of a sultana do not contain, in addition to sultana, a quantity of cake. And that doesn’t follow just from the fact that the boundaries of a detached sultana—a sultana surrounded by air rather than, for example, cake—would contain no cake.

The suggestion, then, is that the claim that Christmas cake is homeomerous might be defensible if we were willing to accept two general claims about stuffs: (1) the contents of an area of stuff can depend upon the contents of more extensive areas of stuff including that area—so that, for example, whether a sultana constitutes a quantity of cake may depend upon whether it is attached to surrounding cake; (2) an area can contain a plurality of fundamental kinds of stuff, including, for example, both sultana and Christmas cake.

The present discussion may also bear on questions about the metaphysical nature of the holes in certain cheeses.

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24 comments
  1. Notwithstanding the point you are willing to make, I would frame this as follows (fallacious as my approach may be):

    – If by “homogeneity” we refer to the possible homogeneity of the matter that forms the christmas cake, then we need to examine/test/prove the constitution of that matter to see whether all of its elements are homogeneous or not — the answer can follow from there.

    – If we only consider the idea/thought of the christmas cake, of whether we think of that cake or “cake-ness” as homogeneous or not, we must draw clear delineations between the cases we examine. A consideration of a cake as such, is not the same as a consideration of its elements which are related in a specific way to derive what we call ‘cake’; just like a consideration of the matter called ‘sultana’ is not the same as a consideration of all the physical elements (atoms, molecules etc.) that interoperate in a very specific way to derive ‘sultana’.

    – A part, when considered as such (when decontextualised), constitutes a whole in as far as that consideration is concerned; so that a sultana per se differs from a sultana that is treated as a part of a christmas cake — its context is different and so may be the meaning it contains/conveys. This suggests that the constitution of the case thus considered is different from another case whose facts/elements in their given interoperation can/do vary.

    – So, depending on whether we are considering the part qua part of a whole or as such, we have (at least) two distinct cases. In the case where the part is thought as part, it is not just “sultana” that we are thinking of, but “sultana that is part of a cake in a given way”. If the “given way” encompasses the specific interoperation of all the facts/elements that form the thing (or higher-order meaning) called “cake” and if a different relationship/interoperation of these facts/elements would yield something other than that specific “cake”, then it can be argued that in this case we have a context-specific homogeneity of meaning (homogeneity of what is thought as cake). But if we are to treat “sultana” as such, and we proceed with the same approach to all other elements that form the “cake”, we do end up thinking of a heterogenous number of elements — heterogeneous with respect to one another, but homogeneous with regard to their own idea/thought; and, if so, we may only proceed to argue for homogeneity in light of the specific arrangements and complementarities of the elements that form the structure called “cake” — again a different case from each fact/element per se, because we include in the consideration something other than the element as such, namely the “arrangements and complementarities of the elements that form the structure…”.

    Thanks! Enjoy the holidays — oh, and the christmas cake 🙂

    • Thanks for your comments.

      1. Your first comment suggests that testing for homogeneity (or homeomerousness) requires examining the constitution of the matter. That’s true. But it doesn’t follow that it doesn’t also involve a priori reflection, including reflection on necessary conditions for homeomerousness, and how they are to be applied to matter. The post concerned mainly the latter, though drew on some obvious facts about the matter.

      2. The suggestion about parts and wholes seems to be more or less in line with what I suggest. I wouldn’t put the point in terms of meaning, since I don’t think that sultanas, quantities of cake, &c., typically have meanings.

  2. Rashers said:

    If it is constitutive of genuine/authentic Christmas cake to contain a lucky Christmas coin, are we then forced to say that the coin is, in sultana-esque fashion, cake?

    If so, must I, on pain of impolitely refusing kindly Christmas cake, digest metal this Christmas?

    • Thanks for your comment.

      The first point to note is that the thought isn’t that a sultana, or any other detachable constituent, is cake. At best, such stuffs can constitute, or partially constitute, cake.

      There are then two broad lines of response. The first accepts that a suitably placed coin can constitute a quantity of cake, but denies that every part of an edible stuff must itself be edible. A natural comparison here would be with bones that partly constitute a quantity of meat.

      The second response denies that a suitably places coin can constitute a quantity of cake. The natural rationale for the response would be the following. It was suggested in the post that contiguity with other cake-stuff might be a necessary condition for a sultana to constitute some cake-stuff, but not that contiguity is alone sufficient. Plausibly, there are other necessary conditions, generically, conditions on being an ingredient in fruit-cake. Since a coin might well be thought not to meet those conditions, we have distinctive reasons to deny that it can constitute a quantity of cake-stuff.

  3. Updated in light of helpful terminological correction from Mark Kalderon, and some timely copy-editing advice from Allen Stairs. And champagne.

  4. Eric Weir said:

    If Christmas Cake is cake stuff *and* sultana stuff, the fact that there are bounded areas of each kind of stuff containing no part of the other kind is irrelevant to whether Christmas Cake is homeomerous.

    Cake stuff without sultana stuff is not Christmas Cake. Christmas Cake is cake stuff *and* sultana stuff.

    Whether a combination of cake stuff and sultana stuff is Christmas Cake depends on how evenly bits of cake stuff and sultana stuff are distributed in the mixture. That cannot be settled in the abstract by argument. It is settled by measurement on a case by case basis.

    The ratio of cake stuff and sultana stuff may vary from case to case. All that matters is that there is cake stuff and sultana stuff and nothing else, and that the bits of each are evenly distributed in the mixture.

    • Thanks for your comments.

      1. Why think that Christmas cake is cake stuff *and* sultana stuff? It might be constituted by either stuff, and its constitution might depend on its containing both. But that doesn’t suffice either for the identity claim, or for requiring that every quantity of Christmas cake contains both. So, I don’t see any grounds for endorsing your irrelevance claim.

      2. About measurement versus abstract argument, the point is obvious and in no conflict with anything in this post. The post explicitly deals with a specific argument, based on assumptions about measurement, to the effect that Christmas cake cannot be homeomerous. It aims to suggest one line of response to that argument. Obviously, showing that an argument against a claim can be answered doesn’t show that the claim is true. Similarly, here: no attempt is made to argue that Christmas cake, or any particular sample allegedly of Christmas cake, is homeomerous.

      3. The ratio claim seems plausible enough, and appears to be perfectly consistent with the suggestions made in the post.

      • Eric Weir said:

        First thanks for the response.

        Regarding (1) two responses: (a) the issue is whether a kind composed of at least two other kinds which are discontinuous can be homeomerous; without at least two kinds there is no issue. (b) the irrelevance claim can be rephrased: failure of homeomerousness does not follow from the fact that the kind is composed of two different kinds.

        Regarding (2) again multiple responses: (a) lacking an explicit statement that the argument is not for homeomerousness, but only against an argument against homeomerousness, a natural reading of the original post is that it is an argument for homeomerousness. (b) accepting that the argument is an argument against, my claim can be revised to be 1(b).(c) I accept your first general claim as a clearer statement of the reason I gave—cake stuff without sultana stuff is not Christmas Cake—but I would rephrase it: the *nature* of an area of stuff can depend upon the *nature* of a more extensive area of stuff containing it.

      • Thanks.

        Your rephrasal is, in effect, half of the suggestion made in the post. However, I think it requires (at least) supplementation by the second half: the claim that more than one fundamental kind of stuff can be found in a given area. Otherwise, the cake stuff in an area would replace, rather than supplement, what would, if detached, have been sultana. And that seems implausible.

  5. Eric Weir said:

    If we move to the atomic or subatomic level, the argument against homeomerousness would seem to imply that detached cake stuff is not cake stuff. Likewise sultana stuff.

  6. Thanks for your comments.

    It’s not clear why the move to the atomic or subatomic level makes a difference, though it may do.

    The argument against homeomerousness implies that *some* quantities of stuff are too small to be quantities of cake stuff, whether or not they are detached. It isn’t required to hold that there are *no* detachable portions of cake that retain that status when detached.

    The suggested response to the argument against homeomerousness is that it matters whether or not those quantities are detached. The claim made in the argument about detached portions–that some of them are not cake–seems plausible to me: a detached sultana doesn’t seem to me to constitute some cake. (Grounds for doubt here might be that if the sultana has once constituted cake, it persists in doing so, even when detached.) The case seems even stronger for detached subatomic parts. Cakes contain hydrogen atoms. But it doesn’t seem plausible to hold that every detached hydrogen atom constitutes cake.

  7. Eric Weir said:

    Again, thanks for the response.

    I see now that the point about moving to the subatomic level is not directly relevant to the issue of homeomerousness. At this point I would only claim an analogy: If Christmas Cake cannot be homeomerous because it is composed of multiple discontinuous kinds, shouldn’t we then say that detached cake stuff is not cake stuff because it is chemically complex?

    I agree with your other observations.

    • Thanks.

      The argument against homeomerousness doesn’t seek to deny that there is cake stuff. It seeks to deny that all areas of cake stuff contain cake stuff: too small areas contain only non-cake stuff, for example by containing only sultana. At most, chemical complexity would be apt to lead them to deny that sultana-free cake stuff is homeomerous. But I take it they’d happily make that denial. The fruitcake example is just an example of a more general issue, and a more general range of claims.

      • Eric Weir said:

        “At most, chemical complexity would be apt to lead them to deny that sultana-free cake stuff is homeomerous.” Exactly, though I was assuming it would be an unwanted conclusion. Off-the-top-of-my-head I don’t know how to respond to those who would “happily” draw that conclusion or others like it. Maybe later.

  8. Eric Weir said:

    The blog is not letting me respond directly to your latest response in the thread of my initial response, i.e., the one about Christmas Cake being cake stuff *and* sultana stuff. Here goes anyway.

    I’m inclined to agree that the second half of your suggestion is needed. I’m not sure I understand the problem you see if it is not included. And when I think about what my argument for including it would be I am led to wonder whether both parts of your suggestion might not be circular. At least I would think those arguing against homeomerousness would find them as difficult to accept as the claim of homeomerousness for Christmas Cake.

    I am also inclined, however, to wonder whether it might not be possible to get along with just the first part of your suggestion. If we have a kind contained in another kind we have a plurality of kinds and the suggestion does not preclude there being more than two. But since I don’t understand the problem you see if the second part is not included, perhaps I am missing something.

    My own argument for the second part of the suggestion? A bit uncertain, but I’m inclined to say it’s a fact that has to be accepted: Almost all stuff is made up of other stuff. Very little is not complex. There is reason to suspect that everything that seems simple is potentially complex. Is anything absolutely simple? If there is, does it follow that it’s the only thing that is?

  9. philori said:

    Since it’s reasonable to say: “I baked a Christmas cake” when I actually forgot to add sultanas, the Christmas cake with sultanas is not homogeneous.

  10. Thanks for your comment.

    I’m afraid that I’m not convinced either by the base claim or by the alleged consequences. As to the base claim, it might be reasonable to say “I baked a Christmas cake,” even though it’s not strictly and literally true. We might even think that it’s not reasonable in the described circumstances; more reasonable, at least, would be to say “I *tried* to bake a Christmas cake.”

    Be that as it may, I don’t see why its being true that Christmas cake can fail to contain sultanas (supposing for the sake of argument that that is true) would entail that Christmas cake that does contain sultanas is not homeomerous.

  11. philori said:

    Well, my suggestion is “Let it be a Christmas cake even if it’s without sultanas, and then Christmas cakes without sultanas are homeomerous, however those with sultanas are not”. Further, I would say that the part of the thread about the atomic and subatomic level is not relevant for mereology. I see that parthood has to be transitive, however this is subject to limitations. Unless limitations of this kind are given, there are no homogeneous or homeomerous wholes at all. A universal wouldn’t be a homogeneous whole, for example…

  12. Yes, I understood what your suggestion was. But you didn’t provide any grounds for taking it to be true, so it’s a bit hard to assess.

    • philori said:

      My witnesses would be linguistic usage (i.e. Christmas cakes without sultanas being still called “Christmas cakes”) plus an argument salva veritate against unrestricted transitivity of parthood (given by the need to let at least universals be homogeneous).

  13. For the sake of argument, I was willing to accept the claim about linguistic usage (although I think it doubtful), and also the claim that linguistic usage reflects truth (which again, I think is doubtful). What I was hoping for was an explanation of why you think the claim that there can be Christmas cake with, and Christmas cake without, sultanas, together perhaps with the claim that Christmas cake without sultanas is homeomerous, entails that Christmas cake with sultanas is not homeomerous. What you offer here doesn’t seem on its face to be such an argument; at best, it alludes to an argument.

    Further, it’s not clear why opponents of homeomerousness of Christmas cake should be moved by the generality of their argument, supposing that the argument does generalise. Why shouldn’t they deny that any substances–or most substances, depending on the generality of the alleged argument)–are homeomerous?

    • philori said:

      My thought is, since a Christmas cake without sultanas is defined as a homeomerous Christmas cake (and you accepted this for the sake of argument) it follows straightforwardly that a Christmas cake with any other addition (e.g. sultanas) is not homeomerous.
      Of course, the opponent of homeomerousness has a point. But she must live with being a nominalist. A consistent argument against homeomerousness implies that there are no universals since universals make sense only as homeomerous/homogeneous wholes whose proper parts are all and only those entities which are of the kind which forms the universal. Since nominalism is logically consistent, why not? The only arguments against this option would be of philosophical nature.

  14. Thanks.

    1. I’m afraid I don’t think it does follow straightforwardly from the existence of homeomerous sultana-less Christmas cake that sultana-ed Christmas cake is not homeomerous. In fact, it’s far from obvious to me that it follows at all, straightforwardly or not. What I was hoping for was some articulation of the supposed argument from one claim to the other.

    2. I’m afraid I don’t understand your reflections on universals at all. Why should universals only make sense as homeomerous, or (a distinct claim) homogeneous, wholes at all? If they must be one or another kind of whole, why should they have parts? If they have parts, why should those parts be entities of the kind which forms the universal? And why should their being so require that they be homeomerous, or homogeneous?

    3. A consistent argument against homeomerousness might only be an argument against the homeomerousness of some possible substances. It needn’t be an argument that homeomerousness is impossible. It might even be restricted further, e.g. to contingent substances. Again, the bearing on issues about universals on issues about contingently existing substances like cake is hard to make out without much more articulation.

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