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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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To a first approximation, physicalism is the view that everything is physical. Reaching a second approximation requires attending to two tasks. (1) specifying further what it is for something to be physical. (2) Specifying the range of the quantifier “everything”.

I don’t want to get involved here in detailed discussion of (1). I take it to be plausible that abstract objects—for instance, numbers—will not trivially be included in the domain of the physical. That’s not to say that they don’t play an essential role in theories in physics. But I take that to present a difficulty for simplistic accounts of the physical—for example, as whatever figures essentially in theories in physics—rather than as a reason for counting abstract objects as physical. It’s anyway natural to think that abstract objects will not be included except via an account of how talk about abstract objects is not to be taken at face value as talk about abstract objects, but is rather to be given some other treatment. Perhaps, for example, statements putatively about abstract objects are true, but are not really about abstract objects; rather, they are indirect characterisations of properly (that is, trivially) physical elements. Alternatively, perhaps statements about abstract objects are apt to be true or false of abstract objects but, despite appearances, are uniformly false, and their function in successful explanations is to be explained without appeal to their truth. As a third alternative, it might be argued that statements apparently about abstract objects are not statements at all; they are more like rules or regulations governing the practice of statement-making proper. I take it that the natural, default position is that no such reconstruction is required and that statements apparently about abstract objects and apparently true are about abstract objects and are true. For present purposes, I will assume that the natural, default position is correct.

If “everything” in the characterisation of physicalism meant everything, then the existence of abstract objects would provide a counter example to physicalism. The defender of that strength of physicalism would therefore be required to pursue a project of reconstruction: either one of those sketched above, or some other means of avoiding our apparent commitment to the existence of abstract objects. In fact, however, it’s common to avoid the need to pursue such a project by allowing that the existence of abstract objects is not an immediate threat to physicalism. Rather than defend the strong view on which absolutely everything is physical, many physicalists opt instead for a weaker view on which everything that is located in space-time, and/or that interacts causally, is physical.

Furthermore, standard arguments for physicalism support only the weaker view. Here is a version of a standard form of argument.

P1. Let e be an element such that (a) e impinges causally on some elements, p, that are trivially physical and (b) the status of e as physical or not is up for grabs.

P2. Wherever there is causal impingement on p, there are physical effects on, or involving, p. (Supposed to be underwritten by conservation laws in physics.)

P3. Wherever there are physical effects on, or involving, p, those physical effects are determined to obtain by other physical elements, q, together with physical laws governing the behaviours of p and q. (From P2.)

P4. Suppose that e is not physical.

P5. In that case, something non-physical impinges causally on p. (From P1.)

P6. But any effects that e has on p are determined by physical q, together with physical laws. (From P3.)

P7. It’s implausible/wrong to suppose that effects on, or involving, p are determined by q and also by independent e. (Supposed general metaphysical principle.)

P8. It’s implausible/wrong to suppose that e is independent from physical q (From P4, P6, P7.)

C9. e is, or is dependent upon, physical q.

Whether or not we think that this, or some successor, provides a good argument in favour of physicalism, it’s clear that it only applies to es that impinge causally on physical elements. So, unless we think that all existent abstract objects do that, the argument will not, on its own, support a form of physicalism that includes in its range all abstract objects. In order to make the argument bear on the status of all abstract objects, one would need a supplementary argument to the effect that all abstract objects impinge causally on the physical realm. Such a supplementary argument might appeal, for example, to a combination of the apparent fact that we know things about abstract objects together with a general principle—in need of detailed defence—to the effect that we can know about things only insofar as they impinge causally on the physical, e.g. on the physical elements that constitute our brains. However, I think that most physicalists who also accept the existence of abstract objects would not want to take that route. Since such a physicalist would have independent reason to hold that abstract objects are not physical, they would have to treat the conclusion either as a ground for viewing the argument with suspicion, or as a ground for giving up their commitment to the existence of abstract objects. Instead, I think most such physicalists would prefer to adopt a form of dualism, according to which there are two fundamental realms of being: the physical realm and the non-physical realm of abstracta.

Even the weaker form of dualist physicalism would be undermined if there were elements that were at least partially located in space-time, and that interacted causally with physical elements, but whose natures depended essentially on abstract objects. In the sequel, I’ll sketch, without attempting to defend, an argument to that conclusion.

The following are some suggestions written for graduate students in the hope of encouraging, and supporting, them in asking questions at talks. They are not intended to be complete, or to provide a decision procedure. Usual levels of intelligence, reasonableness, and sensitivity are required in order to follow them. Two specific forms of incompleteness are worth mentioning: I say nothing here (except implicitly) about either politeness (and so non-agressiveness) or about the specific implementation of the aim of being helpful, e.g. to speaker or audience.  I take it that with respect to both issues, one quickly reaches the point at which written advice ceases to be helpful. But let me anyway say three things. First, philosophy is very difficult. One should view what one takes to be a speaker’s mistakes in that light. Second, rudeness, even when backed up by solid questions or objections, impresses only the foolish, and has a tendency to undermine whatever esteem might otherwise have been attracted by a good question. Third, being helpful includes allowing that others may have other questions to pursue, that there may be a variety of reasons for which the speaker may not be able fully to address one’s question there and then, and generally attending to the needs of all others in the room.

Three laws:

1. You are obliged to (attempt to) ask a question in every talk you attend.

2. In asking questions, the fundamental aim is to help oneself, other attendees, or the speaker to better understand the issues involved in the talk.

3. If you cannot think of a substantive question, then you should (attempt to) ask a question of clarification. (Corollary of Law 1 and Law 2: From 1, you should (attempt to) ask a question; From 2, if you have a question of clarification, there is a good chance that asking it will be of help to at least one of oneself, other attendees, and the speaker.)

Hints and tips:

1. Always bear the first Law in mind when auditing a talk: the pressure is on for you to ask a question once the talk has finished, so you should spend the talk trying your utmost to generate one.

2. It can be helpful to take notes during a talk, especially to note points that you found objectionable or unclear.

3. You may find it helpful to write your question down before asking it. This can serve as a sort of support when you come to ask your question. A side benefit is that some speakers will ask you to repeat/fill out your question, and having a written version to hand can be helpful in that case.

4. Always listen carefully to what the speaker says in response. If you are unsatisfied with the speaker’s response as at least addressing your question, it is often worth pressing them, perhaps simply by saying ‘Sorry, I may be being slow, but I’m not sure how that answers my question.’ My own rule is to try to only respond once in this way. If you are unsatisfied, the chances are that others are too; you can either rest content with that result, or allow others a chance at pressing the same line of questioning. However, if the speaker’s response appears to address your question, but in a way that opens them to further objection, you can (with chair’s permission) press them with the further objection. Again, my own basic rule is to stick to two, or at most three, bits of to-ing and fro-ing.

Some styles of question:

1. The question of clarification. E.g., ‘I wonder if you could say a little more about…’

2. The question of comparison. E.g., ‘You said X, but (insert philosophers name) denies Y [optional: because Z], and it wasn’t clear to me that you had explained why you think (insert philosophers name) is wrong about this [optional: what your response was to the considerations they raise against X].’

3. The counterexample. E.g., ‘If I understood you correctly, you said X. But suppose Y. Wouldn’t that be a counterexample to X?’

4. The putative inconsistency. E.g., ‘You appeared to say X at the start of your talk, and then to say Y later in your talk. Isn’t there at least a tension between X and Y?’

5. The additional case. E.g., ‘If your proposal is viable, one would expect it to cover Y. Do you think that’s right? And if you do, I wonder if you could say something about how your account does cover Y [optional: because there would appear to be the following difficulties].’

6. The distinction. E.g., ‘You appeared to treat the following claims (/case/etc.) as on a par, but there appears to be a distinction between them [optional: because…]’

7. The support. E.g., ‘I wonder whether it might be helpful to consider X in developing your case (/responding to objection Y, explaining claim Z, etc.) [optional: brief expatiation on X].’

A question that has occupied many botherers of the meal–snack distinction concerns the placement of soup: can soup, taken alone, constitute a meal, or is it at best a snack? The following represents an attempt to decide the issue, based on minimal assumptions.
Assumption 1: Necessarily, for all x, if x is such that, were x part of a meal, then it would be at most a proper part of the meal, then x is not a meal.
Assumption 2: Necessarily, for all x, if x is food, then it is either a snack or a meal.
Assumption 3: Necessarily, for all x, if x is soup, then x is food.
Assumption 4: Necessarily, for all x, if x is soup, then were x part of a meal, then it would be at most a proper part of the meal.
Plausibly, it follows from the four assumptions that necessarily, if x is soup, then x is a snack. The putative deduction might be challenged by defenders of modal logics far weaker than S5, or by defenders of some forms of non-classical logic. Assumption 3 might also be challenged by so-called deviant food classifiers, according to whom soup is a drink rather than food. However, I believe that what is presented here will be acknowledged as a proof by all orthodox theorists.

In a previous post (“Permission to believe?”), I briefly discussed a question that arises from a proposal made by Seyed Ali Kalantari and Michael Luntley (and in different forms by others) about a norm governing believing (and, in particular, believing qua believing, in the course of deliberation). The norm that they propose is, in one formulation, the following:

(1) For any S, p: it is permitted for S to believe that p only if p is true. [Their (12).] (Kalantari and Luntley, 2013: 422)

Now one comment that arose from the previous post concerned precedence: it was suggested by Clayton Littlejohn that he, and others, had proposed the same, or very similar, norms as governing believing. I don’t know the relevant literature well enough to comment in detail. But discussion with Kalantari suggested the following perhaps distinctive feature of his own proposal: his view is that (1) is the only norm included in the very concept of belief. (We can leave open for present purposes precisely what inclusion in a concept amounts to.) So, insofar as others who have proposed analogues of (1) held that this was either only one norm amongst others included in the concept of belief, or held that the norm was not included in the concept of belief, their positions are significantly different than Kalantari’s. Now, assuming that that makes it so that (1) is the only norm governing believing per se, there will be further consequences. In particular, because, in that case, no other norm would be available to rule out believing in cases in which p is true, it will follow that where p is true, one is permitted to believe. Slightly more formally, we will have (2) in addition to (1):

(2) For any S, p: it is permitted for S to believe that p if p is true. [Their (12).] (Kalantari and Luntley, 2013: 422)

But crucially—another potential difference between Kalantari’s position and others—(2) is not included in the concept of belief. Rather, (2) is a consequence—albeit an immediate consequence—of the inclusion of (1) in the concept of belief, together with the fact that (1) is the only norm included in the concept of belief.

So construed, the proposal raises a further question. (1) tells us, in effect, that if our deliberations indicate to us that it’s not the case that p, then we are not permitted to believe that p. That is, in those circumstances, we are prohibited from believing that p. But what should we do in case we discover that p is true? In that case, (2) permits us to believe that p. But nothing requires us to believe p. Thus, (1) (even when conjoined with (2)) appears to leave it open that we might discover that p is true, and yet take it that we are not thereby required to believe that p. Moreover, we might do so while perfectly adhering to all the demands set by the concept of believing. In an earlier post (“Remarks on the transparency of belief”), I suggested that we might sometimes find ourselves in that position. The question raised by the proposal that (1) exhausts the norms determined by the concept of believing is whether it’s right to think that there’s nothing special about being in that position: whether, that is, the concept of believing allows that we might perfectly adhere to its demands while consistently withholding belief in the face of discoveries that so believing would be believing truly.

References

Kalantari, S. A. and Luntley, M. (2013). ‘On the logic of aiming at truth.’ Analysis 73(3): 419–422.

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