Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

The ‘How Many?’ and the ‘Why Any?’ Questions and Their Connection

This post continues the ruminations begun here which were inspired by Stephen Maitzen's intriguing paper Stop Asking Why There's Anything (Erkenntnis 77:1 (2012), 51-63).

Let 'CCB' abbreviate 'concrete contingent being.'  For present purposes, the 'How many?' question is this: How many CCBs are there?  And for present purposes the 'Why any?' question is this: Why are there any CCBs?  There might have been none, but there are some, so why are there some?  (I take that to be equivalent to asking why there are any.)

What I want to get clear about is the connection between these two questions.  In particular,  I want to see if the senselessness of the first, if it is senseless, entails the senselessness of the second.

I think it is clear that 'CCB,' like 'thing,' 'entity,' 'existent,' object,' etc. is not a sortal expression.  There are different ways of explaining what a sortal is, but for present purposes a sortal

  • supplies a criterion for counting the items to which the term applies
  • provides a criterion of identity and non-identity among the items to which the term applies
  • gives a criterion for the continued existence of the items to which the term applies.

'Pen' and 'penguin' are examples of sortals.  I can count the pens and penguins on my desk.  There are five pens and zero penguins. (It's a tad warm for penguins here in the Sonoran desert.)  The penguins in Antartica are countable as well, in principle if not in practice.  (This use of 'countable' is not to be confused with its use in set theory.  A countable (uncountable) set is an infinite set the members of which can be (cannot be) placed in one-to-one correspondence with the natural numbers.)

'CCB' is not a sortal because it does not provide a criterion for counting the items to which it applies, say, the things on my desk.  Is a pen together with its cap one CCB  or two?  And what about the particular blackness of the cap?  Presumably it too is a CCB. Are we now up to three CCBs?  And so on.

Maitzen concludes that the 'How many?' question is a pseudo-question because ill-formed, and its is ill-formed because   it features a dummy sortal, a term that functions grammatically like a sortal, but is not a sortal.  As senseless, the question is to be rejected, not answered.

From this result Maitzen straightaway (without any intermediate steps) infers that the 'Why any?'' question is also senseless and for the same reason, namely, that it harbors a dummy sortal.  It is not clear, however, why the fact that the second question features the dummy sortal 'CCB' should render the second question senseless.  We need an argument to forge a link between the two questions.  Perhaps the following will do the trick.

1. If it makes sense to claim that penguins exist, then it makes sense to claim that there is in reality some definite number of penguins.  (It cannot  be true both that there are penguins and that there is no definite number of penguins.) Therefore:
2. If it makes sense to claim that CCBs exist, then it makes sense to claim that there is in reality some definite number of CCBs.  But:
3. It makes no sense to claim that there is in reality some definite number of CCBs. Therefore:
4. It makes no sense to claim that CCBs exist. (2, 3, Modus Tollens)
5. If it makes no sense to claim that CCBs exist, then it makes no sense to ask why CCBs exist.  Therefore:
6. It makes no sense to ask why CCBs exist. (4, 5 Modus Ponens)

I suspect that some such argument as the foregoing is running behind the scenes of Maitzen's text.  The crucial premise is (3).  But has Maitzen established (3)?  I agree that WE cannot count CCBs.  We cannot count them because 'CCB' is not a sortal.  And so FOR US the number of CCBs must remain indeterminate.  But from a God's Eye point of view — which does not presuppose the actual existence of God –  there could easily be a definite number (finite or transfinite) that is the number of CCBs.

On can conceive of an ideally rational spectator (IRS) who knows the true ontology and so knows what all the categories of entity are and knows the members of each category.  What is to stop the IRS from computing the number of CCBs?  We can't do the computation because we are at sea when it comes to the true ontology.  All we have are a bunch of competing theories, and the English language is no help: 'CCB' does not supply us with a criterion for counting.

In short, we must distinguish the question whether the number of CCBs is indeterminate in reality or only indeterminate for us.  If the latter, then we cannot move from the senselessness of the 'How many?' question to the senselessness of the 'Why any?' question.  If the former, the move is valid, but as far as I can see, Maitzen has not given any reason to think that the former is the case.

 

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Bill Vallicella

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25 responses to “The ‘How Many?’ and the ‘Why Any?’ Questions and Their Connection”

  1. Steve Maitzen Avatar
    Steve Maitzen

    Thanks, Bill, for your very helpful argument, which crystalizes reasoning that I unfortunately left inexplicit in my article. I’m grateful for it. If I end up using it in my next paper, I’ll of course credit you!
    You and I agree that “CCB” is supposed to be a category more general than any sort of being. That’s why parts of composite CCBs (e.g., parts of a penguin) automatically count as CCBs (even though parts of penguins don’t automatically count as penguins). Given that degree of generality, then, there’s no reason not to accept mereological universalism about CCBs: Any two or more CCBs (including parts of CCBs) compose a further CCB, even if it’s a “scattered” CCB. Given that starting point, we can show that there’s no total number of CCBs, unless that number is at most 1.
    (1*) N = the total number of CCBs. [Assume for reductio]
    (2*) N > 1. [Premise]
    (3*) Any two or more CCBs compose a further CCB. [Mereological universalism]
    (4*) Therefore: The definite total number of CCBs = 2^N – 1. [From (1*), (3*), power set axiom]
    (5*) (2^N – 1) isn’t N, for all N > 1. [Premise]
    (6*) Therefore: Not (1*). [From (2*), (4*), (5*), reductio]
    So unless there’s at most one, non-composite CCB, there’s no definite total number of them. If you reject (3*), I can try to defend it some more, or I may be able to come up with a cardinality argument that doesn’t require it.

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  2. Steve Maitzen Avatar
    Steve Maitzen

    Retraction: I screwed up! (4*) doesn’t follow. I forgot that the CCBs that compose a further CCB mustn’t overlap. Back to the drawing board.

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  3. Leo Carton Mollica Avatar
    Leo Carton Mollica

    Dr. Maitzen:
    Is (3*) really a widely accepted, or even plausible, claim? I was under the impression that, as generally interpreted, the doctrine of mereological universalism only is committed to any two or more *disjoint* objects forming a further item. Otherwise, I and my hand could form a further whole, which is well-nigh senseless on any good account. Consider a world with just three monads: at most, we can get seven CCBs out of such a world, and any principle allowing for more is thereby discredited.
    As an aside, aren’t there a number of non-sortals about which it makes sense to ask “Why any?” We cannot count red things, bodies of water (which may or may not be entirely surrounded by other bodies of water), or high-pitched sense-data, but it still makes sense to ask why anything is red, why there is water, or whether there are any sense-data. Excuse me if the point is redundant, easily dealt with, or confused.

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  4. William Avatar
    William

    Steve:
    if the CCBs include a, b, and c, is the CCB ( ( a, b) c ) different from the CCB ( (a, b), (a, b) , c)?
    If it is starting from a non-infinite number, your 2^N – 1 argument is only infinitely inflationary if you count sets of sets without reducing them to their component units, right?

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  5. Steve Maitzen Avatar
    Steve Maitzen

    Bill: On further reflection, I’m queasy about premise (1) of your argument, which seems to depend on the general principle that if there are Xs then there’s some definite total number of Xs (finite or transfinite). There are truths, but I’m persuaded by Patrick Grim’s Cantorian argument that there’s no definite total number of truths (finite or transfinite). So unless I can find some other reason for accepting (1) than the questionable principle that seems to be its basis, I can’t accept the argument.

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  6. Dr. Günter Bechly Avatar
    Dr. Günter Bechly

    I think a possible solution to Maitzen’s challenge is to be found in Alfred North Whiteheads process philosophy with its distinction between aggregates / heaps and individual actual entities. There is only a finite and distinct number of actual entities (viz spatiotemporally atomic events within the corpuscular society of ultimate elementary particles, and the presiding “soul” occasions of a regnant nexus within composite individuals like atoms, molecules, cells, and organisms), but there is an infinite and indeterminate number of ways to arbitrarily group them into aggregates or heaps (= macroscopic things). Consequently, the question “why do any actual entities exist rather than nothing at all” does make sense and deserves a reply, at least for those who endorse Whiteheadian metaphysics.

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  7. Bill Vallicella Avatar
    Bill Vallicella

    Steve,
    Let me start with your last comment. I too have made use of Grim’s argument to refute my friend Peter Lupu. Here: http://maverickphilosopher.typepad.com/maverick_philosopher/2009/03/a-cantorian-argument-why-possible-worlds-cannot-be-maximally-consistent-sets-of-propositions.html
    Peter once claimed that possible worlds are sets. I argued that if so, then the actual world is the set of truths, but by Grim’s Cantorian reasoning there cannot be a set of all truths.
    You seem to be giving this argument:
    a. There are truths
    b. There is a definite number of truths
    c. There is a set of truths
    d. There is no set of truths
    Therefore
    e. (b) is false.
    But can’t one question the move from (b) to (c)?
    We need to assume, for the above argument to work, that if there is a definite number of Fs, whether finite or transfinite, then there is a (mathematical, not commonsense) set of Fs. So if there are ten rattlesnakes in my yard, then there is a math. set consisting of those ten snakes. Is that perfectly obvious? I vaguely recall some arguments of my pal London Ed against math. sets. It would not be contradictory to say that there are ten bottles of beer in the reefer, but no set of those bottles. Or would it?
    Following Frege, we could say that numerals such as ‘ten’ are predicates of concepts (not of objects), and so there would have to be concepts. But it doesn’t seem that we are forced to say that trhe extension of a concept is a set. The extension might just be n items referred to plurally.
    In any case my (1) does seem true for finite cases. If there are cats in my house, then there is some finite n such that n is the number of cats in my house. Wouldn’t it be incoherent to claim that there are cats in my house, but no definite number of cats?

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  8. Alfredo Avatar
    Alfredo

    Leo, I think that is a good point. If it makes sense to ask the “Why any?” question of some non-sortals, then it is not clear that Dr. Vallicella’s move from 1 to 2 is justified. It seems he is working with some sort of principle like this:
    (C) If it makes sense to say ‘there are X’s’ then it makes sense to say there is some definite number of X’s.
    Nevertheless, maybe some of those examples, such as the cases of water and high-pitched sense-data, are not analogous to the case of CCB’s (I think our answer in the case of ‘red things’ will be as contentious as the case of CCB’s). After all, even though there is not an answer to the question of ‘How many?’, there is an answer to the question of ‘How much?’, right? If that’s true, then maybe we can reformulate the principle as follows:
    (C*) If it makes sense to say ‘there are X’s’ then it makes sense to say there is some definite number of X’s OR it makes sense to say there is some definite amount of X.
    I’m not sure if that’s adequate. But maybe with something like this Dr. Vallicella’s argument could be reformulated accordingly. So does it make sense to say there is some definite amount of concrete contingent beings? I’m not sure it does.

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  9. Steve Maitzen Avatar
    Steve Maitzen

    Leo and William: Our comments (that the CCBs must be disjoint) seem to have crossed in the mail! If I’ve read you right, we’re on the same page. My (3*) is false without the qualifier “disjoint,” and once you add the qualifier (4*) doesn’t follow. Furthermore, as I said in my immediately previous comment, I’ve got doubts about Bill’s premise (1). (Really, it’s doubts about his premise (2) — my commenting has been sloppy!) There are true propositions but, if Grim is right, no total number of them. In that case, we seem to lack a general reason to accept (2), or at least Grim’s result casts some doubt on (2).
    Leo: I agree with your aside, but I don’t think it affects my thesis. If you ask why there are any red things, someone might reply by explaining how ripe tomatoes reflect a particular range of wavelengths of visible light. Or red delicious apples. And so on. If you insist that such answers can’t in principle explain why any red things exist at all, then it seems to me you’re treating “red things” as if it named a kind whose members require explanation beyond the explanations available for tomatoes, apples, and so on. That’s the mistake I meant to highlight, and I now worry that all this talk of sortals, non-sortals, and dummy sortals may be a distraction! I’ve got to ponder this more.
    Bill: Grim replies to this worry in “The Being that Knew Too Much” (IJPR 2000, at 148). He says his argument doesn’t require (c). As I say, my real worry concerns your premise (2), and I wouldn’t want to assume that only finitely many CCBs exist.

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  10. peterlupu Avatar
    peterlupu

    Bill,
    I am unclear about the concluding paragraph following “In short,…”
    I do not see how the “How Many?” question is senseless whereas the “Why any?” makes sense if the number of CCBs is determinate in reality and that it makes sense to say that some IRS knows what you attribute to such a being. After all, if the number of CCBs is determinate in reality, then there is a determinate answer in reality to the question “How many?”, although we may never know it or even cannot know it. Moreover, according to these assumptions, your IRS should know the answer.
    So given these assumptions, the two questions stand or fall together; at least so it seems to me.

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  11. Bill Vallicella Avatar
    Bill Vallicella

    Peter,
    The IRS does not know what sense YOU attach to a dummy sortal to make it into a sortal so that you can count with it; the IRS is a being for whom the structure of reality is completely determinate.
    Let me see if I can put my point more clearly.
    The question ‘How many CCBs are there?’ has no definite answer that we can supply; it has no definite answer for us. I take Maitzen to have established this in the early pages of his paper. The argument hinges on the correct observation that ‘CCB’ is not a sortal, hence not a count-noun; it is what Wiggins calls a dummy sortal. The argument also hinges on the fact that we have no universally accepted ontological views such as would allow all to agree that, say, mereological universalism is false.
    That’s all he succeeds in showing; he does not succeeed in showing that the number of CCBs is indeterminate in reality. So I grant him that there is a sense in which the ‘How many?’ question is senseless: it is senseless because unanswerable by us.
    But this does not entail that the ‘Why any?’ question is senseless.
    To show the latter, he needs to have shown that the first question is unanswerable period, not just for us. But he didn’t show that.
    For that reason I do not accept his argument.
    The IRS can compute the number of CCBs because he knows all the ontological categories and how many members are in each. Because he possesses the true ontology, he is able to resolve questions that we cannot resolve, e.g., whether the mereological sum of you and me is a third CCB in addition to you and me.
    The weakness of the paper, as I see it, is that Maitzen never explains how he moves from the ‘How many?’ question to the ‘Why any?’ question. There is a leap of logic on the relevant page. Can’t cite it because there are no bloody page numbers! He seems to think the transition obvious. But it is not, and part of the reason it is not is because there is a failure to distinguish the question whether the number of CCBs in indeterminate in reality or merely for us.

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  12. Steve Maitzen Avatar
    Steve Maitzen

    Can’t cite it because there are no bloody page numbers!
    Bill: Now there are. Refresh the page and click the link in line 1 of your post. (Can’t simply email you this info because I can’t find your bloody email address!)

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  13. Bill Vallicella Avatar
    Bill Vallicella

    Thanks, Steve.
    When I was in the professorial ranks it always used to annoy the hell out of me when students turned in a paper without page numbers. Hence my over-strong reaction. My e-mail address is tucked away behind the About hyperlink on the right sidebar near the top. I keep it inconspicuous to keep my e-mail manageable.
    I wrote above: >>The question ‘How many CCBs are there?’ has no definite answer that we can supply; it has no definite answer for us. I take Maitzen to have established this in the early pages of his paper. The argument hinges on the correct observation that ‘CCB’ is not a sortal, hence not a count-noun; it is what Wiggins calls a dummy sortal. The argument also hinges on the fact that we have no universally accepted ontological views such as would allow all to agree that, say, mereological universalism is false.<< Would you agree with that? And the implied distinction between an answer we can supply and an answer simpliciter?
    I think it would be useful to distinguish among various senses of senseless:
    A question is
    senseless 1 iff we (or the community of competent practioners) do not agree on an answer.
    senseless 2 iff we (or, etc.) cannot agree on an answer because of the present state of knowledge.
    senseless 3 iff we (or, etc.) cannot agree agree on an answer because of some irremediable feature or defect of the human intellect.
    senseless 4 iff we cannot agree because there just cannot be an answer in reality. (E.g. the question ‘How fast does time flow?’ in usanswerable because there just cannot, in the nature of things, be an answer to it: not even God could answer it.)
    Now in which sense of ‘senseless’ are you saying that the two questions are senseless? I get the impression that you intend something like the 4th sense.
    But with respect to the first question (How many?)I think all you establish is that the question is senseless in the second sense.

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  14. Leo Carton Mollica Avatar
    Leo Carton Mollica

    Alfredo:
    I’m not sure whether your (C*) can save the argument, since there are seemingly cases of good “Why (not) any?” questions without any corresponding “How many/much?” questions. Take sense-data: it is clearly acceptable to ask “Why are there no sense-data?” But how could we ask for a quantity of sense-data? We can ask for numbers of instances with sortals (like cats), or numbers of measures (like litres) with mass-nouns like “water”, but what can we do in this case? Neither, it seems. The same, I suspect, could also be said of tropes, truthmakers, situations, and other philosophical posits, which are neither sortals nor mass-nouns. And that seems to be the category into which CCBs fall.
    Dr. Maitzen:
    So, am I reading you right in this argument?
    1. If X can explain why there are any A’s, B’s, C’s… Z’s, where all these are the kinds of A* that exist, then X can explain why there are any A*’s.
    2. For every kind of CCB, science can explain why there are any of that kind.
    3. Thus, science can explain why there are any CCBs.
    Is that an accurate summary of the argument?

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  15. Steve Maitzen Avatar
    Steve Maitzen

    Bill: Those are probing questions! I’ll do my best with a two-part answer. I hope the parts cohere!
    1. If ‘CCB’ is being used as a mere covering term (Thomasson’s lingo) ranging over pens, plums, penguins, etc., then I have no quarrel with the questions “How many CCBs are there?” and “Why are there any CCBs?” However, if the questioner isn’t, in principle, satisfied with answers that invoke only sortals (‘pen’, ‘plum’, etc.), then I accuse the questioner of trying to use ‘CCB’ as if it were a sortal. ‘CCB’ is, at best, a dummy sortal because (as you say) it fails at least one of the three criteria you list in your post.
    2. The defective questions are defective not for sociological or epistemic reasons but for semantic reasons: they’re semantically underdetermined. In the perfectly general “How many?” and “Why any?” questions, the term ‘concrete, contingent being’ isn’t defined stipulatively; instead, it’s used as an item of shared language. Now, does it include fusions or arbitrary undetached parts? I don’t think that question has an answer that we merely fail to agree on or know; instead, there’s no semantic fact of the matter about whether the term includes them.
    So I wouldn’t use “senseless” 1-3 to describe them, and I’d use “senseless” 4 only if the reason “there cannot be an answer in reality” is that the questions (pseudo-questions, really) don’t in fact ask anything.
    Leo: I’m inclined to accept your three-step argument provided that ‘A’ through ‘Z’ represent sortals and ‘A*’ represents a dummy sortal.

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  16. Bill Vallicella Avatar
    Bill Vallicella

    Steve,
    Thanks for continuing with this discussion.
    It is true that there is no semantic fact of the matter as to whether or not ‘CCB’ as an item of shared language includes fusions or arbitrary undetached parts. But Tibbles-minus-his tail, which is an arbitrary undetached part of Tibbles, is a CCB if there is such an item as Tibbles-minus-his tail. Ontologically, there is a fact of the matter as to whether there are arbitrary ndetached parts.
    If the fact of the matter is that there are undetached arbitrary parts, then the two questions could be legitimate without collapsing into questions about instances of sorts.

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  17. Steve Maitzen Avatar
    Steve Maitzen

    It is true that there is no semantic fact of the matter as to whether or not ‘CCB’ as an item of shared language includes fusions or arbitrary undetached parts. But Tibbles-minus-his tail, which is an arbitrary undetached part of Tibbles, is a CCB if there is such an item as Tibbles-minus-his tail.
    Bill: I don’t follow. Suppose we agree that there’s no semantic fact of the matter about whether the term ‘superhero’ as an item of shared language includes King Arthur. (Suppose we agree that ‘superhero’ is semantically underdetermined in that respect.) Wouldn’t it then be odd for either of us to say, “King Arthur was a superhero if in fact King Arthur actually existed”? Why would either of us use the term in that way if we agree about its unsettled semantics?

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  18. peterlupu Avatar
    peterlupu

    Bill,
    “The question ‘How many CCBs are there?’ has no definite answer that we can supply; it has no definite answer for us.”
    The pivotal words here are ‘for us’. I think this issue raises some questions about Dr. Maitzen’s views as stated in his article. In order to highlight them let us distinguish between metaphysical, conceptual, and epistemic in/determinacy.
    Thus, if something is metaphysically indeterminate, then there simply is no fact of the matter, in reality and quite independently from any knower or conceiver, about it from any point of view; including your IRS (funny, Bill; very funny!). If something is metaphysically determinate, then there is a fact of the matter in reality, whether we do or can know it or whether we have the suitable concepts to express it.
    Conceptual indeterminacy arises (at least) when certain combination of terms/concepts yields no clear sense: E.g., how many strands of hair are on number two? The question cannot be answered for obvious reasons (this is akin to Ryle’s “category mistake”). Similarly, the question-form ‘how many….’ does not combine with ‘thing’, ‘object’, individual’, and any other dummy-sortal, including ‘CCB’, to yield a question that has a clear sense. Therefore, it cannot be answered.
    Epistemic indeterminacy is when from one knower point of view something is indeterminate, but from another knower’s point of view it may be determinate. Epistemic indeterminacy is compatible in principle with metaphysical and conceptual determinacy.
    Now, after reading Dr. Maitzen’s article it is pretty clear to me that he does not think that the “How many” question is merely epistemically indeterminate. What is not clear to me, or at least not fully clear, is whether he thinks that it is metaphysically indeterminate in addition to being conceptually indeterminate and whether the former indeterminacy, if true, is the result of the later.
    In his argument against your IRS scenario dated Sunday, June 03, 2012 at 05:53 PM, which he subsequently partially and temporarily retracted, he seems to argue that the question how many CCBs there are is *metaphysically* indeterminate.
    However, throughout the article he frequently uses the phrase ‘senseless’ in connection with the question ‘how many’ when conjoined with a dummy sortal such as ‘things’ or ‘CCB’. The problem, he seems to think, is that the question ‘how many things or CCBs there are?’ is senseless because “…its indeterminate just *what* things we’re asked to count in the first place.” (p. 59) (Note the irony that this very statement of the problem uses the dummy sortal ‘thing’; how else could the objection be made?) So it seems to me that Dr. Maitzen does think that such questions are conceptually indeterminate also.
    So I venture to say that we should take Dr. Maitzen as certainly holding that the ‘how many’ question is conceptually indeterminate when conjoined with a dummy-sortal. If so, then he is committed to think (in my opinion) that the question “How many CCBs are there?” is not merely conceptually indeterminate *for us*, as you wish to hold, but it is conceptually indeterminate period; i.e., indeterminate for any being whatsoever, including an IRS. The question is senseless and, therefore, it is senseless even if taken from the point of view of an IRS.

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  19. Alfredo Avatar
    Alfredo

    Dr. Vallicella: Doesn’t an impossibility on the conceptual level also imply a metaphysical impossibility? For example, it is conceptually incoherent to suppose a bachelor is married; thus it is metaphysically impossible for a bachelor to be married. Likewise, I’d be inclined to think that since it is senseless to ask how many CCB’s there are there can thus be no determinate number in reality.
    Back in the post where you argued that the question of “How many?” is senseless, we clarified that an answer to it would not be arbitrary in the same way that an answer to a sorites-case would be arbitrary. So the sense of “indeterminate” being used in this post is not the same as when we say it is indeterminate when someone goes from being non-bald to being bald. *That* type of indeterminacy may be merely semantic. On the other hand, the indeterminacy of the “How many?” question is *not* indeterminate in that way. It is indeterminate in the sense that the question makes no sense, and thus there can be no corresponding fact of the matter in reality. So it is not clear to me the answer in your post adequately addresses your third premise.

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  20. Bill Vallicella Avatar
    Bill Vallicella

    Alfredo,
    ‘Concrete contingent being,’ though semantically indeterminate, unlike ‘bachelor, can be made semantically determinate. Imagine God using ‘CCB.’ it would not be semantically indterminate for him. He would know whether Tibbles-minus-his tail is a proper part of Tibbles or not and is thetrefore to be counted as a separate CCB. And so on for all the ontological questions that are indeterminate for us.
    It is senseless for us to ask how many CCBs there are since for us ‘CCB’ is semantically indeterminate: it supplies no criteria for counting the way ‘bachelor’ does. But this seems consistent with the claim that in reality — from a God’s Eye POV — there is a determinate number of CCBs.

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  21. Bill Vallicella Avatar
    Bill Vallicella

    How many suicides in NYC in 2011? Is this question answerable? Not as it stands. In ordinary English ‘suicide’ is semantically indeterminate. But it can be made determinate by precisifying a dictionary definition. Then one can count suicides. Similarly, if we assign a precise meaning to ‘CCB’ then we can count CCBs.

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  22. Bill Vallicella Avatar
    Bill Vallicella

    Peter sez: >>So I venture to say that we should take Dr. Maitzen as certainly holding that the ‘how many’ question is conceptually indeterminate when conjoined with a dummy-sortal. If so, then he is committed to think (in my opinion) that the question “How many CCBs are there?” is not merely conceptually indeterminate *for us*, as you wish to hold, but it is conceptually indeterminate period; i.e., indeterminate for any being whatsoever, including an IRS. The question is senseless and, therefore, it is senseless even if taken from the point of view of an IRS.<< I think Peter is using 'conceptual' the way Steve uses 'semantic.' One thing is clear: 'CCB' as an item of shared linguistic usage does not supply criteria for counting in the way 'bachelor' does. So the question 'How many CCBs?' is semantically indeterminate, and for this 'internal' reason, unanswerable. But it doesn't follow that 'CCB' is meaningless. After all, it is true that every pen, plum, and penguin is a CCB. It is also true that the proper parts of pens, plums, and penguins are CCBs, though they are not pens, plums, or penguins. Therefore, 'There are CCBs' does not collapse into 'There are instances of sorts.' For example, a proper part of Peter is his torso, but I don't reckon that is an instance of a sort. And what about Peter's blood? That is a proper part of him I should think, but not an instance of a sort. We cannot ask how many blood does Peter contain. We must ask: how much blood does he contain. 'Blood' is a mass term. Admittedly we can ask how may pints he contains. And then there are Peter's property-instances, his particular ruddiness, say. That would seem to count as a CCB. Now if there are CCBs, including those that are not instances of sorts, must it not also be the case that there is a definite number of them?

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  23. peterlupu Avatar
    peterlupu

    Maitzen’s “Stop Asking Why There’s Anything”.
    I agree with Bill’s primary contention that there is something of a gap in Dr. Maitzen’s move from the claim that the ‘How many?” question is senseless to the conclusion that the ‘Why any?’ question is likewise senseless. I am unsure, however, whether Dr. Maitzen intends this move to be a strict logical inference, as Bill suggests, or he sees the move from one to the other in a different light.
    (All references are to Maitzen’s article “Stop Asking Why There’s Anything”, Erkenn, 2012)
    On page 59 (middle paragraph) Dr. Maitzen says that his focus on the ‘How many?’ question is for the sake of illustrating “…the senselessness that arises when we try to use dummy sortals as if they were genuine sortals.” Yet in the final paragraph at the bottom of the same page the move seems to take the shape of an inference. Thus, he reiterates that the problem in the case of ‘How many?’ question arises “…because it is indeterminate just what things we’re supposed to count in the first place. The same problem arises, therefore, when we’re asked to explain why there are any of those things at all: any of which things?” (Note the ‘therefore’; my emphasis)
    I think that I may be able to recast Dr. Maitzen argument so as to reconcile these two attitudes, albeit doing so unveils an unsupported premise. So I will now state what I think Dr. Maitzen has in mind and then I will show what the unsupported premise is and why we should not accept it.
    1) Dr. Maitzen thinks that there is a general problem with a class of terms he labels, following Wiggins, dummy sortals. The class of terms in question includes ‘thing’, ‘object’, ‘individual’, ‘item’, ‘entity’, ‘being’, ‘substance’, Bill’s newly coined ‘CCB’, and others. While these terms seem to behave (grammatically) as if they were genuine sortals, they in fact are not because they “…lack criteria of identity governing the instances that are supposed to fall under them,…” (p. 55)
    2) Now it is important to note that this problem is general in the sense that dummy-sortals lack criteria of identity in all their occurrences. This includes occurrences in questions such as ‘How many?’ or ‘Why anything?”, but also in declarative sentences such as ‘There are two things in your hand’, etc. This problem becomes evident if we think of the proper logical function of dummy-sortal terms as a special class of sortal-variables or perhaps place-holders with genuine sortal terms as their substitution instances. Dr. Maitzen thinks that whenever we treat a dummy-sortal term as if it were a genuine referential general term rather than as a place-holder or variable with genuine referential terms as substitution instances, we get in trouble. (See pp.55-56)
    3)For instance, consider the example of the sentence in the previous paragraph except this time restated so that the dummy-sortal ‘things’ is replaced by a variable, or for purpose of a more illuminating illustration, treated as a place-holder:
    (*) There are two ____ in your hand.
    What are the truth conditions of (*)? Of course, as it stands (*) has no truth-conditions. We cannot state the conditions under which (*) is true/false until we inject some proper referential sortal term into the blank ‘___’. (I think) Dr. Maitzen thinks that dummy-sortal terms behave just like the blank ‘____’ in (*) behaves: i.e., they function as place-holders for some genuine referential sortal and until such a term replaces the dummy-sortal in all its non-mentioned occurrences in a sentence, the sentences has no truth-conditions.
    4) The same general phenomenon is illustrated by questions such as ‘How many?”. Let us say that the content of a well formed and meaningful question has answer-conditions. Answer-conditions are analogous to truth-conditions associated with declarative sentences; they state the conditions under which a proper answer is to be found or at least sought. An expression that has the grammatical form of a question but fails to contain or entail answer-conditions is not a genuine question as it stands. Therefore, it is “senseless” and cannot be answered. In order to avoid the ambiguity between the grammatical versus the logical roles of dummy-sortals, let us consider an example of a ‘How many things?’ question when the dummy-sortal ‘thing’ is replaced by a blank:
    (**) How many ____ you hold in your hand?
    Just like (*) fails to contain truth-conditions, similarly the form (**) fails to contain or entail any answer-conditions as it stands. It is not even a proper grammatical question. The phrase ‘how many’ requires that the blank be filled with a count-noun, a genuine sortal term, in order to convert (**) into a proper question which features suitable answer-conditions. Only then will we have a meaningful question that specifies the relevant domain and the suitable conditions for an answer (whether or not we know how to answer it or even can answer it).
    5) The final step in what I take to be Dr. Maitzen’s overall argument is to apply the same considerations to questions of the form ‘Why anything exists?”. We may highlight the problem by replicating the method applied above and recast this question by replacing the dummy-sortal with a blank:
    (***) Why any____ exists?
    Clearly, (***) contains no answer-conditions as it stands because it is not even clear in which domain an answer is to be found. And in the absence of answer-conditions, (***) is meaningless until the blank is filled with a proper sortal term. Once the blank is filled with a proper sortal term (e.g., ‘penguins’, ‘galaxies’, etc.,), the resulting question will contain answer-conditions and, therefore, will make sense. However, once this is done, then the question will no longer require a blanket answer and, hence, cease to be a threat to scientific explanation and to naturalism.
    6) So Dr. Maitzen’s argument proceed from (i) a general premise about the proper logical function of dummy-sortals (i.e., that they are place holders or sortal-variables); to (ii) an illustration of what happens if this function is ignored in the case of ‘How many?’ questions; to (iii) claiming that the same general problem occurs in the case of ‘Why any?’ questions; and finally (iv) showing that if the proper function of dummy-sortals is respected ‘Why any?’ questions no longer pose a threat to naturalism.
    7) So it seems to me that Dr. Maitzen’s argument does not have the form of a direct inference from the claim that the relevant ‘How many?’ question is senseless to the conclusion that ‘Why any?’ question is likewise senseless. Rather it has the structure of a general premise about so-called dummy-sortal that is illustrated, on the one hand, by instances of the form of ‘How many?” questions and then again claimed to hold in the case of ‘Why any?’ questions.
    8)The General Premise: The logical function of all occurrences of dummy-sortals in declarative sentences as well as in questions is either as a term-variable or as a place-holder. Unless these dummy-sortals are replaced by genuine sortals, declarative sentences have no truth-conditions and questions have no answer-conditions. Therefore, all such sentences are, strictly speaking, meaningless.
    9) So far as I can tell, Dr. Maitzen does not directly defend this general-premise in his article. While he offers considerations in its support for specific cases and illustrates it with respect to ‘How many?’ questions, he does not argue for the generality of the claim regarding all cases. I consider the absence of a defense for such an important premise a weakness of the overall argument.
    10) There are other difficulties with the general premise. There are many sentences in Dr. Maitzen’s own paper that use (not merely mention) dummy-sortals such as ‘thing’, etc. Many of these cannot be easily replaced by any “genuine” sortal”; at least I would not know how to do so. Are we to conclude that all of them are senseless? That will hinder much of the content of the paper.
    Moreover, consider the term ‘sortal’ itself. It is, I suggest, itself a dummy-sortal. If it is, then what are the suitable replacements for it that will turn sentences in which it occurs into meaningful sentences? Are we to conclude that in the absence of such clear replacements, many sentences in Dr. Maitzen’s article in which the dummy-sortal ‘sortal’ occurs are strictly speaking meaningless?
    The same holds for the terms ‘event’, ‘effect’, ‘cause’, etc. All of these terms are dummy-sortals. Are we to conclude that sentences such as ‘All events have a cause’; ‘All effects have a cause’; and many others are meaningless unless we can come up with suitable sortal-replacements for the dummy-sortals? I think that such a verdict would turn much of our discourse into meaningless sounds.
    11) There is a very specific reason why ‘How many ____?” questions demand a count noun or suitable sortal to replace the blank. This reason is dictated by the fact that the answer-conditions for such a question require that the domain of the question must be populated by entities that can, at least in principle, be counted (in a broad sense of ‘counted’). This domain is specified by the term that is placed in the blank. Unless the term in question specifies a suitable domain, the question no longer entails any answer-conditions, since a suitable domain was not clearly specified. It would be like the command: ‘Find him!’ in the absence of any anaphoric background indication to whom the ‘him’ refers. Typically, the ‘him’ does have an anaphoric back-reference, although it may be implicit.
    12) It is not clear to me, however, that the meaningfulness of the question ‘Why anything exists?’ requires a specific domain of objects for which clear and specific identity conditions can be given. Unlike ‘how many’ which clearly demands counting and therefore a suitable domain of objects, perhaps exists does not require any particular domain of objects for which identity conditions exist. Perhaps ‘exists’ in ‘Why anything exists?’ is sufficiently lenient so that it leaves room for any domain of concrete and contingent entities we choose or perhaps even an indefinite disjunction of such domains to be considered. The question then asks why any of these CCBs should exist rather than absolutely no CCBs at all.

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  24. Bill Vallicella Avatar
    Bill Vallicella

    Impressive commentary, Peter.
    If ‘sortal’ is a dummy sortal,then ‘sortal’ is not a sortal. But can’t we count sortals and distinguish them from non-sortals? Consider this list:
    pen, penguin, cat, planet, fact, entity, object, item.
    There are exactly four sortals. Since we can count sortals, ‘sortal’ is a sortal.
    Why did you say that ‘sortal’ is a dummy sortal?

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  25. peterlupu Avatar
    peterlupu

    Bill,
    Thanks.
    You are counting the terms that are called ‘sortals’. If so then we can also count dummy-sortals; e.g., things, object, individual, being. There are exactly four of them.
    When I say that ‘sortal’ is itself a dummy-sortal I mean that there is no one set of identity conditions in common to all sortal terms. Refuting this claim requires providing such conditions.

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