A well-known Christian Philosopher, Mike Rea, picks 8 & 5 as well. I have a paper submitted to a journal on this exact topic – stay tuned – I will probably post it once it is forthcoming. Here’s a readable paper co-authored by him.

But what you say in your comments sounds more like what a unitarian would say… that Jesus is a man, miraculously brought into being by God, in Mary – she supplies the ovum. He doesn’t have a/the “divine nature,” but he is endowed with massive power by God. Trinitarians think that at the miraculous conception an eternally existing pre-human Jesus (the Word) combined with a “complete human nature” at the miraculous conception, yielding a being with both a divine and a human nature, but which is one self. Confusing? Yes!

On your “subset” comments – yes, you would think that Father and Son could not be alike in every way. The Father (but not the Son) will be in some sense the origin of the Son. So, they can’t be numerically identical. And it’s hard to see how they could be one being. (Contra 8.)

Some clarity on this topic IS possible. Don’t get discouraged – just seek out material which is clear and helpful, and prayerfully compare it to the Bible. Here’s some hard but I hope worthy reading which further lays out what Christian thinkers have thought about this matter.

No one anywhere in this debate is supposing God to be material, or created.
If it were true that we could never understand (any of) God’s nature, then the doctrine of the Trinity can’t have been divinely revealed (i.e. something the recipients of revelation now know). Maybe we should all just go read instapundit!

The debaters are using backwards logic. Specifically, they are defining the uniplural Creator (ref. Ecclesiastes 12:1) with the logical laws of Creation. As a result, they are creating a “materially transcendent Creator,” which is an oxymoron.

Now, let us consider John 1:1-2. In John 1:1-2 [Greek], John describes God[*] as “the Logos.” According to Greek philosophical writings, the term Logos describes the underlying foundational source of all reality. As a result, John’s usage of this Greek philosophical terminology communicates that God[*] creates reality itself, not vice versa (cross ref. Acts 17:22-25, 28, Colossians 1:15-17, Romans 4:17, Hebrews 11:3).

What does this mean? ‘Elohiym‘s uniplural nature is self-referential, as in omnitranscendent. As a result, we may never understand ‘Elohiym‘s uniplural nature.

Great summary. I’ll just note that the Cappadocian view, if I am understanding it properly, makes the ‘are’ an ‘are’ of predication, not identity. Gregory of Nyssa, following Basil, argues that the statements ‘The Father is God’, ‘the Son is God’, ‘the Spirit is God’ are logically similar to ‘Peter is human’, ‘Paul is human’, ‘John is human’; it’s the metaphysics of being God vs. that of being human that makes the difference. In this case, deity doesn’t pluralize the way humanity does (because of properties like spirituality, simplicity, etc.); but that’s a metaphysical fact about divine nature rather than a logical fact about the statements. I think Nyssa may argue somewhere that this can easily be made plausible if you’re a Platonist: if you’re a Platonist about human nature, you already hold that Peter, Paul, and John share one and the very same human nature in some sense; they just do it in a limited and derivative way that wouldn’t apply to God. I imagine that taking this line would get much more complicated the less Platonist you get about natures. The full Cappadocian position gets into the processions; when they talk about divine unity the Cappadocians tend to place a lot more weight on the divine processions than on the more purely abstract questions. (As does Augustine, for that matter.) We see this in Nyssa’s treatise “On Not Three Gods.” But that gets into other issues.

Chris,

I think that in a world where Brandon exists through time the maximality defender of (1)-(4) can’t avoid accepting the Brandon + 0 argument. Thus I think the commitment follows, due to the generality (1)-(4) would have to have. But that’s a complicated issue. Have fun fishing.

I’m leaving on a fishing trip so won’t be able to respond for awhile. But I don’t think a defender of the analysis of (4) into (1) – (3) is committed to a view on persistence. That would be bad. Instead, I think it is one who puts forward the Brandon at t + 0 argument that is committed to the view, by virtue of accepting that there is a thing that is Brandon at t + 0 (and even this is not really sufficient for the committment).

But anyway, I’m surprised about the importance of maximality here. It deserves more consideration. I’ll be back after contemplating whether a proper part of a trout is a trout. Thanks for all the great discussion.

Dale,

Great postings. Your summary seems to me apt. Best,

Christian

In the interest of making things understandable even to those who
haven’t done graduate work in philosophy, I think I’ll try to summarize
what just went on – at least, the bulk of it. This is risky, but I’m
going to take a shot at simplifying without over-simplifying. I don’t
intend to hereby end the discussion, and please feel free to correct
me, or throw rotten fruit at me, or whatever. Also, it may help
non-PhDs to read my upcoming posting on the concept of identity – that
provides some important background information.

In “the doctrine” part 3, I listed a number of options of interpreting the traditional claim that Father and Son are homoousias. This is all about option 3, which Brandon says is the position of the Cappadocian Fathers (such as this guy).
In the article I gave a quick objection to this – basically, if Father
and Son both have the universal property of divinity, then there are
two divinities, two gods, and monotheism has been abandoned..

Here’s where it gets tricky. Brandon wants to say that even
though the Father is a divinity, and the Son is a divinity, and they’re
not identical (this is a technical term here, meaning, one and the same
entity, like you and yourself are), it doesn’t follow that there are two divinities. Christian’s initial reaction is (in my words, not his) – What? It obviously follows. That isn’t the sort of thing that even needs arguing.

Brandon fiercely holds his ground, though. He wants to say that what does follow
is that there are at least two non-identical subjects of divinity, but
NOT that there are at least two divinities. Find that hard to get your
head around? A lot of philosophers, including both Christian and I, do
as well. Still, many philosophers, in trying to solve problems outside
of Christian theology (such as material object counting), want to say
that things can be numerically the same without being identical. Thus, though the Father is not the Son, they are the same God.

Now that last “are” I underlined is interesting. It can’t be that both are identical to God (because they aren’t identical to each other), and it can’t be that the two together are identical to God, for identity is a one-one relation, not one-many – this suggestion would be nonsense (and no one here has suggested it). I’m not quite sure what Brandon intends here, though he says he doesn’t want to say that Father and Son are “relatively identical”. Parts &
whole? A relation something like material constitution? (All these options have been explored in the recent literature, and will be the subjects of future postings.)

Brandon’s aim, though, was really defensive. His main point was:
the objection as given won’t stand, as it “begs the question”.
(Compare: a Muslim & a Christian argue, and the Muslim says, “But
the Holy Qur’an itself says that Jesus isn’t the Son of God.”)
That is, the objection assumes something which intelligent Social
Trinitarians like the Cappadocians deny, namely, that if two things are
distinct, and both are things of a certain kind, then there are at
least two things of said kind.

Do the Cappadocians really hold such a metaphysically sophisticated
view? And whether they did or not, is it defensible? Does it provide a
way around the polytheism objection to social trinitarianism? I
certainly hope that Brandon & Christian chime in again, on all
these topics and more.

End of summary.

Other comments: Yes, Brandon, Leftow’s work on all this is mighty
interesting. He’s resolutely anti-Social-Trinitarian (see his big
chapter in the Trinity symposium book edited by O’Collins & Davis -
linked on the main blog page). In this piece he pretty clearly takes my
option #2. (I briefly criticize him for this in my Religious Studies article, “The unfinished business…”) In that big, more recent Faith & Philosophy piece,
he does appeal to time-travel thought experiments, and their alleged
lessons about personal identity. He sails pretty close to modalism
there, and defends against that charge. That is a very difficult piece,
and I hope I can post some time soon on the gist of it. It is a largely
defensive piece; I believe that Leftow still holds to my #2, so I don’t
think I’ve left out an option there.

Dale, with regard to your question about whether there are other options, didn’t Leftow have an article in Faith and Philosophy last year in which he suggested that the identity might be analogous to personal identity. I don’t have it with me, but if I’m remembering correctly, that might be another possible way to understand the unity.

I really like that example. My first response is that maybe (1) and (2) are both false. Being a human being is maximal and so a temporal part of a human being (Brandon at t + o) is not a human being. Hence, once again, maximality explains away the potential counterexample!

I must admit though that maximality doesn’t strike me as plausible here as it does in the synchronic case. I want to think about this one a bit more. Interesting.

(5) is clearly not redundant. Consider this:

(1) Brandon at time+0 is a human being
(2) Brandon at time+1 is a human being
(3) Brandon at time+0 is not numerically identical to Brandon at time+1.
(4) Therefore there are two human beings.

Difference of times is clearly enough to break numerical identity, so (3) is true; (1) and (2) are also true. But (4) is false because difference in time alone is not enough to pluralize human beings. I don’t think there’s anything obscure about this: not all differences pluralize Fs. But any difference of the thing itself breaks numerical identity (it’s perhaps worth noting as a side issue that if there were differences of the thing itself that don’t, #1 on Dale’s list suddenly becomes an interesting candidate, and one that might not need to be modalistic). So lack of numerical identity does not suffice to pluralize Fs. So, for instance, no one would say that the fact that I flaked off a bit of old sunburn makes me a different human being. It makes me different than I was before I flaked it off; but it’s not a difference that introduces a plurality of human beings. It does seem that (5), or something of the sort, is needed.

Fair enough, we have sidetracked a bit. But the sidetrack seems to me an important one since it shows how interconnected problems in metaphysics are to what some might otherwise have thought to be an entirely different issue. I love when this happens in philosophy.

I think you’re right that (A), the claim that (1) – (3) entail (4) needs to consider the Tibbles problem. Initially I claimed that it is analytic and obvious, but you’ve convinced me its not obvious.

Much would need to be said on behalf of Maximality as a solution. I can’t say that here. But a point has been lost in this, one that seems to me important. Whether Maximality is an adequate solution to the task, I think that a constraint on any solution to Tibbles must entail that there is one cat on the mat even though there are many cat-candidates. This does leave open a relative identity solution, one I hope to discuss in the future.

“but it brings its own problems, since it requires either that we be able to formulate a criteria to distinguish parts that are F from all parts that are only proper parts of F in order to identify F itself.”

I’m not seeing your worries for Maximality. It gives you the criteria. Take some object o and property p, to say that p is maximal is to say that if o is p, then no proper part of o is p. There is a worry about which object o is p, of course, but that is a worry independent of maximality. For example, is the brain the person, or the body, or the…a problem whose answer is independently difficult to establish.

“or that we accept supervaluation, which requires saying we know that Tibbles is a cat but we don’t know what part (in the usual mereological sense in which a whole can be part of itself) of him is a cat.”

That doesn’t sound like supervaluationism to me. Isn’t the view just the idea that there are ways to make the extension of a predicate more precise and that we could do this with ‘is a cat’ but we don’t ordinarily do this. So, Tibb is a cat iff “Tibb is a cat” comes out true on all admissible ways of making ‘is a cat’ precise.

I’m not defending this view. I don’t really understand it. But the little I understand about it doesn’t imply the claim about knowledge you’re making.

“but since they don’t necessarily exhibit maximality in cases like the house’s wall over the edge of the property line, where no one thinks the proper part of the house is on its own a house.”

I’m sorry, I’m just not seeing it. The whole house is not over the property line, but we say “Your house is over the property line” and I suggest this is okay because in general we assert Fx when only a part of x is F. But “being over the property line” is not a maximal property since parts of a house can have it in addition to the house (we would have to redescribe the case for this, though).

But if your point is just that it’s not obvious how to distinguish maximal properties from non-maximal ones, I agree, linguistic intuitions are not unequivocal.

A final point:

It is sometimes true to say “There are two F’s” for some F. But this fact, when it is a fact, is not a brute one. The fact is not a basic one. I think (1) – (3) explain why.

1. a is a F, and
2. b is a F, AND
3. a is not numerically identical to b,

4. So, there are (at least) two F’s.

That is, (1) – (3) analyze and explain (4) by telling us a bit more about what the world must be like in order for (4) to be true.

You think (1) – (3) do not entail (4) so then you deny the analysis of (4) into (1) – (3). You’ve offered another condition that you think must be satisfied for (4) to be true.

“It has to indicate that the two things are pluralized in being F, i.e., not ‘there are two things that are F’ or ‘there are two things that are (a single) F’ but ‘there are two F’s’. Nothing about the form of the argument leads to this.”

5. a and b must be pluralized in being F.

Perhaps you think that 1, 2, 3 and 5 entail 4?

Here is my worry to adding “any” other condition to 1, 2, and 3 to analyze 4. First, 1, 2 and 3 seem to me a correct analysis of 4. Second, further conditions like 5, are less comprehensible than 4 and so will not be informative if added to the analysis, but confusing. Third, we can ask: Is 5 analyzable? If so, then does it turn out redundant or simply not a condition on 4?

I think it turns out redundant. It seems a and b are pluralized in being an F just when a is an F, b is an F and a is distinct from b. So, 5 should be left out of the analysis of 4. So, as far as I can tell, a believer in the trinity should deny one of the following:

Jesus is a God
The Father is a God
Jesus is not identical to The Father.

Now, the worry then is which one to deny. Since most trinitarians aceept that Jesus is the same God as The Father, they seem committed to the first two claims. Since trinitarians are committed to the view that Jesus is a different person from The Father, they seem committed to the third. But, if I’m right, then that entails Polytheism.

I think we are coming to more of an understanding of each other.

“I however think that if (1) – (3) are true, then (4) is true.”

I’d be willing to concede this (understanding the premises as you are) if it comes with an adequate defense. Such a defense would have to address the various ‘problems of the many’ in which it appears to be false. Maximality appears to handle these problems, but it brings its own problems, since it requires either that we be able to formulate a criteria to distinguish parts that are F from all parts that are only proper parts of F in order to identify F itself (but this appears to require the ability to distinguish infinitely, or at least, mind-bogglingly many, cat-candidates from one precise cat, which we are never in a position to do actually) or that we accept supervaluation, which requires saying we know that Tibbles is a cat but we don’t know what part (in the usual mereological sense in which a whole can be part of itself) of him is a cat, and thus that we don’t know what part of Tibbles is Tibbles. And that’s even setting aside the question of whether we can formulate supervaluation coherently, which some have questioned.

On the house example, your response just makes my example all the stronger. The argument I was responding to, remember, was that our linguistic conventions include maximality (one of the reasons Sider gives for it); but since they don’t necessarily exhibit maximality in cases like the house’s wall over the edge of the property line, where no one thinks the proper part of the house is on its own a house (even the same house), then a fortiori there’s no reason to think they require it in subtler cases. (And we clearly do apply the label ‘person’ to the person-with-the-clothes as well as to the person-naked-under-them.) And, in fact, it would be astonishing if they did so, since our linguistic conventions don’t seem to be mereologically precise enough to include any clear conventions of maximality. So the linguistic conventions argument is a non-starter. That just leaves as arguments for maximality (1) an argument from intuitions; (2) the argument mentioned above about overpopulation; and (3) the ability of maximality to solve problems. (1) is unreliable; (2), as noted above, is a false dilemma. Only (3) is left — and it depends on being able to handle the vagueness problems associated with maximality.

But, interesting as all this is, since this is a Trinity post on a Trinity blog, I don’t want to hijack the thread for discussing maximality as such; at this point we’re only tenuously connected to my original point, was that, even if one still accepts it, the objection to #3 is much, much less plausible on close examination than it appears on first glance. Right now the sort of questions we are getting into have more to do with the question of relative identity, #8, (its value in comparison with maximality as a solution to these problems, whether it’s the only real way to allow all the cat-candidates to be the same cat, etc.); and as I’ve already noted, I think #3 is more promising than #8; and this line of thought only has relevance to #3 in the sense that it underlines the fact that the objector to #3 needs a serious defense of his claims for the divine case in order even to get the objection off the ground.

That’s fine. I didn’t mean to imply I was doing exegesis. The only interpretation of the trinitarian idea my point would undermine (if I’m right), is one that claims Jesus is a god, The Father is a God, Jesus is not numerically identical The Father and there is not more than one thing that is a God.

However, if trinitarians don’t believe those claims, fine by me. This eliminates one potential interpretation as being consistent.

“It’s nowhere near as easy to make the objection as one might think.”

I agree wholeheartedly.

“I don’t see where you are getting ‘There are two distinct masses of feline tissue that are one single cat’, or what you are doing with it.”

Skip that. It was only meant to illustrate an intuitive assignment of objects and properties in the Tibbles the cat case. It’s incidental.

“As it stands the argument is not valid. It’s a good enthymeme in that when combined with a very defensible premise (about the contrariety of colors) it becomes a sound argument. I think you can draw such a premise simply by serious analysis of what green and red are. But as it stands the inference is not formally valid.”

Here is a place that we are talking past one another. By valid I meant a kind of necessarily truth-preserving inference. I did not mean a property of forms in virtue of which an inference is necessarily truth-preserving. So, I agree on your way of understanding the term ‘valid’ that the move from (1) – (3) to (4) is not (obviously) valid. I however think that if (1) – (3) are true, then (4) is true.

“Someone who denied that colors were necessarily contrary — e.g. someone who held that ‘green’ and ‘red’ were really just dispositions that can be had simultaneously by the same object — would be entirely within their rights to deny your claim about entailment.”

I deny this. I think they would be mistaken.

“On the linguistic convention, try building a wall of the extension on your house on your neighbor’s property and see whether they describe it as ‘Your house is on my property’ — this is a clear case in which, as a matter of linguistic convention, a proper part of F is an F.”

I agree this issue is tricky. But I deny your example support the view in question. Your neighbor does not think a house is opn her property, she thinks a part of a house is. Similarly, when I say I see the Pacific Ocean by seeing a part of it, I do not mean that the small mass of water I see is the Pacific Ocean. I think the pacific Ocean is bigger than Lake Michigan, and I don’t think that the part of the Pacific Ocean I see is beigger than lake Michigan and your view would imply I have inconsistent belief, when I don’t. Another example, I park my car and one tire is on the sidewalk. We would say, your car is on the sidewalk Christian. But really, only part of it is, and that is sufficient for the assertion to be correct. This phenomena is a rather general one. It adequately explains your house example.

“I invite you actually to ask people whether the part of them naked under their clothes is one and the same thing as the person wearing the clothes, despite not being in the strictest sense identical.”

I don’t see how this example helps??? The person under the clothes is a person, the person and the the clothes together is not. It is a person wearing clothes.

“as I see it, it is, in this context, a position about the sameness of cats, since it denies that Tibbs is the same cat as Tibbles.”

It entails that Tibbs is not a cat together with the relevant facts, sure. I don’t think this is sufficient to be about cat-identity. Otherwise, the principle of non-contradiction is about everything, and it is not.

Unless you are understanding the premises in the argument in a weird way, I’d simply deny that the premises have anything to do with the doctrine of the Trinity as usually understood. So discussing it seems a bit moot. But the cat on the mat problem shows that there are at least apparent counterexamples to it, whether we think they can be explained away or not. That’s my primary point here; I don’t feel a comments box is a useful place for elaborating a theory of the Trinity, so I’m primarily confining myself to showing problems with the objection to the Cappadocian position. And the chief problem with it is: It’s nowhere near as easy to make the objection as one might think. It actually turns on complicated issues of identity and sameness that need to be addressed explicitly if the objection is to work against #3.

I don’t see where you are getting ‘There are two distinct masses of feline tissue that are one single cat’, or what you are doing with it; this seems to move the problem from bad to worse, since now you’re introducing new stuff into the subject as well as into the predicate that isn’t in the original argument. What am I missing?

“I say if x is red all over at t then that entails that x is not green all over at t. But the latter claim is not part of the meaning of the other one. Nor is it ruled out by form, in any sense that I can see. But yet the inference is valid and we can see that it is.”

This seems sort of an odd response to me, so perhaps I’m just missing your point. The problem I raised above was not that the latter claim is ‘part of the meaning’ of the former claim; it’s that the meaning of the former claim, when colors like green are understood a certain way, constrains the conclusions you can draw from it in an argument of this form. As it stands the argument is not valid. It’s a good enthymeme in that when combined with a very defensible premise (about the contrariety of colors) it becomes a sound argument. I think you can draw such a premise simply by serious analysis of what green and red are. But as it stands the inference is not formally valid (it is possible to have an inference of the same logical form that draws false conclusions from true premises, e.g., x is material all over at time t, therefore x is not physical all over at time t — the same form, but it fails because ‘material’ and ‘physical’ are not contraries), and a counterpart to A for it would be incorrect unless you are understanding the premise in such a way that it already implicitly implies a premise about the contrariety of colors. (Someone who denied that colors were necessarily contrary — e.g. someone who held that ‘green’ and ‘red’ were really just dispositions that can be had simultaneously by the same object — would be entirely within their rights to deny your claim about entailment.)

On the linguistic convention, try building a wall of the extension on your house on your neighbor’s property and see whether they describe it as ‘Your house is on my property’ — this is a clear case in which, as a matter of linguistic convention, a proper part of F is an F. Such cases are very easy to think up. As I said above, it’s a natural way of speaking even if we choose to explain it as nothing more than verbal convenience. (Another example: I invite you actually to ask people whether the part of them naked under their clothes is one and the same thing as the person wearing the clothes, despite not being in the strictest sense identical. And on the cat, perhaps I just have weird friends, but all the people I’ve ever asked say it’s one and the same cat.) But I don’t consider this a major issue one way or another; I only brought it up because Sider brings it up.

On your claim that (in the cat on the mat case) the maximality claim doesn’t involve putting forward a position about the sameness of cats; as I see it, it is, in this context, a position about the sameness of cats, since it denies that Tibbs is the same cat as Tibbles. And for the reasons I noted above, I think this position has to be defended, because it is implausible. In other words: Maximality is all well and good, and I’m quite sure there are cases exhibiting maximality; but if we’re going to assume that all cases of the sort found in the original argument are cases exhibiting maximality, I’m going to need to see the argument for it.

1. a is a F, and
2. b is a F, AND
3. a is not numerically identical to b,

4. Therefore, there are (at least) two F’s.

You deny that 4 follows from the premises.

Two questions: Can you think of a counterexample? What does follow from the premises?

I suggest there is no counterexample, so the inference is valid. I also suggest we could interpret 4 in at least two ways:

4* Therefore, there are at least two things each of which is an F.

or 4** Therefore, there are at least two things which are each F.

I stipulate that I interpret 4 as 4** and then ask: does it follow validly from the premises? I think so. Then I suggest, if 4** does, then 4* follows too since 4** entails 4*. This corresponds to claim (B) above.

“The mere form of the argument doesn’t rule out ‘There are two distinct subjects that are one single F’; which means that A (which requires that the argument be a rigorously valid deduction) is false unless the premises have to be understood in such a way as to yield the conclusion.”

I understand this response as follows: you don’t think you need a counterexample, rather, you only need to point out that unless a certain proposition is ruled out by the form of the premises, then the argument is not valid. I just don’t know how a form “rules out” a proposition. Perhaps the truth of the premises together with logical rules can jointly rule out the truth of a proposition, is that what you have in mind? That’s fine. I don’t think anything above rules out the proposition you’re interested in in this sense. To be honest, I don’t understand the proposition ‘There are two distinct subjects that are one single F’.

Take a substitution instance: there are two distinct cats that are one single being freckled.

I substituted a property for F and got non-sense. I don’t understand the schema you are interested in enough to be concerned with its being ruled out.

However, it does suggest: there are two distinct masses of feline tissue that are one single cat.

That is understandable. But it is just equivalent to saying that there are two distinct masses of feline tissue that are jointly a cat. In this sense, the subject expression is a plural referring expression attributing a property to a plurality of tissue masses.

Let me stipulate that the ‘is’ in (1) – (3) is the is of predication, and the ‘are’ in (4) the are of predication. I assume that (4) is saying of two things that each of one them ‘is an F’ in the regular sense. For example, Joe is a scuba-intructor.

Additionally, you seem to think its being ruled out is important in that if it is not ruled out, then the argument from (1) – (3) to (4) is invalid. But this is just to say that you deny the entailment. I say if x is red all over at t then that entails that x is not green all over at t. But the latter claim is not part of the meaning of the other one. Nor is it ruled out by form, in any sense that I can see. But yet the inference is valid and we can see that it is.

But now consider the response: but you haven’t rule out that there could be a a thing that is both red all over and green all over at t, so the inference is invalid!

Do you think that is a good response? Or do you deny that we have to rule out this proposition in this case?

About maximality: there is alot going on here, but briefly, I don’t think people are confused about whether a part of a cat is a cat or whether part of a cat is the same cat at the cat of which it is a part. I think most people just deny that cats have parts that are cats and this entails that cats don’t have parts that are cats and that are the same cat as the whole.

Maximality nicely explains this. I don’t see why the case of Jane problematizes this, she is a person and no proper parts of her are also persons.

“My own view of the cat on the mat problem is that anyone who denies that proper parts of cats can be cats is just obviously toying with words, and is not putting forward a plausible account of the sameness of cats.”

I don’t think its a matter of toying with words, the idea is that the instantiation of some properties is border-sensitive, extrinsic rather than intrinsic, and this a substantive and interesting claim intended to solve puzzles and cohere with linguistic intuitions. The claim is a general one, and does not require putting forward a view about the sameness of cats. The point is that since a proper part of a cat is not a cat, the question as to whether the “two” cats are the same does not arise.

“And he’s simply wrong that the usual linguistic conventions don’t count large proper parts of F’s as F’s; in linguistic convention occasionally counts even very small proper parts of F’s as F’s.”

This seems wrong to me. But I’d certainly be open to counterexamples. I mean just ask anyone: “Hey, how many cats are on the mat?” Everybody says “One!” Does that cat have parts, like all of it minus a whisker? Everybody says “Sure.” Is that part of the cat a cat? I think most people will either shrug or say “No way!”

While the path you take for the cat on the mat problem is not uncommon, it has to be understood that it’s not an obvious position and needs considerable defense (pretty much all the solutions to the problem are implausible). And this is sufficient, I think to problematize the objection, if the objector just wants to rely on the original argument as an obvious objection: the objector can’t just throw out the argument without defending it, because it’s not, in fact, completely obvious that it poses a problem. Thus the real objection isn’t the argument, or even the argument as understood in A — it’s set of positions about identity that are on closer view controversial. (My own view of the cat on the mat problem is that anyone who denies that proper parts of cats can be cats is just obviously toying with words, and is not putting forward a plausible account of the sameness of cats; even the relative identity position, which I regard with considerable suspicion, seems much more plausible to me than this view. Jane without her nose ring isn’t just a part of a human being that suddenly leaps into human-being status when Jane takes out her nose-ring; she’s a human being who’s one and the same human being as Jane with the nose-ring, just abstracting the nose-ring. And that seems the most straightforward claim. If we’re going to introduce maximality, it’s possible this is a case to do so; but we need to defend it and define the level of maximality. Which Sider paper on maximality do you have in mind? It seems to me that a problem with Sider’s support for maximality is a failure to distinguish ‘A large proper part of a house is not a house’ from ‘A large proper part of a house is not the same house as the house of which it is a proper part’. The former is ambiguous, and gets some of its plausibility from recognizing that a large proper part of a house is not a different house, to which a denier of maximality is not committed. In fact he makes exactly this conflation at the beginning of “Maximality and Microphysical Supervenience”. And he’s simply wrong that the usual linguistic conventions don’t count large proper parts of F’s as F’s; in linguistic convention occasionally counts even very small proper parts of F’s as F’s, because it’s sometimes verbally convenient to do so, whether we think there’s anything more to it than that or not. We just don’t usually count proper parts of F’s as different F’s, except in jokes. One problem with taking maximality seriously in cases like this is that it requires us to say that there are things that are not cats that, without any intrinsic difference, could counterfactually be cats, and things that are cats that could, without any intrinsic difference, counterfactually not be cats. This looks suspiciously like wordplay rather than a substantive claim.)

I’m still not sure I follow you about (A). The issue has nothing to do with how we understand meaning — it’s the form of the argument. The mere form of the argument doesn’t rule out ‘There are two distinct subjects that are one single F’; which means that A (which requires that the argument be a rigorously valid deduction) is false unless the premises have to be understood in such a way as to yield the conclusion. (And as an objection to the Cappadocian position, how the premises are understood have to be understood has to be fixed by how the Cappadocian would understand them. And the Cappadocian would have no problem with saying that there are two subjects that are F; in fact, Cappadocians have a long history of saying exactly that, and often. What they disagree with is that this implies that there are two F’s. And the objection appears precisely to conflate the two.)

This is why I said that, while the argument itself has a lot of plausibility, A isn’t even remotely plausible. (Burden of proof seems irrelevant here; my view of burden of proof is that, taken seriously, it’s worked out in dialogue and doesn’t magically accrue to any given position; which explains why just about everyone conveniently is inclined to think it’s on the other side. But in any case, if the objection is to succeed against the Cappadocian, it has to put forward premises the Cappadocian would accept, end of story. This has nothing to do with burden of proof and everything to do with relevance.)

By the way, this is a real cool issue. I think I almost completely disagree with everything you are saying here. I’m no dummy and obviously you aren’t, so let’s figure if we are talking past one another, okay?

“I’m not following you; if you are interpreting the premises as ‘The Father is a God’ &c., why do you think they accurately characterize the Cappadocian position (or even any position that might be consistent with #3)?”

I don’t think this accurately captures the CapCreed. I have no view one way or another on that issue. My claim is just that (A) is true and if (1) – (3) capture some essential part of the docttine, then (4) follows from the doctrine. I also do not know if such a view is consistent with #3, I haven’t thought about that.

“the objection needs to come to a more substantive conclusion than ‘there are two things that are F’ (or even: ‘there are two distinct things that are an F’), which is just a summary of the premises. It has to indicate that the two things are pluralized in being F, i.e., not ‘there are two things that are F’ or ‘there are two things that are (a single) F’ but ‘there are two F’s’.”

First, here it seems we agree on one thing: ‘there are two things that are F’ just summarizes the premises. That is what (A) does, it moves from (1) – (3) to a summary of them. That is why I think (A) is analytic, necessary and very plausible. Second, I don’t think (A) must indicate that things are pluralized in being F. That is what a theory of predication does, not a premise. Of course, you might wonder whether the following conditional is true:

(B) If there are two distinct things each of which is a God, then there are two Gods.

Option 1: You might accept (1) – (4), (A) and then go on to deny (B). I haven’t ruled this out.

Option 2: Or, you may accept (B) but deny that it entails polytheism. Perhap one might think that Polytheism requires that there are two things each of which has the property “being God” rather than “being a God” and you deny the move from the former to the latter.

Anyway, that is consistent with what I have been saying so far. I would go on to argue, although I have not argued it yet, that both options are dubious. I think (B) is trivial and I doubt anyone not attempting to save the trinity would deny it. Just ask a layperson. So, the presumption should be in its favor. I also think think the presumtion should be in favor of the vlaim that (B) and a commit to its antecedent entails Polytheism.

Of course, if we had independent reason to doubt this then that should give us pause. That is why I have repeatedly asked for a counterexample since without a counterexample, and given that the claims would be accepted by the average Joe, and given that they strike me as trivially true, I suspect that simply denying (B) or (A) amounts to turning one’s head to the problem of the trinity.

To be clear, I am not suggesting anyone is committed to (A) or (B) above since I am only responding to a conditional claim.

“But the form itself doesn’t even eliminate the possibility of two distinct things being a single F; this has to be entering in from the meaning of the premises. But then it has to be shown that the Cappadocian is committed to the premises in the sense that yields the conclusion.”

So, I don’t think it has to be shown that “it is impossible that two distinct things be a single F” must enter into the meaning of the premises. First, that assumes a false view of meaning. This theoretical claim is certainly not part of the meaning in the premises. Ask most people and they would tell you (4) follows from (1) – (3), but they would also have no view (or a muddled one) on the claim about distinct things being a single F. Second, I think you have the presumption or “burden of proof” backwards since, like you recognize, for tables and chairs and bananas, if two distinct things are each bananas, then we all agree it follows that there are two bananas. What needs to be shown is that it is possible this is false for something. We ought to move from the familiar to the unfamilar with the claims we accept. That is why I am looking for a counterexample.

Incidentally, I like the argument you give to Ocham. I would say that:

“1) Christian is the man Roxane loves.
2) Cyrano is the man Roxane loves.
3) Christian is not numerically identical to Cyrano.”

This is an inconsistent triad so (4) trivially follows from them. This is because I like the Russellian treatment for ‘the’.

Also, “a) Tribbles is a cat
b) Trib is a cat
c) Tribbles is not numerically identical to Trib
you still can’t get
d) There are two cats.”

Also, I would deny that (d) does not follow from (a) – (c). This would be a counterexample to (A) above. But, instead I think that (b) is just false. Parts of cats are not cats. This probably because ‘being a cat’ expresses a maximal property. See Ted Sider’s paper on maximality for the argument.

I’m not following you; if you are interpreting the premises as ‘The Father is a God’ &c., why do you think they accurately characterize the Cappadocian position (or even any position that might be consistent with #3)?

The point about having F (I should have said ‘being F’) is that the objection needs to come to a more substantive conclusion than ‘there are two things that are F’ (or even: ‘there are two distinct things that are an F’), which is just a summary of the premises. It has to indicate that the two things are pluralized in being F, i.e., not ‘there are two things that are F’ or ‘there are two things that are (a single) F’ but ‘there are two F’s’. Nothing about the form of the argument leads to this. It’s very plausible for most of the things we know; but we also have independent reasons for accepting the conclusion given the premises for most of the things we know (e.g., most of the things we know are material objects that are conveniently distinguished by the fact that they don’t occupy the same space at the same time). But the form itself doesn’t even eliminate the possibility of two distinct things being a single F; this has to be entering in from the meaning of the premises. But then it has to be shown that the Cappadocian is committed to the premises in the sense that yields the conclusion.

To Ocham:

But that the relevant description in question is a count noun — that is, a count noun by being a countable unit, rather than by accident of English idiom — can’t be assumed by the objector.* I don’t see your point about the different presumptions at all — but perhaps it’s due to my not sticking rigorously to the standard sort of English predicate format but slopping into a different format. Use ‘subjects of being F’ if you prefer; the ‘subject’ here is the a in the molecule (Fa), whereas the F was simply F. It wasn’t intended to be anything but an anglicizing of the notation; but I was slopping about.

* This is perhaps worth a slight round-about development, by pointing out that there are complications even when the noun is what we would generally take to be a count noun. Cf.

1) Christian is the man Roxane loves.
2) Cyrano is the man Roxane loves.
3) Christian is not numerically identical to Cyrano.

These are all true. But it’s not straightforward that
4) There are two men Roxane loves
without disambiguation, because while the real men are distinguishable into countable units, the object of Roxane’s love is not, so how we take the conclusion has to be kept very close to how we took the premise predicates. It’s real countability — how the noun is actually predicated — that’s at issue, not the fact that the word is typically a count noun in everday grammar; and real countability is precisely what the objector can’t assume — those things are count nouns, properly speaking, that are such that when predicated of subjects they pluralize by subjects.

Also, even considering only count nouns, what would you say about the cat on the mat problem? Tribbles and Trib are not numerically identical because Tribbles is the cat and Trib is the cat leaving out its tail; but from

a) Tribbles is a cat
b) Trib is a cat
c) Tribbles is not numerically identical to Trib
you still can’t get
d) There are two cats
because Trib and Tribbles, while not numerically identical, are only one cat. Numerical identity is a very fragile identity in this way; any difference breaks it.