Dialogue on analogy

[ME] I hear Rome gets busy this time of year.
[YOU] Busy? What do you mean?
[ME] You know, all the hustle and bustle with the tourism season. People going here, people going there, all that stuff. Just like all the crazy hustle and bustle in Chicago over Thanksgiving weekend. People shopping, the sidewalks filled with exponentially more than normal.
[YOU] Ah, I see. What my crazy grandfather likes to call 'Hustley-Bustley'. That's trademarked, by the way.
[ME] You and your crazy grandfather. Always giving things weird labels.
[YOU] That's true. Sometimes he calls his wife 'Big Al'.
[ME] Let's go back to Hustley-Bustley.
[YOU] So you're saying that you think Rome is Hustley-Bustley, and you're thinking of Chicago's Hustley-Bustley when you say that.
[ME] Uh, yeah.
[YOU] But you've never been to Rome yourself, you've never seen it.
[ME] Well, yeah, but I've heard from friends who have visited.
[YOU] So?
[ME] So, I would imagine that Rome's Hustley-Bustley must be like Chicago's Hustley-Bustley.
[YOU] It might be, but it might not be.
[ME] Well, that's true, but I have faith that it is.
[YOU] There's no more reason to believe that it is than to believe that it's not.
[ME] But surely Rome is similar to Chicago in at least some way.
[YOU] Ah, but you've assumed there is something similar between Rome and Chicago. My point would be that you can't compare Chicago to Rome without some similarity between them. And in this case, you don't actually know what Rome is like, so you can't really tell me that you know they're similar.


[ME] Hmm. Can I retract my statement that there's something similar and still compare Chicago and Rome?
[YOU] I don't see any way to do that myself.
[ME] What do you mean?
[YOU] Are you sure you don't want to say there's something similar between Rome and Chicago?
[ME] Yes.
[YOU] Since we both obviously have in our heads similarities between Rome and Chicago and the whole point is to try to work this out without any similarity, let's use a more extreme example. Imagine that I told you they've found a city on one of Saturn's moons, and that we've named the city IHWDANT (short for 'I Hope We Discover Alien Ninjas There'). Everything there is totally different from our cities on earth. The inhabitants, if you can call them that, are different. The buildings, if you can call them that, are different. The whole system, if you can call it that, is different. In fact, it's nothing at all like the cities we know.
[ME] I hope we discover alien Ninjas there.
[YOU] Me too. Anyways, given the difference between Chicago and IHWDANT, would you ever dream of comparing Chicago's Hustley-Bustley and IHWDANT's Hustley-Bustley?
[ME] Why not?
[YOU] Well, on what basis would you make any comparisons?
[ME] I don't know. Let me think. Does it get busy there?
[YOU] What do you mean by 'busy'?
[ME] You know, just regular 'busy'. Lots happening out and about.
[YOU] Well, there's not really any 'out and about', at least not in any sense that we conceive of 'out and about', and there's not really any 'lots happening', or at least not in any sense that we conceive of it. The place is totally different that way.
[ME] Uh, okay, so let's try something else. Are there lots and lots of inhabitants? Maybe I could say that if there are lots and lots of inhabitants, then we could suppose that if they all did something at the same time, that would be like 'busy'.
[YOU] Again, there's not really any 'inhabitants' there, at least not in any sense that we conceive of 'inhabitants'. And further, there's not any number there, at least not in a way that we understand it, so we couldn't say 'lots and lots' in any conceivable way either.
[ME] Okay, I see where you're going with this. To anything which I suggest as a possible similarity between Chicago and IHWDANT, you'll just say that there's nothing in IHWDANT that is like that in any conceivable sense for us.
[YOU] Exactly.
[ME] So what's the point?
[YOU] The point is that Chicago and IHWDANT are so different that if you don't have any similarity to start with, then you have no conceivable way of comparing them.
[ME] How so?
[YOU] Since IHWDANT is so utterly different from Chicago, you don't really know what it means to say there is Hustley-Bustley in IHWDANT. All you really understand is the Chicago case. The meaning of Hustley-Bustley for IHWDANT is entirely mysterious. If IHWDANT is truly nothing at all like Chicago, then Hustley-Bustley means utterly different things for Chicago and IHWDANT.
[ME] So when I say Hustley-Bustley for IHWDANT, I have no idea what it means. I only understand what Hustley-Bustley means for Chicago.
[YOU] Right.
[ME] I guess I need a way to explain how I am to understand the meaning of Hustley-Bustley for IHWDANT.
[YOU] Of course, you could just say that Chicago and IHWDANT are not that different, or at least that there is some similarity between them on which you could base your comparisons. But it seems that you want to stick to the idea that Chicago and IHWDANT are totally different.


[ME] What if I just said that there is Hustley-Bustley in IHWDANT. I could grant that I don't really understand what it is for there to be Hustley-Bustley in IHWDANT, but I do understand what it is for there to be Hustley-Bustley in Chicago, and so I could say there is Hustley-Bustley in IHWDANT, and know that I'm definitely referring to something in IHWDANT, but I don't really understand at all what it is. If I can use a little terminology from Frege, I could say that there is reference, but not sense.
[YOU] Sure, you could say that.
[ME] But?
[YOU] But it would seem to me a strange thing to do.
[ME] Why?
[YOU] Well, in the first place, how would you know that Hustley-Bustley has reference for IHWDANT if you don't understand what it means for there to be Hustley-Bustley in IHWDANT?
[ME] I'm not sure I see why it's a problem.
[YOU] Well, it seems obvious that reference depends on the sense. Let me give you an example. I know that you own a baseball with Don Mattingly's signature on it, and I know that you're putting it up for sale. I also know that you are selling tickets to a fantastic New Year's Eve ball sponsored by the volunteer organization you work for. Given that, suppose I said to you, 'I'm interested in the ball'. What is the reference of 'the ball'?
[ME] That would depend on what you mean. If you mean the baseball, then 'the ball' would refer to my Don Mattingly baseball, but if you mean the New Year's Eve ball, then 'the ball' would refer to that.
[YOU] So the reference depends on the meaning, and meaning is just another word for the sense of the term.
[ME] Okay, I see the point. Reference depends on sense.


[YOU] So the question is: if you don't have the sense of Hustley-Bustley for IHWDANT, how would you know it has reference?
[ME] Suppose that IHWDANT sent us a tour guide.
[YOU] What do you mean?
[ME] Well, I presume that we don't understand the language of IHWDANT, since in IHWDANT, there's nothing like there is in Chicago which we understand.
[YOU] Correct.
[ME] But suppose they understand our language.
[YOU] How do you mean?
[ME] Although we don't understand anything about their world, suppose they understand ours. They would then understand everything, their world and ours, and we would just understand ours.
[YOU] Okay, sure.
[ME] So with their comprehensive knowledge, they put together a brilliant marketing team to prepare a tour guide and send it to us. They write the guide in our language, for us, and they use words like Hustley-Bustley, knowing that although we don't have any idea what Hustley-Bustley is in IHWDANT, we do know what Hustley-Bustley is in Chicago, so the word would have some identifiable meaning for us when we used it and thus it would be useful. Further, even though we don't know what Hustley-Bustley is in IHWDANT, they do, so the word Hustley-Bustley does actually refer to Hustley-Bustley in IHWDANT.
[YOU] Okay.
[ME] Wouldn't that give me reference without sense?
[YOU] Perhaps.
[ME] Wouldn't that establish my case?


[YOU] It depends on the truth of the story about the tour guide. Hustley-Bustley would only refer (without sense) to Hustley-Bustley in IHWDANT if IHWDANT actually prepares a tour guide and sends it to us as you have described. If somebody from Chicago just made up the tour guide and convinced us all that it came from IHWDANT, then Hustley-Bustley would certainly not refer (with or without sense) to Hustley-Bustley in IHWDANT.
[ME] Okay, but suppose the story is true.
[YOU] Well, you'd still have to believe it. Let's suppose that IHWDANT do in fact prepare and send the tour guide to us as you have described. Even still, I'd have to use the word Hustley-Bustley with reference to IHWDANT. After all, I could simply reject your story of the tour guide as pure fantasy about IHWDANT. In that case, I would conclude that Hustley-Bustley in IHWDANT doesn't exist at all. But that doesn't mean I would stop using Hustley-Bustley with reference to Chicago. And every time I, or anyone else for that matter, used Hustley-Bustley with reference to Chicago, Hustley-Bustley would have both sense and reference for the Chicago case.
[ME] But nobody is questioning whether Hustley-Bustley has reference (or sense) with respect to Chicago.
[YOU] We are asking about the reference of Hustley-Bustley with respect to IHWDANT. And that requires that somebody actually uses the term Hustley-Bustley with reference to IHWDANT. There can be no reference (even without sense) to IHWDANT if the term Hustley-Bustley is never used with respect to IHWDANT. And using Hustley-Bustley with respect to IHWDANT requires that I at least believe that I can use the word with respect to IHWDANT. Otherwise, it'd never occur to me to use the word of IHWDANT. So you still have to believe the story before you can even use Hustley-Bustley with respect to IHWDANT.


[ME] But we've granted that the story is true. Hustley-Bustley would then refer to IHWDANT even if nobody believes it.
[YOU] Not really. There might be something in IHWDANT to which the term Hustley-Bustley can refer. But that something is different from its name. I (or the authors of our tour guide) can give it the name Hustley-Bustley, but we could give it any name. We could call it 'widget' just as easily. The point is that even if there is this something, we still can't refer to it unless we use a name to refer to it. Unless someone uses a name, for example Hustley-Bustley, to refer to this something, we can't refer to it at all. So yes, supposing that the story is true, there is a something to which Hustley-Bustley can refer, but that doesn't mean that the particular term 'Hustley-Bustley' refers to it. Somebody has to use the term 'Hustley-Bustley' to refer to it, and that requires that someone believes they can use the term 'Hustley-Bustley' to refer to it.
[ME] I'm not sure I totally understand.
[YOU] It's true that there are cats in our world, right?
[ME] Right.
[YOU] Our word 'cat' refers to particular cats, right?
[ME] Right.
[YOU] Does the word 'plinklet' refer to cats?
[ME] Of course not.
[YOU] Would you grant that God knows all the possible words we could use to refer to cats?
[ME] Sure.
[YOU] So God knows that the word 'plinklet' could refer to cats.
[ME] Okay.
[YOU] But does that mean that 'plinklet' does refer to cats?
[ME] I guess not.
[YOU] Why not?
[ME] Because nobody uses it to refer to cats. It's a word that we could use to refer to cats, but we don't use it to refer to cats. We use the word 'cats' to refer to cats. In order for 'plinklet' to refer to cats, someone would have to actually use it to refer to cats.
[YOU] Right. So reference depends on actual use, not possible use.
[ME] We're distinguishing between possible reference and actual reference.
[YOU] Suppose my cat Felix hasn't given birth to Felix Jr. Would you say Felix Jr. exists?
[ME] Of course not. Felix Jr. could exist, but Felix Jr. doesn't exist now.
[YOU] Reference is the same way. There could be reference for Hustley-Bustley with respect to IHWDANT, but that's pretty much irrelevant. What matters is real, actual reference. What matters is the actual use of words.
[ME] Okay, I'll buy that.
[YOU] Coming back to the story then, do you agree that although there may be something in IHWDANT that Hustley-Bustley could refer to, the actual term 'Hustley-Bustley' doesn't refer to it until someone actually uses Hustley-Bustley to refer to that something?
[ME] Yes.
[YOU] And do you also agree that in order for someone to actually use Hustley-Bustley to refer to IHWDANT, they would have to actually believe the story about the tour guide?
[ME] Yes. If they didn't believe the story about the tour guide, it would never occur to them to use the term 'Hustley-Bustley' to refer to IHWDANT, and then 'Hustley-Bustley' wouldn't refer to Hustley-Bustley in IHWDANT.
[YOU] Right. So explaining the reference (without sense) of Hustley-Bustley to IHWDANT by appealing to your story about the tour guide requires first that the story is true, and second that someone believes it so as to put 'Hustley-Bustley' to use with respect to IHWDANT.
[ME] Agreed.


[YOU] Good. Now you've got your story of the tour guide which gives you the word 'Hustley-Bustley' to refer to the Hustley-Bustley in IHWDANT, but the reference depends on the fact that the story is true and that you believe it.
[ME] Fine. The story is true, and I believe it. Wouldn't I then have reference without sense?
[YOU] You sound like a Christian.
[ME] Is there any other reason why I shouldn't continue holding to my story about the tour guide?
[YOU] There is.
[ME] And what's that?
[YOU] You may believe that the story is true, but how do you know that it's true?
[ME] I don't have to know that it's true. I just have to believe that it's true. I thought we'd agreed on that much.
[YOU] Not exactly. You have reference (without sense) only if the story is true. Merely believing in something isn't enough to make it true. I can believe that Felix Jr. exists and walk around calling out 'Felix Jr.', but that doesn't mean the name 'Felix Jr.' refers to Felix Jr. On the contrary, the name 'Felix Jr.' doesn't refer to Felix Jr. because Felix Jr. doesn't exist.
[ME] Of course.
[YOU] We have reference only if the story is true, and there's nothing in your story to guarantee that it is in fact true. You just have to work on the belief that it is true.
[ME] Fair enough.
[YOU] So you're a fideist about this.
[ME] Sure.
[YOU] Okay, I should just point out that belief may be enough for you, but it may not be enough for others.
[ME] I'll accept that.


[YOU] And I will too. We're both in the fideist camp then. Even so, I'm still uncomfortable with reference and no sense.
[ME] How so?
[YOU] If you go around bandering Hustley-Bustley with respect to IHWDANT, you have no idea what you're talking about. Let's even suppose that we only use Hustley-Bustley with respect to IHWDANT in circles of people who believe the tour guide story. They all believe it, so they all believe that Hustley-Bustley has reference with respect to IHWDANT, but nobody here knows what you're talking about. We just know the word 'Hustley-Bustley', but we don't have any notion of what that's supposed to mean. Essentially, we end up talking about IHWDANT in a way that leaves us with no understand of IHWDANT at all.
[ME] I think I see your concern.
[YOU] Imagine that I build a new room in my house and fill it with various objects. Before you've seen it, I come to you and say, 'You should see my new room. It's incredible'. You say, 'Tell me about it. What sort of things did you put in it?' I tell you that my new room contains a gartnick, a qwinky, and poppeltop (I made these names up, you see, instead of using the objects' common names). You would naturally ask, 'what the hell is a gartnick, a qwinky, and whatever the last one you said was?'
[ME] Naturally.
[YOU] I would just tell you not to worry, because those words have reference to real objects in my new room.
[ME] Please never actually describe objects to me in this way.
[YOU] Now, it seems clear enough that you have a way of talking about the objects in my new room, because you have some names which have reference. Unfortunately, these names don't have any sense. You have no idea what it means for there to be a 'gartnick' in my new room.
[ME] Indeed, I have no idea.
[YOU] So what would you do with this information? Would you run off and tell your friends about the objects in my new room?
[ME] Only if I was a psycho.
[YOU] You can see that it just seems pointless to talk about something if our language has reference but not sense.
[ME] I do see that.
[YOU] On a practical level, what's the point of having reference but no sense if I want to talk about IHWDANT?
[ME] That doesn't seem to be a very productive way of talking about things. At the very least, I certainly wouldn't acquire much understanding of IHWDANT if my words for IHWDANT had reference but no sense.


[YOU] There's more.
[ME] Oh?
[YOU] Not only would you not understand what gartnick, qwinky, and poppeltop mean, you also wouldn't understand how to talk about those things in relation to each other. Could you meaningfully say that in the design of my new room, the gartnick helps to balance the feel of the qwinky?
[ME] Of course not. I don't know what the qwinky is like, so I wouldn't know how it needs to be balanced, and I don't know what a gartnick is, so I wouldn't know how it would balance the qwinky.
[YOU] Right. You wouldn't be able to talk about the garntick in relation to the qwinky or the poppeltop in any meaningful way. Likewise, you couldn't form any syllogisms from the terms gartnick or qwinky.
[ME] Why would I want to form a syllogism from things in your room?
[YOU] You wouldn't, but you might if this was just a big analogy for some other topic.
[ME] Okay, this is getting weird again. The irony is not lost on me, by the way.
[YOU] In any case, my point is, you couldn't meaningfully reason from gartnicks to qwinkys or talk about how they interrelate in any meaningful way if you had reference but no sense.
[ME] Of course, but I still don't see why I would want to.
[YOU] Never mind that. We agree that it seems counter intuitive to try and talk about something with reference but no sense. If I try to describe IHWDANT with terms like Hustley-Bustley which have reference but no sense, I end up with a pretty empty description. I might as well just talk about IHWDANT with words like 'gartnick' and 'qwinky'.

Randal Rauser, Is The Trinity a True Contradiction?

Randal Rauser, 'Is The Trinity a True Contradiction?'. Quodlibet Journal 4 (2002).

http://www.quodlibet.net/rauser-trinity.shtml.

Rauser compares the logical problem of the trinity to 'true contradictions', i.e., contradictions which are true. In classical logic, if you admit one contradiction, you have to admit all contradictions, so to avoid this, everybody believed that contradictions were false. In modern paraconsistent logic, you can localize contradictions so that those contradictions don't entail contradictions in the rest of the system. Consequently, some today can admit contradictions which are true.

Rauser then considers David Cunningham's book These Three Are One because Cunningham seems to claim all over that book that contradictory states of affairs are true. In the end, Rauser concludes that it is not helpful to countenance true contradictions in God. The reason is that God is a necessary being, and thus any true contradictions would ultimately be about God's nature, and it makes more sense to say God is, for example, 'good' only rather than that God is 'not-good' and 'good'.

Hylomorphism and the trinity

In what follows, I would like to examine the shortcomings of comparing the divine persons to hylomorphic compounds. According to traditional classical theism, the divine persons are said to be made up of the divine essence plus a personal property such as being a father or being a son. Throughout the history of trinitarian theology, this occasionally gets construed in terms of hylomorphic composition: the divine essence plays the role of 'matter' and a personal property that of 'form', so the divine persons can be seen as hylomorphic compounds made up of matter and form.

The claim that the divine persons can be seen as hylomorphic compounds shows up mostly recently in a paper by Jeffrey Brower and Michael Rea ('Material Constitution and the Trinity', Faith and Philosophy 22 (2005): 57-76; henceforth, B-R). When they bring hylomorphism into the picture, B-R are trying to solve a much bigger problem pertaining to the identity and distinction of the divine persons. Here I don't want to discuss B-R's larger project. Instead, I would only like to focus on the claim that the divine persons can be seen as hylomorphic compounds.

I will give two arguments against this claim. First, I will argue that hylomorphism does not map onto the divine persons because the constitutive relation between matter and form cannot apply to the trinity in a straightforward way, or at least not in a way that is obvious to me. Second, I will argue that hylomorphism cannot explain the divine persons because neither the divine essence nor a personal property can play the role of matter. Rather, both must play the role of form.

1. The constitutive relation between matter and form cannot apply to the trinity

A hylomorphic compound is any entity composed of matter and form. But that's not the end of the story. These two constituents also stand in relation to each other in some way. Hylomorphism not only brings along with it matter and form, it also brings certain relations between matter and form. There are, of course, many ways that matter and form are related. For example, we can talk about relations of identity and distinction between matter and form (as B-R do throughout their paper). But this is not the sort of relation that concerns me.

Here, I am interested in a constitutive relation. By 'constitutive relation', I mean the sort of relation which explains why matter and form constitute one thing. This relation needs to be a unity-making relation in some relatively strong sense. A hylomorphic compound is not, after all, just a heap or pile of matter and form. On the contrary, matter and form are supposed to combine in a hylomorphic compound to make up one thing. The constitutive relation explains why matter and form make up more than just a heap or pile. It explains the unity of matter and form in a hylomorphic compound.

This is relevant for the divine persons because we would not want to say the divine persons are heaps or piles of the divine essence and personal properties. There must be some unity-making relation which makes the divine essence and a personal property more than just a heap or pile, some unity-making relation which makes the divine essence and a personal property into a single person. My question, then, is this: what is this relation? What kind of constitutive relation can apply to matter and form but can also apply to the divine persons?

One common answer is to talk about this relation in terms of material organization or arrangement, and this is what B-R seem to do. They describe forms as 'complex organizational properties'. Presumably, this means that they take forms to be the sort of property (or bundle of properties) which organizes or arranges material parts in a particular way. For example, the form of a chair would organize slabs of wood into a chair, while the form of a table would organize slabs of wood into a table. The form is what explains why the material parts end up arranged as they are. For B-R, the relation of form to matter seems to be a relation of material organization or arrangement.

But how exactly would this apply to the trinity? According to B-R, the divine essence is immaterial (and presumably simple), so there aren't any material parts. If the personal properties are supposed to be 'forms' and the divine essence is supposed to be 'matter', what exactly would these 'forms' organize or arrange? It's hard to see how a relation of material organization could apply to an immaterial divine essence. The divine essence, in virtue of being immaterial or un-arrangeable, blocks the possibility of being related to form in this way.

As it stands then, B-R's claim that the divine persons can be seen as hylomorphic compounds fails. If B-R take 'forms' as organizational properties, the divine essence cannot play the role of matter because it is immaterial and thus cannot be organized or arranged. If B-R want to successfully see the divine persons as hylomorphic compounds, they must clarify what sort of constitutive relation applies to the divine essence and the personal properties. The relation of organization or arrangement is inapplicable to the trinity, so some other relation needs to be specified in a way that is consistent with B-R's other claims about the divine essence.

Perhaps we could look to the Aristotelian relation of act-potentiality. Perhaps it is clearer to talk about this in terms of acts and recipients. Forms are acts of some sort, and matter is the recipient of those acts. For example, if we press a signet ring into a lump of wax, the wax is the recipient of the act of imprinting the ring's shape. The wax is potential because it could take on some other shape, or no shape at all. Likewise, the ring's shape is actual because it is what actually makes the wax take on its shape. The relevant feature of this picture is that the form is what makes the wax become what it becomes, not the other way around. The form is the actual-maker, not the matter, since matter is only potential.

But again, how exactly would this apply to the trinity? If the divine essence is supposed to be 'matter' and a personal property is supposed to be 'form', then the divine essence would only be potential to the personal properties, which is to say it would only potentially be a father or a son. Yet according to B-R, the divine essence is not potentially a father or a son. It is a father or son in some necessary sense. Indeed, most would want to say the divine essence is actual, not potential. Besides, Aristotle's act-potentiality relations explain change, and that's not the sort of thing B-R want to explain in the trinity. So here too, the act-potentiality relation is inapplicable to the trinity as a constitutive relation.

What other options are there? To be sure, there are many kinds of constitutive relations, but I cannot seem to see any which don't run into the same sorts of problems. This doesn't mean there aren't any good candidates. I have, after all, only discussed two of the more obvious options (organizational and act-potentiality relations). My aim is simply to show that the standard constitutive relations of hylomorphic compounds don't map onto the divine persons in a straightforward way, at least not without some modifications. If we want to pursue hylomorphism as a model for the divine persons, we need to go further than B-R and explain exactly how 'matter' and 'form' are related so as to constitute a person. Otherwise, we're left with some 'matter' and some 'form' which are just supposed to be 'there' in a divine person.

Whatever we say about this, it has to be relevant to matter and form. By 'relevant', I mean it must have something to do with why one would call the divine essence 'matter' and a personal property 'form'. I have argued that the divine essence cannot be related to personal properties by organizational relations or act-potentiality relations, and so without any other candidates for a constitutive relation on the table, there seems to be no reason to call the divine essence and personal properties 'matter' and 'forms' at all. Hylomorphism can only apply to the divine persons if we establish a constitutive relation which is coherently applicable to the trinity, and it is not clear to me how this could be accomplished.

2. Neither the divine essence nor a personal property can play the role of matter

Another problematic feature of hylomorphism is that only the form explains what kind of thing the compound is. Matter can be arranged into numerous configurations. For example, the same slabs of wood can be configured into a chair or a table. In both cases, the form is what makes the hylomorphic compound into the kind of thing it is, not the matter. The form is the chair-making property or the table-making property, not the wood. The matter itself does little to explain what kind of thing the hylomorphic compound is. If I may put it in the following terms, the form is the thing-maker, not the matter.

The same goes for the divine persons. If we consider the divine essence as 'matter' and the personal properties as 'forms', then the personal properties are the thing-makers, not the divine essence. The personal properties will make the divine essence into the kind of thing it is. Consider the property being a father. Such a property would make some matter into a father, just as the property being a chair would make some matter into a chair. Thus, the property being a father would make the divine essence into a father. Considering the divine persons as hylomorphic compounds thus entails that the property being a father is the father-making property, the property being a son is the son-making property, and the property being a spirit is the spirit-making property. But there's more to the divine persons than being a mere father, a mere son, or a mere spirit.

The divine persons are also divine. Hylomorphism explains why the persons are father, son, and spirit, but how does it explain that the persons are divine? What is the divine-making property? If we take the divine essence as 'matter', it cannot play the role of a divine-making property, because matter is not a thing-maker. What we are left with, then, is simply a father (not a divine Father), a son (not a divine Son), and a spirit (not a divine Spirit). Relegating the divine essence to the role of 'matter' prevents the divine essence from being a divine-making property.

Perhaps we might say that matter does in fact contribute to the kind of thing a hylomorphic compound is. After all, if a chair is made out of wood, it is a wooden chair, and if it is made out of iron, it is an iron chair. Likewise, in the trinity, the 'matter' contributes to what kind of thing each divine person is. The Father is made out of the divine essence, so he is a divine Father, the Son is made out of the divine essence, so he is a divine Son, and the same goes for the Spirit. But this would be a mistake.

Consider the case of a clay statue of Goliath. It is true that a clay Goliath is clay because he is made of clay. Likewise, a bronze Goliath is bronze because he is made of bronze. But compare this with the human Goliath. It is not true that the human Goliath is human because he is made of human 'material'. If that were true, animals would count as humans too, because they are made up of the same kind of flesh and blood material. Thus, the matter cannot be a thing-making property. The human-making property for the human Goliath is not his matter, it is his human form. The same goes for clay and bronze statues. To say a statue is bronze is to say the bronze-making property is the form of the bronze, not the matter.

The problem with saying the divine essence plays the role of matter is that the divine essence cannot play the role of divine-maker. One might turn the model upside down and say the divine essence is the 'form' of the divine persons, while the personal properties are the 'matter' of the divine essence. But this won't do either. Although it does make the divine essence into a divine-maker, it relegates the personal properties to the role of matter, so they cannot be thing-makers. For example, if the property being a father plays the role of matter, it cannot be a father-making property, and the same goes for the property being a son or being a spirit. We would end up with three divine things, but not with a Father, Son, and Spirit.

Whatever model we use to explain the constitution of the divine persons, it needs to explain how both the divine essence can be a divine-making property and how a property such as being a father can be a father-making property. Hylomorphism cannot do this. Any model which employs hylomorphism to explain the divine persons faces the difficulty that the matter cannot play the role of thing-maker. When it comes to the trinity, perhaps it would be best to avoid hylomorphism altogether.

Object-constituting relations and the divine persons

Most versions of classical trinitarian theology recognize at least four properties in the trinity – and here I mean to use 'property' in the weakest possible sense as some recognizable characteristic of a thing, without meaning to entail any ontological claims about what such properties are. For example, I do not intend 'properties' to mean universals, tropes, or anything else typically associated with the term 'property'. I simply mean a recognizable characteristic of a thing.

In any case, I label these properties as follows:

(T1) There are four properties in the divinity like so:
e = the divine essence
p = the property 'being a father' (or paternity)
f = the property 'being a son' (or filiation)
s = the property 'being a spirit' (or spiration)

Additionally, classical theism holds that these properties are arranged in a particular way. Each divine person is made up of the divine essence and a personal property as follows:

(T2) Each divine person is made up of the properties from (T1) like this:
Father = e + p
Son = e + f
Holy Spirit = e + s

My question is: why are these properties arranged in this particular way? What explains this particular configuration? Answering this entails some discussion of the relations between all these properties.

To be sure, there are different kinds of relations we could talk about. For example, we could talk about identity and distinction relations here, and indeed this is what much of trinitarian theology invests its time in. But I'm not interested in those kinds of relations here. I'm interested in what I call object-constituting relations. An object-constituting relation is a relation which explains why its relata together constitute an object.

There are many sorts of object-constituting relations. For example, imagine if I could take a number of sand grains and throw them into a heap or pile. The grains would then be related to the whole as elements of a heap or a pile, and the sand pile would be an object (in the sense that heaps or piles are objects). The relations between the grains of sand are thus object-constituting relations, because they explain why the whole of them counts as an object.

But that can't be what we want here, because in heaps or piles, grouping any two elements together would be arbitrary. If the elements of our pile were the properties specified in (T1), I could group any two of them together arbitrarily. I could just as easily say the Father is p + s as I could say he is e + p. Thus, these divine properties cannot all just be 'there' in the divinity, in a heap or a pile, because then we don't get (T2) in any non-arbitrary sense.

What we need is some sort of relation between the divine essence and each of the personal properties which does not obtain between the personal properties themselves. In other words,

(T3) There is some object-constituting relation which obtains between
e and p,
e and f, and
e and s
which does not obtain between
p and f,
p and s, and
f and s.

Additionally, the kind of object-constituting relation we want here must be some kind of unity-making relation in the sense that it must explain the unity of the divine essence and a personal property in each divine person. Thus,

(T4) The constituents of each divine person are related by a unity-making object-constituting relation like so:
e is related to p such that e + p are one,
e is related to f such that e + f are one, and
e is related to s such that e + s are one.

Whatever we say about the object-constituting relation, it must be consistent with (T1) - (T4). So what is this object-constituting relation?

There are, of course, many strategies for answering this question. I'm not going to go into any of them here, mostly because I haven't worked them all out yet. Here I just wanted to put down the conditions (namely, (T1) - (T4)) for any answers to this question.

Analogy and explanation

Analogies intended to help us understand something often break down. When that happens, the question becomes: just how much does the analogy actually explain? By 'explain', I mean that the analogy in some way helps me understand the inner machinery of the matter. But of course analogies breaks down, in which case an analogy only helps me understand part of the inner machinery of the matter.

But how exactly does this 'explaining' happen? How does an analogy A explain some B? In the simplest case, it would seem that analogical explanation occurs when some parts of an analogy A map onto some parts of the inner machinery of B (taking 'parts' in the broadest sense). For example, suppose A and B have parts in the following ways:

A = parts a, b, c, and d
B = parts a, b, j, and k

In this case, if we understand A, we will understand a and b in B but not j and k, since a and b match up for A and B but not the other parts.

So what's the point of using an analogy? If our analogy only explains a and b, why not just explain a and b, and forget the analogy altogether? Well, sometimes we cannot understand parts without the whole. More specifically, sometimes we cannot understand the relations between parts without the whole. It might be the case that I cannot understand how a is related to b individually, but I can understand a and b along with c and d as a whole, while I cannot understand a and b along with j and k as a whole. That is, explaining how a and b are related in A might be much easier than explaining how a and b are related in B. In this case, the analogy serves the purpose of explaining at least some of the parts of the inner machinery of B, or, more specifically, the analogy explains certain relations between parts of the inner machinery of B.

I mentioned that this seems to me the simplest case. It is the simplest case because I have been taking 'parts' to be atomic in the sense that they themselves don't include parts. Of course things can get more complicated if the parts themselves include their own parts. But this makes no difference. A only explains B in so far as parts map onto parts, no matter how far down the tree of parts we go.

For example, suppose A and B have parts like this:

A = parts a (= parts x and y), b, c, and d
B = parts a (= parts x and z), b, j, and k

Here, A's part a has parts x and y, while B's part a has parts x and z. In this case, the first a only maps onto the second a in virtue of its part x. We can subdivide parts into more parts over and over again, but our analogy will only explain the matter insofar as certain of its parts (and the relations between them) map onto the matter in question.

The same applies to the relations between the parts. As I said, I am taking 'parts' in the broadest sense, so any of these parts might be relations. For example, suppose that x and y are certain relations of a to b in A, while x and z are certain relations of a to b in B. In this case, our analogy A explains B in that A helps me to understand that in B, a is related to b by a relation x, but the analogy breaks down when it comes to the relations y and z.

I am assuming that the parts which 'map' are atomic. That is, one part either maps onto another part or it doesn't. A's part x is either the same as B's part x or it's not. If it's not the same, it doesn't map. If it is the same, it does map. My account turns on this claim. In order to compare two things, there must be something which is the same between them.

Thus far I have started from wholes and moved down to their parts to explain how similar the wholes are. But we can explain this picture the other way around. Begin with two atomic things. Either they are the same or they are not. If they are not the same, they are not comparable at all. If they are comparable, then good. Now, add more atomic things to the picture to form some wholes, and the same rules apply. The first whole is comparable to the second whole only in virtue of those parts which are comparable. One whole cannot be compared to another whole by parts which are not the same.

I must confess that I don't see any other way analogies could be explanatory. For simple things, either one thing is the same as the other thing, or it's not. For complexes, either some of the parts are the same or they are not. There must be something the same in order to compare one thing to another. At this point, I can't seem to see another way that analogy could 'explain' something. If none of the parts of an analogy map onto none of the parts of the analogue, then I wouldn't call it an analogy. I would just call it an alternative model.

This is, of course, just Scotus's theory of analogy in a slightly different form. The basic point is that there must be something in the analogy which maps onto the analogue for the analogy to hold. Without some mapping, the analogy is not at all 'like' the analogue.

Testing

Jebus, how many times have I started a blog and then not maintained it. About a million + π. We'll see if this one works.