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Friday, February 19, 2010


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Could you kindly specify in which sense these propositions are mind-dependent?
Because if the reply is the counterfactual: "if God hadn't thought them, then they wouldn't have existed"
then these sentences aren't necessary (assumed that 'necessary'='true in all possible worlds')

saved by the mighty time!

Hi Peter,

To take inspiration from Avicenna, one might distinguish between contingent products and necessary products, where a contingent product is something that is produced in only some worlds, while a necessary product is something that is produced in every world. You would deny that, saying that there is no such thing as product that is produced in every world. If something is produced, then there must be at least one world where it is not produced. Is that right?



That is the kind of comment I like. Pithy and to the point. I agree that if God hadn't thought the propositions, then they wouldn't have existed. But you think this implies that these propositions (not sentences!) do not exist in all possible worlds. (By the way, don't confuse necessary truth with necessary existence: the former is truth in all possible worlds, the latter is existence in all worlds.)

But I deny that the implication holds. For what I am doing is engaging in per impossibile reasoning: If, per impossibile, God had not thought them, then they wouldn't have existed. That is consistent with saying that both God and the propositions exist necessarily.

Here is a different example. Suppose you have a math. set of necessary beings; they could propositions or numbers or whatever. Then both set and members are necessary. But isn't it obvious that the set depends for its exstence on the members and not vice versa? I could put it this way: If, per impossibile, the members did not exist, then the set would not exist either.


But didn't you have some kind of counterargument, perhaps along the lines of what Aresh said?

You are not giving up, are you?


Peter is probably committed to something like that, where propositions are divine products.

Fair enough Bill. And thanks for the clarification. But now I'm wondering what are the truth conditions of that 'per impossibile' implication...


"You are not giving up, are you?"

Not unless I am wrong.

Could God have in his mind the proposition that 2+2=4 the proposition that 2+2=5?

"But isn't it obvious that the set depends for its exstence on the members and not vice versa? I could put it this way: If, per impossibile, the members did not exist, then the set would not exist either."

Not for its existence, but for its identity.

There are sets that have as members contingent beings: e.g., S={Eiffel Tower}. In such a case we can speak about both that the existence of S depends upon the existence of the Eiffel Tower and that the identity of S depends upon having the Eiffel Tower as a member.

But if S={1}; i.e., when both the set and its members are necessary entities, then the relation of dependence no longer applies and the only issue that remains is identity: i.e., if S would not have had the number 1 as a member, then S would have been a different set. For the counterfactual "if 1 would not have existed, then S would not have existed" is vacuously true. How would we give truth conditions for this counterfactual statement in possible worlds terms when both member and set exist in every possible world? (aresh, I believe, raised this concern)


In my last post the sentence "Could God have in his mind the proposition that 2+2=4 the proposition that 2+2=5?" should be replaced by:

"Could God have in his mind instead of the proposition that 2+2=4 the proposition that 2+2=5?"


I could ask you the parallel question: Are there true and false propositions in Plato's Heaven? You will say 'yes' and you won't see any problem with it. So why should there be a problem with my theory?

Why can't the theist say this: Propositions exist precisely as divine accusatives. Some are true and some are not. Don't confuse existence with truth. I am not saying that the truth of a proposition is its being an object (accusative) of the divine intellect; otherwise all propositions would be true. I am saying that the existence of a proposition is its being an object of the divine intellect.

Do you see a problem with that?


You want truth conditions in 'possible worlds' terms for: If, per impossibile, 1 had not existed, then {1} would not have existed.

I suppose you have to widen your semantics and quantify over both possible and impossible worlds. It is open to me to say that your semantic model is defective if it cannot accommodate the obviously meaningful sentence above. It is plainly meaningful whether or not you consider it true.

I believe some work has been done on impossible worlds. I'll have to check.

But you and aresh both raised a good point.


As I mentioned to you, Katz has talked about working on semantic models that are wider than possible world semantics. My recollection is that this semantics was supposed to be precisely the sort of system that would give an account of the sort you have in mind with per impossibile. I do not know whether he ever finished it or whether it was published.

Incidentally, how do you style here (italics, bold etc.)?


I was trying to find a book by Katz at the library, but some turkey had it checked out. Can you believe that? Didn't he know that I would put it to better use than he would?

To put 'Katz' in italics, type this: left angle bracket i right angle bracket Katz left angle bracket forward slash i right angle bracket.

To bold use 'b' instead of 'i' but without the inverted commas.

    Always be sure to turn off any HTML command you turn on by using the forward slash!

I will put your latest Anderson piece at the top of the page. But first I want to read Anderson's article.


Wow! So simple!


It is a good article. It would b e nice to read it in conjunction with Dale Tuggy's article, but I cannot obtain the later.


Why not e-mail him? He might just snail-mail you an offprint. And then you can make a copy for lazy me!

Ironically, when I logged on this morning I discovered that I had failed to do precisely what I told you to do, namely, turn off any HTML commands you turn on. The whole site was in italics. That fits with my Italianate nature, no doubt, but is objectionable nonetheless.


Anderson's is an excellent article. I spent last night and this morning studying it. He holds off Tuggy quite well.


I apologise but I am afraid I am not able to keep up with the discussion any more for time constraints... I know I wanted to respond to certain your comment but I cannot find it...

Regarding the necessary dependence: I think that your formulation of the problem does not do justice to the orthodxy. According to that, the Son is not dependent on Father, although he "proceeds" from him! Dependence is imperfection but the Son is God, that is, absolutely perfect.

So how is the Son "from" the Father without being dependent on Him?
There are two kinds of "being from" - i mean "being from" in the existential sense, "procedere secundum esse". In both cases, if B is from A, then A "infuses esse" into B. But there are 2 alternatives.

Either i) the esse insfused in B is another esse than the esse of A. In this case the infused esse is dependent, that is, it has an extrinsic source. Therefore this kind of A "being from" B entails dependence of B on A, we say that B is caused by A.

Or ii) the esse infused into B is the very same esse of A. If this is the case, and if the esse of A is uncaused, independent, then the infused esse in B is also uncaused and independent (that is, without any external source). In this case, B "is from" A, because B has esse from A, but B is not dependent on A, because it does not have some other esse that is produced by A but shares A's own independent esse. In this way the Son is from the Father and the Holy Ghost is from jointly the Father and Son.

Cf John 5,26: "For as the Father has life in himself, so he has granted the Son to have life in himself."


The English terminology is that the Father BEGETS The Son and that the Holy Spirit PROCEEDS from the Father and the Son. I believe you are mistaken in claiming that the Son proceeds from the Father.

Your solution is actually worse than the problem. At least my solution shed some light inasmuch as I gave a non-Trinitarian example of two necessary beings such that one in some sense 'begets' the second. And then in a subsequent post I gave a second, a set-theoretical, example.

The problem with your solution is this. You say that F and S have the very same esse. But then F and S cannot be numerically-existentially distinct as orthodoxy requires. Each substance has its own esse. If two substances have the same esse then they are one substance not two.

All you are doing is reformulating the original difficulty. If F and S have the same esse, then they cannot be distinct. But if they are distinct, then each has its own esse.
You are doing the same thing you did before in Christology: you make up a distinction that has no independent warrant and that merely repaeats the problem you were trying to solve. You say that the 2nd Person and Christ are two substances but one suppositum, but as I argued in great detail over a couple or three posts, the only warrant for the suppositum-substance distinction is the very problem you are trying to solve.

The solution is purely ad hoc.


I am sorry about the terminology. In Latin, "procedere" is a cover term for both "generatio" and "spiratio", so I surmised it is the same in English. Actually, looking at the translation of Summa Theologiae http://www.newadvent.org/summa/1027.htm I see that "procession" and "proceed" are used that way: for example q. 27 a. 2 co.:

So in this manner the procession of the Word in God is generation; for He proceeds by way of intelligible action...

I did not intend to offer solutions :-) My point in these discussions has mostly become merely to clarify what is the orthodox teaching and what is not. I kind of expected that you will regard the orthodox thesis that the Son is not dependent on the Father as more problematic than the Avicennian notion of "necessary of itself" vs "necessary from another".

Orthodoxy requires that F and S are numerically not existentially distinct. Viewing numerical distinction in terms of existence is just your interpretation. It may be viable (or so some Thomists believe) in created things where esse can be regarded as distinct from the essence, but certainly not in God. The essence of God that is shared by the Persons is just a (not very suitable) name for His esse, so it is impossible that were not shared by the persons. The orthodox teaching is that the ONLY thing that makes them distinct are the relations of origin.

If you mean "supposit" by "substance", then I deny that each supposit necessarily has its own esse. If you mean just individual substance regardles of the question as how many supposits it subsists, then of course every substance has its own esse, because the number of esse's is the same as the number of individual essences and in this sense we are counting substances according to their essences. In this sense there is one God, one individual divine substance ("consubstantialem Patri") with one esse but three subsistences.

I don't buy the "ad hoc" charge, in the first place because the disitnctions or clarifications are there not in order to solve a problem in the doctrine as You state it, but in order to differentiate the orthodox doctrine from the doctrine you state and criticise. The thesis that the Persons share esse is not a solution of anything, it is part of the doctrine, so is the nature-supposit distinction.

Of course, the solution of the counterarguments against Trinity consists mostly in pointing out certain misunderstandings concerning what the doctrine actually is. But this is not "introducing ad hoc distinctions", this is pointing out distinctions that have always been there in the doctrine (since its full articulation) but were disregarded and neglected by the objector.

the orthodox doctrine you state articulates the meaning of the Scriptures by means of the supposita ontology.
This articulation is not directly visible in the Scriptures,
if it were, there was no need of any orthodox doctrine.
In that sense this articulation is an interpretation of the Scriptures; and the Sriptures are the source of this interpretation.
The supposita theory sounds either contradictory or 'ad hoc' in regard with WHAT is stated in the Scriptures and has to be interpreted.


what I am explaining and defending here is the Catholic docrine. Catholicism recognises 2 sources of revelation, the Scripture and the Tradition, while the Tradition has epistemically the more fundamental role because it is the testimony of the Tradition which justifies the belief that there is a Scripture and what belongs to it.

Therefore, the Scripture is not the only ultimate source of the doctrine. The doctrine of the Trinity is NOT just an interpretation of the Scripture, it is also an interpretation of the orally transmissed apostolic tradition. Furthermore, the Tradition is unlike the Scripture in that it is a living process of continuous clarification and more precise articulation, to the effect that it is impossible to draw a line between the "source" and the "interpretation" in a historical way. Simply ALL the dogmas, both ancient and recent, are "the source", whereas anything else is interpretation (in fact, there are certain "degrees" of pertinence to the doctrine, but this does not change the basic picture).

Thus from the Catholic point of view it does not make sense to to reduce the "source" to the Scriptrue, or to some early statements like the Athanasian creed, and consequently it does not make sense to take the full-fledged dogmatized orthodox doctrine, compare it back to the Scripture and criticise it as "ad hoc". Either one is interested in the rational acceptability, epistemic status etc. of the orthodox doctrine and then he has to take it "as is", because it is declared by the Church to be revealed "as is", or if one is not interested in the orthodox doctrine as maintained by the Church, why should he be interested in what the Scripture or Athanasius says and why would he make attempts to make up his own private interpretations of these statements? For the authority that backs up the relevance and reliability of the Scriptures is the same that backs up the reliability and relevance of the full-fledged doctrine. The same Church testifies both that the Bible is Word of God and that the sophisticated doctirne of Trinity has been revealed by God through the Bible and the Tradition. THIS is THE doctrine of the Trinity that has any epistemic relevance. Anything else would be a human fabrication lacking the least reason to be believed in.

- I would be willing to consider the catholic doctrince as a whole if the Scriptures were like a set of assumptions and the rest of the orthodox statemens (e.g. the supposita ontology) were deducible from these assumptions. But it's exactly the other way around.
- Your reasoning at the bottom of your post begs the question:
if the supposita ontology wasn't constitutive part of the doctrine of the Trinity, then the whole doctrine would be a 'human fabrication'
But the whole doctrine is not a human fabrication so the supposita ontology constitutes the doctrine of the Trinity
I can't assume the the whole doctrine is a human fabrication, but neither the opposite. Especially if its putative ontologic assumptions have been developed by men over centuries.


Numerical without existential difference makes no sense. You are making a distinction that is ad hoc and without independent warrant in order to save a doctrine that is incoherent on the face of it.

You say you don't give solutions. Then you don't see problems, and and I have to wonder what the point of this discussion is. Everybody else sees the problems, why don't you?


I am afraid I don't understand you. The set of revealed assumptions according to Catholics is not confined to the Scripture but comprises the Tradition as well. The epistemic reliability, and, ultimately, relevance of the Scripture, depeneds on the testimony of the Tradition. The same Tradition that says that the John's Gospel is revealed and that the Thomas' Gospel is not also says that God is Trinity and in what is the meaning of it. But it seems that I don't understand your point.

I don't understand your summary of my argument either. I assume that the Trinity doctrine is not human fabrication because the Church says it was revealed. I believe the Church because I have strong rational justification to think that it really is what she claims to be, that is, an institution set up by God to protect, transmit and explain the deposit of faith.

There is no problem in the fact that the conctent of the doctrine was "developed by men over centuries": this is how the Church works and claims to work. It claims that it is endowed with special help of the Holy Ghost which guides her in correct explication of the contents of faith and in discerning what is and what is not part of the deposit of faith.

Did I address your points? I am not sure...


it seems that by saying "numerical without existential difference makes no sense" you are simply assuming without proof that numerical difference entails distinct existences. With this assumption, you necessarily arrive at contradiction in the doctrine, of course.

Now: I insist that from the methodological point of view, it is your duty to prove this assumption, not my duty to "warrant" my distinctions or my denial of this assumption of yours. Distinctions need not be warranted, claims of identity need to be warranted. Why? Because false assumptions of identity yield false consequences, whereas false distinctions only prevent you from deriving some true consequences. Denials of assumptions also need not be warranted, for the same reason (I could not legitimately argue, for example, that your denial of my unproved assumption is merely "ad hoc"). A distinction in fact amounts to a mere denial of assumption, namely, denial of assumption of an identity.

Besides: If it is true that making my distinctions is only undertaken in order to render the doctrine consistent and that otherwise the doctrine would be inconsistent, then the distincions are simply implied by the doctrine. They are just the only legitimate way to understand the doctrine. So they are not unwarranted at all, they are, as it were, proved indirectly by reduction to contradiction of the alternative explanations.

I did not say I do not see problems. I said I was not at this point offering solutions. The reason is that I see no point in trying to solve problems in any other but the orthodox doctrine - for example, I am not concerned to solve the problems of the doctrine that the Persons have each their own esse. First because I am only interested in explaining and defending the doctrine I regard as revealed by God, and second because I regard most of these so far sugested alternative doctrines as evidently self-contradictory and so I cannot see how they could possibly be defended. So my only point now is: let us give up our attempts to construe an alternative meaning of the doctrine and try to get the original meaning of the doctrine correct first.

But of course, if you are not interested in this, I will cease to bother you. After all, it is your blog :-) Thank you for the opportunity to discuss with you (and perhaps we meet in Prague this summer?)

Best regards, L.


The notion of numerical identity is used in the sense of absolute identity: i.e., a relation that a thing holds to itself and only to itself. No *two* things can have the relation of numerical identity, for if there are two things, then neither can be self-identical to the other. An no one thing can have the relation of being self-identical to anything else other than to itself.

Thus, if two things are numerically distinct, then it is not possible for either one to have the relation of being self-identical to the other.

Therefore, if we assume that x and y are numerically distinct, then two things must exist. For suppose that x and y are numerically distinct & there exists only one thing. Then it would follow that "x is self-identical to y' as well as 'y is self-identical to x'. But neither of these make sense.

Numerical identity (difference) is contrasted with *qualitative identity* and *relative identity* (qualitative and relative identity are related, but the former is compatible with numerical identity, whereas the later is not). The former simply means that x and y can be numerically different but qualitatively similar: e.g., one might say that two tables are (of course) numerically distinct but are similar with respect to being sturdy or made out of wood. The later is the view that absolute or numerical identity makes no sense and there is only relative identity: i.e., identity is always qualitative (Geach).

Thus, numerical identity (difference) entails existential identity (difference). This just is what is meant by a theory of numerical (absolute) identity.

Of course, it is open to you to deny that the notion of numerical identity makes sense at all and that all identity statements must be interpreted in terms of some notion of relative identity. What you cannot say is that the notion of numerical identity makes sense, it applies to this or some other case, yet deny that in these very cases numerical distinctness entails existential distinctness.


You are using a different concept of existence. In the scholastic sense existence is an ontological priciple that formally makes a thing exist. If you mean by "exsistential difference" merely the fact that if entities of some sort are two in number, then two entities of that sort exist, this is of course analytical truth and it is not denied in the doctrine of Trinity. Yes, there are three Persons, which entails that three persons exist. The point of the "one existence" thesis is that the ontological priciple that makes all the three Persons exist is one and the same for all the Persons.

The "one existence thesis" is quite direct and inevitable implication of i) divine simplicity (implying no essence-existence distinction) and ii) divine uniqueness (there is only one, unmultipliable divine essence). Many existences in God would go against the most fundamental principles of theism.


I think I am using the same concept that Bill assumed above. All Bill says is that if F, S, and HS are numerically distinct, then there are three different things that exist. This is part of the very concept of numerical identity and distinctness. I think this is what Bill said.


Right. Different substances differ in their very existence: each has its own existence. Or can Lukas give us a non-Trinitarian example of two substances which share their actus essendi, their act of existence? If he cannot, then he is making the same ad hoc move he has made before.

Lukas only muddies the waters by bringing in the doctrine of divine simplicity. According to that doctrine, God is devoid of all composition. So Lukas is right to say that in God there cannot be three existences. But then how can there be three distinct Persons?

By judging Lukas' position 'ad hoc', aren't we simply excluding the possibility of talking of special entities at all?
(By 'talk' I mean 'conceptual framework')
There are 2 issues that you treated in separate posts, which may be nevertheless strongly correlated:
- Within the religious talk, God is assumed as a primitive entity which everything else (ontological and natural entities and laws) depends on. So we should expect that whatever a theist says about God, relies on his special role within the theologic framework.
- In the relativity theory there is a physical entity "the light" which plays a very special and unique role within this theory (as it is proved by the second postulate), some of its relevant properties and behavior and corresponding consequences for the whole theory don't look like any other physical entities'. But nobody would consider the second postulate of the special relativity 'ad hoc', even if it is simply postulating something uniquely valid for one and only one physical entity. Of course we have other reasons why we don't consider this 'ad hoc', that means the 'ad hoc' argument relies on a thick set of epistemic standards (like the ones used to evaluate the explanatory power of a scientific theory)
- The chess game is partly a good example because its rules which define entities and model their behavior, form a very limited and artificial system, while the religious talk covers the whole world, natural and spiritual. Just as the theory of relativity covers the physical world. Therefore questioning God may be analogous to questioning the second postulate of the special relativity.
- Of course we can still say, that according to our standards, one's definition of God is 'ad hoc', but where do our epistemic standards ultimately rely on? Education and needs?


You are raising important questions. But this thread is now played out. I will be coming back to some of this.


Thanks for your comments, and I hope I didn't sound curt in my above remarks. I am afraid we are now at the end of productive discussion of the theological questions. Perhaps on some theology-neutral topics we will find common ground and a basis for mutually beneficial discussions. I am still thinking about Prague. It would be good to meet you there.

Peter Lupu,

you may be using the same concept as Bill, but Bill was criticising my comment where I introduced the classical thesis that there is but one existence in God. Therefore if Bill (and you) used a different concept than I, your comments seem to miss the point of my remarks.

Note: I do not deny that there are three different existing "things" or persons. I deny that there are three different existences. This is a claim that cannot be captured by the PL1 semantics and cannot therefore be refuted by anything that can be properly said about identity and distinction in PL1.

The three distinct Persons exist by the same existence in a similar way to a married couple who own a given item of their common property (e.g. a car) by a single and indivisible relation of ownership. The husband has a car, the whole car, the wife has a car, a whole one, and yet there is just one having (and one car). At least according to the Czech law.


you say you agree with Peter Lupu but in fact you say much more than he. Peter speaks of the difference of existents, you speak of the difference of existences. If you think that the former entails the latter, it is on you to prove your claim. Arguing in the way "give us non-Trinitarian example" is pointless. The possibility of the Trinity does not depend on the possibility of non-Trinitarian analogues, so my (a priori) incapability of giving the requested examples does not prove anything. ("There evidently cannot be a Creator. It is the part of the very concept of production that something is produced out of something else. Or can you give a non-theological example of creation ex nihilo?" If you do not regard this as a sound argument that Creator does not exists, apply your personal refutation of it to your "ad hoc" charges of the Trinitarian extraordinarities, mutatis mutandis. :-))

Concerning the divine simplicity: the doctrine applies to God's essence, or rather to His pure esse unlimited by any essence. This is not contradicted by the Trinitarian doctrine, which does not deny but affirm that there is just one single undivided divine esse or essence. Multiplying the existences of God goes explicitly against the naturally knowable fact of the simplicity of God's essence. Multiplying persons with explicit affirming the unity of existence does not. It may perhaps be shown that it implicitly entails multiplication of essences, but this requires a proof - the doctrine cannot be dismissed just out of hand as explicitly denying God's simplicity (in the relevent sense, i.e. in the only sense that is accessible to purely natural reflexion) while it is in fact explicitly asserting it.

Dear Bill,

I have written my previous comment before your last one arrived. Having looked up "curt" in a dictionary (always learning) - no, certainly you have not been curt. It happens to me often when I am trying to keep it clear and short, so I too hope I did not sound nasty... I agree that our discussion becomes repetitive and unproductive, but I will perhaps drop a comment occasionally for others, or if explicitly challenged :-) I hope your thoughts about Prague will yield a positive result!

Sorry if I'm intruding once again on that topic. Since we all keep misunderstanding each other about the usage of some terms from the beginning of the debate on, wouldn't it be better to bring a brief clarification? To me, Lukas is just saying that, in the case of the Trinity (but not in ordinary mundane supposita), the existential predicate "to exist" refers to exaclty the same ontological constituent as the predicate "to be God", namely an exemplification of the sortal and natural kind "Godhood". From analytic ontology point of view though, Lukas's position sounds not only problematic but also relying on really extravagant ontological commitments:
- "existence" and the exemplification of the sortal and universal natural kind "Godhood" are seen as tropes and numerically identified
- multi-inherence of tropes (one and the same trope can inhere in completely different supposita, 2 sortal and natural kind tropes can inhere in the same suppositum): e.g. 2 sortal and natural kind tropes inhere in one thick particular Jesus; three divine Persons share the trope God
- "real identification" of 3 thick particulars, the divine Persons, with the trope God (by the way "God" is a proper name used to denote a trope!)
- the sortal and universal natural kind "Godhood" is not a universal property (because it can't be multi-exemplified)
- according to Scotus, a suppositum constituent ("suppositality") is needed to explain the synctactical behavior of a suppositum (this argument seems aslo to assume the existence of universal negative-properties)!
- Lukas believes also in haecceitas (which in the case of God collapses, with existence and the individual-nature, into the same entity!)
- if we add "transubstantiation", both the chemical structure and the sensory data associated to wine may be not essential to identify what is wine
- See also how Lukas explains the "Full Man" attribution to Jesus
- And all that holds only for 2 correlated cases "Trinity" and "Jesus" , which are believed only within the christian religion.
It's all that what, on my part, support the 'ad hoc' argument
and explains why we don't easily get each other...

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