Every proof has some premises and a conclusion. The premises are:

A) The Prime Cause is possible.
B) If the Prime Cause is possible, it is actual.

The proof of the first premise consists in previous Scotus' argumentation from the possibility of efficient causality.

The proof of the second premise is by reduction to contradiction:

Were the Prime Cause not actual, it would either be total impossible, or merely possible (this is total disjunction, i.e. a tautology). But the first option contradicts the first premise; the second option is further disproved:

1) What is merely possible, can be actualized.
2) Prime cause cannot be actualized.
Ergo, it cannot be merely possible.

The first premise is taken by Scotus to follow from the definition of possibility, the second follows from the definition of the Prime Cause.

As I am looking at it, I cannot see anything wrong with that proof.

Critical analysis:

Logically neat and ellegant. However, non sequitur, at least as it seems to me. Why? I shall try to explain below.

The proof has the logical form of "reductio ad contradictionem", which is a type of indirect proof based on a chosen assumption. Here the assumtion (A) is the non-actuality of the Prime Cause (see above: "Were the Prime Cause not actual..."). Let us concentrate on that total disjunction following from the assumption (A). It allows for two possible interpretations:

[Poss="is possible", Act="is actual", c="cause"]


Interpretation A)

(A) really implies a complete, tautological disjunction (tautology, by the way, follows from any proposition). But if this disjunction is total (non Poss(c) or Poss(c)), then 1) "What is merely possible, can be actualized" is false. For if we understand the "possible" as "Poss(c)" (and that we must, in order to handle the second member of the disjunction then the proposition says that whatever is found in any possible world, is in some possible world caused to be. That would exclude the possibility (and, a fortiorim actuality) of a being that is not caused (whether it exists in all possible worlds or just in some of them). To conclude, 1) is false and cannot be used in the argumentation. Without it, however, the proof does not work.


Interpretation B)

This is most likely the originally intended meaning and the "indulgent reading" interpretaion. If we understand the disjunction in question in relation to 1), 1) at the same time being true (on the first look, at least), so that the proof could work, then the disjunction would in fact read thus: (non Poss(c) or (Poss(c) and non Act(c))). This disjunction, as it seems, follows from the assumption (A) and 1) truly applies to its second member. The disjunction itself, however, is not a tautology, tautological it is only in connection with (A) - that is (non Act(c) => (non Poss(c) or (Poss(c) and non Act(c)))).

That is all right. I will however attack the premise 1) again. This premise says that if something exists in a non-actual possible world, then it exists in a possible world in which it is caused. This claim commits us, in fact, to the thesis that eveything that does not exist of logical necessity, is possibly caused. I personally do not accept this belief; however, I admit that this interpretation of 1) is acceptable for many: they are then really forced to accept the whole proof as it is put forth.

For me a weaker interpretation would be acceptable (and I believe that is also Scotus' own interpretation, taking into account the text we analyzed in the last year's seminar). 1) would then read as follows: "If sometning exists in a possible world, but does not exist in a certain moment of the temporal duration of the world, then it is caused in a possible world. I consider this persuasive, but to disprove the second member of the disjunction it is to weak. If we then understand 1) in this way, the proof is invalid.

> Logically neat and ellegant. However, non sequitur, at least
> as it seems to me. Why? I shall try to explain below.

Because Peter Dvorak attacks the truth of one of the premises, and not the consequence relationship between the premises and the conclusion, I would not call it "non sequitur". (Non sequitur is a logical error consisting in that the conclusion does not follow from the premises.)

> Interpretation B)
> This is most likely the originally intended meaning
> and the "indulgent reading" interpretaion.

Yes.

> If we understand the disjunction in question in relation
> to 1), 1) at the same time being true (on the first look,
> at least), so that the proof could work, then the disjunction
> would in fact read thus: (non Poss(c) or (Poss(c) and non
> Act(c))). This disjunction, as it seems, follows from the
> assumption (A) and 1) truly applies to its second member.
> The disjunction itself, however, is not a tautology,
> tautological it is only in connection with (A) - that is
> (non Act(c) => (non Poss(c) or (Poss(c) and non Act(c)))).
> That is all right.


Mea culpa, I wrote it in too a shorthand way. I meant it of course so that tautology is the whole implication, the disjunction is total only in relation to the antecedent. But we do understand each other :-).

> I will however attack the premise 1) again. This premise says
> that if something exists in a non-actual possible world, then
> it exists in a possible world in which it is caused. This
> claim commits us, in fact, to the thesis that eveything that
> does not exist of logical necessity, is possibly caused. I
> personally do not accept this belief; however, I admit that
> this interpretation of 1) is acceptable for many: they are
> then really forced to accept the whole proof as it is put forth.


Well, the only thing that is objected to then is the premise "what is possible and not actual, is causable (can be caused)". By way of defence, it will be sufficient therefore to put forth the proof of this premise.

Let me make a comment first on the reformulation of the premise in the possible-worlds apparatus. Yes, I do accept the thesis that what exists in a possible world only, but not in the actual world, is caused in some possible world: namely, at least in that world where it exists. But I think that the possible-worlds apparatus makes hardly possible to substantiate this claim, since it does not mirror the mutual RELATIONS among the possible worlds, or, to state it better, the relation of the possible worlds to the actual world, which consists in the fact that the possible worlds are unactualized potencies of the actual world.

And a short note concerning the proof: All the concepts like "actualizable" (=capable of being actualized), "causable", "dependent on a cause with regard to its existence" I mean IN ABSTRACTION FROM TIME - that is without any implication of successivity in time or any temporality at all. The aim is merely to express the dependence of eventual existence on the operation of another being. By the term "merely possible being" I mean a being that is possible but not actual.

Let us prove a modification of the controversial thesis: "Merely possible being is dependent with regard to its eventual existence on another being." This claim, which in fact only better expresses the original formulation, can function in the whole proof as well, because not only actualizability (capability to be actualized), but also dependence contradict the concept of the Prime Cause.

1) What is in potency in relation to existence, is dependent on other being wih regard to its existence.
2) What is merely possible, is in potency.
Ergo.

The major premise follows from the principle of causality - the possible proof would look something like this:
What does not exist, can gain existence either from oneself, or from nothing, or from another being. But from oneself it cannot be gained, since it would have to exist before it exists (logical priority, not temporal), which is a contradiction. Neither from nothing, for then nothingness would be the sufficient condition of its rise, which would imply a permanent eruption of being from nothingness. Ergo what does not exist can gain (meant without temporal implications) its existence solely from another being.

Proof of the minor premise:

What is possible, is either in act or in potency. Therefore what is possible and is not in act with regard to existence (i.e., what is merely possible) is in potency to existence.Q. e. d.

Proof of the antecedent:

1) For every act, every subject to this act does not contradict is either in potency or in act to this act.
2) Existence is an act that does not contradict what is possible.
Ergo.

The minor premise follows from the definition of possibility: that which is not in contradiction to existence.*)

The major premise is evident fom the correlativity of act and potency, which assures the totality of the disjunction (what is not an act is a potency and vice versa).

Which completes the proof.

*) If someone denied that existence is an act, the proof could read e.g. as follows:

If two things differ really, they differ by an act.
Actual being really differs from a merely potential being.
Therefore, that by which these two beings differ, namely existence, is an act.

The minor is evident (were there no difference, there would be no change at all), the major follows from the definition of act as the formal cause (principium quo -"that by which") of reality. If then the distinction is real, its formal cause must be an act. Which is the major stated in other words.

>> 1) What can have existence but has not, is in potency
>> in relation to existence
>
> For me a weaker interpretation would be acceptable (and I
> believe that is also Scotus' own interpretation, taking
> into account the text we analyzed in the last year's seminar).
> 1) would then read as follows: "If sometning exists in a
> possible world, but does not exist in a certain moment of
> the temporal duration of the world, then it is caused in a
> possible world. I consider this persuasive, but to disprove
> the second member of the disjunction it is to weak. If we
> then understand 1) in this way, the proof is invalid.


I do agree that the use of the expression "incipere esse" (If I remember well), suggests temporal successivity. But in my opinion Scotus did not have temporal relations in his mind, but rather logical ones. If I remember well, he says: "quod potest esse, potest incipere esse". I would take him to be saying: "what can exist, can accept its existence" - that is regardless whether this accepting" is in time, so that the being "starts to be", or without time. Possibility of existence is simply possibility of existence, and even a merely possible being of a non-temporal character has "possibility to accept existence" (that is by which it differs from impossible beings), so that if it accepted it, it would have always existed. I think that by "incipere esse" Scotus simply slips back into the old "diachronic" manner of modal talk, but that the idea itself is clear, though expressed in an old way and very succintly. (Scotus, by the way, very often uses temporal models to illustrate logical relations of priority and posteriority - being aware at the same time that whether these relations are manifested in time or not is irrelevant).

My reply focuses on the concept of something being merely possible to the effect that your argument contains an equivocation on it and hence does not prove the conclusion.

The crucial premise of the overall argument in dispute seems to be this: If something is merely possible, then it can be caused. Now, on my interpretation, the modal terms are to be interpreted in terms of broadly logical necessity, which in turn is captured in the conceptual framework of possible worlds. Hence the premise would read as follows: For any individual in any world save the actual one, the (very same) individual is caused (or ontologically dependent if you will) in some possible world. I agree that if this implication were true then the individual cannot be the Prime Cause, for the Prime Cause is essentially uncaused. Yet, in fact, I do not believe the implication is true.

Let us examine the argument you introduce in support of this implication. It consists of two premises:

1. What is in potency [in relation] to existence, is dependent on another being with regard to its existence.
2. What is merely possible, is in potency to existence.

As to the second premise, you offer the following proof: What is possible, is either in act or in potency. Therefore, what is possible and is not in act with regard to existence (i.e., what is merely possible) is in potency to existence. Now I agree that what is possible, i.e. logically possible (an individual substance or an individual attribute existing in some world) is either in act or in potency, the latter being, pace what the empiricist says, an ontological category in its own right. Yet this is at odds with the second claim concerning the merely possible. The merely possible - an inhabitant of a possible yet non-actual world, as I read the term - is not necessarily only in potency in relation to existence, but can be in act as well, though only a (logically) possible act of course. If this be so, then premise 2 above is false (if read "for every merely possible…").

Now I will briefly attempt to explain why I think this needs be so: The notions of act and potency divide up the ontological furniture of every possible world, whether the world be actual or merely possible. To be in act and to be actual are not the same! A similar distinction arises in the case of potentiality and possibility. Act and potency are world relative or inner-world concepts. While "to be in act" is the same as "to exist in a world", "to be actual" means the same as "to exist simpliciter". The former is an a priori matter applicable in the argument, the latter is discoverable only by empirical inquiry. It is to be noted in this context that Aristotle's ontology was limited to one possible world only, the actual one in fact (as Aristotle did not get beyond the temporal interpretation of modality), yet it employed both: act as well as potency. For Aristotle the notions at stake had an in-world application.

It is obvious by now that you and I treat the concept of the merely possible differently. What happens if we assume a different interpretation of the merely possible, equating it with something in potency, which is what you appear to be doing? In this case the arguments seem to go through all-right, but the implication supported by the arguments has to be read differently: if something is merely possible, i.e. in potency to existence within a world, then in any world, in which it is to be actual, it requires a cause of its actuality (or, in other worlds, is ontologically dependent).

This reading of the initial implication does indeed imply that the Prime Cause is not merely possible in this sense, yet this interpretation of mere possibility (as potency) is too weak to supply the needed exclusive disjunct in: If the Prime Cause does not exist, then the Prime Cause is either impossible or merely possible. For consider the case that the Prime Cause does not exist. Then besides impossible and merely possible (in potency), there is a third option open; namely, that it is logically possible and non-actual, yet in act.

I believe your argument to be based on conceptual confusion. It appears prima facie plausible, for it equates the actual non-existence of the Prime Cause with its being in potency. From this its causal dependency is fairly easy to deduce, for the very notion of something being in potency implies causality, the necessity that there is something (in some time and/or in some world) that brings it about, in other words, actualizes the potency. Yet this equation appears to be unjustified. If the Prime Cause does not exist in the world that happens to be actual, then it is not in potency, though it is possible, i.e. existing in some possible world or other at each and every of its time instances, uncaused. I think I understand the essence of your argument: You think the uncaused being could be only actual if it be possible at all, else something actual would have to account for its reduction from possibility to actuality. To me this makes sense only when read in this way: I think the uncaused being could be only in act if it be possible at all, else something in act would have to account for its reduction from potency to act. Yet this is perfectly consistent with the view that the Prime Cause does not exist at all, i.e. in the actual world (on the argument given, yet it might not be consistent with Scotus's own argument, your argument being different from that of John Duns Scotus read in the seminar).

In my previous post I tried to prove the principle (that alone had been denied by Peter):

(A) What is merely possible, is causable/dependent with regard to its existence.

I used the following proof:

1) What is in potency in relation to existence, is dependent on another being with regard to its existence.
2) What is merely possible, is in potency.

I proved the minor premise of this syllogism thus:

What is possible, is either in act or in potency. Therefore what is possible and is not in act with regard to existence (i.e., what is merely possible) is in potency in relation to existence.

In his reply, Peter accepts the major premise 1), but denies the minor premise 2) and attacks the proof I gave in its favour by making a distinction within the concept of potency which enables him to refuse the totality of the disjunction in the proof of the minor premise. Peter claims that potency to existence (potential existence) is not the same as logical possibility. In his opinion, both in the actual world as well as in the possible one, there are both types of beings: those in act as well as those in potency. In other words, logical possibility and necessity are "trans-world" properties of beings, consisting in existence (in a broad sense, comprising both actual and potential existence) in some or all of the possible worlds, whereas being in potency (in relation to existence) and being in act are "inner-world " properties - they "divide up the furniture of every possible world", according to Peter. From this I assume that Peter would state the disjunction in the following way:

(D) What is possible, is either in act in the actual world, or in potency in the actual world, or in act in a possible world, or in potency in a possible world.

From this, I suppose, Peter infers that a merely possible being need not be in potency in relation to existence: it can be in act in relation to existence, though this be only a logically possible existence (existence in a non-actual possible world). This allows Peter to harmonize the independence (which implies being in act in relation to existence) of the Prime Cause, and its mere (logical) possibility: it can be merely possible, but in act in relation to (logically possible) existence.

Now to the criticism of this reply. Peter has already conceded that being in potency in relation to existence implies dependence, and is, therefore, incompatible with the essence of the Prime Cause. But he refuses to identify this potentiality with logical possibility. I shall therefore prove this identity.

I have to say first that I find Peter's refutation of my argument insufficient. He attempts to defend the possibility for the Prime Cause to be merely possible (existent only in a possible world) and yet in act in relation to existence. But I think he fails to achieve that. I had proved (and Peter has not attacked my proofs) that every possible being is either in act or in potency in relation to existence. By that I meant potency to actual existence, that is, existence in the actual world. What Peter shows is that a merely possible being can be in act - but in relation to logically possible existence only! That is not, in my opinion, what should have been proved - for mere logically possible existence is in fact non-existence, it is mere possibility to exist.

Therefore, without change, I can insist on my proof that since such a being - although it is in act to logically possible existence - is nevertheless not in act to actual existence, and therefore it must be in potency in relation to actual existence, and therefore existentially dependent. For this being is no doubt possible, i.e. existence does not contradict it. But privation of a non-contradicting act is what I call potency to that act (being in potency in relation to that act). I can see no escape from this, and am convinced that Peter has not offered any.

Peter claims that act and potency are "inner-world" concepts. On that basis he could claim that it is a confusion to say of a merely possible being that it is in potency in relation to actual existence; that this claim would, so to speak, cross the boundaries of a single possible world. To address this, I shall have to descend to a more profound level.

First let me say that it appears to me that this claim of Peter is incompatible with the thesis of trans-world identity of individuals, which is a common supposition we both maintain. For if the trans-world identity thesis is true, than the very same individual that is actual in a possible world, is possible in the actual world. And what is possible in the actual world, can exist here and is therefore in potency to actual existence.

Indeed, what is the function of the possible-worlds apparatus? To allow us to speak more clearly of what is possible and what not - but possible in our, the actual world. There is by definition no other world, different from ours. But our world contains some possibilities, unactualised potencies, and to describe them we use this apparatus. A possible world is not an entity distinct from the actual world, but it is the actual world as it might be or might have been. The trans-world identity is already stipulated in the very claim that something is possible in the (actual) world: i.e. that one and the very same thing could be such and such, but is not.

This is in fact Peter's own claim. If he denied it, he would no more speak of reality. Suppose he claimed that mere logical possibility does not imply potency to existence in the actual world, because the two worlds are distinct from each other. What would then be this "logical possibility"? How would it relate to the reality? Would it tell us that a merely possible being is not self-repugnant? But how could it be that a non-repugnant being cannot exist (i.e. actually exist)? Such a possibility, a possibility which does not imply potentiality to existence, is not real possibility, it is rather impossibility. The proposed "third option" of a possible world where a merely possible Prime Cause exists (and is therefore in act in relation to existence in its world) appears therefore impossible. Hence, I claim that there is no other reasonable concept of possibility that could be expressed by the possible-worlds apparatus, than that based on the real possibilities (potencies) in the actual world. For either the existence in a possible world implies that the Prime Cause could exist actually - and this is incompatible with its essence - or it does not bear this implication, but then such a world is not possible, for it cannot actually obtain (still speaking in the non-temporal way) and it does not therefore describe any real possibility. To describe the scope of the real potencies of the real world we can no doubt use the possible-worlds apparatus - it is a matter of definition. If we are to use it for anything other, we should have a reason for that. But I cannot see what this could possibly be - I cannot see what the "logical possibility" that does not imply possibility of (actual) existence would mean and be good for. For me, to be in potency in relation to existence in the actual world is to be in act in relation to existence in a possible world, and to be in potency in relation to existence in a possible world is simply to be in act to existence in another possible world. And vice versa, to be in act in relation to existence in some possible worlds is to be in potency in relation to existence in every other possible world, including the actual world. To be in potency to something then means that this something does not contradict it and is not actually possessed by it: which is the sense of "logical possibility", as I understand it.

To conclude, I shall try to formulate a separate argument for the thesis that logical possibility implies being either in act or in potency in relation to the actual existence. Apart from that, I consider the old version still unrefuted.

1) What is not self-repugnant is either in potency or in act in relation to actual existence.
2) What is logically possible is not self-repugnant.

The minor premise is a definition.
Proof of the major premise (by reduction to contradiction):

Suppose that something is not self-repugnant and yet neither in act nor in potency in relation to actual existence (think of the merely possible Prime Cause, for instance). Such a thing would be incompatible with its own existence; for if it were compatible, it would either not actually exist and be compatible with actual existence, which is the definition of being in potency in relation to actual existence, or actually exist, which is the definition of being in act in relation to existence.

But what is incompatible with its own existence is self-repugnant, because the actuality of all its notes (the notes of its concept), which is the actual existence of such a thing, implies the non-existence of such a thing. You may object that the actual existence of this thing is not necessarily implied in its concept, and therefore no necessary contradiction follows. But I would reply that either you consider that thing being actually such and such, and then the contradiction follows, or you do not consider it so, but then it is not in fact that thing. That is to say, actual being such and such implies actual existence. Potential being such and such indeed does not imply actual existence, but to be potentially such and such is in fact not to be such and such. Therefore, if we examine whether a being is self-repugnant, we have to consider it as actually being such as defined.

Therefore, incompatibility with existence is equivalent to self-repugnance, and it is impossible then that a self-consistent merely possible being not existed and yet were not in potency in relation to existence. It is impossible then that the Prime Cause were merely possible, for that would mean for it to be in potency in relation to existence, which is the same as existential dependence.

And there is one more thing left I would like to deal with - it is the matter of Aristotle considering the act-potency dichotomy as "inner-world". In my opinion this does not prove anything about the nature of potency and act. Aristotle's ontology was indeed limited to only one possible world, but the reason why he employed both potency and act is not because there would be some fundamental distinction between logical modalities and potency and act, but because he confined the logical modalities to the actual world as well (well aware of the connection between these two things, in my opinion). Therefore in the way we extend Aristotle's theory of logical modalities, we should also extend his doctrine of potency and act (and I think Scotus made both of these extensions). These two things must go together in my opinion, being two sides of the same coin.

Based on what Lukas writes it seems to me we have reached a stalemate, a sort of impasse. I can only restate the essence of my last reply, perhaps elaborating on it little here and there, so that my point becomes ever clearer. For I am thoroughly convinced Lukas's arguments do not go through. Lukas fails to make crucial distinctions and thus his argument attains a superficial ring of plausibility.

To make my point clear as far as possible, let me present Lukas's argument in his own words and then expose the fallacy of equivocation he, in my view, commits:

1) What is in potency in relation to existence is dependent on other being with regard to its existence.
2) What is merely possible is in potency.
Therefore, what is merely possible is dependent on other being with regard to its existence.
From this it is clear that the Prime Cause cannot be merely possible. Hence it is actual, for this is the only remaining alternative in a total disjunction merely possible or actual.

Now the only sensible reading I can give the argument is the following:

1) What is in potency in relation to existence (call it ontological possibility or potency proper) is dependent on other being with regard to its existence.
2) What is merely possible (call it logically possible yet non-actual) is in potency in relation to existence (i.e. ontologically possible).
Therefore, what is logically possible yet non-actual is ontologically possible.

The second premise is far from obvious. What is more, I consider it false. Hence, the truth of the conclusion has not been established. I hope the equivocation logically possible - ontologically possible is clear. In case it is not, let me say some more about it.

First, my reading of the argument is supported by the fact that Scotus in his argument speaks about effectibility, which is roughly what I term ontological possibility. The notion of ontological possibility restricts the range of what is logically possible simpliciter in any world to that what is logically possible in it relative to its "causal power", i.e. what entities existing within the world are capable of bringing about within the framework of certain physical laws. NOTA it BENE: the distinction is, in other words, that between an alternate reality (with different entities having different [even no] causal powers, possibly governed by different physical laws) and a reality causally possible relative to some world whether it be actual or not.

Now the ontologically possible is ontologically dependent by definition. The clever move of Lukas' argument is in that he wants to make the reader accept that logical possibility of non-actual status also entails ontological dependency. Relative to what (notice that dependency is a relation) one might ask?
(i) Relative to some entity in this very world (alpha), i.e. our world? If so, then the class of ontologically possible entities turns out coextensive with that of (non-actual) logical possibles. Yet that is highly counterintuitive. For we consider logically possible something that is in no causal power of anything existing at any time instance of our world.
(ii) Relative to God, then? This will not do either, for the argument becomes circular.
(iii) Relative to some entity in some non-actual world? Anything logically possible and non-actual would be dependent on something in some world. I fail to see why this view should have any internal necessity at all if it is to be anything more than a mere stipulation. (Needles to say, I take non-actual possible worlds as possible states of the actual world, there being no quarrel between Lukas and myslef, pace what he says).
To sum up, any way you turn, you find a blind alley, a dead end. There definitely is something in some world, which is logically possible and non-actual, yet not causally dependent on anything in any world, something which is logically possible but not ontologically possible (ontological possibility being a sub-class of logical possibility). I do not see any inconsistency in this concept at all. This is nothing but to say that an ontologically necessary being is possible.

Notice also that Lukas' talk does not appear to make sense in another way too: one has to distinguish language-levels: the object language of possible worlds stating truths (and falsehoods) describing the possible worlds themselves. What we have is a set of world-descriptions plus generalizations over the worlds themselves being parts of the descriptions as well depending on accessibility relations between the worlds. No object language description contains within itself the information which of the worlds is the actual one. It is the task of a meta-language to attribute to one and only world the status of the actual world based on empirical enquiry. To put it differently, the meta-language designates one set of world-descriptions as true simpliciter. Only in this meta-language can one express the difference between the merely possible and the possible. As with the case of logical paradoxes one has to keep the language-levels separate. Yet Lukas' treatment of the proof confounds them on a grand scale: There is to be an entity in some possible world, which has the meta-language predicate of always being actual (member of no possible world but the actual one among them), thus introducing among the object-descriptions elements of meta-language. While the object-language is a priori, the meta-language is based on empirical enquiry and is never the subject of definition. The mistake the ontological argument is marred with - and Lukas' argument is a species of it - is that it attempts to make a matter of a priori enquiry (a part of the object-language) what really is aposteriori and a part of meta-language.

To sum up, I have just restated my point in the belief it will not be misunderstood. I find Lukas' argument clever but wanting.

I have long pondered how to formulate best my reply to Peter - it is a clear mark that something is going wrong if the discussing partners start only to repeat themselves. However, contrary to Peter I do not think we have reached a stalemate. There is a clear point of disagreement, which can now be stated in the words of Peter's reply so that I claim that

A) Logical possibility (=existence in a possible world) implies ontological possibility (=potency to actual existence).

whereas Peter denies it. Peter's distinction between these two types of possibility was the response to my argumentation, therefore the normal way the discussion should follow is that I should either give up or have to save the argument from the fallacio aequivocationis by proving that the distinguished members imply each other (or at least that the logical possibility implies the ontological, for the other part of the equivalence is clear) or by proving one of the premises in the denied sense as well. And Peter should then attack my proof - either by negating one of the premises, or by negating the consequence by making some further distinction in some term.

The problem, as I see it, is in that I feel I have given some proofs for this implication in my previous reply, which, however, remained unanswered. The identity of the two kinds of possibility, expressed in the premise that Peter refuses as being "far from obvious"

2) What is merely possible (call it logically possible yet non-actual) is in potency in relation to existence (i.e. ontologically possible).

is not what was presupposed in my argumentation, but what was being proved (whether successfully or not). It seems to me then that if Peter says that I fail to make crucial distinctions, it is an ignoratio elenchi on his part.

I shall therefore first try and reformulate here my arguments for premise 2 and the thesis A (they are logically equivalent), and thus return the discussion to a clearer and more formal level, on which I think it is easier to avoid misunderstanding and determine what each of us is obliged to do at a given point of the evolution of the dispute. Then I shall briefly return to some parts of Peter's last reply.

I will pick up my original argument and make it as clear as possible in reaction to Peter's objections (I shall repeat the immediately preceding argument, in order to gain the context).

1) What is in potency in relation to existence, is dependent on another being with regard to its existence.
2) What is merely possible, is in potency in relation to existence.

Here Peter makes his distinction in the middle term "what is in potency in relation to existence". He accepts 1) in the sense "ontological potency" but denies it in the sense "logical potency", and accepts 2) in the sense "logical potency" but denies it in the sense "ontological potency".

I chose to prove the second premise in the denied sense (instead of proving the equivalence of the distinguished meanings of the middle term):

2.1) What is logically possible, is either in ontological act or in ontological potency.
2.2) What is merely possible is logically possible and not in ontological act in relation to existence.

(This is a slight reformulation of the old argument, which was a bit clumsy, thus perhaps causing the present problems).

Here Peter in his response virtually denied the minor premise "prout secundam partem" - that is, he conceded that what is merely possible is logically possible (which is in fact true by definition), but denied that it has to be in ontological potency in relation to existence: in his opinion both actual and possible beings can be either in ontological act or in ontological potency in relation to existence.

I then tried to prove the second premise thus (in a less formal form than here):

2.2.1) What lacks existence that however does not contradict it, is in ontological potency in relation to existence.
2.2.2) What is merely possible, lacks existence and existence does not contradict it.

Let me turn to the minor premise firs and deal with the objection Peter gives against it. I understand him thus: Peter denies the premise "prout primam partem", that is, he denies that what is merely possible lacks existence, and gives an argument for this. I understand his reasoning (concerning the distinction between actual existence simpliciter and being in act to existence, yet in a non-actual world) in his previous reply as capable of the following formal expression:

O.1) What is subject to generation (and corruption) gains (and loses) existence.
O.2). Some merely possibles (inhabitants of a non-actual possible world) are as such subject to generation and corruption.
(Ergo, some merely possibles do gain existence, i.e. they do not lack existence, which is against 2.2.2)

I respond to this objection by distinguishing the term what gains existence ("terminus maior") thus: either gains (logically) potentially or gains (logically) actually. And I accept the conclusion only in the sense gains potentially. This does not contradict 2.2.2, for there (and ever before) the existence meant is the actual existence or existence simpliciter, not logically possible existence. Simply stated, I concede that merely possibles are in act in relation to logically possible existence, but claim that they still are in potency in relation to actual existence. Since now, I shall by existence always mean existence simpliciter or actual existence (existence in the actual world).

This is formally stated what I meant in my previous reply by the words that Peter did not prove what he had to prove: by this argument he can always save only the possible existence for a merely possible being. Theoretically, Peter could try to keep his objection by proving the O.1 in the required sense gains logically actually, or to give another proof for the thesis I only deny, namely that some merely possibles do not lack actual(-ly) existence, but I think he would not do that, for it seems to me evident that this is false by the very definition of mere logical possibility - all beings and events in a merely possible world lack by definition logical actuality.

Therefore Peter must turn to the other premise (2.2.1) and try to show that in the sense now restricted to actuality it cannot be proved. I have already given some arguments for that premise, and I will keep them. I proved the major premise thus (again not too clearly in my previous text):

2.2.1.1) What lacks an act that does not contradict it, is in ontological potency to that act (since I define ontological potency as the lack of a non-contradicting act).
2.2.1.2) What lacks actual existence that does not contradict it, lacks an act that does not contradict it (since actual existence is an act).

(Both premises are inferred from the propositions in parentheses by illation a recto ad obliquum). The major premise is true by definition; therefore the only point open to objections is the minor. (I fancy Peter will protest against such a definition of ontological potency, but the only consequent thing he should do then is to deny the very first premise 1, to that he had perhaps consented only understanding the notion of ontological potency in some other way. I shall deal with this possibility below.)

I am convinced Peter has to accept the minor either - due to his acceptance of the trans-world identity thesis. For whether Peter accepts the "trans-world" dimension of the concepts of potency and act or not, I can confine the discourse to the actual world alone, and instead of speaking of a being existing in a possible world I can speak of a being existing possibly in the (=actual) world. Thus all beings being in act in relation to existence in all merely possible worlds exist possibly in the actual world. Therefore, in the actual world they lack existence, and, at the same time, existence does not contradict them in the actual world.

There is no problem in that in the actual world perhaps there does not exist any cause that could actually give them existence. It need not. All that is required is that such a cause be possible, that is, existing possibly in the actual world, i.e. actually in a possible world. Actuality requires actual cause, possibility possible cause - exactly as Scotus has it. Real ontological potencies of beings are not limited by existence or non-existence of external causes that could actualise them.

Therefore, the only way out for Peter I see is denying that actual existence understood as existence in the actual world is an act (unlike existence taken in a certain time as opposed to non-existence in a certain time). But here comes my proof I have also already given:

2.2.1.2.1) That by means of which differs what differs really is an act. (In other words: What has a real formal effect is an act.)
2.2.1.2.2) Actual existence is that by what things really differ. (Actual existence has a real formal effect.)

The major is true by definition: since act is defined as real formal cause (formal cause of a reality).
The minor is also difficult to deny. Originally I suggested proving it from the empirical fact of substantial change and mutation: Terms of change differ really, but they differ by actual existence, ergo… However, this proof is no longer valid at this place, for I was forced to confine the argumentation to the concept of actual existence as opposed to existence in a merely possible world. Peter could here rightly deny that terms of change differ by actual existence in the conceded sense.

Therefore what I must prove now is that the distinction between (logically) actual and logically possible is real, and thus that its formal cause is an act. But who would dare to deny it? No doubt there is some reality in the distinction between possible $100 and actual $100, let Kant say what he will. You can, for instance, get in serious trouble by trying to pay by merely possible money at a restaurant.

Formally I could argue thus (I won't trouble you and myself with the numbers): Actual and merely possible differ really, but it is actual existence what is by definition the formal cause of this difference, ergo. Proof of the crucial major: What does not differ really, does not allow for contradictory predicates. But merely possible and actual do allow for contradictory predicates, ergo. Proof of the major: What does not differ really, is one and the same, but one and the same does not allow for contradictory predicates, ergo. The major is a definition; the minor is the principle of contradiction. Proof of the minor of the preceding syllogism is per exemplum: the predicates merely possible and actual are themselves by definition contradictory predicates. Now, this completes this branch of reasoning. There is however a debt left behind, concerning the very first premise

1) What is in potency in relation to existence, is dependent on another being with regard to its existence.

which may be now denied by Peter, due to my explication of what I mean by ontological potency. I even believe that in THIS premise lies the core of the controversy. I shall have to prove it here anew, then (the proof from causality proposed before won't do again, for Peter would not accept my using terms like "receive being" in a non-temporal trans-world way).

1.1) What does not contain sufficient condition of its own existence in itself, is dependent on another being.
1.2) What is in potency in relation to existence, does not contain a sufficient condition of its existence in itself.

Proof of the major premise:

1.1.1) What has a condition really distinct from itself, is dependent on another being (because to be conditioned by something really distinct is to be dependent on it).
1.1.2) What does not contain a sufficient condition of its own existence in itself, has a condition really distinct from itself.

Both of the premises are evident from the definitions of terms, as I believe it is clear. So let us turn to the proof of the minor premise, "in qua sola videtur esse difficultas".

1.2.1) What contains a sufficient condition of its own existence in itself, exists.
1.2.2) What is in potency in relation to existence, does not exist.

The minor is evident from the definition of potency (lack of a non-contradicting act). Let us proceed to prove the major, then.

1.2.1.1) What is a subject that is a sufficient condition of its own existence, exists.
1.2.1.2) What contains a sufficient condition of its own existence in itself, is a subject that is a sufficient condition of its own existence.

The minor only introduces the concept of subject; it can be proven easily: What contains… etc is a subject, because existence is its (actual or possible) act. And it is a sufficient condition of existence, because every being is what it contains in itself, since we use here "to contain" to mean real identity, as opposed to real distinction (see 1.1.2).

So we can turn to the proof of the major.

1.2.1.1.1) A subject does not posses an act of what it is a sufficient condition solely in case that it is a free act.
1.2.1.1.2) No existence is a free act (although it is an act).

This will need some explanation, I suppose. What do I mean by a free act? I mean an act of which existence or execution depends on the liberty of the subject. The major, 2.1.1.1, is evident then: for sufficient condition of X is a cause of X, and every cause produces its effect either by necessity, or by liberty.

But I shall have to explain more, I am afraid. For it seems that the minor contradicts the divine liberty (if there at last turns out some God to exist): since free acts of God are all identical with His being and existence. To face this problem let me say that by liberty I mean here liberty to the act ("libertas actus"), that is an ability to determine freely whether the given act will exist or not. I do not mean liberty to the object ("libertas obiecti"), which is an ability to direct one's acts freely towards one object or the other.

In my opinion only the libertas obiecti can be ascribed to God. For the act of God is really only one, identical with the being of God, and as such it must be altogether independent, perfect, unchangeable and necessary (here I anticipate some conclusions, that, I am convinced, can be proven). However, from the divine independence follows that the free choice of God must be independent of its object(s), and therefore God can by one and the same act want whatever object He will. "Free act" in my proof means an act that can freely not be carried out by its subject. But because God cannot freely refrain from carrying out its own existence (for no subject can, as shall be proven), He cannot refrain from carrying out any of His acts - there is in fact only one divine act, really identical with His essence and existence. Nota bene: that does not impose necessity of creation on God! Since for God the decision "to create or not to create" concerns the object of his act and not the act itself, due to the independence of divine acts on their objects. Thus if God decided not to create, he would do so by the very act by which he in fact created the world (the opposite would mean that God is dependent on the objects He created).

But why no existence is a free act? Because

1.2.1.1.2.1) Every free act is a) conditioned by the existence of its subject; b) really distinct from its subject as its accident.
1.2.1.1.2.2) Neither of these is true of existence.
The minor is clear enough: concerning a) it follows from the impossibility of anything being conditioned by itself, for b) it follows from the fact that as an inner principle of a being (ens) existence cannot be a really distinct being, lest the infinite regress should follow.

The major I prove thus: Any free act can be or not be independently on the existence of its subject - its subject can exist both with it and without it. But that is a sign of real distinction. Moreover, such an act is inherent in the subject - therefore it is its accident. But every accident is conditioned by its subject, ergo.

All this follows immediately from the notions used: free act, subject, accident, real distinction, condition, existence. The proof is finished, then.

I suggest Peter that he should point out exactly where he thinks there is a fallacy in my proof: that is either deny some premise that is not proved by me or attack the correctness of some of the definitions, or point to an equivocation in a term and make a distinction, or point to a formal non sequitur - and I shall then concentrate on the proof of what he will have denied. I believe this will allow our replies to be short and clear.

Now I shall briefly reply to some points of Peter's last response.

A) The concept of ontological possibility: According to my understanding of this term ontologically possible is what is in ontological potency. And ontological potency is lack of a non-contradicting act (I think it is most reasonable to keep this definition, since it retains the totality of the act-potency disjunction.) Therefore there perhaps are in the world ontological potencies that cannot be actualised by any of the existing beings: this lack of such a cause is absolutely irrelevant to the inner passive potentiality of beings.

B) The issue of physical laws: either they are logically necessary (as I suppose the law of causality is), and then there is no possible world they would not govern. Or they are logically contingent, and then they are equally irrelevant for the necessary ontological condition of beings.

C) What is the term of the dependence relation of logically possibles? It may be an actual being, or a merely possible being, God not excluding. (Note that there is no definite term of this relation - I do not say that there is this or that term, but only that there must be some term). The point of the argument is that only an actual being can stop the chain of dependency - since every merely possible being is dependent. This is no stipulation, but a conclusion of a proof.

D) I am afraid I do not understand Peter's argument concerning the meta-languages. I do not share his view that one has to distinguish the levels of language in this case. In my opinion both factual and modal predicates ultimately belong to and are predicated of the things in the actual world - the only world that there in fact is. For from what other reality could the modal concepts be gained by abstraction? If they are not abstracted from reality, they cannot be predicated of it truly. Furthermore, I do not think that there is such a definite connection between the "object-language" and a priori knowledge on one side and the "meta-language" and a posteriori knowledge on the other. There are some truths capable of a priori proof that are neither analytic nor necessary - such are e.g. all of the judgements that are necessary conditions of any cognitive activity. Among them are existential statements as well (e.g. existence of change). I say all this only to demonstrate that one cannot strictly divide up what is knowable into empirical contingent existential facts and a priori necessary conceptual truths. To the degree I understand Peter's reasoning, I think it is based on this false premise. However, I would not like to distract the discussion in this direction, therefore I rather put forth my view on this matter than arguments for it. As I have said, what I would regard as most productive would be if the discussion concentrated to examination of the single concrete inferences that constitute the proof.

An undisputed merit of Lukas’ last reply is a clear re-statement of his argument (partly in response to my objections), making it easier to pin down the points of disagreement. It turns out that the dispute has its deeper roots in disagreements over the basic ontology used, yet it would be desirable to hold fast to the ontological framework the original proof is cast in as much and as long as possible. I feel, however, that unfortunately it is not possible any longer. I can more or less accept all of Lukas’ arguments up to the following point:

2.2.1.1) What lacks an act that does not contradict it, is in ontological potency to that act (since I define ontological potency as the lack of a non-contradicting act).

2.2.1.2) What lacks actual existence that does not contradict it, lacks an act that does not contradict it (since actual existence is an act).

…I am convinced Peter has to accept the minor either - due to his acceptance of the trans-world identity thesis. For whether Peter accepts the ”trans-world” dimension of the concepts of potency and act or not, I can confine the discourse to the actual world alone, and instead of speaking of a being existing in a possible world I can speak of a being existing possibly in the (=actual) world. Thus all beings being in act in relation to existence in all merely possible worlds exist possibly in the actual world. Therefore, in the actual world they lack existence, and, at the same time, existence does not contradict them in the actual world.

There is no problem in that in the actual world perhaps there does not exist any cause that could actually give them existence. It need not. All that is required is that such a cause be possible, that is, existing possibly in the actual world, i.e. actually in a possible world. Actuality requires actual cause, possibility possible cause - exactly as Scotus has it. Real ontological potencies of beings are not limited by existence or non-existence of external causes that could actualise them.

Lukas concludes the reasoning of the first paragraph: ”Therefore, in the actual world they lack existence, and, at the same time, existence does not contradict them in the actual world.” The latter phrase is ambiguous due to distinct senses in which ”actual world” is generally used in the possible-worlds discourse. ”Actual world” (with the capital ”A”, MEANING 1) could be a sort of proper name of the existing reality (a particular set of individuals, their particular properties and relations). The same term (with the lower case ”a”) is an indexical expression denoting any possible world that happens to be actual (MEANING 2). (One could even distinguish a third sense of the word meaning the abstract logical description of the existing physical reality, MEANING 3, yet for simplicity’s sake I will not distinguish this meaning from the proper name use thus, in fact, identifying a world and its description. Later on I will distinguish yet still two additional senses of the term).

If ”actual world” in ”does not contradict them in the actual world” is taken to denote Actual world, then existence simpliciter (all and only the members of Actual world enjoy existence simpliciter) DOES contradict possibles in the general sense (individuals actually existing in some merely possible world) as their becoming members of the Actual world is logically impossible (a particular entity with properties contradicting some of the rest would be introduced). Notice, that I purposely omit the definite article with Actual world in order to stress its proper name-like status. On the other hand, if ”actual world” is taken in the indexical sense, then ”existence does not contradict them in the actual world” means that another world containing them (World 1, World 2…also a set of particular objects with particular properties and relations) could have been actual instead of Actual world. Obviously, Lukas must have had the latter interpretation in mind. Yet when he talks about possibles existing in the actual world, he in fact speaks of worlds other than Actual world.

Now I fail to see how the assumption of the trans-world identity thesis, to which I subscribe to be sure, forces one to accept the minor premise of Lukas’ argument. The supposed role of the trans-world identity thesis in the argument is probably this: There is some individual, call it Max, existing in a merely possible world (say World 1), who fails to exist in Actual world. Lukas would say that Max is nevertheless possible in Actual world thus enjoying a sort of shadowy ontological status in it. In other worlds, he is in some sense there, i.e. in Actual world. Based on the trans-world identity thesis, Max in World 1 and Max in Actual World are identical. Yet compared to Lukas and Me, real inhabitants of Actual world, Max lacks something, i.e. existence simpliciter which ultimately makes him dependent on something else (this will be proved later). What is true of Max, is true for any internally consistent being not existing simpliciter in Actual world.

Now what is wrong with this picture? The trans-world identity thesis says that there are some individuals existing in more than one possible world. It applies to members of Actual world and says that apart from Actual world any of them exists in some other world too (World 1, World 2…). But it does not work the other way round in the sense that any member of any world is a member of Actual world. A member of a non-actual World 1 which does not exist in Actual world is simply not in Actual world, has no properties in it and cannot be compared to members of Actual world! On top of that Max can never become member of Actual world. He can only become a member of the actual world had some presently non-actual world become actual. (That Actual world is the actual world (MEANING 2) is a non-trivial statement).

My response to Lukas ultimately comes to this: I am suggesting that there is a marked difference in speaking about what is possible in Actual world in the sense that certain modal possibility propositions exist and are true in the actual world (MEANING 5 to be distinguished later) due to their non-contradictory makeup, and saying that Actual world contains particular possibles among its members. While the former is an obvious fact, the latter is downright contradictory (Actual world is the set of all actually existing particular entities and none other). I deny ontological pluralism operative in Lukas’ ontological framework (cf. his example: real and possible money in the actual world).

Have I not said previously - in one of my former replies to Lukas - that there are real potencies in possible worlds apart from things in act? Am I not committed to an ontological pluralism of sorts? Actual world is that which enjoys existence - actuality - at this very time instant t0. Actual world* (MEANING 4) is a set of all worlds becoming actual in time, including Actual world but excluding those that could become actual but never, in fact, do. While it does not make sense to speak of anything potential existing in Actual world, it does make sense to speak of potentialities or potencies of Actual world*. In this sense potency and act are inner world concepts: the past and the future of Actual world* are in this sense potential. I claim that this is the picture Aristotle had in mind defining modal terms temporally. How could he work with a synchronic model when Actual world* was a necessary being (now taken synchronically) for him? He simply would not allow for synchronic contingency at all. The idea of synchronic contingency has become meaningful only within the Christian framework (free creation ex nihilo). Hence I do not understand Lukas’ remarks concerning Aristotle in one of his former replies. Let me add that what is true of Actual world* is true for World 1*, World 2* etc. (In the non-actual worlds the possibilities are not real in the sense of existent in the actual world [MEANING 5 to be distinguished shortly] ontologically they would be reduced to propositions).

Now Lukas would probably protest that he takes ”actual world” yet in another meaning (MEANING 5): the whole of existing reality including all that is logically possible for that is surely also in some sense existent, isn’t it? Here, I think, one has to distinguish: there are two levels, the ontological and the logical. That which exists in some sense (in the broadest possible sense of the word), the ontology, encompasses all the members of Actual world* (particular entities) plus all abstract logical entities (sets, propositions, etc.). A non-actual possible world (and its inhabitants) as such, e.g. World 1*, etc., exists only on the logical plane as a maximal consistent set of propositions. In what sense is it part of ontology, part of the actual world (MEANING 5)? I claim that it is part of ontology only as an abstract entity, (maximal and consistent) set of internally consistent propositions. There are no particular possibilia enjoying some sort of semi-reality within the actual world (MEANING 5) apart from propositions describing them. Possibilia cannot be named, they can only be described on a conceptual (logical) level. Thus ”Max” above is shorthand for some description. When one speaks of inhabitants of non-actual worlds, one is talking nonsense strictly speaking. One ought to speak of propositions instead. Yet the talk is a convenient heuristic tool provided that one is clear on the ontological matters and does not take it too seriously. Introducing possibilia into one’s ontology, as Lukas does it, brings about almost unsurpassable difficulties (trouble in providing criteria of identity). The same goes to some extent, I admit, for futura. There one could delegate the difficulties into epistemology, however.

The upshot of all this is that I claim that the minor

2.2.1.2) What lacks actual existence that does not contradict it, lacks an act that does not contradict it (since actual existence is an act).

is meaningless in Lukas’ sense. Actual existence treated as an act is a predicate of the first order. One cannot instantiate the premise for possibila, simply because there are no particular possibilia neither in Actual world, nor in Actual World* nor again in the actual world MEANING 5. However one could instantiate the premise for future particulars and past particulars, i.e. members of Actual world* not being members of Actual world. Now for the sake of the argument forget all I have stated so far. Let me grant Lukas possibilia and his ontology (cf. the initial provision). Consider the second paragraph of his argument for the minor. I fail to see the necessity of the following implication: if there exists something possible in the actual world then there exists its cause (at least possible) in the actual world. On top of that Lukas seems to accept the stronger actual existence version of the necessary implication: if there exists something actual in the actual world then there exists its cause. The latter implication is obviously false if one accepts the conclusion of Lukas’ proof that there is a Prime Cause. I consider the former implication false as well. Where is an argument for it? Lukas would probably point to the sufficient-condition argument. In order to keep the discussion manageable, I won’t go into the argument until next time (if necessary). At this point in the discussion, I think that denying the minor above blocks the whole argument and it is not necessary to go into its other parts.