PETER OHRSTRf0M

ANSELM, OCKHAM AND LEIBNIZ ON D I V I N E F O R E K N O W L E D G E

AND HUMAN FREEDOM

Since the beginning of Christian philosophy it has been widely discussed whether belief in divine foreknowledge of the future is compatible with belief in the freedom of human actions. In most theology this compatibility is assumed. For the Christian philosopher, therefore, it is an important task to explain how the compatibility can be established within a relevant philosophical system. The discussion has not been brought to an end, although many different solutions have been suggested. But according to A.N. Prior's penetrating analysis I the most important solutions are the Ockham theory and the Peirce theory, which according to Prior can be interpreted as a version of the solution due to Thomas Aquinas. The discussion of the problem is not only important in a theological context but it has also played a significant role in the development of temporal logic. In the present paper I will investigate the theories of Anselm, Ockham and keibniz. 1 shall argue that it is natural to interprete the theories as basically the same theory of temporal logic. It will turn out that this theory is slightly different from Prior's Ockhamist theory. I shall compare the theory with the Peirce theory. Finally I intend to argue that the theory can easily be adjusted to the latest findings in temporal logic. It is difficult to handle problems in logic without the explanatory power of a symbolic language. I shall therefore make use of a modern symbolism. In fact I think that the use of symbolism will make it easier for a modern reader to understand the various aspects of the discussion. The basic symbols of the language are: (1) The statement variables i.e. primitive statements corresponding to so-called "temporally pure event descriptors" e.g. "It is raining in ekrhus". (It is willingly admitted that the notion of "temporally pure event descriptors" is by no means unproblematical. But the notion has to be discussed elsewhere.) (2) Binary operators: /h (conjuction), - (negation), D (implication), V (disjunction), --- (equivalence). Erkennmis 21 (1984) 209-222. 0165-0106/84/0212-0209$01,40 9 t984 by D. ReiclelPublishing Company

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(3) Tense operators for any positive number x (P(x), which is read "x time units ago it was true to say:...", and F(x) which is read "in x time units it will be true to say:..." (4) Modal operators: M which is read "it is possible that..." and N which is read "it is necessary that. " (It will turn out that there are different kinds of modality.) (5) Quantifiers: V x which is read "for all x the following is true:...", and 3 x which is read "there is an x for which the following is true: " (6) An operator for divine knowledge: D which is read "God knows that. " I presuppose the usual bivalent logic of propositions and the usual theory of quantification. Details are left to the reader. The postulate of freedom can be formulated as folows:

(*)

3x: MV(x)p A MF(x)-p

for some statement variable p. The assumption of divine foreknowledge can be formulated in the following way: (**)

qx: F(x)p =- DV(x)p

for every statement variable p. Now, the question is whether (*) is compatible with (**). If one wants to argue for the compatibility, it is necessary to show where the following standard argument for the incompatibility is wrong. In this argument a minimal tempo-modal logic, (m), is assumed. (a) F(x+y)p D DF(x+y)p (**) (b) P(y)DF(x +y)p D NP(y)DF(x +y)p (assumption) (c) N(P(y)DF(x+y)p D F(x)p) (assumption) (d) F(x)p D P(y)F(x+y)p (assumption) (e) F(x)p D NF (x)p (from a,b,c,d,m) (f) F(x)-p D NF(x)-p (from e) (g) F ( x ) - p V F(x)p (assumption) (h) NF(x)p V N F ( x ) - p (from e,f,g) (i) Vx(NF(x)p V N F ( x ) - p ) (from h) (j) Vx:-(M-F(x)p A M - F ( x ) - p ) (from N ~ - M - a n d i) (k) Vx:-(MF(x)p A M F ( x ) - p ) (from g,j) Note that (k) is the negation of (*).

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1. A N S E L M ' S S O L U T I O N

Anselm treats the problem concerning divine foreknowledge and human freedom in his work, De Concordia Praescientiae et Praedestinationis et Gratiae Dei cure Libero Arbitrio 2. In this work Anselm answers three questions, of which the first concerns the problem of divine foreknowledge and human freedom directly. The central idea in Anselm's solution of the problem is his distinction between two kinds of modality. In chapter III of De Concordia he considers two propositions: "There will be a revolution tomorrow" and "The sun will rise tomorrow". Using the day as the time unit these propositions can be symbolized as F(1)p and F(1)q respectively. If F(l)p and F(1)q are true, they are necessary on the basis of what Anselm calls subsequent necessity (necessitas sequens) - in symbols: (1) F(1)p D N~F(1)p (and the corresponding for q). But according to Anselm there is another kind of necessity. He calls it antecedent necessity (necessitas praecedens). On the basis of antecedent necessity the proposition F(1)p is not necessary. In symbols: (2) F(l)p/~-NpF(1)p or equivalently (3) F(1)p/~ Mp-F(1)p (where Mp-=-Np-) according to which it is possible that there will not be any revolution tomorrow although it is, in fact, true that there will be a revolution tomorrow. On the other hand the proposition F(1)q is necessary on the basis of antecedent necessity. That is: NpF(1)q. But what is the difference between the two kinds of necessity? According to Anselm subsequent necessity follows from true propositions about the state of affairs, while a proposition is necessary on the basis of antecedent necessity if the proposition is compelled to be true. Obviously subsequent necessity is factual necessity. Following Anselm subsequent necessity can be defined as the logical consequence of the total quantity of truths of facts. A proposition is necessary on the basis of subsequent necessity if and only if a contradiction follows from a con-

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junction of its negation and any number of true propositions. Using Ns as N in the above argument from divine foreknowledge to necessity of the future, the argument and its conclusion are fully acceptable to Anselm. He does not at all hesitate to accept the truth of the thesis: "What will be, necessarily will be", that is (4) Vx:(F(x)p D N , F ( x ) p . Anselm formulates his view as follows: "For when I say, 'If a thing will be, then necessarily it will be', this necessity follows, rather than precedes, the presumed existence of the thing".(p. 51) This acceptance, however, does not imply any reduction of human freedom. To Anselm the necessity involved is only verbal and factual, but it does not force anything to be true concerning the future. Antecedent necessity is stronger than subsequent necessity. If it is necessary on the basis of antecedent necessity that a certain event will occur, then the necessity causes the event to occur. Antecedent necessity can be described as a causal necessity. This distinction between two kinds of necessity is originally Aristotelian. In Prior Analytics Aristotle clearly draws the distinction between absolute and relative necessity: "Further, it can be shown by taking examples of terms that the conclusion is necessary, not absolutely, but given certain conditions. '4 Also in De lnterpretatione the distinction between the two kinds of necessity is expressed. It is very likely that Anselm knew the Aristotelian distinction. In fact a Latin version of Aristotle's De Interpretatione along with Boethius' commentaries was certainly at his disposal. Now, what is the Anselmian reaction to the above argument from divine foreknowledge to necessity of the future if Np is used as N in the argument? It is obvious that Anselm rejects the conclusion of the argument. According to him there is no insoluble conflict between the doctrines of divine foreknowledge and human freedom. He says: It is clear from these considerations that there is no inconsistency in maintaining both that God foreknows all things and that there are many things which, though having before they occur the possibility of never occurring, do actually occur through free will. (p.55) Therefore, according to Anselm there exists a true proposition about the

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future the negation of which is possible. T h e proposition F(1)p about tom o r r o w ' s revolution is such a proposition, which is expressed in (2). It is clear that if there will be a revolution t o m o r r o w , it cannot be possible on the basis of s u b s e q u e n t necessity - that there is no revolution t o m o r row. If it is possible that there is no revolution t o m o r r o w , it has to be on the basis of a n t e c e d e n t necessity, as it is expressed in (2). It is easy to see that an acceptance of (2) implies a rejection of the above argument from (**) to non (*). This being so Anselm has to reject at least one of the assumptions (b),(c) or (g). It seems clears to me that he is in fact denying (b) if N is t a k e n to be Np. In Cur Deus Homo 11.17 A n s e l m is discussing the Virgin's belief that Christ was going to die of his own will. H e says: It is in accordance with this consequent and non-creative necessity that (since the beliel or prophecy concerning Christ, and according to which he was to die voluntarily, and not from necessity, was true) it was necessary that these things should be. 4 H e r e A n s e l m admits the truth of the proposition "It was true to say: G o d knows that Christ is going to die voluntarily". In symbols P(y)DF(x+y)p, where p is the proposition "Christ dies voluntarily" and where x and y are suitable n u m b e r s . A c o r d i n g to A n s e l m , h o w e v e r , this proposition is necessary on the basis of s u b s e q u e n t necessity, but not on the basis of a n t e c e d e n t necessity. That is: he rejects NpP(y)DF(x+y)p. T h e above quotation is therefore a rejection of the assumption (b) if N is taken as equal to Np. With regard to the assumptions (c) and (g) I am inclined to believe that they were a c c e p t e d by A n s e l m . It should be n o t e d that the a s s u m p t i o n (b) is similar to the first of the premisses in the so called M a s t e r A r g u m e n t of DiodorusS: (D1) P(x)q D NP(x)q, w h e r e q is an arbitrary proposition. A n s e l m obviously rejects (D1) if N is t a k e n to be equal to Np and if q is the p r o p o s i t i o n D F ( x +y)p. Nevertheless, it seems that A n s e l m is willing to accept (D1) in s o m e limited sense. In De Concordia he says: Now, the past event has a characteristic which neither the present nor the future event has. For what is past can never become not-past as what is present can become not-present and as what is going to occur without necessity can be not going to occur. (p.52) Since "what is going to occur .. can be not going to occur" the possibility

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in question cannot correspond to the subsequent necessity, but it must correspond to antecedent necessity. His statement "what is past can never become non-past" therefore must be interpreted in the following way: (DI') P(x)q D NpP(x)q. Now, because of Anselm's rejection of the assumption (b), he must presuppose some restriction as to which propositions can be accepted as q in ( D I ' ) . In order to explain which restriction is natural from the Anselmian point of view one should note that Anselm does not say that any proposition with the verb in the past tense is necessary, but he makes his assertion about past events. I do not think that he would accept God's foreknowledge in the past as a past event, for according to him the divine knowledge is different from human knowledge. In De Concordia he says: "We should also understand that like foreknowledge, predestination is not properly attributed to God. For there is no before or after in God, but all things are present to Him at once." (p.68) So, according to Anselm the fact that God knew something in the past cannot be properly characterized as a past event. Following Anselm the knowledge of God should be understood as a timeless knowledge, but it is also true that he assumed that the divine knowledge can be transformed into the temporal dimension. This seems to be how prophecy works. 2. O C K H A M ' S S O L U T I O N

William of Ockham deals with the problem of divine foreknowledge and human freedom in his work Tractatus de praedestinatione et de futuris

contingentibus 6. At the beginning of the Tractatus Ockham asks whether "someone .. who is now predestinate ... can commit the sin of final impenitence". His answer to this question is positive. It therefore seems that Ockham deals with a concept of causal possibility (and necessity). That is: a proposition is possible at a certain time if and only if the truth of the proposition is or can be caused at that time. Obviously Ockham's concept of modality corresponds exactly to Anselm's antecedent possibility and necessity. Ockham's answer to the problem of divine foreknowledge and human freedom is a detailed presentation of a tense-logical system. The basic elements in this system are the statement variables. Ockham presents

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these variables in the following way: "Some propositions are about the present as regards both their wording and their subject matter (secundum vocem et secundum rem)."(p.46) According to Ockham such propositions as "Socrates is seated", "Socrates is walking" and "Socrates is just" are of this kind. Using these primitive statements more complex propositions can be formulated by means of basic operators and symbols of the system as it is explained in the introduction of the present paper. With regard to propositions about the future Ockham is convinced that God has a complete knowledge. He says "It must be held beyond question that God knows with certainty all future contingents - i.e., He knows with certainty which part of the contradiction is true and which is false."(p.48) This assurance can be formulated in symbols in the following way: (5)

D F ( x ) p ~/DF(x)---p

where p is an arbitrary statement variable and where x is an arbitrary number. (5) together with (**) obviously implies (g), which is one of the assumptions in the argument in the introduction. As one of his reasons for holding that God knows the future contingents Ockham refers to "the pronouncements of the Saints" (p.50). It seems that he was fully aware of the ideas of St. Anselm and St. Thomas concerning the nature of God's knowledge. However he did not want himself to contribute to the explanation of how the truth about future contingents comes to the knowledge of God. He says: ".. I maintain that it is impossible to express clearly the way in which God knows future contingents." (p.50) Ockham is mainly concerned about the logical problem that I have posed in the introduction. The theological problems seem to be secondary in the Tractatus. Ockham's solution to the logical problem is a denial of the assumption (b). This denial can be expressed in the following way: "For example: 'God knows that this person will be saved' is true and yet it is possible that He will never have known that this person will be saved." (p.42) Even if God has always known that the person will be saved, it is still possible that He never will have known so. That is: it is possible that God

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has always known that the person will never be saved, for if things were different the knowledge of God would also be different. Therefore it follows that a proposition like P(y)DF(x+y)p corresponding to "God has known that this person will be saved" need not be necessary even if it is true. What is important here is that the proposition DF(x+y)p ("God knows that this person will be saved") is only about the present as regards its wording but not with respect to subject matter since the proposition DF(x+y)p according to Ockham is equivalent to F(x+y)p. With regard to the propositions which are merely about the past i.e. P(x)q, where x is an arbitrary number and q is an arbitrary statement variable, Ockham does not hesitate to accept the truth of (D1). That is: P ( x ) q D NP(x)q. He says: "Every proposition that is merely about the present, if it is true, has corresponding to it a necessary proposition about the past."(p.74) This version of (D1) seems to be harmless since the necessity involved in it cannot be transformed to the future. In the Tractatushowever, Ockham deals with an objection which shows that even the weak version of (D1) can be problematic in a theological context. The objection is the following: "I ask regarding the things that have been revealed by the Prophets whether or not necessarily they come to pass as they have been revealed."(p.44) The problem is this. Is the proposition "The prophet reveals that F(x)p is true" about the present as regards both its wording and its subject matter? In fact Ockham grants that the proposition is merely about the present and that its corresponding proposition about the past is necessary. As an example he considers the prophecy of Jonah: "Yet forty days, and Nineveh shall be overthrown". It seems to follow from Ockham's view that when this prophecy has been revealed the future destruction of Nineveh is necessary. But it is not. Ockham solves the problem assuming that "all prophecies regarding any future contingents were conditionals". So according to him we must understand the prophecy of Jonah as presupposing the condition "unless the citizens of Nineveh repent". It is interesting that the revealed knowledge of God is necessary while the unrevealed knowledge of God regarding future contingents is not necessary. So according to Ockham the revelation of the future destroys its contingency. The revealed future is unescapable. Ockham obviously understands the divine revelation as a part of God's will.

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In the Ockhamistic system Dq where q is an arbitrary proposition, means that G o d knows q and that he could reveal the truth of q to human beings, e.g. to the prophets. In this system D F ( x ) p is equivalent to F(x)p as long as the truth of F(x)p is unrevealed. If the truth of F(x)p is revealed then F ( x ) p will be necessary. For these reasons the operator D is not needed in the formal representation of the Ockhamistic system. The system can be adequately expressed be means of the basic symbols in (1) to (5) in the introduction. According to Prior, however, there is a difference between the propositions F ( x ) p and P(x)p with regard to truth-value assignments. If p represents the proposition "there is a sea-battle", the truth-value of P(x)p is obviously fixed now, since we cannot possibly make it true or false by any decision that is now open to us. On the other hand we assume that somebody could make a decision so that F(x)p is true or a decision so that F(x)p is false. Therefore it seems that the truth-value of F(x)p is not yet fixed since it depends on future decisions. According to Prior F(x)p has a "wait and see" character. For this reason he introduces the so-called "prima-facie assignments". A prima-facie assignment for F(x)p is a truthvalue relative to a given possibility for the future course of events. That is: for one possibility F(x)p is true and for another it is false. It seems clear to me that Ockham was not an Ockhamist (in Prior~s sense of the word). According to Ockham the truth-value of F(x)p is a meaningful concept. We cannot know the value (unless it is revealed), but God knows it. I have elsewhere 7 demonstrated how Ockham's theory can be presented using a concept of the future as the factual course of events. The truth-value semantics for the temporal logic of Ockham can be represented as in Figure 1 showing a line without beginning or end which breaks up into branches as it moves from left to right (i.e. from past to future), though not the other way. One of the routes from the left to the right corresponds to the actual future (this route is marked). A thesis is valid in this system if and only if it is true at all times in the actual history.

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actual history

time axis (numbers!)

;> 3. L E I B N I Z ' S O L U T I O N

Leibniz accepts the doctrine of divine foreknowledge as well as that of h u m a n freedom. He is fully aware of the arguments that can be constructed in order to prove the incompatibility of the two doctrines, but he rejects them as invalid. He says Nor does the foreknowledge or preordination of God impose necessity even though it is also infallible. For God has seen things in an ideal series of possibles, such as they were to be, and a m o n g them m a n freely sinning. By seeing the existence of this series He did not change the nature of things, nor did He make what was contingent necessary, s

It is the idea of Leibniz that God has chosen the best of all possible worlds and made it actual. But in actualizing the creatures He did not change their free natures. So it is not necessary for a man to do what he in fact will be doing according to the foreknowledge of God. It would have been possible to make a different decision than the actual one. But if this is so, how can the foreknowledge of God be infallible'? Leibniz' solution to this problem is very close to Anselm's solution. Like Anselm, Leibniz introduces a distinction between two kinds of necessity: ~For we must distinguish between an absolute and a hypothetical necessity". 9 Leibniz' two concepts of necessity correspond exactly to Anselm's antecedent and subsequent necessity. If N stands for the hypothetical necessity, Leibniz would have no objection to the argument in the introduction. H e says: "Hypothetical necessity is that, which the supposition

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or hypothesis of God's foresight and pre-ordination lays upon future contingents. "1~ This statement is equivalent to Anselm's "What will be, necessarily will be" and it does not provide any information at all about the number of future possibilities. If on the other hand N is taken in the sense of absolute necessity the argument in the introduction becomes invalid since the assumption (b) cannot be accepted in general. Although Leibniz rejects the assumption (b), he is willing to accept a limited version of (D1). In his TheodicyII w he explains that there is a difference between the past and the future with regard to modality. For while it is not possible to cause a past event, it is now possible to cause some of the future events. Therefore if p is an arbitrary statement variable it follows that P(x)p D NP(x)p and regarding the future there is some statement variable q so that it is possible to make F ( x ) q false although it will in fact be true, that is

F(x)q/~M~F(x)q. This means that while there is no alternative to the actual past, there are alternatives to the actual future. These alternative futures correspond to the Leibnizian concept of possible worlds. The connexion between the manifold of possible worlds (and futures) and the modalities is the usual one: What is necessary is what holds in all possible worlds, and what is possible is what holds in at least one possible world. This concept of modality is obviously hypothetical and it is a temporal modality. This means that a proposition corresponding to an event is necessary if and only if the proposition follows from a proposition about the past or the present. It seems that the necessity in question is some sort of causal necessity. The possible worlds of Leibniz represent the ways in which the entire history might have been different from what it is. Therefore it seems to be reasonable to identify a possible world with a possible history. The truth-value semantics for the temporal logic of Leibniz can be for-

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mulated by means of what Hirokazu Nishimura II has called a causal structure. The structure can be symbolized (H,R,V), where H is the set of all possible histories, R is a three-place relation so that R(hl,hz,t ) means that the possible histories hi and h 2 are indistinguishable at all times up to and including t and V is a truth-function so that V(p,t,h) symbolizes the truth-value of the statement-variable p at the time t in the possible history h. It is not difficult to define truth-values for all propositions in this system. Details can be found in Nishimura's paper. Figure 1 can also be used to describe a causal structure. In this case it has to be interpreted as a number of histories that are indistinguishable at all times up to the time to (see Figure 1). A thesis is valid in the causal structure if and only if it is true at all times in actual history. Almost all propositions which are true at all times in actual history according to the Ockhamistic logic, will also be so according to the Leibnizian theory that I have formulated above. Nishimura has, however, formulated an example of an Ockhamistic thesis, which is invalid in a causal structure. This example can be formulated as follows:

-(ANS(H-pA-pAGp)

A ANA(-pDMF-p))

where A stands for "at all times", S for "at some time", H for "at all past times", G for "at all future times" and F for "at some future time". The exact definitions by means of the basic definitions in the introduction are left to the reader. It is not difficult to demonstrate that the above thesis is valid in the Ockhamistic system, but not valid in the Leibnizian system. As I find the above thesis implausible I am inclined to the view that the Leibnizian system should be preferred. 4. THE T H E O R I E S C O M P A R E D

Although the temporal theories of Anselm, Ockham and Leibniz are not identical, they have some very important features in common: (1) A clear idea of the actual future, which makes it possible to accept the doctrine of divine foreknowledge of future contingents. (2) The belief in alternative future possibilities, which implies the doctrine of human freedom.

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(3) The denial of the validity of D1 (the necessity of the past), though a limited version of D1 is acceptable. Since the theories have these three important features in common it is reasonable to classify them as basically the same temporal logic. After all they provide the same answer to the argument in the indroduction. Let us call it the AOL-answer. The AOL-answer can be criticized on the basis of the other important solution to the problem of divine foreknowledge and human freedom: the Peirce-solution, according to which it is impossible for God to have foreknowledge about decisions that have not yet been made. According to the Peirce-answer God knows every fact about the future, but there are simply no facts to know as regards the future contingents. If a proposition can be known now, the Peircians say, it has to be a logical law or there has to be some cause in the past or in the present which together with some law makes it necessary. In short: According to the Peircians, what can be known now, is necessary. Regarding God's knowledge this means that they hold the following thesis D F ( x ) p D NF(x)p. The only way in which the Peircean can explain the doctrine about God's knowledge is to claim that God knows things in an atemporal or timeless way. It seems that the Peircean must assume that the divine knowledge cannot be transformed into a normal knowledge in time, that is: on this assumption God cannot provide temporal knowledge to the prophets, for how can God give a knowledge to somebody, if He does not have this knowledge himself. As regards the argument designed to prove the incompatibility of divine foreknowledge and human freedom the Peircians accept the validity of (b). In order to solve the problem they deny the validity of (g). This denial implies that the Peircian cannot refer to the actual future, but only to the possible futures or to the necessary future. It is my opinion that this is a high price to pay, indeed. It seems to me that a solution following the AOL-answer is the most natural. But how can divine foreknowledge be explained within the AOLtheory? According to Anselm the knowledge of God is atemporal in the sense that "all things are present to Him at once" (quoted in section 2).

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B u t A n s e l m also a s s u m e d that G o d c o u l d t r a n s f o r m his a t e m p o r a l k n o w l e d g e to n o r m a l k n o w l e d g e , that could be u n d e r s t o o d by the p r o p h e t s . It is difficult for the h u m a n m i n d to g r a s p these ideas. F o r this r e a s o n O c k h a m c l a i m e d that he was u n a b l e to explain divine f o r e k n o w l edge satisfactorily. But we should not think that these difficulties can give rise to a p r o o f for the i n a d e q u a c y of the A O L - a n s w e r . I see no logical or p h i l o s o p h i c a l r e a s o n s that force us to d e n y the possibility of s o m e k i n d of n o n - h u m a n k n o w l e d g e . O f c o u r s e we c a n n o t be sure t h a t the A O L - a n s w e r has f o u n d its final f o r m in N i s h i m u r a ' s causal structures. It is an i m p o r t a n t t a s k for philos o p h i c a l logic to i n v e s t i g a t e t h e s e structures a n d to discuss the q u e s t i o n o f t h e i r p l a u s i b i l i t y t a k i n g physical a n d m e t a p h y s i c a l t h e o r i e s into consideration. I t h i n k that the search for an a d e q u a t e t e m p o - m o d e l logic s h o u l d conc e n t r a t e on a f u r t h e r d e v e l o p m e n t o f the A O L - a n s w e r . NOTES 1 A.N. Prior: Past, Present and Future, Clarendon Press, Oxford 1967; and Papers on Time and Tense, Clarendon Press, Oxford 1968. 2 I quote from Anselm of Canterbury, Theological Treatises, vol.III (ed. Jasper Hopkins and Herbert Richardson), Cambridge University Press, Cambridge 1967. 3 Prior Analytic, 30 b 32, trans. Hugh Tredennick, Heinemann, London and Cambridge, Massachusetts, 1962. 4 I quote from Desmond Paul Henry, The Logic of Saint Anselm, Clarendon Press, Oxford 1967 p. 176. 5 See my paper 'A New Reconstruction of the Master Argument of Diodorus Cronus', Int. Logic Rev. 11 (1980), 60-65. 6 In this section I quote from William Ockham, Predestination, God's' Foreknowledge, and Future Contingents (translated by Marilyn McCord Adams and Norman Kretzmann), Appleton-Century-Crofts, New York 1969. 7 Danish Yearbook of Philosophy, 18 (1981), 81-95. s Causa Dei, prop. 104, quoted from Rescher, The Philosophy of Leibniz. Prentice-Hall, New Jersey 1967, p. 39. (Philos. Schrifien, hrsg. Gerhardt, VI, p. 454). 9 The Leibniz-Clarke Correspondence (ed. H.G. Alexander), Manchester University Press Manchester, p. 56. (Philos. Schriften, hrsg. Gerhardt, VII, p. 389). lO The Leibniz-Clarke Correspondence, p. 56. 11 Hirokazu Nishimura, 'Is the Semantics of Branching Structures Adequate for Non-metric Ockhamist Tense Logics?', Journal of Phil. Logic 8 (1979), 477-478. Manuscript submitted 18 February 1983 Final version received 10 May 1983

History of Science Dept. University of Aarhus Ny Munkegade 8000 Aarhus C Denmark