## The Doctrines of Divine Foreknowledge and Human Freedom: A Logical Analysis

Peter Øhrstrøm Department of Communication and Psychology Aalborg University poe@hum.aau.dk

Abstract: This paper focuses on the logical tense between two Christian doctrines which are considered  to  be  fundamental,  i.e.  the  doctrines  of  divine  foreknowledge  and  human freedom, respectively. It has often been argued that the combination of these two doctrines gives rise to a logical contradiction, and that at least one of the two doctrines therefore has to be  dropped.  This  claim  will  be  investigated  and  a  number  of  possible  solutions  will  be considered. The analysis will be based on ideas from the temporal logic originally suggested by A.N. Prior (1914-69).

Keywords: Divine foreknowledge, human freedom, temporal logic

## Introduction: The logical problem

Consider the following two statements:

- (1) Nicolai is drinking beer
- (2) Nicolai is not drinking beer

In  the  temporal  logic  suggested  by  A.N.  Prior  (1914-69)  it  is  very  important  to  note  that  the truth-value  of  (1)  and  (2)  may  change  over  time.  Obviously,  at  any  time  one  of  them  is  true whereas the other is false.

We may of course also consider the disjunction:

- (3) Nicolai is drinking beer or Nicolai is not drinking beer.

Let the letter p stand for the basic proposition in (1). Then the disjunction in (3) can be stated in the following way:

- (3') p or not p

or as logicians will normally put it:

- (3'') p  ~p

Here ~p stands for the negated position, (2).

The combined statement in (3), (as well as in (3') and (3'')) is obviously true at any time. We may of course discuss what it means to drink beer and what beer is. For instance, should a nonalcoholic beer be accepted as a beer? But as soon as questions of that kind have been answered, we may be able to find out by a rather simple inspection  of the facts  which of the two basic statements is the true one and which of them is (right now) the false one. This seems to be based on  a  very  basic  principle,  which  may  be  seen  as  version  of  the  so-called  principle  of correspondence:

- (C) A statement is true now if and only if the statement corresponds to facts about the present reality.

This means that the proposition 'Nicolai is drinking beer' is true now if and only if it is a fact about the present reality that he is drinking beer. If that is in fact the case then it will now and at all  future  times  be  un-preventable  i.e.  it  is  and  will  always  outside  the  control  of  Nicolai  and everybody else that he has been drinking beer at this (present) time. Before he started to drink he may  perhaps  have  chosen  otherwise,  but  even  when  he  is  in  fact  drinking  beer  it  seems  unpreventable (i.e. outside the control of anyone) that right now he is drinking beer, although he may of course stop his drinking perhaps even very soon. Either there are facts about the present reality which makes the proposition in question true or there are no such facts. The existence of such facts may depend on what we did in the past, but it does not depend on what we are doing now or in the future.

Such considerations may lead us to an additional principle, which we may call the principle of now-unpreventability:

- (U) If a statement corresponds to facts about present reality, then there is nothing we can do about the existence of these facts (about the present reality) i.e. the statement is not only true, but it is also now unpreventable that it is true.

What  is  pointed  out  in  (U)  is  that  although  we  may  influence  the  future  by  the  acts  we  are performing or about to perform, we cannot influence the past and the present. The present is as it is - beyond what we can influence now!

The combination of (C) and (U) leads to the conclusion if a statement, q , is true now, then it is now un-preventable that q is  true  now.  Letting  stand for 'it is now unpreventable that', the principle (U) may be restated in the following manner:

- (U') q   q, where q is a statement about the present state.

Taken together with (3'), either it is now unpreventable that Nicolai is now drinking beer or it is now unpreventable that  Nicolai  is  not  now  drinking  beer.  It  all  depends  on  what  Nicolai  has decided to do.

If we turn to what Nicolai may or may not be doing tomorrow at noon then things become more complicated. However, it is normally held that there are two (and only two) possibilities: 1) tomorrow at noon he will be drinking beer and 2) to-morrow at noon he will not be drinking beer. This means that the following disjunction appears to be true:

- (4) It  will be the case tomorrow at noon that Nicolai is drinking beer or it will be the case tomorrow at noon that Nicolai is not drinking beer.

But even if this is so, we don't believe that we can right now sort out by simple inspection or otherwise which of the two components of the disjunction is the true one and which of them is the false one.

Following A.N. Prior's notation (Prior 1962, 2003) we may let ' F(1) ' stand for logical operator 'It  will  be  the  case  tomorrow at noon that…'. Using this formalism (4) can be restated in the following way:

- (4') One of the propositions, F(1)p and F(1)~p , is true now. The other is false now.

This means that the disjunction, F(1)p  F(1)~p , is in fact true now. That is, either it is true now that tomorrow at noon Nicolai is drinking beer, or it is true now that tomorrow at noon Nicolai is not  drinking  beer.  But  how  can  such  statements  be  true  now  given  (C)?  It  follows  from  this principle that F(1)p can only be true now if there is a fact about the present reality to which it corresponds.  But  how  could  there  such  a  fact?  The  scholastic  and  classical  Christian  answer would involve a reference to the doctrine of divine foreknowledge. This means that exactly one of the two statements, F(1)p and F(1)~p ,  is  true  now, since exactly one of them is included in what God knows now. So this statement is true since it corresponds to the facts that God knows. This is at least how William of Ockham (ca. 1287-1347) saw it:

… the  divine  essence  is  an  intuitive  cognition  that  is  so  perfect,  so  clear,  that  it  is  an evident  cognition  of  all  things  past  and  future,  so  that  it  knows  which  part  of  a contradiction [involving such things] is true and which part is false. [Ockham, 1969, p.50]

It follows from the doctrine of divine foreknowledge that F(1)p can be conceived as a statement about the present since it is equivalent to 'God knows now that F(1)p ', from which it seems to follow that the principle of unpreventability of the present can be applied to F(1)p. By the same kind of reasoning, the principle can also be applied to F(1)~p .  Taken together this means that given the doctrine of divine foreknowledge and the principle of unpreventability of the present, we may form an argument based on the following three premises:

- (4') One of the propositions, F(1)p and F(1)~p , is true now. The other is false now.
- (U'1) F(1)p   F(1)p
- (U'2) F(1)~p   F(1)~p

It is very easy to see that these premises lead to the conclusion:

- (D)  F(1)p   F(1)~p

Clearly, (D) is the deterministic (or even fatalistic) claim that either it is now unpreventable that tomorrow at  noon  Nicolai  is  drinking  beer  or  it  is  now  unpreventable  that  tomorrow  at  noon Nicolai  is  not  drinking  beer.  This  means  that  no  matter,  whether  he  is  going  to  drink  beer tomorrow at noon or not, what happens will be now unpreventable and not under the control of Nicolai  or  anybody  else.  Obviously,  (D)  is  the  denial  of  Nicolai's  freedom  of  choice  when  it comes to drinking beer tomorrow at noon. It follows from the premises that Nicolai has only got one option. He simply must 'choose' what God already now knows that he is going to do.

In  short,  the  principle  of  divine  foreknowledge  with  regard  to  future  contingents  can  in  the context  of  this  paper  be  represented  in  terms  of  (4').  Taken  together  with  the  principle  of unpreventability of the present (including God's present foreknowledge) this leads to (D), which may conceived as a denial of human freedom. If both principles are accepted, then the position leads to a kind of determinism or fatalism. Alternatively, as shown in the diagram below we may formulate an indeterministic temporal logic by rejecting at least one of the two principles. In the following, we shall comment briefly on these three kinds of indeterministic theory.

Figure 1: Four kinds of temporal logic introduced in relation to the principle of unpreventability of the present and the principle of divine foreknowledge regarding future contingents.

| Unpreventability of God's Divine present fore- Foreknowledge kwowledge regarding future contingents   | Yes                    | No                               |
|-------------------------------------------------------------------------------------------------------|------------------------|----------------------------------|
| Yes                                                                                                   | Determinism Fatalism   | William of Ockham Luis de Molina |
| No                                                                                                    | A.N. Prior Open theism | Nuel Belnap                      |

## The classical View on the Future

According  to  the  classical  view  defended  by  William  of  Ockham  and  many  other  scholastic logicians, the doctrine of divine foreknowledge regarding future contingent is accepted, whereas the principle of unpreventability of the present is rejected (Øhrstrøm & Hasle, Part 1.9, p. 87 ff.). This means that according to this view statements like F(1)p about the contingent future actually have truth-values now. As maintained in (C) a future contingent is true if it corresponds with what  Gods  knows  now.  The  rejection  of  the  principle  of  unpreventability  of  the  present, however, means that the contingent future is not necessary (or now unpreventable). The point is that God's knowledge now depends on out future free choices. God knows what Nicolai is going to do tomorrow at noon, and if Nicolai had decided to do something else, God would now have known that instead. But here is a problem. In principle, God could communicate his knowledge regarding Nicolai's future acts to a prophet or even to Nicolai himself. If this is done, it seems that  Nicolai's  alternatives  disappear  since  God  cannot  be  mistaken  which  means  that  Nicolai must act according to the divine proclamation. Ockham solves this problem by maintaining that all biblical prophecies about future contingents are conditionals (Ockham 1969, p.44). He gives an  example  from  the  Old  Testament  referring  to  the  prophet,  Jonah,  who  was  asked  to  go  to Nineveh, where he should proclaim: 'Forty more days, and Nineveh will be overturned' (The Book of Jonah, ch. 3 v. 4). However, we learn from the Bible text that the citizens of Nineveh repented and the city was not overthrown at that time. But does this mean that the prophecy was in fact false when it was stated? According to Ockham we should understand the prophecy of Jonah as presupposing the condition 'unless the citizens of Nineveh repent'. Obviously, this is in fact  exactly  how  the  citizens  of  Nineveh  understood  the  statement  of  Jonah!  Viewed  as  a conditional the prophecy may still be true. Ockham's point seems to be that although God knows the  truth-values  of  the  unconditional  prophecies  regarding  the  contingent  future,  He  does  not communicate  this  knowledge  to  human  beings.  In  this  way  God's  unconditional  knowledge concerning the contingent future remains silent (tacit). Still, it is conceptually important that God knows the truth-value of any future contingent.

According  to  the  fatalistic  or  deterministic  view,  time  is  seen  as  a  linear  sequence  without alternatives. Contrary to this view, time may be conceived as a system with alternative possible futures,  but  at  every  moment  of  time  only  with  one  past.  The  system  is  said  to  be  backwards linear, but forward branching. In terms of such a branching time system, the classical view can be illustrated in the following way:

Figure 2: The classical view according to which there is a chronicle ('the thin red line') representing the true story (past, present and future).

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The point is that according to this view there is a special chronicle from the past through the Now and into the true future. This chronicle represents what actually happened, what happens and what is going to happen. In short, this chronicle represents reality (past, present and future). It  is  also  a  part  of  the  classical  view  that  no  human  being  can  have  complete  knowledge regarding  this  very  special  chronicle.  But  it  is  conceptually  important  that  this  very  special chronicle  (representing  reality)  actually  exists.  The  existence  may  be  understood  as  closely related to the divine (fore)knowledge. God knows it in all details! All other routes through the branching time diagram represent possibilities which could have been but which more or less differ from the true story. Nuel Belnap et al. (2001) have introduced the term, the thin red line , in his discussion and criticism of this classical view (see below).

## Prior's rejection of the classical view

A.N. Prior studied the logic of the classical view carefully. He found its indeterminism attractive, but in his opinion it is also rather problematic to assume that a future contingent can be true now. If a statement regarding the future is in fact true now, then there must according to Prior be a strong evidence for it. And when it comes to the contingent future we can in Prior's opinion have no such evidence. Therefore, Prior found it rather problematic to assume that one of the future possibilities has priority as the one which is going to be real. On the contrary, Prior maintained that  all  possible  futures  can  be  real.  His  view  can  be  illustrated  in  terms  of  a  branching  time diagram in the following manner:

Figure 3: The Priorean view according to which there is no chronicle now representing the true future.

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Prior  argued  that  if  a  statement  about  the  future  is  in  fact  true  now,  then  there  must  be  some strong  evidence,  which  in  fact  also  makes  the  statement  now  unpreventable.  For  this  reason, Prior  could  not  reject  what  we  have  called  the  principle  of  unpreventability  of  the  present.  In order to avoid the determinism which follows from the above argument, he then had to reject the principle of divine foreknowledge at least in the strong sense, which leads to (4'). Coming back to  the  above  example,  this  means  that  given  that  Nicolai  is  free  to  decide  to  drink  (or  not  to drink) beer tomorrow at noon, it cannot according to the Priorean view be true now neither that he  is  drinking  beer  tomorrow  at  noon  nor  that  he  is  not  drinking  beer  tomorrow  at  noon. According to this view, both F(1)p and F(1)~p are false. Prior points out that this in fact makes it possible  to  maintain  the  doctrine  of  divine  foreknowledge  in  a  weaker  sense  than  (4').  The weaker sense may simply be the claim that God knows everything which is true. Since there is no truth now about Nicolai's relation to bear tomorrow at noon, the doctrine does not imply that God knows whether Nicolai is going to drink bear tomorrow at noon or not.

While F(1)p and F(1)~p are  both  false  in  the  Priorean  system,  the  proposition  ~ F(1)p is obviously true in the system. This means that  according to this view we should make a clear distinction between the following two propostions:

F(1)~p : 'It will be the case tomorrow at noon that it is not the case that Nicolai is drinking beer'.

~F(1)p : 'It is not the case that it will be the case tomorrow at noon that Nicolai is drinking beer'.

This distinction may of course be seen as difficult to handle at least within the scope of natural language. Most language users would probably, based on common sense reasoning, think that if it is not the case that it will be that Nicolai is drinking beer tomorrow at noon, then it is in fact going  to  be  the  case  tomorrow  at  noon  that  he  is  not  drinking  beer.  The  distinction  between ~ F(1)p and F(1)~p certainly appears to be a very high price to pay in order obtain indeterminism along with an acceptance of principle of unpreventability of the present.

It  is  interesting  that  Prior's  view  has  given  rise  to  a  new  theological  position,  which  has  been termed 'open theism'. This position has recently been discussed by David Jakobsen (2013).

## Nuel Belnap's Open Future

Like Prior, Nuel Belnap and his co-workers (2001) have criticized the classical view rejecting the idea that a proposition about the contingent future can be true now. However, Nuel Belnap et al. don't want to accept the strange Priorean distinction between ~F(1)p and F(1)~p . They have argued that it is in fact possible to have

## (5) F(1)p  F(1)~p

without assuming (4'). This can be done by rejecting the very concept of the absolute truth-value of a proposition at a moment of time. The idea here is that the truth-value of a proposition should depend not only on the temporal moment but also on the choice of route (or chronicle) through the branching time system. This idea had in fact been developed by A.N. Prior who termed it 'ockhamistic'  (see  Øhrstrøm  and  Hasle,  ch.  2.8,  p.  203  ff),  although  William  of  Ockham certainly would have accepted what we have called the classical view.

By  making  truth  relative  to  the  routes  through  the  branching  time  system,  the  idea  of  divine foreknowledge  can  in  principle  be  excluded  from  the  theory,  and  the  branching  time  system becomes the same as  in  the  Priorean  case,  i.e.  the  same  as  in  Figure  3.  The  various  possible futures  have  the  same  status.  None  of  them  represent  'the  future',  but  they  are  all  possible futures.

The  theory  suggested  by  Nuel  Belnap  et  al.  (2001)  is  elegant,  and  it  has  many  followers  in modern temporal logic. However, again it is a rather high the price they have to pay in order to obtain indeterminism without accepting the classical view. The price in this case is that we have to drop the classical and absolute idea of truth and replace with a more relative notion. If this worldview is accepted, the notion of truth (and therefore also the notion divine foreknowledge) will be rather limited. All knowledge will be conditional i.e. truth will in principle only make sense relative to an assumed course of events. In this case there would not be any absolute truth about the contingent future which could or could not be known by anyone.

In terms of the example used in this paper, this means that the statement, 'Nicolai is going to drink beer tomorrow at noon', does not have a truth-value right now. According to the theory the same holds for the proposition, 'Nicolai is not going to drink beer tomorrow at noon'. According to Nuel Belnap et al. (2001) such propositions can only be true (or false) relative to the future course of events. It is like saying that if Nicolai is going to drink beer tomorrow at noon, then he is going to drink beer tomorrow at noon. This is certainly not surprising! And the loss of absolute truth  is  in  fact  a  great  loss.  Very  often  we  want  to  refer  to  the  truth-value  of  contingent statements. For instance, we may be betting. Some say that tomorrow at noon Nicolai will be drinking beer, some may hold the opposite. Some of the persons involved in this must be right (the winners), whereas others are wrong (the loosers). But who is who? We don't know now, but we may of course know later.

## In defence of the thin red line

But what is so wrong about the classical view which was defended by William of Ockham and many  other  great  logicians?  According  to  Nuel  Belnap  et  al.  (2001)  a  model  like  the  one  in Figure  2  does  pay  due  regard  to  the  idea  of  alternative  possibility.  After  all,  the  notion  of alternative  possibilities  is  essential,  when  it  comes  to  a  proper  understanding  of  the  idea  of human freedom. Nuel Belnap et al. have argued that in case the counterfactual possibility has been chosen, there would also in this alternative situation have been one of the possible futures which would have corresponded to the true future. This means that the model in Figure 2 is far too  simplistic.  In  order  to  represent  the  notion  of  the  true  future  correctly,  there  should  be  a 'selected' future route at any choice point in the diagram.

I believe that Nuel Belnap et al. are right. Their criticism should certainly be taken into account. However, their  observation  is  definitely  not  new.  This  point  was  in  fact  well  understood  and defended  by  Louis  de  Molina  (1535-1600),  who  argued  that  God  has  so-called  middle knowledge. This means that God knows what any human being would freely do in any possible situation. In terms of a branching time diagram this may be illustrated in the following way:

Figure 4: A Molinistic model taking divine middle knowledge into account. There is a 'true future' at any choice point in the diagram.

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In fact, it turns out that there are clear biblical examples expressing this idea of divine middle knowledge. One example is this:

Woe to you, Korazin! Woe to you, Bethsaida! If the miracles that were performed in you had been performed in Tyre and Sidon, they would have repented long ago in sackcloth and ashes. Matt. 11.23

If we take the meaning to be that in the counterfactual situation in question the people in Tyre and Sidon would freely have repented, then this would constitute an example of divine middle knowledge. According to Molina one may in this was truly speak of the free choice of human beings even in a counterfactual situation:

God knows that there would have been repentance in sackcloth and ashes among the Tyronians  and  Sidonians  on  the  hypothesis  that  the  wonders  that  were  worked  in Chorozain and Bethsaida should have been worked in Tyre and Sidon … But because the  hypothesis  on  which  it  was  going  to  occur  was  not  in  fact  actualized,  this repentance never did and never will exist in reality - and yet it was a future contingent dependent on the free choice of human beings. (Molina 1988, p. 116-17)

## Conclusion

The analysis of the logical possibilities, when confronting the doctrines of divine foreknowledge and human freedom, shows that it is logically possible to uphold both doctrines in a consistent manner. The problem which has to be solved in order to do so is the logical tension between the doctrine of divine foreknowledge and what has here been called the principle of unpreventability of  the  present  (understood  as  including  God's  present  foreknowledge).  The  logical  analysis shows that there as two ways to go:

1. One can weaken the doctrine of divine foreknowledge. This can be done in Prior's way (leading to 'open theism') , or in Belnap's more radical manner according to which any truth  is  relative  to  a  course  of  events.  -  In  both  cases  the  price  will  be  very  high  in  the sense that essential parts of everyday reasoning have to be abandoned.
2. One  can  accept  the  classical  idea  of  divine  foreknowledge  and  drop  the  principle  of unpreventability  of  the  present.  Then  the  price  is  that  an  even  higher  degree  of  divine knowledge has to be accepted, namely that of the so-called middle knowledge. In addition, we have to accept that what God knows now can be influenced by our future decisions.

It should be mentioned that all this can be formulated in a secular language. As it is shown with the formulation in (4'), the problem can be stated in terms of truth-values without any reference to divine knowledge. On the other hand, if we accept the version of the so-called principle of correspondence discussed here and formulated as (C), then any discussion of truth must give rise to a discussion regarding the facts and the very nature of the present reality. It seems obvious that 1) above can be accepted without involving very much metaphysics - probably even on the basis of a purely materialistic worldview. The other possibility above, 2), seems, however, to call for an assumption regarding a deeply metaphysical nature of reality consistent with the classical doctrine of divine foreknowledge.

## References

- Belnap,  N.,  and  Perloff,  M.  and  Xu,  M.,:  2001, Facing  the  Future.  Agents  and  Choices  in  Our Indeterminist World , Oxford University Press.
- Jakobsen, David: 2013, Arthur Norman Priors bidrag til Metafysikken , Ph.D. dissertation, Department of Communication and Psychology, Aalborg University.
- Louis de Molina: 1988, On Divine Foreknowledge , translated with an instruction and notes by Alfred J. Freddoso, Cornell University Presss.
- Prior, Arthur N.: 1962, 2003, 'The Formalities of Omniscience'. First published in 1962. A New Edition using modern formalism has been published in Prior, Arthur N.: 2003, Paper on Time and Tense . New Edition. Edited by Per Hasle, Peter Øhrstrøm, Torben Braüner and Jack Copeland, Oxford University Press, p. 39-58.
- Øhrstrøm, P. and Hasle, P.: 1995, Temporal Logic. From Ancient Ideas to Artificial Intelligence . Kluwer.
- Øhrstrøm, P.: 2009, 'In Defence of the Thin Red Line: A Case for Ockhamism'. Humana Mente ,  8: p. 17-32.
- William of Ockham: 1969, Predestination, God's Foreknowledge, and Future Contingents , translated by Marilyn McCord Adams and Norman Kretzmann, New York.