Open Theism and the Nelson Pike Argument
5 March 2008
Open Theism and the Nelson Pike Argument
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In November ’07 the old Spectrum blog site posted an article by David Larson titled Richard Rice Discusses Open Theism, to which there was extensive reader comment.
One comment to that article was mine, where I quoted a complex argument supporting Open Theism by philosopher Nelson Pike, from his 1965 essay titled Divine Omniscience and Voluntary Action. I didn’t elaborate much then, and it seemed to me that the implications of Pike’s argument were not generally recognized in later postings. In this article I wish to revisit his argument and propose the admittedly strong position that it is pivotal to substantive discussion of Open Theism.
But first a few preliminary words to add some background. The traditional view, sometimes called Classical Theism, states that God fully determines the future and knows everything concerning the created world, including the actions of responsible agents. However this exhaustive knowledge (which I will term ‘Classical Omniscience’) is usually considered to be compatible with human freedom (Free Will). Open Theism, in contrast, believes there are some human actions that, being free, are thus inherently unknowable. This leaves the future ‘open’ in that not every possible move is known in advance by God.
Adventist theologian Richard Rice was an early proponent of Open Theism, writing, in 1980, an Adventist-published but controversial book titled The Openness of God – the Relationship of Divine Foreknowledge and Human Freedom. He later contributed, with four other co-authors, to a 1994 volume titled The Openness of God – A Biblical Challenge to the Traditional Understanding of God. This latter book had wider circulation and was also quite controversial. One reviewer (http://www.founders.org/FJ22/reviews.html) called it “a frontal attack on the Reformed conception of God as expressed in its confessions of faith and in its orthodox theologians”.
Parallel to the theological debate (although perhaps beginning a bit earlier) there has been a philosophical dialog/debate around the issues of God, foreknowledge and human freedom, stimulated in part by the Nelson Pike article. It appears to me (but I would be happy to be corrected) that these two threads of discussion have had minimal intersection.
Now, on to the purpose of this essay.
When I read defenses of Classical Theism it appears that a significant concern is that Open Theism diminishes God. I would contend that most Christians (myself included) have what I will call an Anselmian concept of God. By that I mean our view aligns with Anselm of Canterbury’s (1033-1109) definition of God in his so-called Ontological Argument for God’s existence. Anselm wrote (addressing God): “we believe that thou art a being that than which nothing greater can be conceived.” (Italics supplied). And when you and I conceive of God, don’t we take every ‘good’ attribute we can think of and try to extrapolate each out to infinity, then say this collectively is what God’s is like?
Yet Open Theism appears to assign something less than that to God. It identifies an ‘open area’ of potential knowledge outside of God’s omniscient view. And the Classical Theist (thinking after Anselm) objects that with such a view God is no longer ‘that than which nothing greater can be conceived’. A presumably greater omniscience would be one that included this open area. Hence the charge that Open Theism diminishes God.
But an Open Theist would reply that this open area is absolutely unknowable, by the definition of freedom, and thus God isn’t diminished by some lack that is really non-existent. A frequently used illustration is the idea of a square circle. The question is posed – can God make a square circle? (Or substitute, for example, a rock so heavy He cannot lift it.) A square circle is a logical contradiction. If you take the intersection of the set of all squares and the set of all circles, the resulting set is empty. There is no such thing as a square circle and presumably God is not diminished by the limitation of not being able to do what is logically impossible.
Now, Nelson Pike’s original article centers on an argument in which he claims that Classical Omniscience is logically incompatible with Free Will. Here is that argument, as I posted it in my comment last November:
1. God's being omniscient implies that if Jones mows his lawn on Saturday afternoon, then God believed at an earlier time that Jones would mow his lawn on Saturday afternoon.
2. Necessarily, all of God's beliefs are true.
3. No one has the power to make a contradiction true.
4. No one has the power to erase someone's past beliefs, that is, to bring it about that something believed in the past by someone was not believed in the past by that person.
5. No one has the power to erase someone's existence in the past, that is, to bring it about that someone who did exist in the past did not exist in the past.
6. So if God believed that Jones would mow his lawn on Saturday afternoon, Jones can refrain from mowing only if one of these conditions is true:
(i) Jones has the power to make God's belief false.
(ii) Jones has the power to erase God's past belief.
(iii) Jones has the power to erase God's past existence.
7. Alternative (i) is impossible. (This follows from steps 2 and 3).
8. Alternative (ii) is impossible. (This follows from step 4).
9. Alternative (iii) is impossible. (This follows from step 5).
10. Therefore, if God believes that Jones will mow his lawn on Saturday afternoon, Jones does not have the power to refrain from mowing his lawn on Saturday afternoon.
At first reading, this certainly is a brain-buster. But for the moment just consider it to be a ‘black box’, i.e. some argument that purports to demonstrate that human freedom and God’s foreknowledge are logically incompatible, as Open Theism contends. We don’t know if this argument is successful or not. Still, it is either true or false. If false then it can be set aside as an interesting attempt and that’s the end of it. But if true then it is just like the square circle case! It’s easy to see and possibly agree to a square-circle limitation. It may be quite difficult to see if Pike’s argument is true, but if it is, Open Theism has made its point on logical grounds.
The contention (buttressed by an argument such as Pike’s) that Classical Theism is actually logically contradictory is why it seems to me that any meaningful discussion cannot properly evade consideration of this point. Pike’s argument (until conclusively deemed incorrect) reframes the discussion.
But resistance to my above conclusion is more likely to be the norm than the exception. The reasons vary widely. Some reference the argument, others do not. Let me consider some of them (the labels are my own).
1) Who Cares? Pike’s argument is far from transparently true. Our eyes glaze over. And life is short. This whole topic, for many, seems too esoteric to be of practical concern. Why should we care? The most important response, in my view, is that the core issue is about whether human freedom is real or not. And lurking behind this discussion is the formidable Problem of Evil that questions whether evil’s obvious existence can be reconciled with a good God. And the only response that seems (to me anyway) to get any traction at all is one that assigns some responsibility to God’s created beings, via free will gone bad. So if human freedom is illusory the buck totally stops with God.
2) Appeal to Transcendence. I am asserting that if Pike’s argument is true then you can only simultaneously believe in Free Will and Classical Omniscience at the cost of violating logic’s Law of Non-Contradiction (see Pike’s Step #3). And that is a very high price to pay. But some would say what do we humans know anyway? God transcends all – perhaps even logic – and for all we know God can make square circles if He wants to. Or at least operate as Classical Theism contends. Consider the doctrine of the Trinity. There’s an apparent paradox. In the original November ’07 discussion one comment was “I find the closer we get to truth, the closer we get to paradox”. And maybe this conundrum is like that. Now I would note that appealing to transcendence is always impossible to refute, and consequently might be correct in any instance. The term ‘for all we know’ recognizes that some things are beyond actual or even potential human knowledge. But also we should also recognize that just because something is irrefutable that doesn’t necessarily make it true (try refuting solipsism).
3) Knowing Isn’t Causing. The idea here is that God can infallibly know our actions without causing them. Hence we are both free and God retains Classical Omniscience. One participant in the November discussion stated:
“I had some friends who got married years ago, and I knew beforehand that it wouldn't last, and it didn't, even though I had absolutely no contact with them during their ill fated union. That is, my foreknowledge had nothing to do with the freedom they used to ruin their marriage”.
Now this view seems very persuasive because it is difficult to imagine how just knowing would also involve causing. And it should be difficult because there is nothing wrong with this argument, per se. The problem is not that the argument is bad, rather that it is not relevant. To better see this it is important to recognize two different types of causation. I will call them direct (or immediate) cause and initial (or first) cause. The error enters if these two different meanings are conflated. The above quotation refers to direct causation. But looking closely at the Pike argument you find nothing there that speaks about causation at all. What the argument attempts to prove is that Free Will is inconsistent with Classical Omniscience. This implies the universe needs to be deterministic (i.e. Hard Determinism). And, if God is the creator, then He created a ‘falling domino’ universe – which is an initial cause. And it is due to this determinism that God (by virtue of His omniscience) can play out the future infallibly. It is not necessary for God to be the direct cause of anything. His knowledge derives solely from the definition of Classical Omniscience and the hard determinism resulting from a first cause. So any response that concerns itself with direct cause is beside the point
4) God is Outside of Time. Some have argued that God created time and can step outside of time as needed. He would then presumably infallibly view past/present/future from this timeless perspective One November participant stated: “God is not just like us and He dwells both outside and inside of our realm of time and space”. Here I would first observe that this response is a really an instance of #2 – an Appeal to Transcendence. ‘For all we know’ God operates this way, and that fixes any problem. But we should also recognize that the words outside and inside are spatial terms and we are being asked to apply a spatial metaphor to a temporal concept. Anyone using a metaphor should be able to demonstrate that there is a genuine parallel, else the metaphor is invalid. And I don’t know how such a parallel could be demonstrated. Given that we are all spatio-temporal beings (and thus conceptually bound) how would one even coherently explain what it means to be outside of time?
5) Open Theism is Un-Biblical. Christian doctrine and scripture should align. Some concerns about Open Theism include, for example, whether God could make trustworthy prophetic pronouncements. Or, whether texts like Jeremiah 1:5 entail Classic Omniscience. Such points are interesting and important to consider. It is, however, frequently less than obvious whether a specific idea is aligned with the Bible or not. And this issue has been intensely discussed by theologians and even summarizing that debate is well beyond the scope of this article.
There are likely other responses I have omitted, and variations on the ones I’ve commented on. Transcendence is always a possible answer and should not be treated lightly as we humans know so little. But appealing to it here means (if Pike’s argument succeeds) that we would be setting aside logic when its conclusion cuts against our preconceptions. Biblical fidelity is also necessary but it appears (at least to me) that there are points well taken on either side of that discussion. Your investigation might conclude that one perspective or the other holds the greater weight of evidence, but I think few would consider either view to be a scriptural ‘slam dunk’.
In the November discussion one participant stated: “I guess I just don't see that what we gain by keeping the future open to God is worth what we are forced to give up”. And Dave Larson, author of the original article, later asked: “’Closed Theists’ disagree with ‘Open Theists’ with enough respectful seriousness to convince any objective observer that something very important is at stake. What is it?” No one really responded to his question then. As I suggested earlier, it seems to me that a key component of what’s ‘at stake’ is the belief that Open Theism diminishes God. And this belief spawns the fear that such a God is not in control. Open Theists attempt to respond to this point, but I wonder whether that response receives an adequate hearing. Various reasons, like the above, can be interposed and possibly obscure this bedrock concern.
Finally, Pike’s argument is certainly not universally accepted by other philosophers. There is a lively debate that has been carried on in the years since he published it. But the various replies have all implicitly or explicitly acknowledged the necessity of dealing with it. I submit that they have good reason for doing so.
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Rich, I appreciate the time and thought you put into this article. Thank you for enlightening us. The open theist position has always intrigued me, but I have a couple of questions.
On point 3, doesn't the knowing isn't causing argument also apply to first causes. In what sense is God's knowledge the first cause of anyone's activity?
In point 4, you ask if we have a valid conception of what it would mean for God to dwell outside time and space. Have you considered what theories of multiple dimensions say about the possibility of going in and out of linear time? I highly recommend this twelve-minute video: Imagining the Tenth Dimension
David: Concerning my point #3 you asked 'In what sense is God's knowledge the first cause of anyone's activity?' This is an interesting question. But (correct me if wrong) it seems to assume humans are capable of initiating first causes due to Free Will and it also seems to assume that God has knowledge of such first causes. Of course, this is the very point of contention. I think an Open Theist would reply that God's knowledge has no relationship to human 'first causes' because, while these causes happen, they are inherently unknowable. A Hard Determinist would, I think, answer that first causes, for humans, are illusory. And Pike's argument is trying to demonstrate that you cannot have it both ways. A reframing statement might be: does Classical Omniscience entail Hard Determinism? Pike, I think, is trying to demonstrate that it does. If so, there are no human first causes. But an Open Theist would reject Classical Omniscience (Pike premise #1).
On my #4, thanks for pointing me to the video. I found it very interesting. However, that author is also using a spacial metaphor for time as all his dimensions above 3 are temporal. For example, he makes a statement in the video, referring to time: 'as if a line'. And we use this metaphor widely in our culture (e.g. time line). And multiple dimensions can mathematically be represented the same way with no concern whether they are ontologically similar. My point is: how can we justify comparing time to space? If we can make such a move we then can envision some temporal 'God's eye view' where past/present/future can be observed simultaneously and it 'feels' like we can do an end-run around an argument such as Pike's. But I question the legitimacy of this. And the video just assumes it is ok to use space as a metaphor for time.
Rich,
John Frame says as to the arguments of temporality and spatiality being equally strong, "We could...argue that a space-less, immaterial being cannot create items in spatial relationship to one another without Himself being in spatial relation to them. Or,we could argue that God cannot know that something is "here" without himself having spatial location.Or, we could argue that if God is nonspatial, then space must be unreal." ...it is significant that arguments for divine temporality are largely philosophical. Open theist complain that the arguments for divine supratemporality come from Greek philosophy, but their own arguments are philosophical."
PS. Simultaneous and instant are also temporal expressions."If God is atemporal, there is no "instant" at which He gains an item of knowledge."
No Other God by John Frame, p.149.
Pat: I am totally clueless when it comes to God's (a)temporality/(a)spaciality. And I don't think it is merely because He has not clued me in. It's more like the last time I tried to explain quadratic equations to my cat. She just blinked and threw up a hairball.
Given that I suspect humans are inherently incapable of understanding something like atemporality, when I read something like 'If God is atemporal' I'm not sure that is a coherent statement for a human to make. If it is (and my ignorance certainly should admit the possibility that it is) I would like someone to explain what it means to be atemporal without resorting to a spatial metaphor - unless that can somehow be shown to really apply.
Rich,
If God is "Spirit" where is that with regards to spatiality? Is space therefore not real?
If God can be temporal and atemporal (outside space and time as we know it and in it as He chooses) then that atemporality would not have to use temporal terms like "instant" and "spontaneous" because they would not apply to when He acquired the knowledge.
pat
Rich
Thank you for this!
Agree or not, all will concur that you have done your homework and expressed yourself clearly and effectively.
I particularly appreciate your emphasis upon the kind of freedom we may or may not enjoy and the conjunction you achieve between two different philosophical/theological traditions. As you say, their interaction has been inadequte so far.
I hope to participate in this discussion again; however, now I must run to a meeting. But before I take off I say "many thanks!"
Dave
So has most of the philosophical discussion focused on premise 3? There are alternative logics (paraconsistent or dialethic logics) that allow for true contradictions. These are motivated, in part, by a desire to avoid the possibly disastrous consequences of the Liar Paradox. Via a simple proof, one can show that from a contradiction anything at all can be derived, and that result is taken to have serious consequences for classical logic. You avoid that by allowing true contradictions or by throwing out one of the rules (all of which are deeply intuitive) used in the proof. There is no one "correct" logic, as I'm sure you know. And the only way to judge between them without begging questions is to do so pragmatically. So perhaps classical theists ought to go in for alternative logics.
Sounds like hokum to me. Does it sound that way to anyone else?
Either believe in God or don't beleive in him, but don't complicate things to the point where you no longer know which way is up.
Tim: you asked "has most of the philosophical discussion focused on premise 3?". No, not as I recall. There have been attempts to differentiate between so-called soft facts vs. hard facts, as well as consider whether God is atemporal and if that deals with the problem. But you should take my recollections with a grain of salt. Remember, you can't trust any Software Engineers :-).
Rich,
I'll get back later, but let me just restate your syllogism (inserting an alternate term, description for belief), in the following manner:
God's being omniscient implies that
if Jones mows his lawn on Saturday afternoon, then God believed (knew for a fact) at an earlier time that Jones would mow his lawn on Saturday afternoon
So if God believed (knew, had prior knowledge of the fact/event) that Jones would mow his lawn on Saturday afternoon, Jones can refrain from mowing only if one of these conditions is true:
i) Jones has the power to make God's belief (knowledge) false.
(ii) Jones has the power to erase God's past belief (knowledge).
(iii) Jones has the power to erase God's past existence
Therefore, if God believes (knows in advance) that Jones will mow his lawn on Saturday afternoon, Jones does not have the power to refrain from mowing his lawn on Saturday afternoon.
Pikes argument still doesn't make logical sense to me. It is quite complex I have to say and this article does a good job to outline some of the difficulties of having a discussion which attempts to introduce multiple initial possibilities and argue them through to conclusion concurrently to prove one is logically contradictory.
For a human free will to have any power to make a future fact that God knows false, the human would have to know what God knows about his specific position. If the human took a choice without knowing conclusively what the fact that God knew was, then I do not see any contradiction with the idea that the human chose what God knew they were going to choose as there is no causal element. The argument is based on the premise that logically God's knowledge must cause events, which implies in itself that perfection causes imperfection. If you don't insist on this causal link between knowledge and events then you don't get into the position of having to deal with a syllogism without questioning its premises, of which many are not stated in the "simple" steps and possibilities as given.
The whole example is not real anyway, because it relies on a free-will based on a blank slate for the given example, ie, that none of the past events will make any choice more likely than others. Is it possible that free-will is the ability to make a choice based on possibilities with a history? I don't see why not, as to ignore this would be to make every philosophical more fictional than they already acknowledge themselves to be.
In relation to the comment about the Liars Paradox, it is only applicable in open systems where directional temporality governs ones knowledge of the reality. Saying it might be avoided preferring that there is no truth and God is simply following temporally as best he can given imperfect agents which implies that he is subject to the Liars Paradox. It never ceases to amaze me how much is assumed in philosophical discussions which are purported to be the epitome of human intelligence, such as the idea that a logic system has rules which can be filled in in any order, effectively making the Liars Paradox a possibility because of the temporal argument mechanism, not because the nature of the system inhibits a possible truth.
Number 4 contradicts the possibility of any knowledge outside of what we assume to be a closed temporal system, why are you discussing an entity that you really just want to redefine to be inside of the system so that the inherent logical contradictions inside of any closed system with temporal observers whose observations change the nature of the system in unpredictable ways. By implying that there has to be a perfect parallel inside of our imperfect time guided system you are in effect rejecting the possibility of any other event outright using your knowledgeably imperfect logic.
Number 3 follows on from that, it implies that the exists a first cause which necessarily causes everything, implying that there was a blank slate before the closed system, that we assume the universe to be, was created from nothing by something with no history before that. If there was no first cause, for which there is no humanly philosophically acceptable argument as the method of philosophy is governed by first causes, then there cannot be a closed system effectively, so you can't relate a particular piece of knowledge to a cause blindly with any certainty. The creator of a discrete temporal system with events and choices, has been in the past outside of he system by our human definition of the word creator, so why should we put him into the system by "Open Theisming" up the closed system that we created because we couldn't argue against god in the open system.
Why would a consistent agent ever desire to refute solipsism btw? To do so would be to break the rules that make up the argument, and philosophical arguments can't comment on the rules other than to say their consequences are invalid when the rules are taken as a whole. It can't even comment on individual rules other than to complete a sequence of logical statements after eliminating or adding a rule, or which the conclusions are still a result of each rule set, and philosophy only assume that the added or removed rule itself was the sole cause of the problem, instead of having an inconsistent set of axioms for which the weakness was only found when another dimension was added to the stakes.
Tim
As I think I've said before, I do not know how to reduce my ignorance without exposing it; therefore, here goes:
1. As you see it, is Nelson Pike's reasoning valid if we stay within the confines of classical logic?
2. In very broad outline, what would a case for God's total and absolute foreknowlege look like if it moved forward on the basis of alternative logics?
When it is convenient for you, I would appreciate any help you can give me. These questions are not disquised challenges. They are true inquiries.
Thank you!
Dave
Dave. Pike looks valid to me. And I don't think there are any hidden premises regarding causation or temporality (I agree with Rich's comments on temporality/atemporality), though I certainly could be wrong.
I'll get back to you on the alternative logics. I've not had formal training in that area, and have only read discussions about the consequences of and motivations behind such logics rather than actually learning one and doing proofs. I'll do a little research and let you know what I find. Tim.
Allow me first to allay the concerns that have been expressed regarding the usefulness of logic. Understanding logic can help us detect fallacies in our reasoning or determine the validity of our arguments. Since true conclusions can only be deduced from true premisses, the truth of our premisses must either be assumed or determined by other means, such as by scientific observation, special insight or revelation. Logic cannot tell us whether the premisses we use as presuppositions are true or false.
Continuing, for the sake of both simplicity and better clarity, let's make a couple of substitutions in Pike's syllogism (argument) so that in place of "belief" we'll write "foreknowledge". Thus:
God's being omniscient implies that
1) if Jones mows his lawn on Saturday afternoon, then God [had foreknowledge] that Jones would mow his lawn on Saturday afternoon
2) So if God [had foreknowledge] that Jones would mow his lawn on Saturday afternoon, Jones can refrain from mowing only if one of these conditions is true:
i) Jones has the power to make God's [foreknowledge] false.
(ii) Jones has the power to erase God's [foreknowledge].
(iii) Jones has the power to erase God's past existence
3) Therefore, if God [has foreknowledge] that Jones will mow his lawn on Saturday afternoon, Jones does not have the power to refrain from mowing his lawn on Saturday afternoon.
All three are conditional (if... then) statements, but note that #1 has a different form than #2 and #3. IMO, #1 "If Jones mows his lawn on Saturday afternoon, then God [had foreknowledge]..." begs the question in regards to God's omniscience or foreknowledge. Whether or not you agree with me on this, I'll confine our discussion of Pike's argument to #2 and #3, since both have the same form and address the same issue regarding God's foreknowledge.
God's omniscience/foreknowledge implies that
Either #2 "Jones can refrain from mowing his lawn on Saturday, or #3 "Jones cannot refrain from mowing his lawn on Saturday.
These two conditional statements taken together are known as contraries which may be represented, respectively, as follows:
p or not-p
'Hartshorne maintains that, “the semantic analysis of truth with reference to future events should not be so formulated as to make ‘will’ and ‘will not’ the sole possibilities” (Hartshorne 1965, 48). Following Hartshorne's suggestion, George Shields says that, “Z will occur” and “Z will not occur” should not be symbolized in the propositional calculus as p and not-p but as p and q, where “If p then not-q” and “If q then not-p.” The conjunction of these propositions, “If p then not-q and if q then not-p” mirrors the truth value semantics of contrariety, not contradiction, which is mirrored by “It is false that ‘p if and only if q,’” or exclusive disjunction. Shields argues that it is question begging to assume that “Z will or will not occur” must be an instance of “p or not-p”. The question at issue is the formalization of future tense statements; thus, it will not do to assume that verb tense makes no difference in the formalization (Shields & Viney 2004, 220).'
http://plato.stanford.edu/entries/process-theism/
Joselito
I agree that #1 begs the question, or perhaps bootlegs an answer.
I also agree that when speaking of the future we can be unconditional and conditional and that Hartshorne's holds that most of our predictions should be understood as conditional or hypothetical: "If this occurs, that will happen."
Don't we SDAs learn from EGW, and more importantly from the narratives of Scripture themselves, that the promises and threatenings of God are conditional?
I take it that this is one of the big lessons we can learn from the story about "Jonah and the Whale." Yes, I know it really wasnt a "whale!"
This is one of the things that our colleagues on the more Calvinist side of the aisle sometimes have difficulty accepting. But at least some of them are coming along!
Is Hartshorne saying something more than this that I am overlooking?
Tim
Maybe the value of references to paralogics is not they require us to formulate alternative lines of reasoning but that they remind us that ours may not be the only way ["logics]of doing so.
Thank you both!
Dave
A conditional statement asserts that its antecedent implies its consequent. It does not assert that its consequent is true, but only that its consequent is true if its antecedent is true. What an antecedent implies regarding its consequent may have different meanings depending on the context. What's common to all conditional statements is their material implication. No real connection between antecedent and consequent is suggested by a material implication. (The force/reasonableness of Cliff's argument: "If p then q"?)
Let us return to Pike's conditional statements. We have a disjuction of two conditional statements: Either p or not-p. Only one of them but not both may be true. However, both consequents may also be false.
Does our experience not suggest that both consequents are true regardless of what the antecedent seems to imply? That Jones was free to choose which course of action he wished to pursue: to mow his lawn or not? A false consequent cannot admit a true antecedent. False premisses do not yield a true conclusion. If so, we need to revisit what is meant by God's omniscience/foreknowledge.
One final point: Does omnipotence not imply omniscience? Does God not have the power to know all things and events? Rightly or wrongly, we substitute one for the other. Still we need to revisit what we understand about divine omniscience and foreknowledge. Rather than omniscience or foreknowledge, I believe the real issue here is between God's power and will vs human freedom. According to process theists, divine self limitation is not the answer. Persuasive instead of coercive power best describes the true nature of God. I agree.
Well, yes, God has the power to know all histories, possibilities, probabilities and actualities. But isn't it also the case that no one can have the power to know something that is not one of these?
Does the Bible specifically say that God has omniscience? Omnipresence? Or, is it merely a consensus of some who interpret scripture with a preconceived opinion? Aren't there scriptures showing both his omniscience and lack of?
Dave, it looks to me like there are a couple of options regarding strategies to get around the contradiction. One can either deny the law of the excluded middle (ie, assert additional truth values), or the law of non-contradiction. There are multiple languages/logics for doing both.
Denying non-contradiction works best if you can get your contradiction to be the result of self-reference, like the Liar sentence ("This sentence is false") or Russell's paradox (set of all sets that are not members of themselves). I don't see this in Pike or how to get there. If you don't restrict your denial of non-contradiction to special cases, you risk irrationality.
Going for multi-valued logic makes more sense, and has been done with reference to very similar problems. Here again there is a choice between opting for a third value that is either neither true nor false, or both true and false (it looks like it is more common to settle for three truth values than to do more, though fuzzy logics have infinitely many more). The route you go depends on what you are willing to give up - implication (if, then), disjunctive syllogism (A, ~A or B, therefore B), etc.
Like Joselito, I went to the Stanford Encyclopedia of Philosophy - entries on Dialetheism, Contradiction, Paraconsistent Logic. The Free Will entry is also interesting.
Speaking of free will, this little gem popped up on my podcast directory this morning:
Thomas Pink on Free Will
It's interesting to not the similarities between the argument for determinism and Pike's syllogism. Also interesting is Pink's solution to the 'problem' of free will.
Rich
Somehow along the way we have lost you. Sorry!
It would be helpful to know if this time around we are focusing upon your essay where you'd like the discussion to be. If not, let us know where you want us to focus. We may have gotten off course again.
My impression is that you are reminding us that, in addition to what other ways there may be, classical logic helps make the case for open theism; i.e. it is another arrow in the quiver.
David
Thinks for the link to Pink on free will, a topic that is roaring in our Sabbath School at the moment. Having the book and having thumbed through it, it was good to hear him speak. He covers a lot of ground in not much time.
Learning about the site "Philosophy Bites" is a prize.
Tim
You state one of my worries very well: "If you don't restrict your denial of non-contradiction to special cases, you risk irrationality."
Perhaps a defender of the classical view could argue that when speaking about God we have a "special case."
Unless this is an arbitrary assertion, I think that person bears the burden of proof, though "absolute proof" is probably too high a standard.
But we also plausibly learn from you that "The route you go depends on what you are willing to give up."
But does this not depend in part upon where you "want" things to end up?
If I have a nonnegotiable conclusion that is invalid by classical logic, then perhaps going for some paralogic is my next move. But, then, does this not beg the initial question.
Am I tracking the argument?
In the end, I guess I still wonder if the paralogics establish that Nelson Pike's line of reasoning is invalid. I gather from everyone that it passes the requirements of classical logic.
I looked up things at Wikipedia. SEP would have been better. Good example!
Thanks!
Dave
Dave: Thanks, I've been tracking the thread. However, I figured it had mostly died out, as they all do. What I wanted to do with the essay was put the admittedly challenging question on the table: if Pike's argument is logically valid/sound shouldn't then the onus be on Classical Theism to show why it is the preferred view? Of course it might not be valid/sound but that would take investigation. Most of what I wrote, however, had to do with reasons people might have problems accepting Open Theism - reasons that, if they are problematic, can be used to avoid squarely facing the issues. And I attempted to demonstrate what I saw as some problems. I guess the November discussion left me thinking people frequently were hesitant to revisit their beliefs on this one. The idea of diminishing God seems to me a probable underlying cause, but one that doesn't need to be addressed if you think you have a pretty good reason for holding your current view. But, if that reason has problems - what then? I think many people are likely to turn away from confronting a problem anyway. Ambiguity is never comfortable.
Let's represent with the letter "M" the Middle Term of Pike's syllogism, which is: "God had foreknowledge that Jones would mow his lawn Saturday."
1) if Jones mows his lawn on Saturday afternoon, then God [had foreknowledge] that Jones would mow his lawn on Saturday afternoon
S is M
2) So if God [had foreknowledge] that Jones would mow his lawn on Saturday afternoon, Jones can refrain from mowing only if one of these conditions is true:
M is P
3) Therefore, if God [has foreknowledge] that Jones will mow his lawn on Saturday afternoon, Jones does not have the power to refrain from mowing his lawn on Saturday afternoon.
Therefore, M is not-P
Summarizing:
S--M
M--P
Therefore,
M--not-P
Briefly, the Middle Term ("M") links #1 and #2 premisses. The standard form of this categorical syllogism/argument should conclude by establishing a connection between the subject and predicate terms, "S" and "P", which it doesn't. It violates the Law of the Excluded Middle. It's an invalid argument.
Let's make our deduction by connecting the "dots":
if Jones mows his lawn on Saturday afternoon, then Jones does not have the power to refrain from mowing his lawn on Saturday afternoon.
S--not-P
Are we not back to where we started? False premisses cannot yield a true conclusion. We need to revisit our Middle Term: the nature of God's omniscience/foreknowledge. Psalm 139 is the classic statement of God's power, according to Scriptures, inclusive of prescience and presence.
I don't think putting this in syllogistic form captures the argument. You have turned conditionals into statements of identity ("A>B" becomes "A is B"), which is, I'm pretty sure, invalid. Also, the Law of the Excluded Middle is not about an excluded middle term, but an exclusion of any value between true or false.
Dave, I know what you mean about feeling like switching logics constitutes question begging, but I still think it is a valid move so long as you are consistent with it. Even logic is subject to the process of reflective equalibrium. If giving up God's omniscience seems more wrong then giving up disjunctive syllogism, then give up disjunctive syllogism and have a go at it. I think, though, it might be much easier to affirm the validity of Pike but deny one of the other premises (besides 3). Plantinga, I think, denies i.
Joselito - On a second look, the problem in this case is not so much with turning conditionals into identities (though I wouldn't want to make a habit of doing that). Explain a bit more about what you mean by "Law of the Excluded Middle." As you've schematized it, the argument goes S>M and M>P therefore S>~P, which doesn't capture how the "~" gets there, but it does have a middle term that links S and P. Going from S to P is consistent with the rule generally called "hypothetical syllogism." What am I missing? You may be right in calling Pike's premises false, but I don't think the argument is invalid.
Josilito, you wrote: "It's an invalid argument" and later, "False premisses cannot yield a true conclusion". But false premises would make the argument unsound, not invalid (although it could be both). I presume this partly is why Tim wrote: "may be right in calling Pike's premises false, but I don't think the argument is invalid".
As for me, formal logic is not my strong suit, although I have some rusty background. I will attempt to get some time to examine Josilito's comments more carefully. Josilito, I do however, appreciate that you address the argument. I suspect most don't because a) it's a bit daunting; b) they don't want to go where acceptance might force them to go.
Josilito, off the top of my head (dangerous, I know) I am skeptical of your rebuttal because in the book where I originally read Pike's article (God, Foreknowledge and Freedom, ed. John Martin Fischer) none of the other authors produced responses questioning Pike's validity. Now, concerns about premises were another matter. And here some of the difficulty is definitional. Note, however, that just because those respondents didn't go down your track, doesn't make your comments incorrect.
Admittedly, the issue of foreknowledge and free will is far more complex than appears on the surface.
"Regardless of what one thinks of the argument for theological fatalism, there is a more general problem in the logic of time and causation that needs to be addressed."
http://plato.stanford.edu/entries/free-will-foreknowledge/
In sum, the soundness of the fatalism argument is not beyond reasonable doubt. This is why the conversation continues.
I took the liberty of substituting categorical propositions for Pike's conditional statements, hoping someone would notice and correct me.
Let S = the class whose members include "Jones mows his lawn Saturday afternoon; M = God's infallible belief (foreknowledge) that Jones would mow his lawn on Saturday; and P = Jones can refrain from mowing his lawn on Saturday.
Thus, the proposition S is M (S--M) doesn't imply S = M. The Principle of the Excluded Middle asserts that no statement can be both true and false. The application of this principle, excluding the Middle Term from the conclusion of a categorical argument (either S--P is true or P--S is true) is my own invention. It simplifies matters, when I'm trying to decide whether the form of my argument is valid or not.
Evidently, complex issues cannot be resolved simplistically (which I tried to do, unconvincingly:-) neither on rational grounds nor appeal to authority.
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