Cam’s Kalam and the Unsatisfiable Pair Diagnosis

I’ve had the privilege of helping both Stephen and Cameron in their fruitful debate on the Kalam. (For those interested, I’ve also discussed the Kalam on numerous occasions with Alex Malpass, Josh Rasmussen, and others in this playlist here.) Today, I want to briefly discuss Cam’s response to the Unsatisfiable Pair Diagnosis (UPD) in his closing statement video.

Grim Reaper Death Scary - Free image on Pixabay
“Felt cute, might delete later”

First things first: I will assume that you understand the current dialectic. I will assume you know who’s arguing what, who has the burden of proof, what the UPD and causal finitism are, and so on. If you don’t know these things, watch the debate.

Briefly, here’s the Grim Messenger story: Infinitely many grim messengers are assigned a unique natural number; each messenger writes its number on a piece of paper iff no earlier messenger writes their number on it; and the infinitely many messengers converge to noon from the later than direction, such that messenger #1 is set to activate and instantaneously write its number on the paper at 1 pm; messenger #2 at 12:30 pm; messenger #3 at 12:15 pm; and so on ad infinitum. Each messenger has a clock specifying the messenger’s activation time. This story entails a contradiction.

Here’s the Benign Messenger story: everything is the same as the Grim Messenger story, except messenger #1 is not set for 1 pm but is instead set 25 hours earlier — noon the day before. This story does not entail a contradiction.

Here is my rendition of Cameron’s response to the UPD:

  1. If there could be infinite causal chains, then the Benign Messenger story is possible.
  2. For any possible clocks, changing their intrinsic features does not necessarily change the intrinsic features of any other object. (C)
  3. A clock’s activation time is an intrinsic feature thereof.
  4. If (2) and (3) are true and if the Benign Messenger story is possible, then it is possible to change the activation time of messenger #1 in the Benign Messenger story so that it activates 25 hours later without changing the activation times of any of the other clocks or any other intrinsic properties of anything.
  5. If it is possible to change the activation time of messenger #1 in the Benign Messenger story so that it activates 25 hours later without changing the activation times of any of the other clocks or any other intrinsic properties of anything, then the Grim Messenger story is possible.
  6. The Grim Messenger story is impossible.
  7. So, there cannot be infinite causal chains.

The argument is valid. Premise (1) requires continuous time, but the stories can be modified and the argument will apply mutatis mutandis assuming there could be both an earliest messenger and infinitely many messengers whose activation times are spread out over an endless future. (The patchwork principle, (C), will allow us to move from this benign set-up to a paradoxical, infinite-past set-up.) So, premise (1) seems reasonable enough for present purposes, and I’m fine to grant it here.

Premise (3) is (or at least can be spelled out in a way that is) true. Premises (4) through (6) are also true (at least if dialetheism is wrong concerning (6)).

GRAHAMPRIEST.NET
Got gluts?

That leaves premise (2), i.e., the patchwork principle (C). I will argue here that by the theist’s own lights, (C) is false, and that the theist’s way to avoid this problem will render the argument above unsuccessful. I offer my argument as a tool for service, not as the final word that conclusively settles the debate.

Recall (C): For any possible clocks, changing their intrinsic features does not necessarily change the intrinsic features of any other object. This is equivalent to: For any possible clocks, it is possible to change their intrinsic features without changing the intrinsic features of any other object.

But if it is possible to change a clock’s intrinsic features without changing the intrinsic features of anything else, then it is possible to change the activation time of a clock without changing the intrinsic features of anything else. And so consider a world w in which God exists and a clock is set to noon. By (C), it is possible to change the clock’s activation time to 1 pm without changing the intrinsic features of anything else. But then it’s possible to change the clock’s activation time to 1 pm without changing God’s beliefs (since God’s beliefs are in God’s mind, i.e., they are intrinsic features of God), so that a world w* results such that the only thing that intrinsically changes/varies from w to w* is the clock’s activation time. Since God’s intrinsic features remain the same in w* as they are in w, and since God’s beliefs are intrinsic features of God, it follows that God believes, in w*, that the clock is set to activate at noon. But the clock is set to activate at 1 pm in w*. So God has a false belief. But God cannot have a false belief. Contradiction. Since this contradiction results from the conjunction of theism and (C), by the theist’s own lights (C) is false.


Objection: What if the theist denies that God’s beliefs are intrinsic (and thus denies that God’s beliefs are in God’s mind)?

Reply: This is a very valuable objection. I have three responses, ones that I’m still playing with.

First, this proposal is deeply counter-intuitive. (At least by my lights.)

Second, given divine providence, there must be some sense in which God intends the clock, in w, to have the activation time it has. And surely this intention is at least part of the explanation of why the activation time is as it is. And because the intention partly explains this extrinsic fact, it cannot consist in this extrinsic fact. But this fact seems to be the only fact extrinsic to God which could plausibly constitute (or ground) God’s intention about the activation time. Hence, God’s intention, in this case, is intrinsic — it is not constituted by (or grounded in) things disjoint from him. So, by (C), we could keep this intention unchanged as we move to w*. But that means that in w*, God intends the activation time to be different than it in fact is in w*. But that’s surely absurd — God is omnipotent, and so whatever he intends to occur will occur. It’s not as though God’s intention could be frustrated and fail to be realized. And so we could run the argument in terms of intention, and the extrinsic-belief-reply does nothing to resolve this.

Third, theists will surely grant that God can reveal things to finite creatures, such that the finite creatures’ beliefs are intrinsic to them even though God’s beliefs aren’t. And so surely God could reveal to a finite creature what the activation time is in w. It seems plausible, moreover, that there could be [not that there must be, but that there could be] some distinctive intrinsic phenomenological character associated with this true and veridical revelation that gives the creature utter assurance that the revelation is from God, and that this distinctive intrinsic phenomenological character is only grantable by God through the revelation [a ‘gift of certitude in revealed truth’, we might call it]. Suppose, then, that w is one such possible world wherein God grants the gift of certitude in the revealed activation time to the creature. We can then move from w to w* without changing any intrinsic feature of the creature or God. The creature will then have a false belief in w*. Now, either God revealed this belief to the creature in w* or not. If so, then God is a deceiver, and surely that’s absurd. So, God did not reveal this belief to the creature in w*. But then the creature would not have the distinctive intrinsic phenomenological character associated with the revelation, since that is only grantable by God’s revelation, and we just concluded that God did not, in fact, reveal something to the creature in w*. Contradiction! Remember, moving from w to w* did not change the intrinsic features of the creature; and yet we just concluded that in w but not w*, the creature enjoys this distinctive intrinsic phenomenology. Thus, extrinsicalizing God’s beliefs won’t help, since we can still get a contradiction just by humdrum theistic commitments about God’s ability to reveal things to creatures and grant them distinctive intrinsic phenomenologies associated with such revelations.

For these three reasons, I don’t think the objection at hand succeeds. But I’m still exploring all this stuff right now.


To avoid this problem, it seems that the theist must say that (C) is true so long as its application, when considering certain global features of reality (e.g., that there is an omniscient being with intrinsic belief states), doesn’t entail a contradiction. But then the step-by-step argument above fails, since it applies (C) precisely to a situation wherein its application, when considering the fact that all the messengers apart from #1 are arranged in the contradictory first-member-less way, entails a contradiction.

Overall, then, we seem to have a serious problem for Cam’s response to the UPD on our hands. Obviously I don’t claim the problem is insuperable. Perhaps I have missed something. But I think my criticism can be a valuable part in advancing the discussion. 馃檪

Author: Joe

5 Comments

  1. Michael Gonzalez

    I think your third reason is mistaken in that it is God who has an effect on the creature; not the changing of the clock directly. Moreover, God’s revelation to the creature is certainly not *necessary*, and Cam doesn’t claim that changing the features of the clock doesn’t ever change other things, just that it doesn’t *necessarily* do so.

    More broadly, I don’t see how God’s beliefs (or, in this case, knowledge) about contingent reality are “intrinsic features” of His. You draw the connection with His intention, but that only holds on some views of providence. On some views (like Open Theism), contingent reality can turn out all sorts of ways that He did not intend. And the only intrinsic property God has in any of those cases is omniscience. Which things He knows is relational (i.e. extrinsic). Compare it to the proposed property that He sustains everything in being. If contingent changes beyond His intention can alter which things exist, there is no *intrinsic* change to Him; just a relational change of which particular things out there are being sustained by Him.

    Even more to the point, I wonder what *Cameron* means by “intrinsic property”. All of Cam’s examples had to do with the composition and arrangement of parts of objects. If that’s all he means, then God (having no parts at all) is obviously immune from changes to His “intrinsic properties” in that sense.

    Just a few thoughts that may or may not be of any use.

    I personally think moves like UPD are epistemological poison, but not for any reasons Cameron brought up. It strikes me as incredibly obtuse and a very bad example for when we run into similar problems anywhere else in philosophy or science. But, I digress….

    • Thanks for the comment! I have to be exceedingly brief because I’m very busy. 馃檪

      You say: ” Moreover, God鈥檚 revelation to the creature is certainly not *necessary*, and Cam doesn鈥檛 claim that changing the features of the clock doesn鈥檛 ever change other things, just that it doesn鈥檛 *necessarily* do so.”

      Yes, but my argument *doesn’t* assume that it *necessarily* does so. I kindly invite you to re-read the relevant paragraph. Therein I point out that according to Cam’s principle, it is *possible* to change the intrinsic properties of clocks without changing the intrinsic properties of anything else. But then it simply follows that it’s possible to change the property of that clock while keeping the creature’s intrinsic state the same. And yet we supposed that this intrinsic state is one God alone can ensure by revelation. (This doesn’t at all say God’s revelation to the creature is necessary.) And hence the creature’s intrinsic state is mistaken in this other possible world (since the clock was changed) despite the fact that God revealed, in this other possible world, the clock time. And so God would deceive in this world, which is impossible. So (C) does, in fact, lead to absurdity.

      As for your points about knowledge: yes, the *fact* or *thing* known is extrinsic. But the *act* of knowing is intrinsic, as is the *belief* as a mental item of which subjects are consciously aware. Those are within minds.

      Thanks again for your comment, and sorry I have to exceedingly brief! I’m on vacation plus have a number of R&R’s and ref reports due. So I can’t address your whole comment.

      • Michael R Gonzalez

        No worries, I appreciate you giving even a brief response. I really love your work. Take care.

  2. Alexander Delaney

    Great stuff, Joe! But why is premise 5 true? Doesn鈥檛 changing the activation time of messenger #1 necessarily change the intrinsic property of the piece of paper? After all, changing the activation time of messenger #1 necessarily changes what is written on the paper, from the number 1 to something that is not the number 1.

    Also, if Cam鈥檚 argument is sound, can we use it to show that finite causal chains are not possible? For example, consider the Finite Grim Dialer scenario:

    A dial with three numbers, 0, 1 and 2, is set to 0 at 10:00. Two grim dialers, assigned numbers 1 and 2 and each with their own alarm, are each programmed so that when its alarm goes off, it instantaneously sets the dial to its assigned number iff the dial is set to 0.

    Benign case: The alarms of grim dialers 1 and 2 go off at 11:00 and 11:01, respectively. Grim dialer 1 observes the dial as 0 and so sets the dial to 1. Grim dialer 2 observes the dial as 1 and so does nothing.

    Degenerate case: The alarms of grim dialers 1 and 2 both go off exactly at 11:00. Both grim dialers observe the dial as 0 and both instantaneously set the dial to their corresponding number, so at 11:00 the dial is set to both 1 and 2, which is not possible.

    Using Cam鈥檚 argument:
    1. If finite causal chains are possible, then the Benign case is possible.

    5. If it is possible to change the activation time of grim dialer 2 in the Benign case so that its alarm goes off one minute earlier, at exactly 11:00, without changing the activation times of any of the other clocks or any other intrinsic properties of anything, then the Degenerate case is possible.
    6. The Degenerate case is impossible.
    7. So there cannot be finite causal chains.

  3. I haven’t read or watched everything in the debate but I wanted to highlight that your example of changing the clocks without changing God’s knowledge or belief leading to a contradiction is not adequate due to the fact that God’s knowledge, by definition, is intrinsic and infinite, he has knowledge of which world the person changing the intrinsic activation time ( or anything ) to which value and what time and under what circumstances and what could have happened in this world and all the infinite variables following and preceding that, so, his knowledge is encompassing all possibilities; therefore, his belief can’t be changed with or without our desire because knowledge hasn’t changed! neither can his other intrinsic attributes be changed ( power, goodness, etc .. ).

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