Wednesday, May 28, 2025

An End is in Sight: Schmid’s Response to My Paper

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1. Intro



Put concisely:
  1. Joseph C. Schmid wrote “The End is Near: Grim Reapers and Endless Futures” in a peer-reviewed journal published by Oxford University Press called Mind.
  2. I (Wade A. Tisthammer) wrote paper responding to his paper “A Grim End Is at Hand: Schmid’s Grim Reaper Symmetry Argument, Precognitive Grandfather Paradoxes, and an Intrinsicality Test” in that same journal.
  3. Schmid wrote a blog article responding to my paper.
  4. And now I’m responding to him.
Perhaps fittingly, the main title for Joe Schmid’s blog post is “No End in Sight.”

Before moving on I wanted to say that it’s a privilege to interact with Schmid. I’m not the dumbest guy in the world (Oxford University Press publishing one of my philosophy papers convinced me of that) but vis-à-vis philosophy Schmid is way smarter than I am. It’s no accident that he got into one of the finest PhD philosophy programs in the English-speaking world (Princeton University).

In section 2 of this article I’ll describe Schmid’s paper and my paper. In section 3 of this article I’ll describe Schmid’s blog article and my response.


2. Background



2.1 The Topic of the Papers



The papers relate to arguments against an infinite past, which is relevant to First Cause arguments for the existence of God. Schmid’s original paper discusses a certain kind of argument against an infinite past that uses something called the patchwork principle (which comes in various forms). Robert C. Koons’s paper “A New Kalam Argument: Revenge of the Grim Reaper” is an exemplar of such an argument against an infinite past (be warned though that his paper is highly technical). Very roughly (I’ll go into more detail later), the patchwork principle says that if X is possible at some region and Y is possible at an adjacent region, then it’s possible to have a situation where X and Y happen together. For example, if it’s possible for me to be at a particular stop sign, and it’s possible for Joe Schmid to be at that same stop sign one meter away from the location where I would be standing, then it’s possible for there to be a situation where I and Joe are near the stop sign at our respective locations, preferably discussing philosophy or commiserating over my receding hairline. One can use the patchwork principle by copying-and-pasting possible situations together along an infinite past such that they lead to a contradiction (whereas no contradiction would exist for a finite series of such situations), and from this one can infer the impossibility of an infinite past.

Joe Schmid cleverly constructs a symmetry argument: using the patchwork principle, it seems that one can construct an argument against an endless future using an infinite sequence of situations where among other things God reveals the future. The paper I wrote in response argues that Schmid’s symmetry argument doesn’t quite succeed. How? There’s one important caveat to the patchwork principle I left out in my oversimplification: the qualities you’re copying and pasting for the patchwork principle must be intrinsic, and if God’s foreknowledge is of a certain type, then God revealing the future isn’t necessarily intrinsic to a situation. What the heck does “intrinsic” mean, and what type of foreknowledge am I talking about? I’ll explain that soon, starting with God’s foreknowledge.


2.2 God’s Foreknowledge



Among other things, God is a soothsayer and God foreknows all future events, or at least so certain religions would have us believe. One type of foreknowledge called simple foreknowledge is knowing what the future will be in a kind of direct way (such that this foreknowledge isn’t inferred from anything; one would just kind of know the future in an “immediate” fashion). Another type of foreknowledge is subjunctive foreknowledge where one knows the future because of one’s knowledge of what would happen. For example, the Christian could believe that Jesus’s foreknowledge worked this way: Jesus knows that if he were to tell Peter that he will deny Jesus three times, Peter would deny him anyway. Using this subjunctive foreknowledge, Jesus tells Peter that he will deny Jesus three times.

In my paper I provide a motivation for the theist to ascribe subjunctive foreknowledge to God for soothsaying instead of simple foreknowledge. The rationale for this is similar to the famous grandfather paradox for time travel (in what follows I’ll be referring to a specific type of backwards time travel where traveling back in time alters your own past, instead of e.g., creating a separate parallel universe). If a man goes back in time before his parents were born and kills his grandfather, then he couldn’t have been born and thus couldn’t have gone back in time to kill his own grandfather: a contradiction. The grandfather paradox has been used to argue against the possibility of time travel (again, I’m referring to the aforementioned specific type of backwards time travel).

We can construct a similar paradox for soothsaying, what is known in the literature (thanks to my paper) as the precognitive grandfather paradox. Here’s an excerpt from a post-print version (the version after referee comments but just prior to the journal’s proofreader and copyeditor) of the paper that explains it:
Consider the following scenario that I will label (MM1). Miss Murder commits to herself that she will kill Smith if and only if Smith will have a grandchild. The world is such that if Miss Murder did not kill Smith, then Smith would eventually have a grandchild. To see if Smith will have a grandchild, on November 9th at 8:55 a.m. Miss Murder enters the room of an infallible soothsayer who has simple foreknowledge. The soothsayer waves her elegant hands over the crystal ball which, at precisely 9:00 a.m., will reveal whether Smith will have a grandchild. What will it show? If it shows that Smith will have a grandchild, then Miss Murder will kill Smith and prevent him from having a grandchild, in which case the crystal ball couldn’t have shown that Smith will have a grandchild. A contradiction. If however the crystal ball shows that Smith will not have a grandchild, then Miss Murder will not kill Smith, but then Smith will have a grandchild, and the crystal ball couldn’t have shown that Smith will not have a grandchild. Another contradiction. Either way, Miss Murder killing Smith if and only if Smith will have a grandchild creates a contradiction….The result is a sort of precognitive grandfather paradox.
In this paper I say that this motivates the theist to favor subjunctive foreknowledge over simple foreknowledge for God’s future-revealing abilities. Joe Schmid replies thusly:
Note, though, that this motivation strikes me as very weak. The paradox only shows that it cannot be the case that someone acts on the basis of simple foreknowledge in a way that successfully refutes the content of that very foreknowledge. But that doesn’t imply that simple foreknowledge (or acting on the basis of simple foreknowledge) is impossible; it simply implies that, in any world in which someone acts on the basis of simple foreknowledge, no such action successfully refutes the content of that foreknowledge.
What’s the basis for my thinking that the precognitive grandfather paradox provides the aforementioned motivation? Think back to our grandfather paradox for time travel. Intuitively, it seems that if time travel were possible then something like the grandfather paradox could happen. Similarly, it intuitively seems that if we had a soothsayer who could report on whatever will happen in the future with her simple foreknowledge, then something like the precognitive grandfather paradox could happen.

I say “intuitively” but in reality intuitions differ. One might reject libertarian freedom in favor of the whole world being deterministic, and think that it’s a brute fact that there just can’t be any deterministic system that’s self-contradictory like that. For example, in response to the grandfather paradox argument against time travel, one might think that you could not shoot your gun to kill your grandfather upon going back in time because it’ll be determined that some interfering event will inevitably thwart you, like slipping on a banana peel or your gun jamming. The same sort of principle could be applied to the precognitive grandfather paradox; e.g., deterministic forces resulting in Miss Murder not asking whether Smith will have a grandchild (perhaps she slips on a banana peel before she can consult the soothsayer) or thwarting her attempt to kill Smith (such as her gun jamming or her falling victim to a notorious banana-peel-slipping epidemic). Some people will find this kind of thinking to avoid a possible contradiction ad hoc (like me) but others will find it reasonable. As with many things in philosophy, your intuition mileage may vary.


2.3 Intrinsicality



To explain intrinsicality I’ll quote from the great 20th century American philosopher David Lewis (1941–2001).
A sentence or statement or proposition that ascribes intrinsic properties to something is entirely about that thing; whereas an ascription of extrinsic properties to something is not entirely about that thing, though it may well be about some larger whole which includes that thing as part....If something has an intrinsic property, then so does any perfect duplicate of that thing; whereas duplicates situated in different surroundings will differ in their extrinsic properties….Two things are perfect duplicates iff they have the very same intrinsic properties.1
In my paper I used the phrase “intrinsic copy” instead of “perfect duplicate” to mean “having the very same intrinsic properties” but in retrospect perhaps “perfect duplicate” would have worked better.

Schmid’s paper also refers to “dispositions” and “powers” (I suspect that’s largely because Robert Koons does in his paper) and I’ll explain those next.


2.4 Dispositions and Powers



In philosophy, a disposition is pretty much what “disposition” refers to in ordinary language. What in philosophy jargon is called a canonical disposition or overt disposition is along the lines of “the disposition to M when S” where S is the stimulus and M is the manifestation. For example, sugar has the disposition to dissolve (the manifestation) when placed in room temperature water (the stimulus). The stimulus part is optional for canonical dispositions; e.g., an object might have a disposition to emit radiation regardless of whether a stimulus is present. Another conception of disposition is called conventional dispositions and are more directly adjectival such that it includes examples of “solubility,” “fragility,” and “loquaciousness.” Conventional dispositions can arguably be reduced to canonical dispositions. In this article I will primarily be using canonical dispositions.

In philosophy, powers are the underlying reality responsible for dispositions; or to quote Alexander Bird, “powers are properties that are dispositional in nature.”2 For example, the powers behind a glass’s fragility might be the underlying natural properties responsible for that glass being fragile.

In this article I’ll primarily focus on dispositions, but powers are a good thing to keep in mind when seeing phrases like “powers and dispositions” in the philosophy literature. For more on this topic, see this Stanford Encyclopedia of Philosophy (SEP) entry on dispositions and Dispositions and Powers from the Cambridge Elements series (though be warned that the SEP and Cambridge Elements often assume some background philosophy knowledge, so be prepared to look up things when reading them if you haven’t studied philosophy before especially in the analytic tradition).


2.5 Schmid’s Paper



The patchwork principle can be used in various ways to argue for causal finitism (the view that all causal chains have a finite length) via patching together an infinite sequence of intrinsic units containing entities that have certain powers and dispositions. Consider for example the famous Grim Reaper Paradox. Suppose a Grim Reaper has the following disposition: he checks on Fred at a certain time, and if Fred is alive the Grim Reaper swings his scythe and kills Fred instantly, otherwise the Grim Reaper does nothing. Turns out if we stack an infinite number of these Reapers (or the same Reaper checking on Fred an infinite number of times) such that Grim Reaper 1 checks on Fred at 12:00 + 11 hour (1:00), Grim Reaper 2 checks on Fred at 12:00 + 12 hour (12:30), Grim Reaper 3 checks on Fred at 12:00 + 14 hour (12:15), and so forth, this results in a contradiction. Fred cannot survive to 1:00, since a Grim Reaper would have killed him. However, there is no Grim Reaper who could have swung his scythe; for any Reaper you point to, there is a prior Reaper would have killed Fred if he were alive then.

Multiple variations and inspirations of this paradox are a dime a dozen, including the highly technical one that Rob Koons wrote. I won’t go into the details here because (a) that would take too long; (b) it’s highly technical; and (c) this blog article is aimed more at a lay audience. Suffice to say though that it operates on the same sort of principle as the Grim Reaper Paradox and it uses the patchwork principle to patch together infinitely many Grim-Reaper-like units to generate a Grim Reaper style paradox. At any rate, Schmid’s paper aimed to show that one can construct a parallel argument against an endless future using the patchwork principle.

How does that work? Consider the following situation S:
In [situation] S, the Reaper has the power and disposition to swing its scythe if it’s divinely revealed that no future Reaper swings its scythe, and to refrain from swinging its scythe if it’s divinely revealed that some future Reaper swings its scythe. (In the case at hand, Reaper 1 proceeds to swing its scythe.)3
But if you copy and paste situation S infinitely many times onto an endless future (Grim Reaper 1 for tomorrow, Grim Reaper 2 for the day after tomorrow, etc.) the result is a contradiction similar to the Grim Reaper Paradox. Remember, Grim Reaper 1 (and every other reaper) will swing its scythe if and only if God reveals to it that no future reaper swings its scythe. So does Grim Reaper 1 swing its scythe? Grim Reaper 1 swinging its scythe and not swinging its scythe both lead to impossibilities. Let’s consider each one at a time:
  • Grim Reaper 1 does swing its scythe. If so, then no Reaper after it (i.e., a Reaper with a higher number) will swing its scythe, but that’s impossible because Grim Reaper 2 would swing its scythe if no Grim Reaper after it will swing its scythe.
  • Grim Reaper 1 does not swing its scythe. The only way this can happen is if some future Grim Reaper, call it Grim Reaper n, will swing its scythe. But Reaper n swinging its scythe is impossible because Grim Reaper n + 1 would swing its scythe if no Grim Reaper after it will swing its scythe (so basically the same sort of situation as Grim Reaper 1 swinging its scythe).
So whether Grim Reaper 1 does or does not swing its scythe leads to a contradiction when you have infinitely many such reapers mapped onto an endless future.

Notice that the aforementioned paradox, which we can call the Schmid Reaper Paradox, requires these two components for the situational unit in question: (a) the Grim Reaper; and (b) God revealing the future about whether a future Reaper will swing its scythe. In my response to Schmid, I argue that God revealing the future needn’t be intrinsic to a situation. To aid this I proposed an intrinsicality test, which I discuss next.


2.6 Intrinsicality Test



Quoting from section 6 of the post-print version of my paper:
A test for quality Y being intrinsic to situation X is this: if some logically possible situation X has quality Y yet an intrinsic copy of X in a patchwork does not replicate Y without resulting in a logical contradiction and non-contradictory options exist for satisfying the conditions of the patchwork, then Y is not intrinsic to X. In implementing this test, one must take care to accurately identify the intrinsic powers and dispositions of elements in the situation being copied to determine what would (or at least might) happen in the patchwork when seeing if non-contradictory options are available, since it is easy even for intelligent philosophers to inadequately identify the intrinsic powers and dispositions of elements in a situation. Before considering some quality Y of a situation to be intrinsic, it may be advisable to see if there are intrinsic powers and dispositions that led to Y obtaining, and then implement the aforementioned intrinsicality test to see if Y is preserved.
Call this intrinsicality test (IT). Roughly (i.e., I’m oversimplifying), the rationale behind (IT) is this: an intrinsic property is entirely about that thing, so if whether a thing has a given property varies depending on what is outside that thing (i.e., some surrounding situation), then the property is not intrinsic to that thing. For example, if whether Sally has the property of being taller than Alice varies depending on what’s outside Sally (in this case, the height of Alice) then the property is not intrinsic to Sally; it’s an extrinsic property (the property is not entirely about Sally).

More precisely, the rationale behind the test is something similar that Koons wrote in his definition of intrinsicality, where a “region” is a subset of a “world” (where a “possible world” is a complete description of the way things are or could have been like, and “counterparts” are the same things in different worlds; e.g., Abraham Lincoln in the actual world had a beard, but there is a possible world in which Abraham Lincoln never had a beard and this Abraham Lincoln would be a “counterpart” to the Abraham Lincoln of the actual world):
Definition of Intrinsicality: A property P is intrinsic to a thing x within region R in world W if and only if x is P throughout R in W, and every counterpart of x in any region R' of world W' whose contents exactly duplicate the contents of R in W also has P throughout R'.4
To make things more concrete, let’s apply the intrinsicality test to the following scenario. A certain dosimeter has the powers and dispositions to accurately measure X-ray radiation from 0.01 microsieverts per hour to 10,000 microsieverts per hour, reporting the detected radiation level through a loudspeaker. Suppose this dosimeter is in an environment of 0.3 microsieverts per hour, and so it says “There are 0.3 microsieverts per hour of X-ray radiation per hour.” Let’s label our existing dosimeter situation X, and label the quality of the dosimeter Reporting that there are 0.3 microsieverts of X-ray radiation per hour quality Y. Is Y (the radiation report) intrinsic to X (the dosimeter existing)? First let’s ask ourselves: what are the intrinsic powers and dispositions that led to Y obtaining? Among other things, it’s the disposition to accurately report the X-ray radiation level within a certain range in the dosimeter’s environment. With this in mind, suppose we place a perfect duplicate of X (the dosimeter existing) in a patchwork where the dosimeter is in an environment of 0.6 microsieverts of X-ray radiation per hour.5 Is Y preserved? It is not, because the specified powers and dispositions imply that the dosimeter would report 0.6 microsieverts per hour in this patchwork, not 0.3. So Y (the 0.3 microsieverts report) is not intrinsic to X (the dosimeter existing) according to this intrinsicality test. The following factors were relevant when applying the intrinsicality test here:

(i)Some logically possible situation X (the dosimeter existing) has quality Y (reporting 0.3 microsieverts per hour).
(ii)A perfect duplicate of X in a patchwork does not replicate Y without resulting in a logical contradiction (the intrinsic powers and dispositions of the dosimeter don’t replicate reporting 0.3 microsieverts per hour in the patchwork without contradiction, because the specified dispositions imply it would report 0.6 microsieverts).
(iii)Non-contradictory options exist for satisfying the conditions of the patchwork (the patchwork has (a) an environment of 0.6 microsieverts; and (b) a dosimeter with the specified disposition to report 0.6 microsieverts and not 0.3 microsieverts in such a circumstance).
(iv)When considering some quality Y of the situation to be intrinsic, we see if there are intrinsic powers and dispositions that led to Y obtaining (in this case, the dosimeter’s disposition to accurately report the radiation level of the environment it’s in) when implementing the intrinsicality test to see if Y is preserved.

If someone instead expected the dosimeter to report 0.3 microsieverts per hour in the patchwork of there being 0.6 microsieverts per hour, one might suspect that person didn’t correctly understand the specified powers and dispositions of our hypothetical dosimeter. A response like, “But the report of 0.3 microsieverts per hour is a matter of the circuitry, the loudspeaker, etc. which are intrinsic to the dosimeter; so the report is intrinsic to the dosimeter” would fail to properly apply factor (iv) of the intrinsicality test (and/or suffer from some other sort of confusion in applying the test).


2.7 My Paper’s Response to Schmid



Say that to “reveal a relevant future” means to give a correct and straight “Yes” or “No” answer to whether some future specified event will occur. For example, in the precognitive grandfather paradox, the soothsayer was not able to reveal the relevant future with respect to whether Smith will have a grandchild. Recall that Schmid’s symmetry argument requires that God revealing a relevant future be intrinsic to a situation.

To see how revealing a relevant future isn’t necessarily intrinsic, suppose we have a soothsayer with subjunctive foreknowledge who knows that e.g., Smith would have a grandchild if nobody kills Smith. Call this individual soothsayerj. Soothsayerj has the disposition to reveal the relevant future to Miss Murder upon request if and only if soothsayerj is capable of doing so (she has the option to not prophesy the future if she is not so capable). Suppose we modify scenario (MM1)—the one with the precognitive grandfather paradox—as follows: the soothsayer with simple foreknowledge (call her soothsayeri) is replaced with soothsayerj. Call this scenario with soothsayerj scenario (MM1+), and in this scenario soothsayerj’s dispositions are such that she would not reveal the relevant future in these circumstances.

But there are circumstances in which she would reveal the relevant future. To borrow from the paper, suppose in world w3 Miss Murder walks into soothsayerj’s room and asks whether Smith will have a grandchild. In w3, a meteor instantly kills Smith at 9:01 a.m. (though the world is such that if a meteor had not killed Smith, Smith would have a grandchild). So in w3, soothsayerj reports that Smith will not have a grandchild. Let’s label the situation of soothsayerj and Miss Murder (soothsayerj would use her subjunctive foreknowledge to reveal the relevant future to Miss Murder upon request if and only if soothsayerj is capable of doing so, Miss Murder’s determinations, etc.) Sw3.1. Note that Sw3.1 does not include a meteor killing Smith. If we made a perfect duplicate of Sw3.1 and placed it in a world in which the surrounding situations are like (MM1+), then soothsayerj would not reveal the relevant future. So soothsayerj revealing the relevant future in Sw3.1 is not intrinsic to that situation. Applying (IT):

(i)Some logically possible situation X (situation Sw3.1 with soothsayerj etc.) has quality Y (soothsayerj revealing the relevant future to Miss Murder).
(ii)A perfect duplicate of X in a patchwork does not replicate Y without resulting in a logical contradiction (the intrinsic powers and dispositions of soothsayerj do not replicate revealing the relevant future in the patchwork without contradiction).
(iii)Non-contradictory options exist for satisfying the conditions of the patchwork (soothsayerj has the option to not reveal the relevant future).
(iv)When considering some quality Y of the situation to be intrinsic, we see if there are intrinsic powers and dispositions that led to Y obtaining (in this case, soothsayerj’s disposition to reveal the relevant future when she is capable while also being disposed to not reveal the relevant future when she is incapable of doing so) when implementing the intrinsicality test to see if Y is preserved.

Thus soothsayerj’s revealing the relevant future is extrinsic rather than intrinsic to Sw3.1 largely due to the specified intrinsic dispositions of soothsayerj. In my paper I also describe soothsayerjt which is like soothsayerj except that intrinsic features guarantee that she never utters anything false, and the result is the same as before for the same reasons; e.g., she still has the disposition to not reveal the relevant future when she is incapable of doing so (factor (iv)), and so her revealing the relevant future is still extrinsic according to (IT). A similar principle applies to the Schmid Reaper Paradox. Quoting from section 3 of the post-print:
Suppose we add some additional details to Schmid’s situation S to be as follows, designating this variation of Schmid’s S to be Sj. The version of God in Sj, which we can designate as Godj, is powerful but cannot do anything to bring about logical inconsistencies. Godj uses subjunctive foreknowledge for soothsaying decisions and he has some inclination to use his subjunctive knowledge to reveal the relevant future to the local Reaper, but Godj is disposed to not reveal any set T of relevant futures if he is incapable of revealing T (in such a case, God has the option to not prophesy the future) and using his omniscience he decides in advance what relevant futures he will reveal.
In a world where there is a single instance of situation Sj (where among other things there are no other reapers) Godj reveals the relevant future and the Reaper swings his scythe. However, if we make a perfect duplicate (also called “intrinsic copy”) of Sj and paste it onto an endless future, Godj does not reveal the relevant futures since it is part of his specified dispositions to not do so in such circumstances. More explicitly:

(i)Some logically possible situation X (situation Sj with Godj etc.) has quality Y (Godj revealing the relevant future).
(ii)A perfect duplicate of X in a patchwork does not replicate Y without resulting in a logical contradiction (the intrinsic powers and dispositions of Godj do not replicate revealing the relevant futures in the patchwork without contradiction).
(iii)Non-contradictory options exist for satisfying the conditions of the patchwork (Godj has the option to not reveal the relevant futures).
(iv)When considering some quality Y of the situation to be intrinsic, we see if there are intrinsic powers and dispositions that led to Y obtaining (in this case, Godj’s disposition to reveal the relevant futures when he is capable while also being disposed to not reveal the relevant futures when he is incapable of doing so) when implementing the intrinsicality test to see if Y is preserved.

In my paper I also describe Godjt, which is like Godj except it is explicitly specified that God cannot utter a falsehood. Again, the result is the same since e.g., God is still disposed to not reveal the relevant futures when he is incapable of doing so (factor (iv)).

Note that whether we get a contradiction along the lines of the Schmid Reaper Paradox depends on what God’s specified dispositions are. If the details of situation S are like Sj then we do not. However, consider the following (quoting from section 3 of the post-print):
[I]f we have a version of the Schmid situation S (call this version Sn) where God has the power to reveal the relevant future to a Reaper no matter what (at least in the sense that God would reveal the relevant future to the Reaper regardless of what the other situations were like) then this would create a contradiction in the Schmid Reaper Paradox when Sn is intrinsically copied and patched onto an endless future.
So on the “reveal the relevant future no matter what” deity, which we can label Godn, a contradiction results largely because of Godn’s specified dispositions, but a contradiction does not result in the case of Godj largely because of Godj’s specified dispositions.


3. Schmid’s Response to My Paper



As mentioned earlier, Schmid wrote a blog post responding to my paper. One thing to keep in mind in the following quote is my explanation for why an intrinsically copied soothsayerjt would be disposed to not reveal the relevant future in a (MM1+) type patchwork, and my explanation for why an intrinsically copied Godjt would be disposed to not reveal the relevant futures in the endless future patchwork. A big upshot of all this is the existence non-contradictory options in their respective patchworks.
But whether a non-contradictory option is available to satisfy the conditions of the patchwork is the very question at issue! Whether a non-contradictory option is available depends precisely on whether an intrinsic copy of the soothsayerjt would also utter the relevant sentence (since if an intrinsic copy would utter the relevant sentence, contradiction ensues), which in turn depends on whether uttering the relevant sentence is intrinsic to the individually possible localized situation. We therefore cannot non-question-beggingly appeal to the presence of a non-contradictory option to establish that uttering the relevant sentence is extrinsic to the individually possible localized situation.

Tisthammer then applies the same maneuver to the God-Reaper case, but the same problems arise: first, appealing to the claim that non-contradictory options exist for the patchwork presupposes, rather than establishes, that God’s revelation to the Reaper is extrinsic
One might wonder, “Where does Schmid address your explanation for why an intrinsically copied soothsayerjt would not reveal the relevant future?” The answer is simple: he doesn’t. He asserts there are no non-contradictory options without taking into account the specified dispositions of what an intrinsically copied soothsayerjt would do in those circumstances. The same applies to Godjt: in his blog post, he never addresses my explanation for why an intrinsically copied Godjt would be disposed to not reveal the relevant futures in the endless future patchwork.

At first I was frustrated, but then it occurred to me that what was perhaps obvious to me and Robert Koons (with respect to Koons’s application of the patchwork principle and relevantly similar applications) wasn’t obvious to everyone when it came to using the patchwork principle: what exactly are we copying when copying and pasting things onto a patchwork. Schmid has not, I think, correctly understood the nature of the “perfect duplicate” (what I also called “intrinsic copy” in the paper) in the application of the patchwork principle (at least in the context of the paper). In retrospect and in fairness to Schmid, I probably didn’t pick the best descriptions for “intrinsic” and “intrinsic copy” for my paper given how I was using the terms.

To help see what I and Koons seem to have in mind by a perfect duplicate vis-à-vis the patchwork principle, consider what one might mean in ordinary language when we say one thing is a “perfect duplicate” of something else. We can conceive of a machine, similar to the replicators in Star Trek: The Next Generation, that perfectly replicates a device like our hypothetical dosimeter at the molecular level, and that the two (qualitatively) identical dosimeters are then placed in different environments with different radiation levels. Suppose I have one of the perfectly replicated dosimeters and La Forge has the other. If my dosimeter accurately reports 0.3 microsieverts per hour, and I say, “La Forge has a perfect duplicate of my dosimeter” and La Forge’s dosimeter accurately reports 0.6 microsieverts per hour to due to the environment La Forge is in, the objection “They’re not perfect duplicates because they give different radiation readings” would seem to obviously misconstrue what I mean by La Forge having a perfect duplicate of my dosimeter. It would seem that part of what I mean by “perfect duplicate” here is that the dosimeter is copied in a way to preserve its intrinsic powers and dispositions.6 This type of perfect duplicate (copied in a way to preserve its specified intrinsic powers and dispositions) is how I interpreted Koons’s writings. It would seem that Schmid didn’t correctly understand this important aspect of a “perfect duplicate,” apparently interpreting it in a way so that a “perfect duplicate” of my dosimeter entails that La Forge’s dosimeter would also report 0.3 microsieverts per hour despite La Forge being in an environment of 0.6 microsieverts per hour. I thought my interpretation of Koons was obvious, and I thought this interpretation of my paper would be obvious, but in hindsight assuming that people would naturally interpret it in this way was a mistake.

How could I have explained myself better about what I meant by “intrinsic”? What I could have done is something like an intersection of Lewis’s definition of intrinsic I quoted (noting that an intrinsic property is entirely about that thing) and Koons’s definition of intrinsic I quoted (roughly, quality Y being intrinsic to a thing means that every other-world counterpart of the thing has Y) for my definition of “intrinsic” and by extension “intrinsic copy,” in addition to using the illustration of perfectly replicated dosimeters placed in different environments (which would be analogous to one dosimeter being an other-world counterpart of another). If I did that it would’ve been a lot clearer. I could have also quoted from Cambridge Elements’s Dispositions and Powers where on p. 18 it defines intrinsic dispositions as, “roughly, that whether an object has them or not is independent of whatever is going on beyond them.” A key factor for an “intrinsic copy” of a thing is preserving specified (intrinsic) dispositions. For example, situation Sn has Godn revealing the relevant future as intrinsic to Sn largely due to Godn’s specified disposition (part of the definition of Godn is the ability to reveal the relevant future no matter what), but revealing the relevant future is not intrinsic to Sj due largely to Godj’s specified dispositions (dispositions that are specified in the definition of Godj). With inter alia Godj’s specified dispositions we can then use (IT) to show that Godj revealing the relevant future is not intrinsic to Sj.

At any rate, if part of our conception of an “intrinsic copy” is that we are copying the thing in a way to preserve the thing’s specified intrinsic dispositions (as in the case of the perfectly replicated dosimeter given to myself and La Forge), then it follows that soothsayerjt will not reveal the relevant future to Miss Murder because her specified dispositions entail that she won’t in those circumstances. Similarly, Godjt’s specified dispositions entail that he won’t reveal the relevant futures in an Sj endless future patchwork. (Recall the applications of factor (iv) for soothsayerj and Godj; they similarly apply to soothsayerjt and Godjt.)


4. Conclusion



To summarize, Schmid critiqued an argument against an infinite past by arguing that an application of the patchwork principle could be used to argue against an endless future. However, Schmid’s symmetry argument relied on God’s revealing the relevant future to be intrinsic, and I argued that isn’t necessarily the case with Godj, though it would be the case with Godn. Really it depends on the specified dispositions of the deity in question. My intrinsicality test (IT) showed that there were non-contradictory options available for when Sj is intrinsically copied onto an endless future thanks largely to the specified intrinsic dispositions of Godj.

Schmid’s response that no non-contradictory options were available apparently relied on not correctly understanding what a “perfect duplicate” was in the context of how the patchwork principle was used in the paper; namely, something analogous to perfectly replicated dosimeters with the same specified dispositions in the scenario where I say that La Forge’s dosimeter is a perfect duplicate of my own even when his dosimeter gives a different reading due to being in a different environment. In Schmid’s defense, I didn’t specify the “copied in a way to preserve the specified powers and dispositions” aspect of a “perfect duplicate.” I assumed that this aspect was obvious (I thought it was an obvious interpretation of Koons, and that it would similarly be obvious in my paper) but in retrospect that assumption was not a good one to make and I should have better described what I meant by “intrinsic” and by extension “intrinsic copy;” the description I did provide in the paper was at best incomplete.

I’m glad Schmid wrote his blog article because it exposes the importance of asking the following question when using the patchwork principle: what exactly are we copying when pasting these perfect duplicates onto a patchwork? I think it should be made clear that we are duplicating in a way to preserve a thing’s specified intrinsic powers and dispositions; e.g., the disposition of the dosimeter to accurately report the radiation level of the environment it’s in. I think this more or less matches what we often mean in ordinary language by a “duplicate” of something. For example, if I’m holding a dosimeter in an environment of 0.3 microsieverts per hour and I claim La Forge is holding a perfect duplicate of my dosimeter when La Forge is in an environment of 0.6 microsieverts per hour, you likely would not say that my “La Forge has a perfect duplicate of my dosimeter” claim is false merely because La Forge’s dosimeter reports a different radiation level than my dosimeter; that would seem to clearly misconstrue what I meant by the phrase “perfect duplicate.”

Similarly, in the patchworks I was using I was duplicating soothsayerj and Godj in a way to preserve their respective specified intrinsic dispositions when placed in patchworks. How I had interpreted Koons in his use of the patchwork principle is that the kind of duplicates he was using were those that preserved a thing’s intrinsic powers and dispositions. I was using that sort of duplication in my paper, but I didn’t make this aspect of duplication for the patchwork principle as clear as I should have.




1 Lewis, David. 1983. “Extrinsic Properties.” Philosophical Studies, Vol. 44, No. 2, pp. 197–200.

2 Bird Alexander. April 2016. “Overpowering: How the Powers Ontology Has Overreached Itself”, Noûs, Vol. 125, No. 498, p. 341.

3 Schmid, Joseph C. 2023. “The End is Near: Grim Reapers and Endless Futures.”, Mind, p. 9.

4 Koons, Robert. June 2012. “A New Kalam Argument: Revenge of the Grim Reaper”, Noûs, Vol. 48, No. 2, p. 258.

5 I’m making some implicit assumptions here, like the X-ray radiation not inexplicably stopping right before reaching the dosimeter’s radiation sensitive material. On that note, even if Schmid’s symmetry argument doesn’t work, that doesn’t mean there aren’t other successful objections. One problem is that Schmid has convincingly argued that patchwork principles of the sort Koons has in mind are at best insufficient for getting the desired outcome when patching together intrinsically copied situations. For example, when sending a signal to pass information between adjacent spatiotemporal regions, one needs to assume that the signal doesn’t inexplicably stop at points between those two regions. I think this could be repaired by making those implicit assumptions more explicit, but (a) those assumptions could be challenged; and (b) Schmid has a valid point such that at the very least further specification of those supplemental assumptions is required for a tighter and more effective argument.

6 David Lewis said, “if two things (actual or merely possible) are exact intrinsic duplicates (and if they are subject to the same laws of nature) then they are disposed alike” (1997, “Finkish Dispositions,” The Philosophical Quarterly, Vol. 47, No. 148, p. 147). Of course, God isn’t necessarily bound by natural laws, but we still have a similar sentiment here vis-à-vis intrinsic duplicates having the same dispositions. (I’m not saying all dispositions of elements in a hypothetical situation are intrinsic, but I think some are depending on what is specified.)

Wednesday, May 10, 2023

The Moral Argument (A Quick Version)

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Intro



The moral argument is a family of arguments that use morality as a reason to believe in God. The version of the moral argument I’ll be discussing:
  1. If God does not exist, then objective moral wrongness does not exist.
  2. Objective moral wrongness does exist.
  3. Therefore, God exists.
But for this, it’s important to define our terms.


Moral Semantics



To roughly define what I mean by “morality” I’ll explain the sort of “ought” used in moral obligations. Some oughts are purely descriptive, e.g., when “If you want to do well in school, you ought to study” just means something like “As a matter of practical necessity, you need to study to do well in school.” Some oughts prescribe in a way that is not purely descriptive; e.g. someone saying “You shouldn’t torture infants” might be using this sort of ought, and this is the type of “ought” I’m using in my definition of morality (e.g., an action is morally wrong for someone only if they ought not to do it). Very roughly, by “moral wrongness exists” I mean that there are true facts of what people ought not do using the aforementioned not-purely-descriptive sort of “ought,” e.g., it is a fact that it is morally wrong for a man to torture infants just for fun.

An important feature of this moral semantics is that it implies that moral wrongness is non-natural; i.e., it is not part of the natural, physical world. (Facts of physics, chemistry, etc. are purely descriptive, whereas the property of moral wrongness is not purely descriptive.) Another implication of this moral semantics is that, barring the supernatural, non-natural moral properties like moral wrongness would be causally inert (since anything outside the natural world causally influencing the natural world would be supernatural) and empirically undetectable (such causally inert moral properties could not interact with photons etc.).

To illustrate, imagine a moral nihilist (who does not believe in moral wrongness) and a moral realist (who does believe in moral wrongness) observe some jerk kick a dog just for fun. The dog whimpers in pain and runs away. Both agree on all physiological and psychological facts, e.g., that the dog felt pain and suffered minor injury. The moral nihilist says, “I don’t think moral wrongness is attached to that action.” The moral realist says, “I think moral wrongness is attached to that action.” There is no empirical way to determine who is right here; both views agree on all the same empirical facts. In this sense, moral wrongness is empirically undetectable. Notice also that moral wrongness being non-natural is largely why it is invisible and empirically undetectable in this scenario.

In the context of the moral argument, by moral wrongness being objective I mean that it exists independently of human belief and perception of it.


Arguing for Moral Objectivism



Perhaps the quickest way to argue for moral objectivism is to simply point to an example of an objective moral truth, i.e., one that holds independently of human opinion. Consider the largely uncontroversial fact that it is morally wrong for a man to torture infants just for fun. That this is objectively morally wrong can be shown with this thought experiment: would it remain morally wrong if a baby torturer thought otherwise and killed everyone who didn’t agree with him? It seems that it would be, and thus we have an example of an objective moral truth. The step-by-step reasoning goes like this:
  1. In the thought experiment, something remains morally wrong even when all human opinion thinks otherwise (since the torturer killed off everyone who doesn’t agree with him);
  2. in which case the moral truth “It’s morally wrong for a man to torture infants just for fun” would be holding despite human opinion;
  3. in which case it seems we have an example of an objective moral truth (i.e., holding true independently of human opinion) thereby giving us objective morality.
If (a), (b), and (c) are all true as they seem to be, then we have an example of an objective moral truth. (For those who disagree, do you disagree with (a), (b), or (c)? If so, which one(s)?)


Arguing for the First Premise



It is a theorem of mathematics and propositional logic that “Given A, probably C” entails “Probably, if A then C.” Applied here, “Given God’s nonexistence, objective moral wrongness probably doesn’t exist” entails “Probably, if God does not exist then objective moral wrongness does not exist.” My general approach then is to assume arguendo that atheism is true and see if that leads to objective moral wrongness probably not existing. That approach can be broken down into two components:
  1. If atheism is true, we do not have good reason to believe in objective moral wrongness.
  2. If atheism is true, we have good prima facia grounds to disbelieve in objective moral wrongness.
For (4), I’ll argue that barring the supernatural, we don’t have any good reason to believe that objective moral wrongness exists. Recall that moral wrongness is empirically undetectable, but if so, how do we know about it? In practice we rely on moral intuition (intuition in the philosophical sense of the term, which is about what is immediately present to one’s consciousness and what the consciousness immediately apprehends). How does moral intuition deliver knowledge of moral truths? The theist could say that God designed our cognitive faculties (as via superintended evolution) in such away that when they are functioning properly we intuit certain moral truths, just as we intuit elementary truths of logic and arithmetic.

But for atheism, moral intuition delivering moral knowledge is problematic. Recall that objective moral wrongness is non-natural, and since anything outside the natural world causally affecting the natural world would be supernatural, then barring the supernatural such moral properties like moral wrongness are causally inert and would have no causal influence over whether our brains would produce moral intuitions, and so we'd have the same moral intuitions regardless of whether moral wrongness existed. This would seem to undercut such intuition from properly justifying our belief in morality.

To illustrate, suppose a cyborg has a metal-detecting implant that is designed to give her the intuition that a widget in her hand contains metal if and only if the widget contains metal. But suppose her metal-detecting implant malfunctions and it delivers the cybernetic metal intuition regardless of whether the widget contains metal. Then even if the widget in her hand contained metal, and she believed it contained metal solely on the basis of her cybernetic metal intuition, her true belief wouldn’t be knowledge. The same applies to brains producing moral intuition if such intuition would exist regardless of whether morality existed. Like the malfunctioning metal-detector implant, even if the belief in moral wrongness were true, this belief wouldn’t be knowledge. Moreover, if the cyborg knew that her implant would deliver the cybernetic metal intuition regardless of whether the widget contained metal, this would serve as a defeater for her belief (where a defeater is something that undermines the justification of a belief). The same applies to knowing that one’s brain would deliver the intuition of moral wrongness existing regardless of whether moral wrongness existed.

Of course, this all assumes that moral wrongness is causally inert and that no relevant supernatural intervention takes place. The atheist could get around this problem by positing us humans having supernatural clairvoyance of these invisible and non-natural properties, but this seems awfully far-fetched. It is more likely on atheism that we do not have moral knowledge.

Further analogies could be made. For example, suppose we define a “spirit” as an incorporeal conscious being; e.g., (to borrow a bit from Carl Sagan) an invisible, incorporeal dragon that has no causal influence of the physical world. Consider the following Invisible Dragon Scenario, where nearly everyone in the world believes in an invisible dragon that approves and disapproves of certain behaviors we do. The invisible dragon is of course empirically undetectable, and the only reason people believe in it is via an intuition of its existence due to a quirk of evolutionary development. If it were pointed out that people’s brains would give them the intuition for their invisible dragon beliefs regardless of whether the invisible dragon existed, this would provide a defeater for people’s invisible dragon beliefs. The same, I think, would go for moral wrongness on atheism, and I see no relevant difference between moral beliefs in what we could call the Atheism Scenario (people believe in moral wrongness on the basis of intuition, but moral wrongness is causally inert and has zero causal impact on whether our brains would give us moral intuitions) and the Invisible Dragon Scenario. Some potential rebuttals:
  • Moral supervenience is metaphysically necessary. One could say that moral wrongness associates with certain behaviors by metaphysical necessity (i.e., that it couldn’t have been otherwise), and this results in moral knowledge. This rebuttal is easily accommodated by modifying the thought experiment so that the invisible dragon is metaphysically necessary. It still seems the dragon intuition wouldn’t deliver knowledge.
  • Reliabilism. Another objection is that our moral intuitions and therefore beliefs are produced by a reliable process, and thus moral intuitions deliver knowledge. This is dubious on atheism, since it’s just as easy to conceive of evolution producing a species with very different moral codes (note the vast differences within our species regarding moral beliefs among different cultures throughout history). Even so, this can be accommodated. Imagine that the physical laws have a high probability of producing accurate intuitions about the invisible dragon, though the dragon still has zero causal impact over what intuitions would emerge. Again, it seems like the dragon intuitions would fail to deliver knowledge.
The argument from moral knowledge in a nutshell:
  1. The dragon believers in the Invisible Dragon Scenario do not have knowledge for invisible dragon beliefs.
  2. If the dragon believers in the Invisible Dragon Scenario do not have knowledge for invisible dragon beliefs, then moral realists in the Atheism Scenario do not have moral knowledge.
  3. If moral realists in the Atheism Scenario do not have moral knowledge, then on atheism we do not have good reason to believe in objective moral wrongness.
  4. Therefore, on atheism we do not have good reason to believe in objective moral wrongness.
The justification for (8) is that the Atheism Scenario is more or less the situation we are in right now if atheism is true and moral wrongness exists (again, us having supernatural powers of clairvoyance is far-fetched). The justification for (7) is that no relevant difference exists between the Atheism Scenario and the Invisible Dragon scenario such that the dragon believers have knowledge for their dragon beliefs but the moral realists do not have moral knowledge in the Atheism Scenario. Two proposed relevant differences (metaphysical necessity and reliabilism) were already discussed, those two differences being incorporated into the Invisible Dragon Scenario.

Premise (6) seems fairly obvious. Even so, one could bite the bullet and say that the dragon believers would have knowledge of the dragon (particularly in light of the reliabilist rebuttal), but for such a person I invite them to imagine them living in a world where belief in the invisible, incorporeal dragon is as common as belief in gods. Suppose you inform these dragon believers that they would have their dragon intuitions even if this invisible dragon did not exist. Wouldn’t this fact provide a defeater for their invisible dragon beliefs? It seems so, and that doesn’t seem like this should occur if the dragon believers really did have knowledge that the invisible dragon exists. Moreover, that sort of defeater also seems to apply to objective moral wrongness if atheism is true, and if that is the case then on atheism we do not have good reason to believe in objective moral wrongness.

Having justified point (4), i.e., that if atheism is true, we do not have good reason to believe in objective moral wrongness; I’ll turn my attention to point (5), that if atheism is true we have good prima facia grounds to disbelieve in objective moral wrongness. My justification for this relies on what is known in philosophy as the argument from queerness.

To illustrate the general idea behind the argument from queerness, imagine someone saying that an invisible unicorn is floating above their head. This claim is possible but not plausible and one would be prima facia justified (i.e., justified in the absence of further evidence) in disbelieving in this claim, because the invisible unicorn is “queer,” i.e., it wildly diverges from the types of things we know exist in a way to make it unlikely in the absence of evidence for it.

On atheism, objective moral wrongness likewise seems queer: it is invisible, non-natural, and we would need something like supernatural clairvoyance to know it exists. This is wildly different from the types of thing we know exist, and thus on atheism we would have prima facia justification for disbelieving in objective moral wrongness.


Conclusion



The moral argument being discussed here is this:
  1. If God does not exist, then objective moral wrongness does not exist.
  2. Objective moral wrongness does exist.
  3. Therefore, God exists.
The type of moral semantics being used here is such that the moral “ought” is that type of ought that does not have only descriptive qualities. This leads to moral wrongness being non-natural and empirically undetectable. The justification for premise (2) is a proof by example: it is objectively morally wrong for a man to torture infants just for fun, as revealed in a thought experiment in which a man who doesn’t think it’s morally wrong kills everyone who doesn’t agree with him (in that situation, it would still be morally wrong).

The justification for premise (1) is that given God’s nonexistence, it is likely that objective moral wrongness does not exist. The approach for this justification was twofold:
  1. If atheism is true, we do not have good reason to believe in objective moral wrongness. There is no relevant difference between the Invisible Dragon Scenario and the Atheism Scenario, and if that is so, then on atheism we do not have good reason to believe that objective moral wrongness exists. To oversimplify somewhat: if atheism is true then we’d have our moral intuitions of objective moral wrongness existing regardless of whether it existed, and this seems to prevent such intuition from being a good reason to believe in objective moral wrongness (recall the illustration of the cyborg and her faulty metal-detecting implant).
  2. If atheism is true, we have good prima facia grounds to disbelieve in objective moral wrongness. This was justified via the argument from queerness. If moral wrongness exists, it is non-natural and we’d need something like supernatural clairvoyance to know it exists.
Both premises of the moral argument seem justifiably true, and if the premises are true the conclusion is correct regardless of what else might be true.

Friday, June 24, 2022

Conjunction and Conditional Probability

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Intro



In this article I will prove that the probability of “Given A, probably C” is greater than or equal to the probability of “A and C are both true.” This has implications for the moral argument for the existence of God, for reasons I’ll explain next.

Background



Behold the following moral argument:
  1. If God does not exist, then objective morality does not exist.
  2. Objective morality does exist.
  3. Therefore, God exists.
In a previous article I provied via some basic mathematics and elementary propositional logic that “Given A, probably C” entails “Probably, if A then C”, e.g., “Given God’s nonexistence, objective morality probably does not exist” entails “Probably, if God does not exist then objective morality does not exist.” A lot of atheists disagreeing with the moral argument who concede that “Given God’s nonexistence, objective morality probably does not exist” are thus rationally committed to believing the first premise of the moral argument.

However, some atheists who believe objective morality does not exist say they don’t agree with the first premise despite rationally committed to doing so (or at least rationally committed to the first premise being probably true). In this article I argue that atheists who believe that objective morality does not exist are rationally committed to believing Given God’s nonexistence, objective morality probably doesn’t exist which in turn implies If God does not exist, then objective morality does not exist is probably true.

More precisely, I will use the power of mathematics to show that anyone who believes God does not exist and objective morality does not exist is rationally committed to believing Given God’s nonexistence, objective morality probably does not exist.

The Proof



For brevity’s sake, I’ll use a bit of symbolic logic, where ∧ represents “and” and ¬ represents “not” as part of my abbreviations:

G =God exists.
¬G =God does not exist.
M =Objective morality exists.
¬M =Objective morality does not exist.
¬G ∧ ¬M =God does not exist and objective morality does not exist.
P(¬G ∧ ¬M) =The probability that ¬G and ¬M are both true, i.e., the probability that God does not exist and objective morality does not exist is true.
P(¬M|¬G) =The probability of ¬M given ¬G, i.e. the probability of objective morality not existing given God’s nonexistence.


One assumption I will make is the person who believes that ¬G ∧ ¬M is true also believes that ¬G ∧ ¬M is at least probably true. Generally speaking, to be rationally consistent, if you are to believe that some proposition P is true, you should also believe that P is at least probably true.

To generalize, I’ll use two propositions A and C. The goal is to prove this is true:
P(C|A) ≥ P(A ∧ C )
To start with, note the following equation familiar to many high school graduates and intelligent middle school students:
P(A ∧ C) = P(C|A) × P(A)
What is the highest P(A ∧ C) can be if we hold P(C|A) constant? Well, we would want P(A) to be as high as it can be, which is 1. Thus, in finding an upper limit for P(A ∧ C), this inequality is true:
P(A ∧ C) ≤ P(C|A) × 1
    ⇔ P(A ∧ C) ≤ P(C|A)
After finding this upper limit for P(A ∧ C), there’s just one more step:
P(A ∧ C) ≤ P(C|A)
    ⇔ P(C|A) ≥ P(A ∧ C)
Since A and C were of course arbitrary placeholders, we can use all sorts of propositions, including ¬G and ¬M. So for example this is true:
P(¬M|¬G) ≥ P(¬G ∧ ¬M)


Conclusion



Thus anyone who believes God does not exist and objective morality does not exist is rationally committed to believing Given God’s nonexistence, it is unlikely that objective morality’s existence, since P(¬M|¬G) is going to be greater than or equal to the probability of ¬G ∧ ¬M.

Since God does not exist and objective morality does not exist being probably true entails Given God’s nonexistence, it is unlikely that objective morality’s existence, which in turn entails that If God does not exist, then objective morality does not exist, one who believes God does not exist and objective morality does not exist should also believe that the first premise of the moral argument (If God does not exist, then objective morality does not exist) is at least probably true.