Grim Reapers, Causal Finitism, and the Kalam | Dr. Alex Malpass

[@rationalityrules]

Extremely insightful conversation, and an absolute treat for me for obvious reasons : ) I've just been reading about the Unsatisfiable Pair Diagnosis after Malpass suggested a few papers, and seeing him talk it through with another sharp and informed person has been really useful. Thank you, sincerely.

[@MajestyofReason]

Hey! Really glad you liked it. I've really enjoyed the fact that you and Cameron are raising the discourse on the 'theism vs non-theism' scene. A few years ago I would have never imagined that two very popular KZbinrs, one theist and another atheist, would be quoting Oppy, Pruss, Rasmussen, Benardete, etc. in their videos. Such great stuff! Cheers my dude.

[@danglingondivineladders3994]

sophist

[@jacksonhoward740]

YES!!! This is wonderfully done, Joe. Also, can we please get Rationality Rules to watch this before his next rebuttal?

[@MajestyofReason]

EGG-ZACTLY

[@rationalityrules]

You leave my horrid accent alone! :P

[@Hello-vz1md]

@@rationalityrules After your Kalam series kindly also make more series on philosophy of religion With Joe like your current Kalam series It will be really great

[@DarwinsGreatestHits]

Great stuff. Here's another example in the literature but from a different context. I think it's in the same spirit as the Eulerian circuit. There's a mother with 23 strawberries that wants to distribute them equally to her 3 children. The problem is that it's impossible, because 23 doesn't divide by 3 without remainder. It's a mathematically impossible situation. Presumably there is no mysterious mathematical force stopping her. We can alter the situation slightly by adding a single strawberry and suddenly it becomes possible! If one is possible why isn't the other?

[@MajestyofReason]

[@c.guydubois8270]

Mom can eat 2 too..

[@AskYourself]

This is great, hope this channel does well.

[@bigolboomerbelly4348]

what is your discord?

[@ajhieb]

If I told you to go stand in the corner of a perfectly circular (aka "cornerless") room, there is no paradox here. I've simply instructed you to do something that is incoherent. I haven't disproven the concept of a perfectly circular room, nor have I disproven the concept of corners. I've simply stuck two incompatible concepts together that are obviously incompatible. The only difference between this example and every infinity "paradox" I've encountered is the incompatibility is less obvious. But in some way shape or form the supposed paradoxes all rely on starting at the end of an endless series. Of course it's never phrased that way because phrasing it that way _does_ make the incompatibility obvious. You can't get to the end of an endless series. Period. That's not a paradox. It isn't a contradiction, it's simply an incoherent concept that _seems_ coherent because it's described poorly. It doesn't matter if the endless series is convergent or divergent. You can't get to the end of an infinite series. If you could, it wouldn't be an infinite series. Benedetti's wall guy... starting at the end of an endless series. Grim Reaper... starting at the end of an endless series. Grim messenger... starting at the end of an endless series.

[@joshuabrecka6012]

Alex is so great. He was such a big influence on me when I first got into philosophy via the internet. Thanks for having him on Joe. He's got a paper coming out in Mind on the GRP I think (Haven't finished listening yet)

[@MajestyofReason]

Much love

[@ApologeticsSquared]

I think that logic alone doesn’t explain why contradictory grim reaper scenarios don’t occur if you allow for a reasonable sort of branching modality. Say I have countably infinite reapers each with a natural number. I order them to “kill Fred 2^-n hours [blank] 12:00.” I can fill that blank with either the word “after” or the word “before.” Say I decide how to complete my command by flipping a truly random coin. Heads means I put in “before” and no contradiction. Tails means I put in “after” and there is a contradiction. Since there is no contradiction with me getting heads, the causal infinitist seems to need to maintain that there is a possible world where I get heads. But, since there is a truly random coin used, it seems that there should also be a possible world branching off where I get tails. But getting tails yields a contradiction. So there isn’t such a possible world. So, the causal infinitist seems to need to have some way of barring the entire scenario. Have a nice day! :)

[@MajestyofReason]

Thanks for the lovely comment!!! I truly appreciate it. Here's my take on your comment: I don't think the scenario you've described avoids the UPD. For if the set in question is truly infinite, and the coin is truly indeterministic between O1 and O2, such that O2 is a scenario in which each P holds for each member of the infinite set iff P holds for no 'earlier' member of the set, then you've simply described to me a contradictory scenario. The coin *cannot* be indeterministic between O2 and O1 while holding the infinity fixed; this is just contradictory. The unsatisfiable pair here is just this: (A) the set is infinite (B) (i) The coin is genuinely indeterministic between options O1 and O2, (ii) hold (A) fixed, and (iii) O2 is such that P holds at member m of the set (for any m) iff P holds nowhere before m. This (A) and (B) is just as contradictory as the original conditions (A) and (B). But this is precisely the scenario you've just described. There is thus no special need to debar the scenario here, by my lights. It's just as contradictory as before. :) Think of it like this. Suppose I tell a long story about how Cameron Bertuzzi gets into a taxi, and while in the taxi he makes memes about classical theism being false, debunks new atheists, and so on. Then, at some point later in the story, I mention that Cameron has never been in a taxi (simpliciter). You would stop me right there and say that I've contradicted myself. It would be odd for me to say "yes, and I have an *explanation* of why the story cannot obtain: because taxis are impossible! By contrast, you've only said that the story is contradictory. That's no explanation." I think this is a wrongheaded response. But now imagine the following. Suppose I tell the same long story about how Cameron Bertuzzi gets into a taxi, and while in the taxi he makes memes about classical theism being false, etc. Then, at some point later in the story, I say this: "now, God is going to flip a truly indeterministic coin. If he flips tails, then he makes it such that he never creates taxis. If he flips heads, he does nothing. And we are holding fixed the other portion of the story about Cameron's getting into the taxi [just as you needed to hold fixed the other part of the story that the set of grim reapers is infinite]." Now suppose I say: "Since there is no contradiction with God getting heads, the taxi-believer needs to maintain that there is a possible world where God get heads. But, since there is a truly random coin used, it seems that there should also be a possible world branching off where God gets tails. But getting tails yields a contradiction. So there isn’t such a possible world. So, the taxi-believer needs to have some way of barring the entire scenario." It seems to me that this second taxi story it just as wrongheaded as the first. The correct response for the taxi-believer is to say "you haven't given me any reason to abandon my belief in [the possibility of] taxis, since you've just described a contradictory scenario." Intuitively, moreover, I just don't see any force in the second story I told. And it seems structurally identical to the story you told, such that--for me--my epistemic evaluation of the latter is the same as the former. Hope *you*, my good friend, likewise have a nice day!!! :)

[@ApologeticsSquared]

​@@MajestyofReason Thanks for your reply! I was almost at the point of abandoning my objection because I found your reply to be so forceful. But I thought of something that might salvage it, so I would love to hear your thoughts! I think that you're right in that I can't ask you to hold arbitrary parts of a story constant, and change other parts. So I need to go a complete other route that doesn't make you do any such thing. So here's a reformulation of the argument that (as far as I can tell) doesn't ask you to hold any arbitrary facts constant. Here's the story: I have an indeterministic coin that if it lands tails, will cause infinity grim reapers to create a paradox (roughly in the same way I described in my previous post). Let W be the world where the coin lands heads. Now, W has no contradictions in it. There aren't any Freds who are both decapitated and not decapitated or anything like that. If you asked me, "Hey, are there any true contradictions in this world that we're in?" I wouldn't be able to tell you any. So, W is a consistent world. (By a "consistent world," I mean one that violates causal finitism, but contains no contradictions beyond that.) Now, without causal finitism, it seems that consistent worlds should also be possible worlds--there aren't any contradictions in W, so it seems totally possible! But... if W is a possible world, then any maximal world segment in W is also possible. Let W' be the maximal world segment which contains all of W up until I flip the indeterministic coin. If W' is indeed possible, then we should expect only possible worlds to follow from W'. But, an impossible world where the indeterministic coin lands tails (call this world V) can follow from W'. Contradiction! Here's the whole argument: 1) If causal finitism is successfully dodged with UPD, then any consistent world is a possible world. 2) W is a consistent world. 3) For any possible world X, a maximal world segment of X is a possible maximal world segment. 4) W' is a maximal world segment of W. 5) Only possible worlds follow from possible maximal world segments. 6) V follows from W'. 7) Therefore, if causal finitism is successfully dodged with UPD, then V is a possible world. (From 1-6) 8) V is not a possible world. 9) Therefore, causal finitism is not successfully dodged with UPD. (From 7-8) This gets around your taxi-coin-analogy story, because holding that there are taxis and that God is flipping a coin to choose whether or not to make taxis is not a maximal world segment. I think that I either have come up with a very intriguing argument or that some imprecision in my language will cause the whole argument to collapse. One of those two. :)

[@MajestyofReason]

@@ApologeticsSquared Thanks for *another* lovely comment!!! You are on a roll, good sir! :) [I do want to say that it's great fun talking with you. You articulate ideas *very* clearly and precisely, and you also *present* them in a non-tribalistic manner. And I'm all about such a presentation!] So, I guess I'm still not convinced. For why can't I simply parallel this *further* argument? Like: Here's the story: God has an indeterministic coin that if it lands heads, God wills to prevent the existence of taxis (at all) to create a paradox [with Cameron's having stepped into the taxi while it being the case that God--an omnipotent being--wills to prevent the obtaining of taxis]. Let W be the world where the coin lands tails. Now, W has no contradictions in it. There aren't any Camerons who both enter and do not enter a taxi or anything like that. If you asked me, "Hey, are there any true contradictions in this world that we're in?" I wouldn't be able to tell you any. So, W is a consistent world. (By a "consistent world," I mean one that violates 'taxi impossibilism', but contains no contradictions beyond that.) Now, without taxi impossibilism, it seems that consistent worlds should also be possible worlds--there aren't any contradictions in W, so it seems totally possible! But... if W is a possible world, then any maximal world segment in W is also possible. Let W' be the maximal world segment which contains all of W up until God flips the indeterministic coin. If W' is indeed possible, then we should expect only possible worlds to follow from W'. But, an impossible world where the indeterministic coin lands heads (call this world V) can follow from W'. Contradiction! Here's the whole argument: 1) If taxi impossibilism is successfully dodged with UPD, then any consistent world is a possible world. 2) W is a consistent world. 3) For any possible world X, a maximal world segment of X is a possible maximal world segment. 4) W' is a maximal world segment of W. 5) Only possible worlds follow from possible maximal world segments. 6) V follows from W'. 7) Therefore, if taxi impossibilism is successfully dodged with UPD, then V is a possible world. (From 1-6) 8) V is not a possible world. 9) Therefore, taxi impossibilism is not successfully dodged with UPD. (From 7-8) It seems to me that these arguments are well-nigh identical, and yet I think we rightly take my argument to be wrongheaded. I think the underlying problem is that--completely ignoring my taxi analogy--we still have an Unsatisfiable Pair in the initial description of W *itself* (and, also, W'), such that we have merely contradicted ourselves in the construction of the world. For, again, if the set in question [of reapers, in this case] is truly infinite, and the coin is truly indeterministic between O1 and O2, such that O2 is a scenario in which each P holds for each member of the infinite set iff P holds for no 'earlier' member of the set, then we’ve simply described a contradictory set-up from the get-go regardless of whether the coin lands in O1. If the coin is genuinely indeterministic, it doesn’t matter if we land in the no-contradiction-preserving O1 world; what matters is that-in describing the coin as genuinely indeeterministic-we have ipso facto committed ourselves to the possibility of O2. But O2’s coming to be is simply contradictory, since then we satisfy (A) and (B) of the original UPD [since then we have the infinite set and P holding at m (for any m) iff P holds nowhere ‘before’ m (where ‘before’ simply expresses the ‘infinite’ direction along the total ordering relation on the infinite set)] PS: Idk if you saw it, but at some point in this video, I give your channel a shoutout :) kzbin.info/www/bejne/iZjdm6yVfMlljJI

[@ApologeticsSquared]

​@@MajestyofReason Well, let's hope I continue on my roll! :) [And I also really enjoy this. I love cordial discussions on metaphysics, so I love your channel! :) ] To clarify things, if I'm talking about a premise or world or something from your analogous post, I'll add a hashtag (e.g. W#, V#, premise (3)#, etc.) and if it's from my post, I'll leave it unchanged. Now, I find it hard to understand precisely what you mean by, "God has an indeterministic coin that if it lands heads, God wills to prevent the existence of taxis (at all) to create a paradox [with Cameron's having stepped into the taxi while it being the case that God--an omnipotent being--wills to prevent the obtaining of taxis]." I know you aren't saying that God annihilates all taxies, because then V# is a possible world. So, it seems that you are saying that God wills that at no time there are taxis. So, at the moment God sees heads (we're assuming God is in time, right?), He wills to perform some sort of backwards causation, where He reaches back into the W'# and takes out all the taxis (since in W'# there are taxis), so that the world segment which leads to V# is both the taxi-containing W'# and not the taxi-containing W'#. Even if that's not what you meant, I think I understand that when God sees heads, He makes a contradiction actual (and the nature of the contradiction doesn't really matter). Now, if that's the right interpretation, then I can reject (1)#. To explain why, let's look at (1): 1) If causal finitism is successfully dodged with UPD, then any consistent world is a possible world. You can maintain that (1) is false if you add some other metaphysical principle in the mix, like Necessitarianism. A Necessitarian could say, "Yep! I endorse the UPD, but I don't think that any consistent world is automatically a possible world because there are a bunch of consistent worlds but there is only one possible world." Fine. That seems like a terrible way of rejecting (1) because Necessitarianism is, like, a bajillion times more of a commitment than causal finitism. But my point is, if you throw other metaphysical principles into the mix, then you can reject (1) without a problem. Now, it seems that I can dodge (1)# with a fairly uncontroversial additional metaphysical principle: God does not have the ability to bring about any contradictions. So, even though W# is consistent# (it doesn't violate taxi impossibilism (which is the best name of a metaphysical view ever) and it has no contradictions), I am not committed to the possibility of W# because it violates my extra metaphysical principle that God has no ability to bring about contradictions, and the description of W# includes that there is a God who has the ability to bring about contradictions. So, it seems that to dodge (1), then you need some sort of extra metaphysical principle. So, the Grim Reaper Paradox stands unless one can come up with such a metaphysical principle that is itself weaker than causal finitism. Also THANKS!!! That wasn't just a "Hey, nice channel." You said, "I don't know why he doesn't have more subscribers!" I really appreciate it! :)

[@ApologeticsSquared]

​@@MajestyofReason Another thought: The UPD seems to me to allow too much. Let's say "roundsquare possibilitarianism" is the belief in the possibility of machines which, if activated, could draw a picture of a round square. Now, the only way such a machine can produce a contradiction is if it is actually activated. If it's sitting in the corner deactivated, then there's no problem. So, the only way to bring about a contradiction is: A) There are machines that can draw round squares when activated. B) These machines are activated. Can't I just use the UPD to maintain roundsquare possibilitarianism? Sure, holding both (A) and (B) is contradictory. But holding just (A) isn't. Have a nice day! :)

[@blamtasticful]

We know it's getting interesting when Dr. Malpass drops some David Lewis!

[@PaulQuantumWales]

Alex is a great thinker. He's no Darth Dawkins or Saul Kripke but a fine guest nonetheless.

[@gotterdammerung6088]

You think Darth Dawkins is a brilliant mind?

[@carsonwall2400]

@@gotterdammerung6088 Of course! He's arguably the greatest presuppositionalist since Ken Ham!

[@gotterdammerung6088]

@@carsonwall2400 LMFAOOOO

[@carsonwall2400]

@@gotterdammerung6088 You mean you *didn't* read any of Darth's treatises in your symbolic logic class?

[@gotterdammerung6088]

@@carsonwall2400 Quit trolling

[@gianniryansmith614]

Malpass is the OG philosoChad

[@LogosTheos]

Dr. Malpass is a very careful thinker!

[@MajestyofReason]

Very true!!!

[@anglozombie2485]

@@MajestyofReason Has malpass ever said what he thinks about the beginning of the universe since he doesn't seem to be a big fan of oppy's intial state being necessary.

[@Mojo_DK]

Okay so I have a question in regards to the unjustifiable pair. I understand that the scenario A (an infinity) is not consistent with the rule B (do something if it has not been done one step prior) to put it simply. So the only thing that we can be sure of at that point that (AandB) is wrong. So either A is wrong, B is wrong or both are wrong/impossible. That are the options at that point. But we know that the rule B is something that can be done both in reality and mathematically. The rule is just to look back one step and check if the task you are suppose to do has already been done. So wouldn't that just mean that infinities in general (A) cannot exist in reality? That would resolve all contradictions. It also works well with science....the Planck length...the quantization of fields....and the hope to finally quantize gravity to unify relativity and quantum mechanics. So I basically don't understand how we can ignore the entire pair if the rule B is so obviously possible. Like isn't that the entire point of logic/philosophy? The same is true for the hight example right? A is taller than B or B is taller than A but not both can be taller. So either A is taller or B is taller. If we know which person is taller, we know which person is smaller. Yeah two things that can be true individually can in combination contradict each other. But once the example hits reality the contradiction still has to be resolved. If infinities exist then it is impossible to execute the rule (B) by some magic mechanism. But if infinities do not exist the rule (B) is possible and I don't see a reason that would make the rule (B) impossible. I would say that the rule (B) actually is possible. The time travel paradox is the same. Either I can time travel or I can shoot my grandfather. Shooting a person is clearly possible...so time travel is not possible. Yeah the pair is unjustifiable but the fact that one part of the pair is possible, still makes the other part impossible. And a last thought...even if we cannot tell if A is false or B is false, wouldn't that still mean, that there is only a 1/3 chance that infinities (A) are possible?...'cause either A is wrong, B is wrong or both....your opposition has no problem if A and B are both wrong at the same time...the point is just, that A is wrong.

[@pancakefist4716]

Hello, Joe. I am new to this channel but the content here seems beautiful and worth watching, I will watch it in my own time, as I am deeply interested in philosophy. I just have some comments on some things in this video. I would like to comment on "Causal finitism does not imply a finite past". Don't you think that one has to discuss the nature of time before making such a claim? For example, on an A-theory of time, or tensed theory of time, objects and events which are wholly present is all which exists, and the future comes after the present. So future events are caused by present events. Doesn't that make time a causal chain, and causal finitism applies to that chain, therefore a finite past? However, I think a consequence of this would be causal non-finitism, because if one accepts a tensed theory of time, every event has a preceding event which caused it, so when an object X begins to exist at time (Tn) on an A-theory, there is a time (Tn-1) at which the object did not exist, and time (Tn+1) at which the object exists. How does this lead to causal non-finitism? well, a finite past means that time itself began to exist. But how can time begin to exist on a tensed theory of time? if time began to exist , this means that there is an earlier time at which time did not exist. This is contradictory. There must be a past event causing a future event, but there is no past event causing the "first moment of time", therefore, infinite past, therefore causal non-finitism. I think Quentin Smith (an A-theorist) writes about this in his "Time, change and freedom". However, on a B-theory (tenseless time), I am not sure as its complicated. All events are equally real and there is no distinction between the past and present and future. So real change does not exist because if a banana was unripe at time T1, but ripe at T2, the banana did not really change and become ripe, because T2 existed and has always existed, T1 is just prior to T2, but T2 is somehow independent and uncaused by T1 because its a moment which always existed. So a finite past is not really a finite past because the first moment of time has always existed, and is equally real as all events on the timeline, time began in the sense that it is the first event on the timeline, just like the first point on a ruler, the ruler fully exists and all points on it are real, just like time as viewed by the B-theory. I think the B-theory just leaves us with an eternal changeless block universe, in which all events are equally real and independent, and to prove that an infinite past exists on a B-theory, we just need to prove that a set containing an infinite number of objects can exist. But I think I am misunderstanding something about the B-theory as I am not well-read on it. Can the B-theory account for something "beginning to exist"? Does the B-theory demolish the cosmological argument because it shows that an event cannot really "begin"? Perhaps you can help me out here, but I heard Dr. William Craig suggest that the cosmological argument can work on a B-theory. Second of all, does time exist independent of events (this view is substantivalism) or is time just the mere consequence of events causally or temporally related to each other (relationalism)? I think that this plays part in answering whether causal finitism results in a finite past or not. If we adopt relationalism about time, then yes, causal finitism does lead to a finite past, this is because time is not an independent substance, it is dependent on events, events causing each other is time, time is dependent upon change and events, if no real change exists, then no time. However, if we adopt substantivalism, this means that there is the possibility of an infinite past with causal finitism, because time is not dependent upon causes and change and can exist independent of causes. Thank you, Joe. I will be on the wait for your response and opinion on the topic of the nature of time and how it affects the cosmological argument. Keep going with the amazing content and thought-provoking discussions! :)

[@GeneralZod99]

There is something about Alex's appearance that I find appealing. I cannot quite put my finger on exactly what it is.... He may rise before Zod.

[@logos8312]

Good conversation as always! So I've been thinking about this unsatisfiable pair diagnosis solution, and I can't really get on board with it. I have a few reasons I think that way. 1. Direct solutions that explain why things don't work are better than indirect solutions, where we can swing it. 2. Causal Finitism solves other paradoxes which aren't formal contradictions, but do need a resolution nonetheless, and these paradoxes don't necessarily take the form excluded in the unsatisfiable pair solution. I'm thinking chiefly of the counting problem. 3. My model of solving the Grim Reaper Paradox is consistent with Causal Finitism, but actually is inconsistent with the unsatisfiable pair solution, which tells me the unsatisfiable pair solution is incomplete. So let me get into my solution to the Grim Reaper Paradox and go into these 3 points, hopefully they'll be clear. We're going to start with 3 first. The Grim Reaper Paradox has the following rules: (i) Fred is alive at the beginning (agree) (ii) Fred can only be killed by a reaper (agree) (iii) Multiple reapers can't kill Fred simultaneously (agree) (iv) Once dead, Fred stays dead (will be altered) (v) There are an infinite number of reapers (agree) (vi) The Reaper Rule (agree) What I'm going to say is that: while the unsatisfiable pair hypothesis says that it's the infinite reapers juxtaposed with the Reaper Rule that gives the contradiction, my solution will allow the infinite reapers, the Reaper Rule, and it just throws in another element by conjunction which resolves the contradiction. If the unsatisfiable pair hypothesis thought that (v) and (vi) were contradictory, then if that's true it should be the case that (v), (vi) and P is still a contradiction, for any proposition P. If I can find even one proposition P for which the contradiction dissolves, then it's not a contradiction in-and-of itself, so it won't work as a rule for dissolving all the paradoxes. To modify (iv) I'm going to add an extra element to the Reaper Paradox called an Angel, and an Angel has the following properties: (I) Angels can be any subsequence of indices occupied by reapers, (i.e. angels replace or "move" reapers, they are not "outside" reaper sequence). (II) An Angel will make Fred alive if Fred is not already alive, (just taking the same reaper rule and applying it to angels). (III) There can only be a finite number of sequential reapers, and a finite number of sequential angels at a time. In other words, the following rules apply: (i) Given a reaper, it is a finite number of indices away, in either direction, from an angel. (ii) Given an angel, it is a finite number of indices away, in either direction, from a reaper. Putting this together means that the infinite sequence can be organized like: ... -> (finite sequence of reapers) -> (finite sequence of angels) -> (finite sequence of reapers) -> ... Now, does this solve the paradox? Yes. Normally: 1. Suppose at some index k, Fred is dead. 2. This means that Fred is killed by some prior reaper. 3. But in order for this prior reaper to kill Fred, Fred would have to be alive, meaning the reaper before IT would kill Fred, ad infinitum. C. Fred is never killed by a reaper because the previous one should have done it already. Now: 1. Suppose at some index k, Fred is dead. 2. This means hat Fred is killed by some prior reaper. 3. The sequence of reapers with a reaper rule is finite before some angel appears. 4. As of that Angel, Fred is alive, made alive by the first in the sequence of angels. C. the first reaper after the last angel kills Fred. Repeat for the case where Fred is alive. So this solves the paradox by dissolving its contradiction. There are an infinite number of reapers, the reaper rule still applies. All we've done is add MORE things to the sequence with yet another variation of the reaper rule (a paradox lands if Fred is dead and is encountered by in infinite sequence of Angels). This means that, under the unsatisfiable pair hypothesis, my solution shouldn't be a solution. Because my solution is of the form: infinite reapers, and reaper rule, and also angels. The rules involving the angels are my "P" such that conjoining P to the infinite reaper / reaper rule conjunction failed to produce a contradiction, so it must be that those two by themselves weren't sufficient to do it. It also turns out that the angel rules are consistent with causal finitism, since every point in the angel sequence has a finite causal history, and likewise with the reapers. What we have, though, is an infinite number of causal histories (each with finite nodes) alternating back and forth such that each is independent of the previous and independent from the next (so you can't just glue the chains together and go AHA!). This is causal finitist solution through and through. Bonus 1 for this solution: Consider the counting problem. You see someone counting "-5, -4, -3, -2 -1, 0!" and they say they've been counting from -infinity. What's the reason, in principle, that they stop counting at 0 when you see them? It can't be their rate of counting, nor when they started, since each of those things would be finite. But this is nonetheless a nontrivial question that demands an answer, and an answer that the unsatisfiable pair solution isn't equipped to give, but my causal finitist solution is. Consider instead that the person was counting: "-32,334, -23,445,223, ..., 0!" Then the person is counting purely at random, and the randomness juxtaposed with their rate and starting time will get the explanation needed. But how is this consistent with my solution? In the reaper case, Fred is alive or dead, so the outcome is binary, but what's important is that the angels "reset" the causal priority. Suppose in more advanced versions of the paradox with a plurality of results, the angels reset the causal priority by adding a stochastic element to it. Here's an example using the Grim Messenger paradox. Suppose that we have the same angel rules as before, but owing to this paradox, we give angels another job. New angel messenger rule: Each angel takes the message, erases it, and adds a new number at random before passing the message on. So, given a finite sequence of angels, at the end of that sequence, a random number will be handed to the next reaper, who follows its rule and hands the number to the next, and so on, until the next angels are reached. Due to the random nature of the angels resetting the number, juxtaposed with the finite uninterrupted sequences of reapers, this paradox too is avoided, AND it ends up having a very similar solution to the counting problem paradox, even though the Grim Messenger paradox has a grim reaper rule (in its unsatisfiable pair) but the counting paradox does not (and thus isn't in the jurisdiction of the unsatisfiable pair hypothesis). The final thing I like about this is that it's direct and concrete. Rather than throwing our hands up and saying "well, just seems these two don't work well together, but exactly why is mysterious!" we can say "it seems the way to get these two to play nice is to ensure there's some extra rule that looks like this... and it works because... and it can be adopted to any paradox by...". To the extent that causal finitism is costly (I'm still pondering whether time must be discrete under this framework, or merely causally measurable in a measure theory sense) I think the clarity and concreteness in the solutions it provides make up for it and then some. My instinct is to look at the extra costs one at a time and see if they're really things you have to commit to on the model.

[@Brunofromaraguari]

I think the problem to invert the paradox to deny the infinity future is that even if the future is infinity, it is just potentially infinity. Because an infinity future is never complete, it just mean that it will be add to it one more day again and again. So infinity future is not exactly a real infinity, it is just an eternal incomplete series of events. The past, otherwise, is really infinity if it regress timeles. That's why I think the point of grim reaper paradox is not just about infinity regress, but about actual infinities. And as an infinity future is not an actual infinity, but just potential (because it never completes itself) the paradox can not apply to it. Even if you invert the paradox to mean that a rapper can't do such thing if there is a future condition.... But I think denying infinity past regress using this paradox it would be the same of denying the existence of moviment because of Zeno's paradox, because they are very similar paradoxes

[@MajestyofReason]

Thanks for the comment! (1) I respond to this potential infinity point elsewhere in this comment section, so check out my responses there!🙂 (2) more importantly, I explain in my recent video “Hilbert’s Hotel: A Comprehensive Response” why an endless future is an *actual*, rather than *potential*, infinite. I recommend checking that out❤️

[@Brunofromaraguari]

@@MajestyofReason thank you. :) I will check it.

[@VeNeRaGe]

Love everything that you do. Your attitude is awesome, it's always a pleasure seeing you!!!

[@MajestyofReason]

I appreciate you

[@carsonwall2400]

Joe coming in clutch with the great content

[@alittax]

Thank you for your awesome videos!

[@Sveccha93]

Kills 99.9% of paradoxes 🤣🤣🤣

[@physics_philosophy_faith]

This was a super helpful and insightful and fun discussion. Is there a good paper that shows how to do the abstraction to prove a logical contradiction before applying any given scenario like time or causes or anything? "The Form of the Benardete Dichotomy" by Shackel? That looks like it attempts to abstract a general form.

[@MajestyofReason]

Thank you!!! The two derivations I know of are Shackel (2005, pp. 400-401) and Malpass' paper under review. :)

[@physics_philosophy_faith]

@@MajestyofReason Awesome, thank you so much!!

[@folamialamudun1915]

I think the Grim Reaper paradox is invalid. We are focusing on the infinite grim reapers and completely ignoring fred. Unless you are dissociating time, i.e. t_fred and t_reaper are two independent continuums, the paradox is only an apparent one. Observe: If we assert that there are infinite gradations of moments on the reaper side of the equation, which gives us the infinite number of reapers. This infinity holds if and only if there are infinite gradations of moments on Fred's side of the equation too. The two paired possibilities are: There are infinite reapers and Fred never moves because there is an infinite gradation of moments between the initialization of this experiment and Fred's movement; or there is a finite number of reapers and Fred moves because there is a finite gradation of moments between the experiment and Fred's movement. Either way, i feel this is a very bad objection to infinite causal chains. Not that I believe the latter is logically valid.

[@homeyjeromy]

Could it be the case that the reason the GRP is impossible is because of how it attempts to apply infinity to something that is finite? It seems to be setting up an impossible scenario and them demanding that it be possible. This is to say the infinite set of grim reapers are assigned only one person to kill, and each grim reaper has infinite competition that will kill the person before they will. This makes it impossible for any individual reaper to win, and yet the scenario demands a winner. If we keep all of the rules of GRP, except now: each grim reaper is assigned their own person to kill at a particular time, and if any grim reaper fails to kill their assigned person, the next grim reaper in line will kill that person instead. So it would look like: GR1 --> P1 GR2 --> P2 GR3 --> P3... If GR1 fails to kill P1 at the assigned time, then when GR2's time comes, it will kill P1 instead, and GR3 will kill P2 and so on. In this modified version there is no longer a contradiction. It will still be the case that every person is killed, even in the event that an infinite amount of grim reapers fail to kill their assigned person. It seems to me, if the problem can be solved soley by introducing another infinity, then the problem with GRP to begin with, is how it attempts to apply infinity to a finite object. Let me know what you think.

[@m.l.pianist2370]

Hi Joe, I don't know if this question is dumb, but regarding the unsatisfiable pair diagnosis, what's the explanation why the pairs are unsatisfiable? In Eulerian circuit example, there's a mathematical explanation. In the taller-than example, there's an explanation involving the logical properties of the taller-than relation. It seems unsatisfactory to merely point out that two conditions cannot both obtain without providing an explanation. Am I missing something? Thank you for the consistently great content that you put out!

[@MajestyofReason]

Thank you for the lovely comment! So, I think the explanation for why the pair is unsatisfiable would just be the logical proof that it entails a contradiction. It's just like the case of the mathematical proof of the Eulerian circuit example, but this time it's a logical proof. The proof is a bit too complex to copy and paste here, but Alex includes it as an appendix in his paper on this (the paper is currently under review). :)

[@MajestyofReason]

Each is individually possible, but their conjunction alone entails a contradiction! It's just like how each of these is possible, though their conjunction implies a contradiction: (1) Alex is taller than me; (2) I'm taller than Alex.

[@m.l.pianist2370]

@@MajestyofReason Hi, sorry I deleted my previous reply, I thought my question was confused. Thanks for answering it anyway, haha! :) I guess what I have in mind is that "I'm taller than Alex" and "Alex is taller than me" aren't explicitly contradictory, and so further premises are needed to bring out this contradiction. If this is right (I'm not sure that it is!) then what would the crucial premise be that leads to an explicit contradiction?

[@MajestyofReason]

@@m.l.pianist2370 Well, so long as we define our terms (i.e. 'taller than' will be defined such that it's an asymmetric relation: a's being taller than c entails the falsehood of c's being taller than a), then we don't need a further premise. It just falls out of the meaning of 'taller than' plus the LNC. The deduction for the incompatibility of (A) and (B) in the UPD doesn't require any further premises beyond (A), (B), and the classical rules of inference like modus ponens and the LNC. [the latter of which technically isn't a rule of inference]

[@m.l.pianist2370]

@@MajestyofReason I see, that clears up my concern!

[@TheLilKimooo]

@Majesty of Reason i feel like im missing something here, isnt the whole point of the paradox was to prove that an infinite past and causality are unsatisfiable? It seems to me like what the unsatisfiable pair did was to emphasise causal finitism rather than offer an alternative. What am I missing?

[@craigmcloughlin9361]

Absolutely loved this, thank you both. Can someone point me in the right direction on which bit of Hulme's work the term "Hulmeian Modesty" references? (t=3888)

[@davec-1378]

Zeno’s paradox of motion

[@d.f.4489]

Hey Joe when's the project going to be done concering Ed Feser's 5 proofs for the existence of God? I hear those arguments every single time, multiple times, when engaging in discussions and I don't really have good objections.

[@luizcarlosrviana3724]

18:22 Isn't Alex assuming some form of Pythagoreanism or structural realism here? To say that space and time are continuous is *not* the same thing as to say that there are such things as concretely existing independent points which have causal powers, unless you assume that mathematical structure exists in reality much in the same way that it exists in the mind, and that this structure can stand in causal relations with other concrete objects (which to me seems a very weird commitment to have). A causal finitist could say that space and time are continuous *in the sense that* given any concrete spatio-temporal distances between distinct concrete regions of space-time (defined up to finite measurement precision, rather than as abstract indivisible "points") we can divide these distances into smaller distances either (1) in a purely theoretical mathematical way, as a mental experiment, or (2) physically. Points are then just a mathematical abstraction for this process of division, and do not concretely exist, nor have causal powers. The same could also apply for abstract velocity and acceleration vectors and for any other sort of abstract mathematical structure. So it just doesn't follow that a causal finitist is in any way commited to the idea that space-time consists of a finite number of points because he doesn't have to grant that space-time is concretely being composed of actually existing individual points (endowed with causal powers) to begin with.

[@MajestyofReason]

I think that's our point, though. The point is precisely that causal finitism entails that time isn't continuous, i.e. that there do not actually exist these distinct points. Sure, the Aristotelian view is one way of working this entailment out, but that it is an entailment is all that Alex was trying to emphasize (and Pruss essentially agrees with Alex here). And this is a theoretical cost, since it commits one to an additional claim about the structure of spacetime (such additional ontological baggage is not needed by the UPD).

[@HyperFocusMarshmallow]

A way of putting these paradoxes is to compare them to solutions of equations. You can have an equation for x with a solution and then another equation for x with a solution but yet there is no x that’s a solution of both. Is that surprising? The “Causal finitism” route seems to solve it by saying we can’t have one of the equations ever. Problem solved. But you don’t need it. If you get a contradiction from two assumptions then that combination doesn’t work but the assumptions might work on their own or in combination with other assumptions. Same as with the bridges of Königsberg and square circles etc. The bridges of Königsberg could be solved though if there is teleportation. Or helicopters.

[@KamikazethecatII]

It seems actually fairly plausible to me that the Stoics might have stumbled on a similar problem since they believed in the conflagration

[@ceilingspirits1592]

Question: when you mention that causal finitude could be true but the past could be infinite I wonder how those overlapping causal chains would relate to each other. What causes each series? Thanks

[@chad969]

This should be good!

[@helsharidy123]

This is amazing!

[@goldenalt3166]

The funny thing about the time travel scenarios, is the contradictory assumption that time travel is possible and yet causality is purely past-> future. Paradoxes are geometrically impossible, just try to draw one in a comic strip. It is only by introducing another time dimension that you could have one space-time point with different contents.

[@richardguyver6676]

I came here via Rationality Rules and his Kalam debate with Cameron. Really interesting. Out of interest if someone was studying philosophy, at what level in their study would they likely study unsatisfiable pair diagnosis/causal finitism etc? Thanks

[@MajestyofReason]

Thanks! So, I think it depends on what specific area/domain of philosophy one is studying. If one is studying epistemology, say, then causal finitism and the UPD will never come up. But if one is studying philosophy of religion--and if, in particular, one is studying the Kalam in the philosophy of religion--then one will pretty quickly come upon causal finitism, UPD, and whatnot. Hope this helps!

[@CMVMic]

Thanks for this! Where's Oppy though?

[@anitkythera4125]

Joe...it's videos like this that make me want to employ a team of mechanical Turks to create an infinite set of KZbin accounts for the express purpose of giving this more than one thumbs up...but each Turk can only give a thumbs up if the Turk to his left gave a thumbs up...

[@MajestyofReason]

ahahah much love

[@anitkythera4125]

@@MajestyofReason seriously Joe, Your intelligence combined with your guileless enthusiasm.and ability to articulate complexity and is a boon to humanity...or at least to the subset that interacts with you ;-)

[@romanbesel4759]

Very nice that you got Alex on to speak about this topic in detail. I find the GRP not easy to understand and so this helps me a lot. Thanks for doing this channel, keep up the good work!

[@MajestyofReason]

Much love

[@moonhouse3540]

Woohoo!!!! Can’t wait to get off work so I can listen to this!

[@richardjb25]

Alex /Joe; How does Graham Oppy's (favorite?) theory of modal possibility relate to causal finitivism.

[@MajestyofReason]

Good question. The branching/Aristotelian view of modality which Oppy favors is actually independent of the truth or falsity of causal finitism! If past causal chains are finite, it will still be the case that possibilities are simply what could branch off from the actual past. And if past causal chains are infinite, it will still be the case that possibilities are simply what could branch off from the actual past. :)

[@richardjb25]

@@MajestyofReason Thanks for that. Hopefully you didn't have to hold Oppy's toes to fire in order to answer this.

[@williamkeller5541]

I am unsure about the argument that the Grim reaper Paradox implies the end of the furure. If the argument does work does it mean that causal finitism implies the end of the future or that a certain version of the grim reaper Paradox implies an end to the future or are they the same thing?

[@MajestyofReason]

This is an excellent question. Out of the three options you presented, it is the second one. Essentially, Koons (2014) uses the GRP to argue for the finitude of the past (where a GR kills Fred iff no earlier/past GR does). Alex and others have argued that the argument can be run in the other direction (where a GR kills Fred iff no later/future) GR does. So, it's not that causal finitism entails the finitude of the future ( I don't think it does--you might want to check out my discussion with Elephant Philosophy :) ); rather, its that the GRP can arguably used to equally justify an infinite future.

[@williamkeller5541]

@@MajestyofReason Ok. This is what I was hoping. I think Causal finitism is true but I am not sure I buy the grim reaper Paradox as evidence for it. If one accepts the paradox could one run an argument for athiesm that would argue that if God is necessary in time and that time will come to an end God would cease to exist. Since God could not cease to exist he does not exist. Once I typed it out it seems less promising than I originally thought. Do you think the idea behind it might work with a little polishing?

[@MajestyofReason]

@@williamkeller5541 That would be very problematic if God is necessarily in time. It's a good thought, and it would be interesting to explore how this interacts with other views on which God isn't necessarily in time. I've puzzled over whether God might be temporal until the end of time, and then--somehow, mysteriously, perhaps unintelligibly--'transition to' or 'become' timeless upon the end of time. So, it's like WLC's view but w.r.t. the end of time. I'm not even sure this makes any sense (since I'm not sure WLC's view makes sense), but it's certainly ripe for investigation!

[@williamkeller5541]

@@MajestyofReason Thanks for the response. I really appreciate your time.

[@HyperFocusMarshmallow]

Do you guys have a good list of sources, to get into this topic. I have a physics background so I might need to get a bit of guidance on the philosophy.

[@MajestyofReason]

An excellent place to start is Mike Huemer's "Approaching Infinity" :)

[@HyperFocusMarshmallow]

@@MajestyofReason Thanks!

[@dimazhyvov170]

TREMENDOUS!! LOVED EVERY BIT OF IT!!!!

[@howlong1248]

if god can't whisper secrets to grim reapers it would seem to undercut any possibility of prophecy.

[@williamlight2393]

MOOOOOORE! WE NEED MOOOOOORE! nice talk :D

[@vincentiormetti3048]

Great convo, lots of food for thought

[@tionarry]

Have you ever tried getting Dr Craig or Dr Pruss on?

[@MajestyofReason]

Pruss, unfortunately, doesn't generally do KZbin discussions. And Craig is very hard to reach, but I could try at some point!

[@matthieulavagna]

So far so good! Joe, what is your view on the nature of time? Do you believe it is discrete or continuous?

[@MajestyofReason]

I need to study that question in far more detail to have a considered view! The literature there is massive and highly technical lol.

[@matthieulavagna]

@@MajestyofReason I'm sure it is. If I'm not mistaken, paradoxes like the grim Reaper or Thomson's lamp tend to show time has to be discrete. This is my view for the moment. I believe that it would also be tough to solve Zeno's paradox if time is continuous.

[@MajestyofReason]

@@matthieulavagna That is one motivation that some philosophers cite. There are some plausible considerations favoring both sides, and defenses of both sides against the allegations of the other! I can't take a firm stance on this issue without looking into the literature in some depth. I'll do that at some point in the future [ or maybe some discrete moment in the future rather than a point! ;) ]

[@matthieulavagna]

@@MajestyofReason lol, nice one! I'm getting Pruss' infinity causation paradox and Oppy's arguing about Gods for Christmas btw😛

[@eytanscher8674]

Thanks so much this was great! I'm a big amateur but when I think about your A is taller than B and B is taller than A example it strikes me differently than the GRP. In a possible world that "A is taller than B" doesn't that by definition mean that B is shorter than A? so by saying there's a possible world where "A is taller than B" you're also saying B is shorter than A. It's a contradiction in definition to not say that second part. Isn't that different than the GRP? I don't see how the "no beginning" proposition definitionally contradicts the P conditional added. It seems that the contradiction "arises" as a consequence of the putting the 2 together. I feel like that I didn't make sense but maybe your smart brain will understand what I'm struggling with :)

[@MajestyofReason]

Thank you for your comment! So, I think the reason for some of your reservations [which are wonderful! I can tell you're a truth seeker :) ] is that the contradiction between conditions (A) and (B) isn't immediately self-evident. For our primate brains, we can't automatically and immediately see the contradiction. But it is most definitely there, since it can be demonstrated via formal proof! So, just as when one says "A is taller than B" one thereby says that "B is shorter than A", it is also true that when one says that "condition (A) is satisfied:, one thereby says that "condition (B) is not satisfied" (even if one does not realize this).

[@eytanscher8674]

@@MajestyofReason Thanks for your kind words and I'll definitely mull that over. If you're correct then what do those smart people like Pruss say to that?!?!?! It seems so obvious with your height example that there is no need for a mysterious force lol.

[@MajestyofReason]

@@eytanscher8674 I think there's lots of room for reasonable disagreement. Maybe we shall see what Pruss says in response to Alex's article once it's published! :)

[@New_Essay_6416]

love u Joe

[@blbphn]

Can someone please explain to me how it makes to say both that "no particular G kills S", and, nevertheless, "S is necessarily killed (by some G)"? Why not rather say, "If no particular G kills S, then S is not killed (by a G)"? (For only a particular G could kill S, as there are no non-particular Gs, assuming that the infinite series of Gs is a series of particular Gs.) And if it is the case that "S is not killed", then where is the paradox? No G kills S, and S is not killed -- seems perfectly consistent. What am I missing?

[@MajestyofReason]

Thanks for the comment! :) I think your analysis misses the fact that S is certainly going to be killed. So, the paradox is: "No G kills S, and so S is not killed, but S is also killed". Why is S also killed? Because think about what would have to be true if S *isn't* killed. S would be surviving until 1 am. But for S to survive to 1 am, the reaper at 12:30 would have already killed S!

[@blbphn]

@@MajestyofReason But (back to Zeno) doesn't "S is certainly going to be killed by 1 am" already assume that an infinite series can be exhaustively realized (which seems be the very point in question)?

[@blbphn]

@@MajestyofReason In other words, if S is to reach 1am (be it dead or alive), either finitism is true or an infinite series can be exhaustively instantiated. Now no contradiction is entailed on finitism, but a contradiction does seem to be entailed on infinitism. Isn't that the fundamental issue?

[@blbphn]

@@MajestyofReason Just to add a little more (sorry!), you state: "S would be surviving until 1 am." But IF, in order to reach 1 am (dead or alive), an infinite/unending/inexhaustible series of temporal moments is exhaustively traversed (exhausting an inexhaustible), then there seems to be a straight forward contradiction. How can this conclusion be reasonably avoided? But on finitism (discrete space/time) there is no such contradiction (making it the better theory). So, if finitism is true, then S is killed at 12:30. But if infinitism is true, then 1 am can never be reached (since an inexhaustible series of moments cannot be exhaustively traversed). In fact, if infinitism is true (here in the sense of a temporal continuum), then, starting from any moment in time, there is (by definition) no next point to go to. It logically doesn't exist. So, if the traversal is to be sequential and continuous, then the traversal can not even begin, for there is never any next moment/point; it is logically undefined. Thus, continuous movement through space/time would be logically impossible if infinitism (continuous space/time and exhaustive traversal through it) were true. Where has this analysis gone wrong? Thanks!

[@goldenalt3166]

To me it looks like the continuous probability distribution. The probability that any given value is chosen is 0 but the sum of all is 1. Just because you can't identity a reaper doesn't mean there isn't one.

[@GodOfThe]

Hello

[@LouigiVerona]

Am I the only one who doesn't understand why the pair is unsatisfiable? Can someone please explain?

[@MajestyofReason]

So, recall the pair: (A) the set is infinite, e.g. {..., -5, -4, -3, -2, -1, 0} (B) property P holds at member m [for any member m] of the infinite set iff P holds nowhere before m in the set (where 'before' refers to 'earlier' members within the ordering relation. So, in this case, it would be all the negative numbers below a particular given number. So, if we let m = (-3), then 'before m' refers to -4, -5, -6, -7, -8, and so on.) So, with these two in mind, we can get a contradiction. Here's how that goes. Pick some arbitrary member, n, from the infinite set. Now, by (B), P holds at n iff P holds nowhere before n. (1) Suppose P holds at n. Then, P holds nowhere before n. But then consider the member located immediately before n. Call this member n*. Does P hold at n*? Yes and no. [Which is a contradiction]. Why yes? Because by (B), P holds at a given member iff it holds at no previous member. But in the case we've been considering, P holds nowhere before n*. This is because P holds nowhere before n, and a fortiori it holds nowhere before any point located before n [and, you will recall, n* is one such point!]. So, P holds nowhere before n*. By (B), it follows that P holds at n*. Why no? Because we assumed that P holds at n. In which case, by (B), P holds nowhere before n. But n* is before n. Therefore, P does not hold at n*. So, we have a contradiction: P holds at n*, and P doesn't hold at n*. So, by assuming P holds at n, we derived a contradiction. But n was just an arbitrary member of the set. Thus, our conclusion is perfectly general, holding for all members of the set. It is a contradiction to suppose P holds at any member of the set, since we assumed it held for some member (labeled 'n') and derived a contradiction. So, P holds *nowhere* in the set. (2) But... if P holds *nowhere* in the set, then a fortiori it also holds nowhere *before* member m in the set. [For some member m.] By (B), it follows that P holds at m. Contradiction! We just showed that if P holds nowhere in the set, then it holds somewhere in the set. So, either way, we get a contradiction. We began by assuming P holds at some member in the set. We got a contradiction from that. [This happened in (1).] But then we assumed that P holds at *no* member in the set, and we similarly derived a contradiction. [This happened in (2).] So, either way--whether P holds at some member of the set, or whether P does not hold at some member of the set--we get a contradiction. So, we get a contradiction from assuming the conjunction of both (A) and (B). Hope this helps!

[@LouigiVerona]

@@MajestyofReason Huge thanks for that! Now I get it! Would it also make sense to link to Alex's paper in the description of the video? And again, thank you for taking the time to explain.

[@MajestyofReason]

@@LouigiVerona Much love

[@LouigiVerona]

@@MajestyofReason Ah, got it! :)

[@crabking6884]

Nice! I had to watch this video over several days so my memory of everything in this video is kind of all over the place. Where would I be able to find more papers on this subject? One more question, this is only somewhat on topic, but what would you say about the objection to the Kalam that says “god’s will is eternal so that means the universe has to be eternal”. I know Aquinas has responded to this objection, but whenever I ask a Thomist what Aquinas means in his response, they don’t even completely know what’s he’s saying, they just copy and paste the passage thinking I’ll be convinced.

[@MajestyofReason]

So, Koons (2014) "Revenge of the Grim Reaper" and Pruss (2018) "Infinity, Causation, and Paradox" are relevant. They'll be quite technical, though. Alex's paper on Grim Reaper Paradox and Mysterious Forces is currently under peer review, so it can't be shared (there is some probability--I know not what--that if you email him, he will send you a copy). Finally, this has some helpful, accessible sections: www.academia.edu/5188902/Gods_Existence

[@Midzyful]

This just seems like special pleading. Imagine if Cantor said to Russell. Naive set theory is correct. The only problem is you are combining sets and self reference. There’s no problem with the rest of the sets.

[@MajestyofReason]

This is a valuable point. But now imagine if someone said all self-reference is impossible. (Or, alternatively, all sets are impossible). Surely that's not the right solution. But that's precisely what causal finitists do with condition (A): they jettison the entire condition wholesale as impossible. So I think your analogy might cut both ways here. I'm also not sure if it's analogous at all. From my very limited understanding of the history of mathematics, the very *axioms* of naive set theory jointly entailed contradiction. So, one can't just say "oh, the problem is when you combine them; the rest is fine." The very foundations of the theory, the very axioms, entailed contradiction. And this isn't resolved by saying that their combo simply cannot be true, since if p is an axiom of system s, then according to s, p is true. This is part of what it means to be an axiom in a system. Hence, if two claims, p1 and p2, are both axioms of some system s, then s requires that both p1 and p2 be true. And if p1 and p2 are both true, it automatically follows that their conjunction is true. So, if it can be shown that their conjunction is actually contradictory, so much the worse for the system--the system itself entails contradiction. You can't just say "oh, we just won't combine p1 and p2", since such a combo is strictly entailed by the system + the rule of inference known as conjunction introduction. But this isn't what's happening with the UPD at all.

[@Kanendd]

Great discussion 👌