tag:blogger.com,1999:blog-3891434218564545511.post4731049539978917715..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: From the Grim Reaper paradox to the Kalaam argumentAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger70125tag:blogger.com,1999:blog-3891434218564545511.post-24882570886202839962020-11-02T14:40:51.444-06:002020-11-02T14:40:51.444-06:00@Ross. Well, I have not read the book, nor is the ...@Ross. Well, I have not read the book, nor is the book in the post above. I do not however consider the fact that subsequences between two points of sequences are never infinite even if the sequence itself is infinite to be a paradox at all. Its a rather trivial mathematical observation. But as I say above, it doesn't really prevent infinite causal sequences in finite time, nor does it deal with anything other than causal sequences ie causation that follows a countable sequence of distinct points in time. The very fact that we are talking about infinities over finite periods of time would suggest a continuum rather than discrete functions. There is nothing preventing a form of causation that is ordered in time and infinitely divisible over a finite period. In fact the equations of quantum dynamics are continuous not discrete so this would seem to be the expectation. The problem with bringing quantum dynamics into the picture however is that if you were to try to divide it up infinitely you would not be able to find out anything about it beyond a given resolution (plank length) even if, in reality, such an infinitely divisible causal function exists. Quantum mechanics suggests that the vast majority of events are either uncaused (random) or we simply cannot determine the cause due to the nature of the physics involved, and all other events are a combination of the consequences of these possibly uncaused events. If time is finite in the past then there are two possibilities, it is a closed set and had a single point in time where it started and there was a first event, or it is an open set with no first event.<br />Timothy Whiteheadhttps://www.blogger.com/profile/11646757021200031878noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-24251607412126737032020-11-02T13:31:02.574-06:002020-11-02T13:31:02.574-06:00TW:
The paradox is only one of many I consider. T...TW:<br /><br />The paradox is only one of many I consider. The main thought in the book is that the hypothesis that there are no infinite causal histories kills *many* paradoxes in one fell swoop. You're right that if this paradox were the only one, it would at most establish that we cannot have an infinite causal chain between two events. But the latter hypothesis is insufficient to handle some of the other paradoxes in the book.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-56236651829218561072020-11-02T12:11:47.629-06:002020-11-02T12:11:47.629-06:00A slightly more formal analysis than my previous c...A slightly more formal analysis than my previous comments:<br /><br />The basic apparent paradox is built on the fact that in an infinite sequence there is never an infinity between any two terms. But that does NOT prove the sequence is not infinite. So although I agree that there cannot be an infinitely long causal chain BETWEEN two events, it does NOT prove that causal chains cannot be infinite.<br />Of course the original post only refers to subdividing causality infinitely, it does not deal with the possibility of an infinite past timeline, nor does it deal with the possibility of a bounded timeline that is nonetheless infinitely divisible eg if time is the open set of times after 11:00am.<br />And finally, there is the assumption that causation is pointlike and thus countable ie there is a definitive list of a causes b causes c etc. I am sure that with some thought one could come up with concept of causation that did NOT require countability or exhibit pointlike behavior and could thus be uncountably infinite.<br /><br />Food for thought:<br />The set of rational numbers is countable. That means that we can find a sequence such that any given rational number has a previous number and a next number in that sequence. The sequence is infinite. But it is apparently NOT possible to create such a sequence that follow size order. Between any two rationals you care to pick there is always another rational. The hard part is given one rational, can you find the next biggest rational in the sequence? Does no such number exist?Timothy Whiteheadhttps://www.blogger.com/profile/11646757021200031878noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-59524462223926702472020-11-02T11:42:18.832-06:002020-11-02T11:42:18.832-06:00Hallo Mole,
If educated assumptions work, why wou...Hallo Mole,<br /><br />If educated assumptions work, why wouldn't you make those? Because there are "just" assumptions?<br />There is a fine difference between educated assumptions and "just" assumptions. The difference is, that educated assumptions tend to work most of the times. If they wouldn't work, then they would be adjusted, till they do work. You can't state that also for "just" assumptions.<br /><br />Also here is an infinite causal-chain for you without any contradictions:<br /><br /><b>After a chicken comes another egg.</b><br /><b>After an egg comes another chicken.</b><br /><br />So where is the contradiction in that infinite causal-chain. Why would it be impossible, if there is no contradiction in that infinite causal-chain?<br /><br />Best regards, <br />Zsolt NagyZsolt Nagyhttps://www.blogger.com/profile/11519070636926516031noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-21967171111808364242020-11-02T08:15:00.147-06:002020-11-02T08:15:00.147-06:00@Mole
I'll ignore your unnecessary rudeness fo...@Mole<br />I'll ignore your unnecessary rudeness for now.<br />Regarding infinite causal chains, all this is is rehash of Zeno's paradox (Achilles and the tortoise). So is it your claim that that paradox proves that time is not infinitely divisible?<br />Unfortunately he has NOT demonstrated that there cannot be an infinite causally related sequence. A sequence may be both infinite and bounded. He does not seem to understand this most basic finding in mathematics. It is this same issue that Zeno's paradox plays with. It presumes an infinite sequence that is bounded by but does not include a point then points out that the point is not part of the sequence. Interesting, but not a paradox. The paradox occurs when you demand that the point IS part of the sequence. But this is a problem with your demand, not with the mathematics.Timothy Whiteheadhttps://www.blogger.com/profile/11646757021200031878noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-86731305356737706152020-11-02T07:35:58.382-06:002020-11-02T07:35:58.382-06:00There is no "approximate determinism" th...There is no "approximate determinism" there is only determinism. The moment you add randomness to a decision or a result, even one which is 99.99% on one side, it becomes undeterministic. A good way of understanding why this should be obvious is that there is no clear threshold probability p we can choose so that only upto p things are undeterministic. <br /><br />We collect information about people only because we are operating under some assumptions and models of determinism which are only approximations. Predictions of consumer behavior is based on machine learning models and if you've taken a course in ML you'd have learn how much these things are based on so many assumptions and giving different extents of probabilistic confidence. <br /><br />And please don't randomly throw in pop culture speculations on quantum computing.Molehttps://www.blogger.com/profile/06314516106468362013noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-25523918370266809732020-11-02T07:24:10.254-06:002020-11-02T07:24:10.254-06:00"If your argument were valid, then you would ..."If your argument were valid, then you would have demonstrated that there isn't an infinite number of points in an interval"<br /><br />No. He doesn't claim to do that. There are different kinds of infinities and this paradox gives evidence that there cannot be a infinite causally related sequence. Numbers are abstract objects and do not stand in causal relations. LOL @ you saying that this isn't already published works, instead of being grateful that important works in philosophy are being discussed by the author himself on a blog site. He's literally written a book on this published by Oxford and it seems you are the one who needs some reading on the philosophical implications of the existence of infinities. It's quite striking that you're ignorant of the fact that actual learned philosophers who disagree with Pruss still don't respond with the nonsense Muh Number Line Objection. <br /><br />If you want to learn more read the published works. Btw, here's a post by an atheist philosopher who disagrees with Pruss and doesn't respond with these childish objections.Molehttps://www.blogger.com/profile/06314516106468362013noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-33220525948131220202020-11-02T02:38:28.069-06:002020-11-02T02:38:28.069-06:00You have NOT demonstrated that there cannot be an ...You have NOT demonstrated that there cannot be an infinite sequence of events. You have merely demonstrated that dealing with infinities is difficult and confusing. If your argument were valid, then you would have demonstrated that there isn't an infinite number of points in an interval on the numberline in which case you would have demonstrated a fundamental flaw in modern mathematics for which you deserve the most prestigious prize in mathematics. That your proof is found on a blog not some mathematics journal, and the fact that you mention God in a mathematical proof suggests you need to do a bit more studying of the mathematics of infinities.Timothy Whiteheadhttps://www.blogger.com/profile/11646757021200031878noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-55860118424975800752020-10-02T17:51:25.290-05:002020-10-02T17:51:25.290-05:00Even if reality should present itself indeterminis...Even if reality should present itself indeterministic on the fundamental level, this won't stop <b>Laplace's demon</b> from calculating and determining, that can be calculated and determined.<br /><br />Even if Jill's brain or consciousness should be indeterministic, this won’t stop Facebook, Google and Amazon from gathering all the information about Jill and from that determine her actions. Jill is going to a casino, because Jill already has shown her tendencies for gambling.<br />Her winning 10 $ with a specific expectation from general understanding of gambling and stochastics and spending that money on a drink, because Jill already has shown her tendencies for alcoholism. From that it’s not far to conclude and to determine her carambolage with her car given her physical, her mental, weather and car state in combination with her route, that she takes regularly from casino to her home.<br /><br />You see, even if consciousness might be indeterministic, the rest of the world still might be determinisltic or a lot of the times approximately deterministic. And one day we might even could approximate and simulate the indeterministic mind via quantum computers.<br />Zsolt Nagyhttps://www.blogger.com/profile/11519070636926516031noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-70537093142078007982020-10-02T14:29:31.815-05:002020-10-02T14:29:31.815-05:00We don't know whether in our brains we even ha...We don't know whether in our brains we even have approximate determinism. It depends on how much quantum-level stuff is relevant to our brain function.<br /><br />On standard views of quantum mechanics, the indeterminism is NOT merely due to incomplete knowledge. In fact, given some assumptions such as locality (basically, that one cannot have causal influences that are faster than light), it can be proved that the quantum indeterminism cannot be merely due to incomplete knowledge.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-3141533979231427532020-10-02T12:12:34.511-05:002020-10-02T12:12:34.511-05:00Then I guess, that by probability p=1 we got deter...Then I guess, that by probability p=1 we got determinism and by probability p≠1 or 0≤p<1 we don't got determinism.<br />What about a very high probability with almost 1=100% (p≈1)? Is that determinism or not? I suggest we could say, that it is approximately deterministic.<br /><br />Further it still appears to me, that all considered causes and effects only appear to be not deterministic with probability p=1 cause of our incomplete knowledge.<br />What about <b>Laplace's demon</b> with his completed knowledge? It seems to me, that it is capable of determining all causes and effects.<br />Even if we have incomplete knowledge, approximated determinism is still achievable.Zsolt Nagyhttps://www.blogger.com/profile/11519070636926516031noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-58526210528061710252020-10-02T11:18:16.139-05:002020-10-02T11:18:16.139-05:00All we need for satellites is high probabilities, ...All we need for satellites is high probabilities, not determinism.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-18715984493556872142020-10-01T18:04:46.783-05:002020-10-01T18:04:46.783-05:00If our physics is not deterministic, then why woul...If our physics is not deterministic, then why would anybody care to shoot satellites into our or other planets orbits? Every nation, that can and does shoot satellites into orbits, does it, because our physics is deterministic.<br />Also why would Facebook, Google and Amazon gather so much information about everybody?<br />Sure, we might be not purely physical, yet I still think, that <b>Laplace's demon</b> would be capable of determining Jill's and anyone's actions.Zsolt Nagyhttps://www.blogger.com/profile/11519070636926516031noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-58612113089795484952020-10-01T17:13:50.313-05:002020-10-01T17:13:50.313-05:00But our physics is not deterministic. And we are n...But our physics is not deterministic. And we are not purely physical anyway.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-84751270225409586542020-10-01T12:44:20.267-05:002020-10-01T12:44:20.267-05:00Hallo Dr. Pruss,
I agree to, that causal chains ne...Hallo Dr. Pruss,<br />I agree to, that causal chains need not be deterministic. Yet why shouldn't <b>Laplace's demon</b> be capable of determining Jill's actions?<br />It appears to me, that if Laplace's demon has all the knowledge about physics and has all the knowledge about all the actual physical objects and further has enough capacities and power to do the necessary computations, then Laplace's demon is capable of determining all of Jill's actions and further is capable of determining all of external actions, that might happen to Jill.<br /><br />Best regards,<br />Zsolt NagyZsolt Nagyhttps://www.blogger.com/profile/11519070636926516031noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-24376766100920779862020-10-01T09:06:59.570-05:002020-10-01T09:06:59.570-05:00Mr Nagy:
Causal chains need not be determinstic. ...Mr Nagy:<br /><br />Causal chains need not be determinstic. Jill won $10 at a casino. Then she took that $10 and bought herself a drink. Then she drove and smashed up her car. We have a chain: going to a casino, winning $10, buying a drink, driving, smashing car. But all the links in the chain are indeterministic.<br /><br />Unknown:<br /><br />I am inclined to accept one direction of Phenomenal Conservativism: if something seems to me, that fact is evidence for it. I don't accept the other direction, that that's the only evidence there is.<br /><br />And, yes, it still seems to me that a HH is possible. And my current view is that a HH is possible, but that one cannot have an infinite number of things cooperating to a single effect, so the denizens of the rooms cannot cooperate for a single effect.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-68339801223113394092020-09-30T21:28:35.710-05:002020-09-30T21:28:35.710-05:00Hey Dr. Pruss,
A couple of questions. For one, do...Hey Dr. Pruss, <br />A couple of questions. For one, do you subscribe to Phenomenal Conservatism? I saw your comment about "seemings" as evidence and was wondering. Also, does it still seem to you that a HH is possible? What about transfinite operations done on the occupants in the hotel, does that sway you in any way? Blessings!Anonymoushttps://www.blogger.com/profile/15178155758999986485noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-7090643893126004692020-09-09T15:06:36.022-05:002020-09-09T15:06:36.022-05:00Thank you Dr. Pruss for your response and clarific...Thank you Dr. Pruss for your response and clarification.<br /><br />I agree with most of the things, that you stated in your response and I like to add, that I for myself also think, that there is something deeply flawed in the general concept of causal chains. From a pure physical standpoint causal chains appear to be very deterministical and if actually there would be the Laplace's demon, then it would appear, that all causal chains would be already determined. That would be very off putting.Zsolt Nagyhttps://www.blogger.com/profile/11519070636926516031noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-16411142498295876422020-09-09T14:19:05.795-05:002020-09-09T14:19:05.795-05:00I think "seems" is always evidence, but ...I think "seems" is always evidence, but defeasible like most forms of evidence. That it seems that an infinite past is possible is evidence that it is possible. Indeed, this is why for decades before I came to the argument in this post, I thought that an infinite past was possible: it seemed to be! It *still* seems to me to be, but I have stronger seemings behind the arguments to the contrary. (And in a sense I think an infinite past is possible. Just not an infinite past *causal* chain.)Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-89335856657280086172020-09-09T13:44:33.190-05:002020-09-09T13:44:33.190-05:00It seems clear to me that an infinite past is logi...It seems clear to me that an infinite past is logically possible. "Seems" isn't enough, is it?<br /><br />I suppose I would be interested to see if you could actually produce an argument against an infinite past that doesn't fail trivially, as this one has, but "yeah, but read my book" doesn't really move me as a response to "your argument doesn't work."<br /><br />I have very little incentive to spend time and money on a book, if this argument is any indication of the quality of the intellectual work therein.<br /><br />I do actually think, that one could produce an argument against actual infinities of things with *certain* kinds of causal interconnections--indeed, I think if you had aimed your argument here differently, it could have been not-bad, but I don't believe for a second that you actually have a competent argument for causal finitism more generally, and I also don't care enough to pay money to find out. <br /><br />Calehttps://www.blogger.com/profile/17231108214219274750noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-58490699723447933352020-09-09T13:31:49.459-05:002020-09-09T13:31:49.459-05:00We certainly have models of universes without an a...We certainly have models of universes without an absolute speed limit: Newton's gravitational model.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-87516885003381568342020-09-09T13:31:06.532-05:002020-09-09T13:31:06.532-05:00Huemer's book on paradoxes infinity, btw, embr...Huemer's book on paradoxes infinity, btw, embraces the solution to a lot of paradoxes by limiting parameters to the finite, including having a metaphysically necessary requirement that there be an absolute speed limit. That seems to me to be very implausible. It seems clear to me that teleportation is logically possible.<br /><br />I agree that with infinite space and infinite stuff all causally connected and no speed limit one also gets the GR paradox. So that's a reason to reject the possibility of an actual infinity. I don't think it's a conclusive reason: what I end up rejecting in the end in my book on paradoxes of infinity is an actual infinity of things with certain kinds of causal interconnections.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-89551195226151946742020-09-09T12:08:06.433-05:002020-09-09T12:08:06.433-05:00Honestly, it gets worse even than that.
Let's...Honestly, it gets worse even than that.<br /><br />Let's imagine that it's possible for there to be a universe with infinite space and infinite physical stuff (both of which are required for your GR scenario). Let's imagine that this universe can also be one without a maximum speed for physical signals, since that is also required for your GR scenario. In this case, we can run into the GR scenario even with a finite past. After all, with infinite space and infinite stuff, we can have our infinitely many factories build our infinitely many GRs all at the same time. An infinite past isn't actually required at all! <br /><br />So. Whatever factor or conjunction of factors is impossible, thanks to the impossibility of the GR supertask (assuming we even agree that the GR supertask is impossible, which we don't actually have to do at all) doesn't even include an infinite past. <br /><br />An infinite past might be incidentally impossible, but (again) this argument absolutely fails to support that claim. It is flawed at every level of examination. Calehttps://www.blogger.com/profile/17231108214219274750noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-76082841169538171322020-09-09T11:53:40.175-05:002020-09-09T11:53:40.175-05:00It's kinda funny, too, that, while the *value*...It's kinda funny, too, that, while the *value* of the speed of light, or the maximum speed of physical signals, isn't metaphysically necessary, that doesn't really matter. Even if it is metaphysically necessary just that there is *some* upper limit on the speed of physical signals, your argument would fail in the same way. <br /><br />And it isn't nearly so "obvious" that this isn't the case. <br /><br />Indeed, fine tuning arguments generally go the opposite direction: this maximum speed is one of those parameters which must be given a finite value. I actually think if you look around, you'll find far more skepticism directed at the proposal that there could be a physical universe without a maximum speed for physical signals than at the proposal that there could be a physical universe with an infinite past. After all, actual physicists are pretty well on the fence about the latter, but we are all quite certain about the former. We have plausible models of hypothetical universes with infinite pasts, but none without finite maximum signal speeds. Calehttps://www.blogger.com/profile/17231108214219274750noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-42782497801759125572020-09-09T11:28:13.555-05:002020-09-09T11:28:13.555-05:00It seems obvious that that is not really a defense...It seems obvious that that is not really a defense against my objection.<br /><br />Sure, we can imagine a universe in which instantaneous action is possible. Maybe (maybe, though your argument still certainly doesn't establish this) a universe *like that* can't have an infinite past, but so what?<br /><br />This is the same basic problem, again. The problem with the GR scenario is not an infinite past: it's all of these other unstated factors.<br /><br />What's more likely: that instantaneous action over physical distance is impossible, or that an infinite past is impossible? That both are possible, but not in conjunction? Oh, right, and that doesn't actually cover it: your GR scenario needs infinite stuff. It needs an infinite past without an information pinch-point, like our universe seems to have in its past. It needs infinitely subdivisible time, and machines capable of arbitrary chronological precision.<br /><br />At *best,* the argument only points to the impossibility of the conjunction of all of these things. It remains that your suggestion, that this argument establishes the impossibility of an infinite past, is laughable. <br />Calehttps://www.blogger.com/profile/17231108214219274750noreply@blogger.com