Alexander Pruss calls my argument "VERY CLEVER"! (Grim Reaper Paradox)
ฝัง
- เผยแพร่เมื่อ 9 พ.ย. 2020
- In this video, I explain the Grim Reaper paradox as well as an argument I came up with that strengthens it.
Alexander Pruss's post on the Jolly-Givers: alexanderpruss.blogspot.com/20...
My original comment: alexanderpruss.blogspot.com/20...
![[TH] VCT Pacific Stage 2 - Playoffs Day 2 // PRX vs GEN | DRX vs TLN](http://i.ytimg.com/vi/gmrSk-_ahlA/mqdefault.jpg)
Typo: "12:30" is supposed to be "11:30"
Congrats bro. Not every day mad genius' like alexander Pruss call someone clever. You're pretty smart.
Did you or have you done a video in cyclical causality?
Nope. The closest thing I did was a video on time travel. :)
@@ApologeticsSquared Make a video on it. It should be interesting.
It's the same thing as the "Achilles paradox", you just exchange the time period of overtaking with causes for change and devide them into infinity... causing your brain to melt ;)
So the guy Pruss thinks is clever can't figure out that 12:30 comes after 12:00. Says all you need to know about religious apologists right there.
Congratulations. Craig called Pruss scary smart and Pruss called you clever. Therefore both Craig and Pruss think you are clever :)
I won't believe it until its put in modus ponens.
Yeah Criag said that in his interview with the catholic apologist I'm sure of his name. He remember he said he would be a great competitor of Dr. Graham Oppy if he wasn't his competitor.
That logic doesnt follow.
You are everywhere josh :)
Pruss is a literal genius PhD in Math and Philosophy and he called you clever if that happened to me my ego would sky rocket lol
I've found that the cure is to post other arguments in the comments on his blog and have him obliterate them with genius counterpoints. :)
"don't get emotionally attached to Fred cause he's gunna die soon"
Or will he..
🤨 Michael here
If I ever get a large ego, I just go to Pruss’s blog and ask him a question. Then I realize I can’t amount to anything because I will never have a doctorate in math and philosophy. 😂
Fun story about Pruss, I was trying to learn about probability and he found me resources from Oxford and stuff. He’s a super nice guy :)
David Chalmers's rendition of the Grim Reaper Paradox (in a sense, he was the guy who originated the paradox in the first place) actually prevented the mereological summation explanation from working by making it an explicit part of the scenario that "you can only die through the motion of a grim reaper’s scythe" and if you are already dead "his scythe remains immobile throughout". Since no Grim Reaper moves their scythe, you can't be dead, and yet you can't be alive either. Contradiction.
The response I envision from the causal infinitist is: “Well, that scenario so described is impossible. In the real world, there would always be at least two things that could kill you: swings of reapers’ scythes or the powers of mereological sums of reapers.”
It sounds crazy, but it would allow one to maintain the mereological summation explanation to the bitter end.
Have a nice day! :)
@@ApologeticsSquared
_The response I envision from the causal infinitist is: “Well, that scenario so described is impossible. In the real world, there would always be at least two things that could kill you: swings of reapers’ scythes or the powers of mereological sums of reapers.”_
That sounds crazy.
_It sounds crazy, but it would allow one to maintain the mereological summation explanation to the bitter end._
In that case it's nice to have a Jolly Giver argument. Incidentally a similar approach happened with the Eternal Society Paradox from Adelia Brown. I'll have to do a video on that some time (albeit it'll probably be part of a larger "Eternal Society Paradox" video).
Thanks to your video, I think I _finally_ understand the GRP. Your explanation was much easier to follow than others that I’ve seen. Thanks!
The Grim Reaper seems to be a simple case of mathematical limits. Without going into the intricacies, any number divided by infinity is zero. Thus, by dividing the interval between 11 and 12 into infinite partitions, we can determine that the shortest partition will have zero duration. Thus the reaper that kills Fred will be the one that arrives at 11pm on the dot. It sounds counterintuitive, but that, in and of itself, is not a contradiction.
Without going into the intricacies, a limit only tells you how a function behaves as you approach a value. For example, f(x) = sin(x)/x approaches 1 as we get closer and closer to x=0, but that function is actually undefined at 0 on the dot. Likewise, the distance between the reapers and 11pm approaches zero as we look at earlier and earlier reapers, but there is nonetheless no reaper that is scheduled to kill Fred at 11pm on the dot.
Here's another way of looking at this. The number of hours between the Nth reaper and 11pm is 2^-N hours. That is, we have reapers numbered {0, 1, 2, 3, 4, ...} who sit around waiting to kill Fred after 11pm for a portion of time equal to {2^0, 2^-1, 2^-2, 2^-3, 2^-4, ...} hours. Now, the reaper that kills Fred is going to be the reaper whose number in the latter set has the smallest value. This corresponds to whichever reaper has the largest number in the former set. But the set {0, 1, 2, 3, 4, ...} has no largest value! The limit* of the set is infinity, but that isn't actually in the set. There is no biggest value in {0, 1, 2, 3, 4, ...}, so no reaper kills Fred.
you assume that it has to be the "first" grim reaper that kills him but why should think that? its jjst one of them that happens to be at the right place and have actual luck of killing him,
What great explanation and video editing. Thanks for this.
Glad you liked it! :)
Just discovered your channel, fantastic stuff! Absolutely love the Minute Physics-style videos plus the clear explanations. As an atheist, always love to find high-quality theist content. Instant subscription!
Thanks! Much appreciated!
Every reaper who sees a reaper ahead of him realizes that he'll have nothing to do and goes home.
Then they all go home and Fred survives!
@@ApologeticsSquared what would you say to the response that an infinite series like this with r=.5 equals one mathematically so there is a finite sun.
@@ApologeticsSquared what's the point of this thought experiment? I'm not saying it's pointless, rather, I genuinely want to know. If you respond to this question please add a heart to my comment or at least upvote it or else TH-cam won't notify me that you responded.
@@elgatofelix8917 The point of the Grim Reaper thought experiment is that it's supposed to support a view called "causal finitism": the view that all chains of cause and effect cannot be infinitely long. This would imply that there must be a First Cause, which an apologist will go on to argue is God.
@@ApologeticsSquared Thank you.
Good video, and congrats on your argument being acknowledged. 👍
Love the extension of Pruss’ argument. Shows you’re thinking through things well
Bro, your channel is awesome!
Thanks!!! :)
I no longer believe the, grim reaper killed Fred, what a relief
Isn't this argument just a more complicated version of Zeno’s Arrow?
My thoughts exactly.
This is brilliant.
The problem here is, that if time is quantized - as is strongly indicated - this paradox doesn't actually translate to the real universe - it's only a paradox in the hypothetical universe where Fred lives & dies.
In quantized time, there is a first reaper one quanta after 11:00, and it kills Fred.
THANK YOU
while thats true, that also implies that there isn't an infinite series anyways, which just demonstrates the position they're already going for.
@@mohidkhan9819 exactly.
So you agree actual infinity doesn't exist and therefore causal finitism makes sense. Awesome.
That's good. The sum total nothing to infinity is still nothing.
The original version of the Grim Reaper Paradox was thought up by Jose Benardete in his book Infinity: An Essay in Metaphysics. Pruss later came up with an unbounded version of the paradox.
I believe causal finitism, but am skeptical of this line of argumentation. I think what really causes the contradiction in the first place is not merely the hypothesis of a causal infinite, but of an actualized infinite by itself. The very concept of an actualized infinite is contradictory, so it doesn't make sense to say that no grim reaper could be the one who killed him, because that requires that there is an actual infinite number of grim reapers, which is contradictory.
Of course, this, by itself precludes causal infinitude as well...
A causal infinitude isn't actualized all at the same time though, so throughout it is there ever a contradictory state of an actualized infinite? :)
Nice video. I've had a similar thought with the grim reaper paradox with scythes. Suppose we perform an autopsy on Fred at 12:00. What does his body look like? Does it have a scythe mark though none of the scythes have blood on them? Or maybe the mereological sum of reapers shot a bullet instead. There's no reason why it should be a scythe wound rather than a bullet wound.
Add 1 GR at 11:00. Now which GR killed Fred? The one at 11:00. But there are an infinite number of reapers. So it IS possible for there to be an infinite number of GRs. So the argument doesn't prove causal finitism.
This is just the door closing argument reframed.
If I start to close a door, it must travel half the distance before closing, and half again, and so on, so clearly the door will never close because it will always have half the remaining distance left to cover.
Yeah, we have calculus for that.
The door does close.
Yeah. That was my exact thought but instead with how people shouldn't be able to travel from one place to another.
I'm unsure how a mathematician could allow this argument since I would think most calculus students have had a similar idea conveyed and know there is a problem with the logic.
Who else got emotionally attached to Fred
This paradox is a time-reversed lamp super-task paradox.
What do you think of attempts to reverse the tense in the argument, thus showing that in addition to a beginning, the causal chain must have an end?
It was discussed on Majesty of Reason not too long ago. I think it might just be enough to reduce the Grim Reaper paradox to absurdity.
good job
Amazing.
You deserve much more subs, also if Pruss called me clever I would literally explode!
Thank you very much!
I only figuratively exploded. :)
@@ApologeticsSquared :)
@@ApologeticsSquared did you consider making a video about gap problem or the arguments against Kaalam brought forth by Malpass and Morriston?
@@g-7km231 I need to read up on Malpass and Morriston.
And a video on a gap argument would be a good idea! :)
@@g-7km231 oh Well now your a theist? 😂😂😂 Why are You acting like an atheist in EP's channel but all of the sudden when I find You in mathomas or AS channel your a theist 😂
The point of the "set" is to showcase an attribute of the set, by that changing the mechanics of the paradox and solving it. You can't change the attribute of the set because you don't address the point, who is the changing of the mechanics. You can have infinite sets of infinities, with specific properties. For example , when the properties manifestate, a new set of infinities emerges that includes by necessity, the properties of previous set , but in the same time excludes all the infinite sets that the 1st property never manifestate.
‚Good video! And yes, Alex Pruss is great.
"clever" his words. lmao! This vid is great.
I wish i could understand the blue/yellow argument.
It seems to me if they individually have the ability to make blue, then some case could be made that collectively they have thar ability to make blue. I just didn't understand why they should have the ability, collectively, to make yellow.
Sort of like if one dragon can burn me up with fire, then i suppose an infinite number could, but i guess im not sure why that would mean that theres just as much reason to believe that an infinite number of dragons could shoot lasers out of their eyes.
I'll watch again.
Nevermind, I get it.
@@godfreydebouillon8807 I don't haha
Extraordinary claims require extraordinary evidence.
That’s quite an extraordinary claim. Got any evidence for it?
Man i see you everywhere from EP to here. Its like i know you at this point lol
@@KT-dj4iy as InspiringPhilosophy has said, a claim which establishes the validity of all other claims is itself an extraordinary claim
@@vaskaventi6840 The problem is that the level of evidence, above ordinary, required by any claim should presumably match the level of the claim itself, again above ordinary. But then look at the implications of your position. You claim that Inspiring Philosophy claims that claims attempting to establish the validity of all other claims constitute “extraordinary” claims, yes? Assuming so (although I might, myself, have termed them meta-claims) then what classification would you claim for such extraordinary claims? Are they _extra_ extraordinary? And then what of _those_ claims? And so on. You are already laying on Inspiring Philosophy a burden of producing at least ExtraExtraOrdinary evidence. But by doing so, you yourself assume the burden of producing ExtraExtraExtraOrdinary Evidence. And, as I say, so on. Before you know it, you’ll be wishing for more wishes, some poor genie will be getting her rump paddled, and Frege, Russell, and Gödel will all be turning in their graves. Where are all the recursive acronyms when you need one!
@@KT-dj4iy Well, forgive me for butting in but the evidence for that would be your own standard of evidence. If your friend said he had dinner last night, that's a claim you wouldn't think to question. It's an extraordinarily ordinary claim. You probably hear claims like that every day and never think to question it. Why would you? It's so ordinary. But if your friend said "I had dinner last night with the president of the United States." Well, I don't know about you but I'd need something a little more there. Maybe your friend is honest but still, you're going to want some kind of scenario in which that made sense. Maybe a neighbor is related or friends with his extended family or something. Some connection somewhere. Or maybe the president is doing some kind of outreach program where he has dinner with a typical American family or something. Something like that would be fine if you knew your friend was usually honest. But what if your friend said "I had dinner with the president. Abraham Lincoln. He rose from his grave just to eat dinner with me." At that point, if it were me, there's almost nothing you could say to convince me. If he had video evidence of this I'd probably just remark about what a good look alike they managed to get. Even if I went to his eternal resting place in Springfield IL and saw the claw marks coming from the inside going out with no body, there would always be part of me that doubted. I would think it strange that they were taking the joke this far but that's really extraordinary. Maybe if I went to the hospital with Lincoln himself where he had tests that indeed confirmed he was in fact a dead man walking around and if he knew details about the life of Lincoln that I Googled in advance, and I saw the empty grave, maybe I'd very reluctantly accept that maybe something I don't understand happened.
It's not that extraordinary claims require extraordinary evidence as such. It's more like, "I hope so. I hope you don't just believe every crazy thing you're told." Because, I happen to have this really great investment opportunity. I'm telling you this thing is so great, whatever you can shove in my Paypal right now, you'll get back tenfold. But it's got to be right now. As much as you can. You see what I mean? I wouldn't do that but there are people all over who wouldn't think twice about it. There's always another scam another huckster. And we all like to think we'd never fall for it but millions do. Very intelligent people fall for it.
That's a category error. Okay I'm not some big shot mathematician/philosopher but infinity is not an amount. If it could be represented by any one integer, it wouldn't be infinity. It would just be that number. By asking "Which reaper killed Fred?" that's like saying "How much is infinity?". If there are infinite reapers, there is no one reaper at the end. It's not so much a paradox as it is a description of infinity.
Exactly, so you concede that causal finitism is true.
Someone tell this guy about the difference between actual and potential infinites.
Im not sure if I quite agree. I have two possible points of contention one of which I feel I can explain better so I will divide this comment into two halves with a line break. I will get the complex rambling objection out of the way first as im still mulling over my exact thoughts on that matter and am more so just looking for feedback. The second objection however I will include after the break.
I would argue that just because we can’t pinpoint a specific value at which an action occurs doesn’t mean we can’t have such an infinitesimal value at which an action occurs. Perhaps it is just the difference in the properties of finite vs nonfinite values.
I understand that the mathematics involving infinite series is likely one possible objection to this as it seems you mentioned, unless I misunderstand, and while I partially agree I can’t shake the feeling that even if an infinite series did converge it would be off by an infinitesimal value.
For example if I have written this correctly ½+¹/⁴+¹/⁸+…¹/n should converge to equal 1 however It doesn’t seem like this series should ever actually reach 1 since there is a constantly diminishing value of each subsequent input.
I suspect that there may be a similar issue as the one which arises when multiplying an infinite decimal expansion of 1/3 by 3. When we multiply the fraction itself we get
“(1/3)x3= (3/3)= 1”
But if we put this in decimal expansion we get
“(0.333_)x3= (0.999_)”
And since (0.333_) is said to be equal to (1/3) that means (0.999_)= 1. But that can’t possibly be accurate, rather its more likely that one of these values is our best approximation of how to divide 1 in to 3 equal parts but is slightly off by an infinitesimal margin since such a value can’t be pinpointed exactly in a finite amount of time. Not enough to notice or really matter in most cases but if you’re picky enough about your numbers its enough to differentiate between them.
Im not sure exactly what kind of proof would be required to demonstrate that infinite series actually converge at an infinitesimal value infinitely close to their suspected value but I suspect it would be rather complex due to the tedious nature of infinitesimals.
---------
My second objection is with your claim that the red ball turning yellow after 11:00 is equally as plausible as it turning blue.
This to me strikes me as similar to Zeno’s paradox whereby there’s an infinite partitioning of a finite distance and yet the distance is crossed anyways. The only difference here seems to be that instead of distance we are measuring duration. Nevertheless the infinite partitions of each are reached in a finite amount of time even if it seems like no first or subsequent partition should be reached.
Looking at this with your analogy of colored balls we do see that there is in fact several points whereby when the duration reaches that value it will change the ball from red to blue, and yet we also see there are no points in the duration that would turn the ball from red to yellow. Just because we can’t pinpoint any first shift doesn’t mean no shift occurs if by the end of a set duration we observe that shift.
When you say after 11:00 is the ball red or blue It needs to be specified how long after 11:00 we are measuring because this would drastically change the results. If its any finite value of measurement then the ball will be blue however if it’s an infinitesimal value of measurement the ball might still be red unless the infinitesimal value occurs at or after a point in which the ball already turns blue. But as stated previously Infinitesimals are tedious and not really something that can be easily pinpointed when approaching from a strictly finite value.
I realize in hindsight my second objection kinda relies on the presupposition of the first but I don’t think I have quite explained the first as well as is possible so I will gladly attempt to clarify any questions anyone might have. Honestly questions might help me understand what needs to be addressed in how I present the information so it’d be helpful to both of us.
You do understand that the Reaper story is a variation on Zeno's paradox. You do know that pure mathematicians post Cauchy and Kroenicker have their useful techniques for summing some types of infinite regress. That said, IMPO, such arguments recapitulate the mediaeval theological debates about angels dancing on pin heads: it is irrelevant since their is neither measure no consequence. It is philosophical and logical gymnastics predicated on the assumption that infinitudes - and infinitessimals - are in any sense meaningful outside the domains of philosopy, logic and set theory.
Hi! Great video, very clear. And congratulations on the touch with fame!
I think inferring causal finitism is a very unparsimonious, 'ontologically costly' explanation of what's going on with these scenarios. Are you familiar with the _unsatisfiable pair diagnosis?_
Basically all these scenarios boil down to two rules that logically contradict: (1) There is no first member, (2) the first member does something.
Recognizing these are in logical contradiction is enough, we can stop there without inferring anything about the world outside our heads.
Well not so fast. This assumes that making the decision to kill Fred doesn't take any time. Each grim Reaper has to make a decision based upon the current situation. Since there is only a finite amount of time it doesn't matter how many grim Reapers there are. There can only be a finite number of decisions in one hour.
Can you help me understand one point? I'm having a bit trouble understanding. So would the collection of "Blue Makers" turn into nothing due to it being a collection? I may have misunderstood the point but if we parody the reasoning for why a yellow ball shouldn't appear due to a lack of a Yellow Maker, does this mean we are also saying there is a lack of a Blue Maker due to the collection? Thank you!
Another reason you cannot treat the collection of reapers as the cause of Fred's death is that no one reaper will kill (or take any action) Fred if he is already dead. There is no collective action because all individual action is dependent on the former state of Fred.
That's an excellent point!
Isn’t an infinite sum between 11 and 12 a potential infinity and not an actual infinity?
I don’t get it surely the first one at exactly 11 killed him? Or are we saying that between 11:00 and 11:01 time can be split infinitely?
Why can't we argue something like this:
1. The red ball will become blue if there is at least one blue-maker present at a time between 11:00 and 12:00.
2. There is at least one blue-maker present at a time between 11:00 and 12:00.
3. Therefore, the red ball will become blue.
P1 Seems obvious, that allows any arbitrary number of blue-makers to be present at any time between 11:00 and 12:00, say a single blue-maker is present at 11:05.
P2 describes any scenario where at least one blue-maker is present between 11:00 and 12:00, which doesn't seem to be a problem.
The conclusion is just a simple MP deduction from P1 and P2, logically valid.
This argument seems to obviously work with a single blue-maker, or two, or a trillion, so what causes it to entail a contradiction or some kind of absurdity if there is an infinite number?
I love Pruss and I find his GR and Apple arguments compelling, so I am posting this in hopes of discovering where my argument fails. Thank you.
Thanks for the comment!
P1 is false, because a yellow-maker or a green-maker could precede all blue-makers.
So, what you need is:
1’. The red ball will become blue if there exists some time t such that at t there is a blue maker and at no time before t is there something capable of changing the ball to a color different from red.
This leaves open the question wether mereological sums of infinite blue-makers have the power to turn balls yellow, or only if they can turn balls blue.
Have a nice day! :)
@@ApologeticsSquared Ah, I should have thought about it a little bit more. Thank you for the reply!
A casual loop avoids this problem. Also, the paradox assumes time is infinitely divisable if so a blue maker could never meet a red ball because there would be an infinitely divisable segment of time that would be a boundary between the blue maker and the red ball.
I'm not sure how a causal loop would avoid the problem. Granting for the sake of argument that it does, though, it seems to be jumping out of the frying pan and into the fire. For, I suspect things like the Grandfather Paradox make causal loops more controversial than infinite chains.
And yes, it assumes that there is a possible world where time is infinitely divisible (though it makes no statement about the actual world).
Have a nice day! :)
@@ApologeticsSquared Why do you say it would be jumping out of the frying pan and into the fire? Only if it faces more problems than it solves but I don't think it does. The grandfather paradox is a temporal paradox against the idea of time travel. I do not think time travel is possible nor do I see why time travel must be possible for a causal loop to exist. Well, I disagree with Leibniz, I agree with Spinoza. There is only one possible world that necessarily exists. Using counterfactal conditionals in the GR scenario should take into account metaphysical considerations.
The problem people have with the grandfather paradox is usually pinpointed in the backwards causation within the scenario. Backwards causation is entailed by causal loops.
I find Necessitarianism to be too counterintuitive. How can we all grasp the notion of possibility, or "could-ness" so easily if the only things that could be are that which are?
Also, how is it that "A casual loop avoids this problem"?
:)
@@ApologeticsSquared
“The problem people have with the grandfather paradox is usually pinpointed in the backwards causation within the scenario.”
The GF paradox has to do with time travel, not backwards causation. Backwards causation and causal loops are two different things. Backwards causation faces the bilking problem. However, regarding the GF paradox “it is hard to make them work in detail when we remember that changing the past may be impossible” However, there is another response is that of Vihvelin (1996), who argues that there is no contradiction here because ‘Tim can kill Grandfather’ is simply false (i.e. contra Lewis, there is no legitimate sense in which it is true). According to Vihvelin, for ‘Tim can kill Grandfather’ to be true, there must be at least some occasions on which ‘If Tim had tried to kill Grandfather, he would or at least might have succeeded’ is true-but, Vihvelin argues, at any world remotely like ours, the latter counterfactual is always false. plato.stanford.edu/entries/time-travel/#GraPar
“The idea of backward causation should not be confused with that of time travel… The difference, however, is that time travel involves a causal loop whereas backward causation does not” plato.stanford.edu/entries/causation-backwards/
“Backwards causation is entailed by causal loops.”
One might think that causal loops are impossible-and hence that insofar as backwards time travel entails such loops, it too is impossible. Lewis (1976, 148) raises the question whether there must be causal loops whenever there is backwards causation; in response to the question, he says simply “I am not sure.” Mellor (1998, 131) appears to claim a positive answer to the question.[22] Hanley (2004, 130) defends a negative answer by telling a time travel story in which there is backwards time travel and backwards causation, but no causal loops.[23] Monton (2009) criticises Hanley’s counterexample, but also defends a negative answer via different counterexamples.
Second, are causal loops impossible, or in some other way objectionable? One objection is that causal loops are inexplicable. There have been two main kinds of response to this objection. One is to agree but deny that this is a problem. Lewis (1976, 149) accepts that a loop (as a whole) would be inexplicable-but thinks that this inexplicability (like that of the Big Bang or the decay of a tritium atom) is merely strange, not impossible. In a similar vein, Meyer (2012, 263) argues that if someone asked for an explanation of a loop (as a whole), “the blame would fall on the person asking the question, not on our inability to answer it.” The second kind of response (Hanley, 2004, §5) is to deny that (all) causal loops are inexplicable. A second objection to causal loops, due to Mellor (1998, ch.12), is that in such loops the chances of events would fail to be related to their frequencies in accordance with the law of large numbers. Berkovitz (2001) and Dowe (2001) both argue that Mellor’s objection fails to establish the impossibility of causal loops.[24]
plato.stanford.edu/entries/time-travel/#CauLoo
"I find Necessitarianism to be too counterintuitive."
Not everything that is counterintuitive is false. Eg.It was once counterintuitive to think the earth was round or that the earth revolved around the sun.
How can we all grasp the notion of possibility, or "could-ness" so easily if the only things that could be are that which are?
There is a good paper on Spinoza’s metaphysics for strict necessitarianism. One should first understand Spinoza’s definition of necessity, as it has to do with things and not propositions, etc.. Spinoza himself wrote in a letter that the subject of necessity belongs to metaphysics. “In raising the question of whether Spinoza’s metaphysics can account for his strict necessitarianism, it is, moreover, important to explain that Spinoza’s strict necessitarianism applies to things, rather than propositions, truths or events. The notion of necessity in Spinoza is connected to the notion of a thing (Latin: res)….. necessity for Spinoza is always de re and not de dicto”
dspace.library.uu.nl/bitstream/handle/1874/368566/A%20Vindication%20of%20Spinoza%27s%20Strict%20Necessitarianism%20-%20Thesis%20Research%20Master%20-%20Lennard%20Pater%20-%204160959.pdf?sequence=2&isAllowed=y
It is causality that is necessary, there are no contingent modes even though there may be contingent truths/propositions. There is only one possible substance that necessarily exists.
Also, how is it that "A casual loop avoids this problem"?
Apart from the assumption that time is infinitely divisible and I am able to cross an infinitely divisable segment of time, a causal loop connecting 10:00 and 11:00 will solve the paradox i.e no reaper is able to put an apple in my sack, my sack will always be empty and the jolly givers will always have an apple. I will never cross the temporal boundary i.e. 11:01.
Also, I can say the scenario is impossible because it implies I can cross over an infinitely divisable segment of time, yet a jolly picker cannot. If the claim is there is no first jolly picker, then there can be no first instance of time after 11:00. For if there were a first instance of time, then the jolly picker at that time would put whatever he had in my basket. The BOP would be on you to justify why there can be a first instance of time after 11:00 but no first jolly picker. To claim there can be a first instance of time after 11:00, a parallel argument can be made that there must be a first instance before that if time is infinitely divisable.
Ah, you're right. I was using the term "backwards causation" too loosely to encompass vanilla backwards causation as well as causal loops. Thanks!
// One should first understand Spinoza’s definition of necessity, as it has to do with things and not propositions, //
Possible worlds are based on propositions; not things. So if necessitarianism (the notion that there is only one possible world) would need to entail not only a necessity of things, but a necessity of propositions.
A possible world where a causal loop avoids the problem is all fine and dandy. But I think you would need to maintain the extra thesis that necessarily, any such paradox would have a loop associated with it. Otherwise, we can just ask what happens in the possible worlds where there aren't those causal loops! But I see no reason to see why causal loops must be necessary.
The defender of the paradox isn't saying that there is a first instance of time after 11:00; they are saying that (at least in the world where the paradox occurs) time is continuous, so for any two times t1 and t2 such that t1 < t2, there exists some t such that t1 < t < t2.
Have a nice day! :)
great
Question? In mathematics this paradox refers to a limit, which technically ends and avoids paradoxes without actually being infinite, how about that, like would it still be paradoxical or would it just count as “limit” causal finitism?
A limit neither ends nor avoids a paradox here. What this paradox is getting us to do (via the way causation works) is pick out the smallest member of a set. However, there is no smallest member of the set {1, 1/2, 1/4, 1/8, ...}.
@@ApologeticsSquared ok thanks 👍
soo, the point is nobody can say that a collection of bluemakers should itself be a bluemaker?
...but...what about the first reaper in line??!? My brain ...
The grim reaper paradox isn’t any more interesting than Zeno’s or Melissus’s. It assumes actual infinities to disprove the eternity of the world instead of potential infinity.
Infinitesimal =\= an infinite with members of equal size.
How can you possibly use the first to rule out the second?
Btw. I also don’t get the yellow-blue ball point. In mathematics we know how to treat infinitesimals, the set is a convergent series so the ball will become blue at 11:00 on the dot.
You put in as a set up to the scenario that there are “blue ball makers” which converge at 11. So that’s why the ball is blue and not something else.
Sorry, but to respond to your comment, I'm going to need to get into some technicalities:
Infinitesimals aren't used anywhere in this thought experiment; there are only non-infinitesimal real numbers being considered. Each reaper is scheduled a distance which is a finite, positive, *non-infinitesimal* real number away from 11:00.
// ...the set is a convergent series... //
This statement is confused. A series is a summation of members of a set. But the reapers aren't being "added" together. So I'm not sure what it is that you are trying to convey with this statement.
// ...so the ball will become blue at 11:00 on the dot. //
Actually, no. There is no Blue-Maker scheduled to make the ball blue at 11:00; they are all scheduled to make the ball blue at some time *after* 11:00. So, the ball is red on the *closed* interval [10:00,11:00], and blue on the *half-open* interval (11:00,12:00]. 11:00 "on the dot" exists on the former interval.
// You put in as a set up to the scenario that there are “blue ball makers” which converge at 11. So that’s why the ball is blue and not something else. //
But how does that work, if none of the Blue-Makers used their blue-making powers? Literally *none* of them used their powers to change the ball's color, yet it changed color!
Have a nice day! :)
@@ApologeticsSquared Yes okay, fair enough it’s not a series it’s a sequence but my point will still stand.
This is an infinitesimal because the time we’re talking about is getting smaller-and-smaller and there’s a limit set at 11. Which means the guy will die at 11 after an infinite number of Reapers. We know how to deal with these infinites pretty well in maths and I don’t think this is very controversial.
*”There is no blue ball maker schedule at 11”*
I’m not saying there is, it’s a convergent sequence with a limit set at 11 (that was defined in the initial conditions of the thought experiment). Guass taught us how to deal with these sorts of problems, if an infinite sequence converges to a point then after and infinite number of “Reapers” it will hit that point.
I think it’s also odd to cite Craig in this video, given that Craig believes these sorts of infinites are perfectly okay. He’s defended with James Sinclair the idea, for example that a universe with a singularity has no initial instant of creation but an initial interval.
@@andrewwells6323 You seem to be thinking that this question is akin to, "Find the limit of the sequence: 1, 1/2, 1/4, 1/8, ..." (which represents the number of hours each reaper is away from killing Fred). This is, as you say, fairly uncontroversial and very straightforward; the answer is 0. But that's not the question. We have a set of reapers each with a specific value assigned to them, {1, 1/2, 1/4, 1/8, ...} and we use the death-warrant setup (i.e. "Kill Fred if alive at such and such time") to force the reaper with the *smallest value* which was assigned to them to kill Fred. However, there is no reaper with a smallest assigned value. For any reaper assigned with a value x, there is another reaper assigned the value of x/2. So none of the reapers kill Fred. But, Fred must die (or else he escapes an infinity of inescapable reapers). Contradiction. Now, since the death-warrant setup seems like it can be done in the real world, and it allows us to pick the least element of a set of things acting upon something causally, it seems like you cannot have these kinds of sets without least elements in the real world. This means that you can't have these sorts of infinities of causally interacting reapers.
Hope that helps. Have a nice day! :)
I don't see how the reapers are a causal history. It's not like the first reaper caused the second one and so on. If one reaper kills Fred, then Fred's causal history is finite: it includes one reaper and only one. If no reaper ever kills Fred, then Fred's causal history is also finite: it doesn't include any reaper. Both of these scenarios are impossible, as the paradox shows. But nowhere in this paradox do we actually have an infinite causal history. What are your thoughts on this?
Also, you should be wary of these kinds of paradoxes. They tend to assume that causes happen inside of time (which is obvious, we have only ever observed causes happening inside of time), it would be unwise to use them to support the idea that something "outside of time" (whatever that means) is a cause to anything.
I believe the casual relationship between the reapers is that each one will only act if the one temporally prior to it fails to act. The scenario is pointing out a contradiction that arises in a past-eternal universe: none of the reapers have killed Fred despite his death. This article may make it a bit clearer since Apologetics Squared was just presenting the essentials of the reaper paradox in the video and didn't have time to go into all of its complexities: reasonablefaithutd.org/2019/09/01/grim-reapers-and-the-infinite-past/
As for your second point, that appears to stem from another misunderstanding. The purpose of this paradox is to show the contradictory nature of a past-eternal universe in which time would always exist not to make a claim about the nature of reality without the presence of time.
I hope this helped.
The problem here is definitely happening because there are the causal powers of infinitely many things being used; if all but finitely many reapers were stripped of their power to affect anything, the paradox would be resolved.
So, where does the infinite causal history come into play? I have three possible answers:
1) An infinity of grim reapers would need to be caused in the first place to even exist, violating CF.
2) The reapers checking to see if Fred is alive is itself a part of Fred's causal history.
3) The existence of the reapers entails the POTENTIAL of an infinite causal history, which is an impossible thing, even if that potential is never used.
Now, I think that CF applies to timeless chains of cause and effect, but even if it didn't, it would still be useful for apologetics.
Have a nice day! :)
@@ophidiandove4575 The version presented in this video is fairly different than the one in the article :) Furthermore, the one in that article can be resolved by a really simple assumption: the message (or Fred, or even the reapers!) can't just exist infinitely into the past. It needs a cause and thus it must have begun to exist at some point in the past. This solves the paradox without any need for causal finitism and without claiming that the universe is finite into the past. Now, in that last paragraph, it proposes that the reapers just add a photon to the universe if a previous reaper hasn't already done so. But, the reapers need a way (like a message) to let the others know if they've added a photon or not. This way would then need to exist without a cause, so we go back to my previous objection.
@@ApologeticsSquared "The problem here is definitely happening because there are the causal powers of infinitely many things being used" I agree.
1) doesn't really violate causal finitism. The causal history of every single reaper is finite. 2) seems a bit sloppy. Would there be no paradox if the reapers were omniscient and didn't have to check on Fred? And I don't see how 3) is true (that is, I don't see how the existence of the reapers entails the potential of an infinite causal history, as I said, every causal history in this scenario seems finite). Does the existence of infinitely many things always entail the possibility of an infinite causal history or are the reapers a special case?
Even if 3) were true, you have a scenario that
1) Has the potential of leading to X
2) Is contradictory
That doesn't mean the contradiction stems from X, unless you directly show that of course. For example, the grim reaper scenario also entails the potential of one grim reaper buying ice cream. That doesn't mean there's anything wrong with ice cream :)
"I believe that CF applies to timeless chains" Well that'd be an interesting argument to hear, I hope you do a video on that. Is there one of these paradoxes to support causal finitism that doesn't require a timeline?
@@Nickesponja // "The problem here is definitely happening because there are the causal powers of infinitely many things being used" I agree. //
Then I'm not super sure what your beef is with causal finitism. I don't know if you could actually not be a causal finitist and yet think that it's impossible for infinitely many things exercise their causal powers.
// 1) doesn't really violate causal finitism. The causal history of every single reaper is finite. //
Yes, but whatever caused them to exist would have an infinite causal history. Unless of course there were infinite creators. But now I think that this argument loses force, because if you're not already a theist, then it seems you'd be less adverse to the idea of infinite reaper-creators.
// 2) seems a bit sloppy. //
Here is Pruss himself giving a more thorough treatment of (2):
"It is, however, a little less clear how exactly causal finitism rules out the story, in that in the story as given none of the reapers actually do anything, and hence it seems that there are not infinitely many causes in the history of the final outcome, namely Fred’s being dead at 11. There are, however, multiple ways of spelling out the details in causal finitism that allows the view to rule out the paradox-that is why I called “causal finitism” a family of views.
One attractive way to proceed is to say that ensuring an outcome counts as an interaction that falls within the causal history of an event, even if in ensuring something one in fact does nothing but observe. For instance, my wife may tell me to ensure that my son is in bed. I may tiptoe to his room, gently open the door, and notice that he is in bed. I have thereby ensured
that he is in bed, even though I did nothing to him. For me to count as having ensured, however, I had to be disposed to bring it about that he is in bed if he weren’t already in bed. We can then say that an appropriate causal finitism should also rule out infinitely many ensurings in the history of an event. But each reaper ensured Fred’s being dead at 11. So the story is ruled out by an appropriate version of causal finitism."
Source: alexanderpruss.com/papers/kalaam.pdf
// Even if 3) were true, you have a scenario that
1) Has the potential of leading to X. 2) Is contradictory. That doesn't mean the contradiction stems from X, unless you directly show that of course. For example, the grim reaper scenario also entails the potential of one grim reaper buying ice cream. That doesn't mean there's anything wrong with ice cream :) //
That's a good point. But if we have some Y that is impossible, like drawing a square circle, then something with the potential to actualize Y, like a robotic arm that can draw a square circle if turned on, should itself entail contradictions, even if that power is never used. If I had such a robotic arm, and never turned it on, I still think that we would find ourselves in a contradictory scenario. For example, I could look at the machinery and the programming of the robot. Would I find the program is one that guides the arm in a round yet straight path at the same time? Would I find a piston that has the power to make straight lines while simultaneously curving? If there is a thing with the ability to actualize an impossibility, you should expect that thing to itself be contradictory. Now, a causal finitist believes that the infinite grim reapers could actualize an infinite causal history -- an impossibility. So even if they never actualize that power (which I'm not convinced they don't in their killing of Fred), the causal finitist is unsurprised that these beings could bring about a contradiction -- they have the potential for making the impossible happen! But if you're not a causal finitist, then it becomes very unclear what exactly the problem is.
// "I believe that CF applies to timeless chains" Well that'd be an interesting argument to hear, I hope you do a video on that. Is there one of these paradoxes to support causal finitism that doesn't require a timeline?
//
I don't think it needs a video. Imagine there are an infinity of timeless beings, each who has a natural number on their forehead. Timelessly, this is true of every being:
-Being with n on their forehead timelessly looks to being with n+1 on their forehead.
-The beings can timelessly cause a number to appear on their back by timelessly thinking about it.
-For every being with n on their forehead, if the being that they're timelessly looking at has no number or a number less than n on their back, then that being is going to timelessly think of n. Otherwise, they're going to timelessly think of the number they're timelessly looking at.
The above scenario is basically the Grim Messenger scenario construed timelessly. It leads to a contradiction, even though no time is passing.
Have a nice day! :)
No reaper killed Fred, because the smallest fraction of time would negate movement. A static (frozen) appearance out of nowhere (how?) would completely consume the shortest fraction of time.
None of these scenarios are actually paradoxical. They're simply don't conform to our intuitions that are based on our experience with finite math. It boils down to a scenario that both requires a starting point, and also defines the scenario such that there is no starting point.
If I gave you a geometry problem that started with a circle (a 2-dimensional object, that by definition, has no corners) and then for the first step of the problem I told you to start that the corner of the circle, I haven't created a paradox, I've simply setup a nonsensical scenario.
Same with all of these various infinite regress "paradoxes." They all set up a scenario of some sort that defines an infinite set that is either unbound in the positive or negative direction, but then later in the scenario attempt to reference a boundary where it was previously established there is none.
To use my circle example, and made it more tangible, if I put you in a circular room, then told you to go sit in the corner. Obviously you can't do that, as there is no corner to sit in. Have I just debunked the concept of corners? Of course not. Have I debunked the concept of round rooms? No of course not. All I've done is created a _linguistic_ contradiction that reduces down to "the corner of a corner-less room."
Or to put it another way, let's take a section of sidewalk... Between two expansion joints there is a distance of one meter. Let's call the expansion joint that I'm standing at Point A, and then a meter away is the 2nd expansion joint we'll call Point B. Halfway between those two points is a point we'll call Point Z. Halfway between A and Z is another point, Y, halfway between that one is point, X and so on. This gives us an infinite series that is unbound at "my" end of the line. That is to say there is no "first" point that I will encounter when traversing the sidewalk. Does this mean I'm unable to traverse that sidewalk? Is there some metaphysical law preventing me from taking that first step, simply because I've invented an arbitrary labeling system for distances on the sidewalk? No, of course not. I walk from point A to point B just like I always did, despite the fact there is no identifiable, individual point where I started.
7:00 I don’t understand what do you mean by after 11am. Do you mean at 11:00 precisely (then it’s no apples of course) or something like 11:00:00.1 (then it’s obviously an infinite number of apples)? I don’t see what is the paradox.
Doesn’t this paradox include Zenos paradox, in which case, it has been debunked, I think? Because of Planck time and Planck space, we know that there is a smallest possible space and time, therefore there aren’t such things as infinitesimal infinites.
Did not explain that causal finitism stops this paradox, only implied and asserted it
I dont understand why the answer isn't just the grim reaper at 11 killed Fred, since it was the first scheduled grim reaper.
The reason is that we made sure to not schedule any reapers at 11:00, so there is no *first* reaper. There are reapers at 12:00, 11:30, 11:15, etc. but no reaper at 11:00.
Have a nice day! :)
@@ApologeticsSquared Ah okay now it makes sense to me! Thanks for taking the time to respond. Great work :)
Can you link the video of Dr Craig being interviewed?
intresting.my argument is that time is not infinetely divisible.there is a quantum of time else the sorter value of time an event can occur!therefore at elevel plus that time we will find the reaper who kills poor fred!right?
That is a response, but a follow-up question is, “Is an infinitely divisible timeline at least possible? If so, then I can talk about what would have happened if such a timeline were actual.”
Have a nice day! :)
When you insert a backward chain of infinite events into a finite timeline you are going to get some peculiar results. It is the thought experiment self that is impossible.
Would you be able to have an actually infinite set of things in an infinite timeline?
why would an infinite amount of grim reapers avoid the death of Fred when one grim reaper already guarantees his death?
I've never apriciated how this counts as evidence for causal finitism. If the scenario is contradictory, it's contradictory. It's not possible on any view. So how does it count against infinite causal chains?
The idea is that you should be able to explain why the scenario in question is impossible, and causal finitism gives a really nice explanation.
Have a nice day! :)
@@ApologeticsSquared
Hey, you have a nice day too :)
But it seems to me, the fact that the scenario generates a contradiction is enough to explain why it's impossible. As much love as i can give to Priest, I don't think it's particularly controversial to say something is impossible just in virtue of being contradictory. What more explanation is needed?
Like i don't think i need to decide between competing view to explain why the sun can't be both yellow and not yellow, all that's needed is rejecting dialetheism
The next step for the causal finitist is to block that simple answer by invoking some recombination principle: “If x is possible and y is possible, and certain conditions are met, then ‘x and y’ is possible.” Having infinite reapers can make a contradiction, so its possibility must be denied.
@@ApologeticsSquared *"and certain conditions are met"*
-- It's going to come down to what you alluded to here, and I don't know how to cache it out in a way that would avoid Mar98co1's solution, which I think was spot on :)
x = I am taller than you.
y = you are taller than me.
A world where both of these is true is logically impossible. Individually they are logically possible, but they cannot be recombined together. I'm betting any recombination conditions you can come up with to handle this, will also handle the Grim Reaper scenario in exactly the same way. (Because the same thing is going on there.)
I’m a bit confused as to what would be the solution to this paradox? How does accepting causal finitism change the situation?
Kalam cosmological argument
Because you concede the position that there can not be an infinite amount of Grim reapers assigned to Fred metaphysically speaking.
This below verison of grip reaper paradox is more easy & general in my opinion. Thoughts?
*) The Grim Reaper Paradox:
(The absurdity of an actualized infinite regress)
Consider the following situation.
Let's assume an infinite regress of past events is not only possible, but actually occurred.
Now, in our hypothetical universe let's assume a person "P" is being hunted by grim reapers. Now, consider the following premises:
1. P can only be killed by a Grim reaper.
2. A grim reaper never fails to kill P.
3. Every hour a new grim reaper will appear. It will first check to see if P is alive. If P is alive, it will kill P.
Now, consider this question:
Is person P dead or alive?
For person P to be dead, a grim reaper would have had to kill him. However, no grim reaper would have ever had the chance. This is because, before a grim
reaper can kill P, another grim reaper would have killed P an hour ago (and so on ad infinitum),
No grim reaper would have ever gotten the opportunity to kill P, because the grim reapers before him would have slain him by then.
However, person P cannot be alive. For if he was alive for but an hour, he would be killed by a grim reaper.
Consequently in this hypothetical universe, person "P" could not have died, nor could he be alive (therefore leading to a contradiction) ...
As long as you have an infinite past, the Paradox remains But the moment you have an absolute beginning, the paradox ceases to exist.
This is the problem of applying actual infinities to actual events or objects.
Consequently, since time cannot have an infinite past, it must have had a beginning point.
(Confusion) I don’t see what any of this has to do with causal finitism. What about infinite things means that they cant have 1 cause.
Interesting paradox. But I'm confused. At 2:19, you say that a single grim reaper is assigned exactly at 12 o'clock. But when it comes to exactly 11 o'clock, there isn't a single grim reaper assigned. Rather, there is an infinite number of grim reapers that get ever closer to 11 o'clock, but not quite so. Why can't there be a grim reaper assigned exactly at 11 o'clock, so that whenever it hits 11.0000...., Fred dies? If time has no smallest unit of measure, that doesn't necessarily mean no assigned grim reaper does the job, since time can be expressed as an irrational number like the square root of 2.
The only way I can see this resolved is to declare exactly 11 o'clock to be the last moment Fred is alive. If that's the case, then yes, it appears impossible to pinpoint an exact time (and hence grim reaper) at which Fred dies. And even if that time is an irrational number, there's no such thing as the smallest irrational number. It's turtles all the way down. And maybe one (if not the only solution) to this is that there must be a finite fundamental limit, such that there is a bedrock unit of time that cannot be broken down further.
Not buying it... Oranges and Pears might've convinced me, but I guess, we'll never know...
Im confused, wouldnt the guy die as soon as the first reapers time struck? The fact that theres an infinitum amount of reapers just means his death is an absolute certainty at that time.
Just because there is an infinitum amount of repears doesnt mean 11pm wont exist from future to present.
The way the paradox is structured, there is no reaper scheduled at 11:00. The timeline is reaper free on the interval [10:00,11:00], and there are reapers within the half-open interval (11:00,12:00]. The idea with putting each reaper halfway between another reaper and 11:00 is to ensure that there is no *first* reaper. Asking which reaper is first is like asking what the smallest element is in the set {1/2,1/4,1/8,1/16...}. There is none.
Have a nice day! :)
There's no such thing as first in a set of infinite things.
This argument seems to seems to go like this:
1) lets imagine something physically impossible (such as an infinity of things that don't exist anyway)
2) look: this leads to something confusing or impossible
3) look: I've proved something contradicts something
4) therefore I'm right
Where is my argument wrong?
I'd formulate it thusly.
1) If the Grim Reaper scenario is impossible, then causal finitism is probably true.
2) If the Grim Reaper scenario is possible, then in w, ∃r(K(r)).
3) If the Grim Reaper scenario is possible, then in w, ∀r∃r₀((r₀
Jup, it’s just sophistry.
Let’s invent a purely hypothetical scenario with no possible analogy in the real world that leads to a logical contradiction and then pretend that this leads to any conclusions about the real world.😂
You seem to agree with his argument since you claim an infinity of things is impossible, correct?
So, you're dismissing the relevance of supertasks by presupposing that they're physically impossible. And then calling this whole discipline of supertasks "sophistry." Okay. I guess it's your first time encountering discussion of supertasks. So maybe you would like to familiarize yourself with the literature on the subject before making sweeping statements that just make you sound ignorant. The argument is about metaphysics, so we're concerned with formalizing a strong, principled reason why supertasks should be logically impossible. It doesn't seem, at a glance, that they violate any laws of logic. Indeed, some philosophers think they are certainly logically consistent and some even believe a supertask machine could be physically built, in this universe. I'll recommend an article for you to read that concerns both types of possibilities of supertasks.
But in any event, if they are possible, that seems to cause paradoxes. Some approaches to defusing the issue of _some_ supertasks just say that the outcome is causally disconnected from the supertask. So the infinite number of events doesn't have a predictable outcome. It's indeterminate. That is how Zeno's paradox is famously "solved." But the grim reaper paradox can't be solved in this way. It's not indeterminate whether the person lives or dies, because unlike in other supertasks, he doesn't flip back and forth between living and dying. Only the first grim reaper in the set can kill him, according to the description of the supertask. All other grim reapers (an infinite number of them) that come later simply do nothing.
So whether the person lives or dies comes down to our understanding of infinite set theory. Can infinite sets have a first member? Of course they can! So it seems that the paradox persists. A physical solution isn't really a solution, but philosophers will say that the paradox has less force because it isn't physically instantiated. But why couldn't it be? There seems to be no principled reason. A much better solution is that infinite sets _can be_ physically instantiated, but they can't all be causally connected. This is causal finitism. And it's not merely referring to the physical universe, but to all possible universes.
I'd also like to point out that, formally, your argument isn't similar to the argument in the video. #4 doesn't follow from #3. "therefore I'm right" about what? The conclusion is that the grim reaper paradox is _metaphysically_ impossible, not merely physically impossible. The fact that something is physically impossible is irrelevant to this argument, which concludes that supertasks are impossible in all possible universes. Something that is metaphysically impossible, e.g., a logical contradiction, could not possibly be physically instantiated, because the material universe behaves self-consistently, for example operating according to conservation laws. But something that is physically impossible is not necessarily metaphysically impossible. Some things are physically impossible just because of the incidental facts of the universe.
That is well-understood by philosophers and physicists, who employ thought experiments all the time, whether they describe scenarios that have a reasonable chance of actually happening in the world or not. You could make the same argument against all manner of thought experiments, including the ones Einstein used to demonstrate special and general relativity. The fact that something is physically impossible is irrelevant if you can't derive a principled reason for it to be physically impossible. And here, we can. Supertasks are physically impossible, and that's not simply an incidental fact about our universe. It's true in all possible universes. And the reason it's true is because of causal finitism. Here, the reason supertasks are physically impossible is similar to the reason logical contradictions are physically impossible: both are not just physically impossible, but _metaphysically_ impossible.
If you deny causal finitism, but you want to have a cogent philosophical worldview, then you need to find some other principle which ensures the impossibility of supertasks and related paradoxical states of affairs. But how can you? Are you going to insist that all possible universes can't possibly have infinite numbers of things? But why? We don't even know if our own universe is finite in dimension or energy. Until about a century ago, the popular theory among secular cosmologists was that the universe is infinite and homogeneous in space and time. It's the Hubble flow that shattered that assumption, but it actually doesn't demonstrate that the universe is finite in spatial dimensions, only in the dimension of time. We assume it is finite, but it could be otherwise. Certainly nothing in the laws of nature say it _couldn't have been_ infinite in space. There's nothing logically contradictory about that, without causal finitism.
Surely you understand that the set of "physically impossible things" is greater than the set of "logically impossible things." Many things that are physically impossible are physically impossible for purely incidental reasons. All sorts of conceivable states of affairs are impossible in our universe only as a result of the seemingly arbitrary values and initial conditions of the universe. And that could prevent certain formulations of infinity paradoxes. But it doesn't prevent all of them. If you were at all familiar with the literature on supertasks and hypertasks, you'd know that there are many proposed infinity paradox machines that are not physically impossible. A paper you might want to read is Stanford Encyclopedia of Philosophy's article on Supertasks. I prefer the Spring 2011 edition.
You also need to explain why an infinite number of grim reapers acting on a person is somehow less possible than an infinite number of grim reapers spread out across an infinite universe. See, the vast majority of skeptical philosophers do not believe that actual infinities are impossible. The denial of actual infinities is an argument common to theists, which is why Mr Doctor Schultz is remarking about the irony of you mocking the video's argument while apparently presupposing its conclusion, the impossibility of actual infinities. If you're a skeptic on the question of God, then you might want to speak to some skeptical philosophers. They should be able to disabuse you of the notion of finitism. They overwhelmingly do not accept that actual infinities are impossible, because they don't accept any of the proposals for principled reasons as to why they shouldn't be impossible.
Again, there's a difference between impossibility and mere incidental facts of history. To say "there can't be an infinite number of protons because the universe started with a finite amount of mass-energy and the universe obeys conservation laws" is very different from saying "there can't be an infinite number of protons in ANY unvierse because every universe will have a finite amount of mass-energy and obey conservation laws." Philosophers are concerned with the former kind of statement, because philosophy is not physics. We're dealing with logical possibility, not mere physical facts.
And if you accept the notion common to secular philosophers, that actual infinities are not impossible for some principled reason, then you're gonna have trouble explaining why infinite grim reapers are impossible. Surely you can imagine a universe that extends infinitely in space, if not also in time. And surely you can imagine a universe that's homogeneous, largely consisting of the same density of galaxy filaments and voids throughout. Because that's how our universe is. Now, it's limited by observability. Because causal influence can only be exerted by interactions via quantum fields and spacetime curvature, both of which are limited to the speed of light, causal influence propagates at a maximum speed of c. Because of this maximum speed (which isn't logically necessary by any means), and the accelerating expansion of the universe, everything in the universe exists within a causal bubble: the observable universe. There's plenty of universe outside of it, but it can't causally influence us or vice versa, because it's expanding away from us faster than light can cross the distance.
Given this fact, it would be reasonable to say that certain types of infinities are impossible, even if our universe were infinite, because although there may be an infinite number of galaxies, they're not all causally linked. Their causal influence is locally constrained by the speed limit of the universe. But that's only a property of a particular subset of universes that includes ours. There are just as many conceivable universes that do not expand or that stop expanding at a certain time. Besides, this is all a metaphysical exercise. If we can imagine a universe that is slightly different from our own, why can't we imagine a universe where there's an infinite number of grim reapers all capable of existing in a single room on Earth? There's no logical contradiction. Again, you may need to refresh your memory on the distinction between logic and physics. Jumping to the moon isn't logically impossible. It's just incidentally not possible for you in this particular state of affairs.
Given that there's certainly no principled reason to deny that an infinite universe could exist, and there's no principled reason to insist that something like the Pauli exclusion principle operates in all possible universes, that means there's no principled reason to deny that a universe could exist where an infinite number of grim reapers all exists in a single room. But that causes metaphysical problems. Which is exactly the point. We're trying to formalize a _principled reason_ for such a situation to be fundamentally impossible. But why can't it be possible in some worlds?
Another good example might be imagining a 20-dimensional time machine. This just happens to be impossible in our universe due to its dimensions. But so what? Isn't it interesting to know whether a time machine is logically possible? You can't just dismiss a philosophical question about the logical possibility of something merely by declaring that it doesn't matter, because it could never be created in the real world anyway. I mean, you can, but can't you see how that would be chauvinistic and anti-intellectual? Surely you don't believe that all thought experiments are invalid and worthless unless they describe scenarios that could reasonably come to exist in the real world? That nothing of value can be gained by considering scenarios that could conceivably exist if things were different, but don't exist?
Your comment (and Rami's especially) kind of reminds me of Stephen Hawking's remark in his final book, about how "philosophy is dead" and physicists have "picked up the torch." Pretty rich analysis, coming from someone who was so ignorant of philosophy that he didn't recognize that he himself was engaging solely in philosophy throughout the book. Well, maybe it was his coauthor who contributed that gem of irony. But either way, it's a common sentiment among people who've had a basic scientific education and have been awed and mystified by the findings of modern cosmology, biology, and so on, but have never been educated in philosophy. Philosophy isn't dead, people just don't understand what it is because they're philosophically illiterate.
Everyone wants to have an opinion on the ultimate questions, but not everyone wants to put in the work to develop the kind of fluency that's needed to even gesture at answers. It's so much easier to just dismiss everything that can't be seen, as if that's the "mature" thing to do. But if Plato and Aristotle could discover truths about reality just by thinking in a time when scientific technology was practically nonexistent, why can't we? Philosophy isn't dead and can't ever die. It's simply a stuffy name for the study of everything. Today, there are specialized disciplines for studying many parts of "everything," so experts on those parts become specialists in those disciplines, rather than philosophers. So who becomes a philosopher? What IS philosophy, now that so many parts of it have branched off into separate disciplines? Well, it's everything that can't be investigated by specialized empirical methods: namely, reasoning about the abstract. This, like many things, is shared between philosophy and mathematics. Just like mathematics will never die, philosophy will never die. And we will never run out of things to reason about, because that set of things _actually_ is infinite. Some people may lose interest in philosophy from time to time, but eventually they'll realize that there are things worth knowing that can't be queried by interacting with the material world.
Similarly, there are also facts about the material world (such as the nonexistence of paradoxes) that are worth trying to understand at a deeper level. We'd like to know not merely _what exists_ but also _why_ it exists. Why are paradoxes never instantiated? This is a worthy question for philosophy. Physics can only answer questions about what is. It may be able to show us that certain paradoxes are incidentally impossible (perhaps because the speed of light prevents a wide variety of paradoxes from physically instantiating), but it can't tell us if there are any deeper reasons. To be fair, physics is a new science. It's not a competitor to philosophy. It's built on the back of philosophy. The earliest physicists were philosophers, and they made their theories within the current of mainstream philosophy. So the laws of logic and the broader view of metaphysics are baked into physics.
Consequently, the first physicists already knew that paradoxes are impossible for deeper reasons than mere physical accidents. But we can't empirically investigate other universes to validate those deeper reasons. The only tool we have for that is reason. That's why physics, philosophy, and mathematics branched off into separate disciplines that nonetheless interact at significant depth and frequency. All have influence on and implications for each other. That's why Stephen Hawking presumed to write a philosophy book and call it physics. Pushing the boundaries of physics means punching through the wall into philosophy. Max Tegmark presumed to write a mathematics book and call it physics, in similar fashion. In both cases, the authors were writing about metaphysics. About multiverses, mathematical structures, the ultimate, foundational layer of reality that philosophy and mathematics are concerned with.
Far from tossing philosophy into the dustbin of history, the development of physics has shown that philosophy is more relevant than ever, with people from all disciplines fighting over it, not understanding when they've crossed outside their intellectual jurisdiction. And they can be (and frequently are) criticized for this, but that's actually the higher _goal_ of science. Science originally started as one unified thing. It branched out into many disparate disciplines as scientists became more specialized, and different methods were developed for each field of inquiry. In order to answer as many questions as possible concerning life, it was necessary that biologists specialize within this narrow field of study. So the disciplines have proliferated and siloed themselves to some extent. But this was always with the understanding that eventually, they should be re-unified under the banner of a grand theory of everything.
If that seems to you a little comically naive, even Orwellian, you're certainly not alone. A grand theory of everything may not be a realistic goal (I doubt anyone presently knows how realistic it is), but it's certainly a noble goal. And the standard-bearer of a grand theory of everything _is_ philosophy. All other disciplines are simply studies of narrow slices of reality. Even physics, which is the study of the fundamental observables of our universe (and to some extent, the implication they may have for other possible universes). It's really under the umbrella of philosophy, both historically and actually. Of course, before their division into disciplines, all science was called philosophy. Then the natural sciences were called natural philosophy. And only relatively recently was that broken down into discreet disciplines like biology, chemistry, and physics.
That's not a coincidence. Philosophy is very reasonably referred to as the study of everything. The word means "love of wisdom." It broke apart into separate disciplines for a time, but the hope is that it will once again be unified in a bottom-up theory of everything, from foundations to accidents. Like the ancient Greek cosmology of chaos sublimating into matter, differentiating into complex forms and composite objects, a theory of everything would start with nothing (nonexistence), develop to a unity that grounds everything, a foundation of reality, and describe all aspects of reality that stand upon it - including all substances, and both form and matter.
If such a theory is ever formalized, its foundations will be philosophical, not physical. The physical aspects of the theory rest upon the abstract: the laws of logic, the mathematical relationships and structures, and so on. The physics isn't the foundation of everything; if anything, it's just the epiphenomena that emerges from the abstract. The quantum fields are clearly just instantiations of geometric forms. So clearly geometry is more fundamental. And knowledge of pure geometry is clearly valuable. So knowing what is geometrically impossible is just as valuable as knowing what happens to be physically impossible in our universe. Similarly, knowing what is metaphysically impossible (i.e., infinite causal structures) is valuable too.
Why can’t you use the same collective idea that was used on the reaper. It is a collective of blue wizards who turned the ball blue and would could not (by the definition of the blue wizard) turn the ball yellow.
3:42 Between 11:00 and 12:00, the number of reapers waiting for Fred is infinite, but at every possible point in time, only 1 reaper is waiting for Fred. Which means at 11:00, there's exactly 1 reaper waiting, and it is that very first reaper that kills Fred. What do you think?
That isn't at all what it said. The directions given to the reapers were to start checking at 12:00, then divide the hour in half and check again 11:30, then the next one to divide the remaining time in half and check again 1115, then the next one to divide the remaining time in half and check again 1107 and 30 seconds, then the next one to divide the remaining time in half and check again, and all infinity of grim reapers to do the same. Dividing in half for infinity means they'll never get to 1100. You're trying to solve the argument by pretending there was a finite number of time intervals involved and a finite number of reapers involved, and thus pretending like 11:00 was reachable by traversing an infinite number, when the whole point is, it is not.
Obviously by 12:00 one of the infinite number of reapers must realize he isn't dead and kill him, however it is impossible that any single one killed him because theres an infinite number of them, and they'd ALL be preceded by one who was ordered to kill him if they found him alive at their appointed time.
This leaves Fred having been killed with no particular grim reaper having killed him. That is a logical contradiction, which is what all atheist arguments are. Atheists cannot argue for a single thing as it pertains to "refuting" theistic logical arguments, without appealing to provable logical contradictions and incoherencies.
@@godfreydebouillon8807
Hi. Thanks for responding. If we assume that time is incremental, then there is no grim reaper paradox, because there must be a smallest possible amount of time after 11:00, and only a single reaper occupies that point in time.
@@alittax Well that's true, but such a "refutation" only serves to reinforce the argument. The argument is meant to demonstrate there CAN'T be an infinite chain of anything, including time, or Grim Reapers, or sequences in a series in the universe. If Planck time for example is the smallest unit of time and cannot be further subdivided, then there is a finite rather than infinite number of units of time between Fred being asleep at 11:00 and 12:00 when the grim reapers sequentially are assigned a point to check if he is alive (the first assigned to check at 1200, the next assigned 1130, the next 1115 and so on).
To say that "that's impossible, there can't be an infinite number units of time" only demonstrates that the argument is correct and that appealing to a theoretical infinite would not be possible.
If, for the sake of argument, it WERE possible to divide the units of time infinitely, then it would lead to a logical contradiction (Fred was killed but nobody killed Fred).
It's the same when appealing to an infinite number of sequences in the universe, or anything else. If we were preceded by an infinite number of occurrences, it would not be possible that the current events we are observing would ever be realized.
This is the correct understanding of what the argument is attempting to demonstrate.
@@godfreydebouillon8807
>> such a "refutation" only serves to reinforce the argument
Not necessarily: my refutation (if we accept it as a solution) just shows that there must be a smallest possible unit of time. It doesn't follow just from this argument alone that not only time can't make up an infinite chain, but nothing else can either (e.g. space, chain of causes, etc). In fact, it might even be possible that there is a smallest unit of time, but the sequence of these individual units can extend indefinitely to the past and to the future (so that you could have these smallest units of time follow each other from the infinite past into the infinite future, like an infinite amount of pearls that look exactly the same, which are strung on a single piece of infinitely long string). So the number of reapers between 11:00 and 12:00 (or any other specific points in time) is finite, but the number of reapers from those two points in either direction (to the past or future) is infinite. What do you think?
Well, you absolutely have a point, but you have to remember there's different major kinds of infinity that philosophers of math and mathematicans talk about. Infinite sets, infinite sequences, potential infinites and actual infinities.
This particular example unfortunately seems to be an infinite sequence that is a set. In other words it's an infinite sequence within a short period of time (like a half hour or whatever it is in the example). Not much unlike making a one inch spread between my index finger and thumb and saying "how many potential points are between my finger and thumb?" Well there's an infinite potential points, but there certainly isn't an infinite number of real things like molecules or atoms or space between your two fingers. We can conceptualize infinity (which is a fascinating fact in and of itself), but as per the great mathematician David Hilbert, in the real universe, infinity is nowhere to be found.
However, the point of this argument is to demonstrate that an infinite sequence, ANY infinite sequence, leads to logical contradictions. It's true that you could rephrase (as you correctly did) with different scenarios of infinite sequences , but they all run into the same problem.
I think this analogy is used to help people see the problem because most people can more easily conceptualize 1/2 hour of time than they can an infinite number of Planck units going back in time forever. If one were to make the claim (which atheists do) that we have traversed an infinite number of units to get to the present point, that would be a positive claim that an infinite number of points have been traversed, and here we are. The Grim Reaper Paradox is meant to demonstrate that making appeals of traversing an actual infinite from the past to the present is logically incoherent, but is the basis for scientific atheist beliefs. It is meant to show that it is not possible that we would have ever arrived to the present moment, nor any moment for that matter, if one appeals to an infinite sequence.
Now, some other atheists may try to get around these problems by appealing to infinite sets (like a timeless, infinite, space-time block), but this opens up a whole new set of logical incoherencies.
Either way, minds exist and the physical exists. Atheists have faith that matter is more fundamental than mind and theists believe that a mind is more fundamental than matter (and since it's more fundamental than matter, isn't composed of matter). This argument is just one example, of many, why the atheist account doesn't work.
In my mind, all of these arguments are just a drop in the bucket, because Thomistic Scholastic Metaphysics and their arguments, which take much, much longer to understand (so they are no good for conversational arguments with most atheists), literally prove that God exists, however they certainly aren't going to convince most people who aren't willing to spend a lot of time studying it.
All of this long windedness to say, I get your point, but this was meant to be a simple to understand example of the problem when atheists appeal to actual infinities.
Let's number the reapers, start with the 12:00 and call him number 1. What is the number of the closest reaper?
Suppose its X. Your answer is wrong, because X+1 is closer.
You cannot assemble a set of reapers which is infinite in size and has a closest reaper. Your scenario is self-contradictory and proves nothing.
I think a more reasonable explanation would be to accept that weird things start happening when you deal with philosophical concepts like "infinity".
It's sorta like dividing by zero. There should be a way to divide by zero, but you can't. If you try to, all sorts of peculiar things happen. Look up the video where a math teacher "proves" that 1 = 2 by subtly dividing by zero when solving an equation.
In this case you would have to deny the law of non contradiction to say infinities are just strange.
Could one say this isn’t evidence against an infinite regress. Rather it’s evidence against infinite divisibility?
This specific paradox, yes. However, if time is only finitely divisible *but* you have an infinitely old universe, then you can get the same sort of paradox.
Have a nice day! :)
@@ApologeticsSquared like, a grim messenger paradox? Or do you have a different one in mind?
@@markslomp8607 That is indeed what I had in mind. :)
In first place, this is nothing more than mental masturbation, In reality it doesn't apply. In second, this is to much ado about nothing, to much construct just to end with the infinite halves paradox. And finally, the paradox or the problem is not that no reaper killed Fred, the problem is determinate which reaper killed Fred, because all reapers had not been identified previously, once you identify all the reapers, the first is the one who kills Fred. This is the same that to say that if someone is killed by a mob, and if you can't point the one who gave the fatal stroke, then nobody killed him, ergo, the victim is still alive.
This paradox doesn't seem to have anything to do with time or causality, but rather with infinity itself. Isn't this just an argument against the existence of real infinities in general?
Not really. If we had infinite ghosts that cannot cause anything to happen at all, no paradox ensues. But we could get paradoxes by giving them causal powers.
Have a nice day! :)
@@ApologeticsSquared
I don't think that's true. It seems like the paradox comes from describing some property of the final element of a series, which is understandable for finite series, but infinite series don't have a final element, so it becomes incoherent.
The thought experiment is equivalent to saying there is an infinite number of reapers that will kill Fred, starting with the last reaper in the list. Well, there is no last reaper because the list is infinite.
It doesn't have to be an action, though. If we say that the reaper's cloaks start white and each successive reaper has a cloak that is half as bright as the last, does the last reaper have a cloak which is completely black? Well, no. Every reaper in the series has some white left in their cloak. Ok, so if every reaper has some white left over, then the last reaper must as well. No, there is no last reaper.
It's incoherent to talk about what happens at the end of infinity because there is no end. The contradiction is contained within the question.
I don't think I'm understanding this quite well. Grim Reaper 1 kills Fred at whatever time he kills him at. Fred is dead. The other Reapers now need to find new jobs. How is this an argument against the existence of actual infinities?
Forgive the smol brain moment, but I've watched this twice and still don't get it. The time between moments isn't infinitely divisible, since at some point we reach planck time. So won't the grim reaper waiting one planck instant after 11PM be the one to kill Fred?
The physics in this scenario doesn’t have such a constraint.
Have a nice day! :)
@@ApologeticsSquared you don't have time without a unit that makes it up. Your scenario isn't worth more than a division by zero.
@@bluellamaslearnbeyondthele2456 I don’t understand. The unit of time used in the scenario was hours.
Have a nice day! :)
@@ApologeticsSquared thanks for the reply, I'm still trying to find the right word. Unit is sometimes used to mean composing elements. I guess elemental unit or atomic unit or a Planck unit or... I should get a dictionary. But nothing is infinit. Nothing.
@@bluellamaslearnbeyondthele2456 If I understand your objection, you’re working under the assumption that the present moment of time needs to have some “length” to it to exist, because if the present moment had a length of zero... well that’s just saying that it doesn’t exist! However, the present is usually thought of to be a single point. That seems *possible* at least, which is all this scenario needs.
Have a nice day! :)
That kind of logical paradoxes demonstrates only one thing : our minds do not work perfectly.
It’s the exact same kind of paradoxes as Zeno’s Arrow or Achilles and the Tortoise.
It doesn’t prove anything, except that our minds can’t really wrap themselves around our reality.
What is your point? How does that have any bearing on his argument?
@@MrDoctorSchultz nothing, except if he wants to get out of the « imagination » corner of logic.
This paradox has no practical bearing on reality. Like Zeno’s paradox or the paradox of Achilles and the tortoise. Those paradoxes show that or minds can extrapolate things about reality that have no implications for reality itself. So they are useless if you want to make a point other than about the way the mind works.
The grim reaper paradox tells nothing about reality, so using it to prove a point is useless and even misleading.
That’s what my comment was about
That’s what I can say right now, based on what I remember. I can’t rewatch the video right now, but I will rewatch in tonight and correct my point if need be.
@@vynne3888 So this paradox only seems impossible because our minds aren't able to comprehend such a thing? But in reality, it is perfectly possibly to have an infinite set of grim reapers such as the one he puts forth?
If we can't understand the problem with such a series of grim reapers, what can we understand? Are we incapable of applying the laws of thought (aka the 3 laws of logic) to anything at all?
@@MrDoctorSchultz no it’s not possible! Because infinity is not a thing that exists!
The “infinity of grim reapers” is an abstraction based on reality but ultimately not fueled by it. If your reasoning contradicts your observations, then check your reasoning first. The fact is that conceptually you can put an infinity of grim reapers between two points in time, but in reality there are two problems : 1/ infinity isn’t a number, you can’t really do anything with it. It’s by definition unusable except for very specific scenarios, so don’t wonder how it’s bizarre when infinity doesn’t work when numbers work. And 2/ reality cannot be segmented ad infinitum. Time isn’t cutable in smaller and smaller parts for ever. Space isn’t either. So this paradox can’t exist in reality, since there would be no place to fit all those grim reapers.
What you call laws of logic are in reality principles, tools that you have to use the right way. Do not wonder why your hammer cannot screw or your axe cannot take out a nail from a plank. Hammers and axes have specific uses, outside of those there is no use in using them.
Just as without an anvil a hammer is pretty much useless, without a reality to base themselves, the “laws” of logic are useless.
@@vynne3888 The interesting thing about logic is that you have used the laws of logic in your very comment! The laws of logic are unavoidable; no matter what you do, you will be using them (I should clarify what I mean by the laws of logic):
A is A
A cannot be both A and non-A at the same time and in the same respect
A is either true or false. There is no middle ground
I am curious, are you a theist? Since you seem to agree in a way with Apologetics Squared that reality can't just keep being reduced farther and farther into a infinity. Does that mean you think reality is eventually reduced to God, or atleast something like God?
Saying "no being used their power to turn it Yellow" isn't the only explanation you can give, though. You can also say "There did not exist a being who had the power to turn things Yellow." This statement obviously does not apply to the blue case as those beings did exist.
You could also just accept that contradictory things are impossible. That has just as much power to explain all of these paradoxes as causal finitism. As it is contradictory to say "no one turned the ball blue" and "someone turned the ball blue" then the situation could not have existed in the first place. This is the same conclusion causal finitism leads to but without requiring us to make any statements about causality.
Would this argument still be valid if scientists later proved that time is discrete/quantized?
It would be weakened, but not destroyed. It just relies on time *possibly* being non-discrete. :)
@@ApologeticsSquared Thanks for your response. I've recently come across your channel and love it to pieces! I was kind of dissatisfied with Craig's response to Euthyphro's dilemma but your video made it much clearer for me. Thanks for all the content you make! God bless! :)
That's an interesting question. Well perhaps even if so, time could still possibly be infinite on a metaphysical/spiritual/conscious level, since they only disprove it on a physical level.
Sure, drop the ball, prove on paper it never hits the floor. Keep dividing by two for infinity ... except the ball does stop and rebounds with some stored energy so there must be an end and it's not infinite in our corner of the universe.
There would be a first Reaper for the same reason.
You can play word games or do mental gymnastics and they are fun and interesting but they prove nothing other than that.
You totally miss the point. It isn't they who are doing mental gymnastics, it's the people appealing to "infinites" as having caused or done anything who are doing the mental gymnastics.
Your example of a ball hitting the ground is yet another example. There isn't an infinite number of anything between your hand and the ground, points, molecules, or anything else, which is why the ball hits the ground. The smallest unit of space is a Planck unit and they are finite, thus the ball hits the ground. If there were an infinite number of PHYSICAL points between your hand and the ground (there are not), then the ball could never hit the ground. The points you describe are imaginary or abstract in some other reality, not the physical one.
You entirely miss the arguments. They are arguing AGAINST the infinite being able to have actualization or actualize anything else, in the concrete world (atheists appeal to the imaginary "infinite" for all of their arguments, from infinite universes, infinite causal series, infinite parallel universes etc etc). They don't and can't exist.
To illustrate why an infinite number of causal events are not possible to actualize another event, they are granting, for the sake of argument, that an infinite number of things can exist (grim reapers) and then to demonstrate that they could have no causal power.
You're correct, we do exist, there is cause and effect, the ball does hit the ground, all because these claims of "infinity" as being the supposed explanation for everything are all nonsense. That's the entire point.
that's a stupid approach to logic
What you're doing is appealing to pragmatism (I think) -- which is actually a very strong move. The expectation for Bob to be dead should _directly contradict_ the expectation for any particular Grim Reaper to _kill_ Bob, if none of them are ever allowed to actually go and kill him. If one is to argue that the "collection" of Grims kill Bob, then they can just as easily say that they would give him a box of chocolates -- as the outcome of the scenario may as well be arbitrary.
nice thought (like the apple part). but is it even possible to make infinite apointments with the grim reaper in two hours? the smales lengt is the planck length. would it not be true, that the smalest time length is the time the light needs to travel one planck length? when that is true. the question wich grim reaper killed Fred is easy to answer.
But to the important point. the beginning of time does not point to a good. its just a gap where u can put god, when u lack knowledge. a clever person would withhold his answer till he has knowledge. he would just say "i dont know" and keep searching. how long did it take humanity to find a explanation for lightning? how many clever people have put their bets on gods and got it wrong? dont be one of them. dont get drunk on little thought experiments that can be entertaining when u are ignorant of your own ignorance. u are certainly clever, but the whole point is to prove god, is it not? this thought does not accomplish that. even when even smarter people think that. even the smartest are often wrong. but it would be funny, seeing a thought experiment destroying atheism.
The thing is.... that if causal finitism is true, you cant avoid God. I mean... this raises the question ¿how long in the causal chain (per se or per accidens) does science can go and not reaching God? For example, there was a time when we didnt know the cause of lighting, we said it was God and then we discover it was an electrical charge of some sort, then we said that those electrical charges were caused by God, but then we discovered that those electrical charges were made by another thing, and so on and so on. BUT, if causal finitism is true (which we see it is), then of course we would get to the causal beginning, which logically need to be God because that cause contains God atributes.
@@lollalo1 U can avoid god, when u put any other explanation in that place. When u use god in that way u just use him, as saying "period". saying period is no explanation. god is not even a end to the question just because u define him as the end to a causal chain. defining god as uncaused is no honest explanation. when u can define god as eternal and uncaused. i can define the essence of the universe as uncaused and eternal. at this point we would just talk smack. cant we agree, that we lack a good understanding and should refrain from claimimg to know the truth? or call our thought an explanation when it is clearly not anything close to a explanation!?
@@lollalo1 I f u say that the beginning of the known Universe has attributes, i would like to hear them. Even if u define a God that has the same attributes as the one u give the big bang, that does not make them the same. having the same attributes is no prove. but please start by proving the excistence of god, then show his attributes, then show the attributes of the big bang. and then we can talk. till then your argument is circular. to this point, your argument counts on me buying that there is a god with some specific attributes. pointing to the big bang, and saying: that thing is described like i like to describe my god, is not convincing.
@@tonolinus No, i do not consider that the expanse of some point of compressed space time (aka big bang) has the same atributes of the classical theism God (simplicity, impassibility, atemporality, etc.) Neither i think that big bang is the strict beginning of the universe. When im refering to universe im refering to all the existence, all the possible worlds and "universes" included beyond our boundaries of space time. We can keep talking about hypothesis of what things are existing out of this "universe" but we wont gain anything. Instead, the question that this video is trying to "debunk" is the notion that this "universe" is past-infinite (and probably future-infinite too)
For example; it is possible to someone to count from the negative infinite to 0? Of course not.
The true infinite cant be real because the evident notion that we exist now is contradictory about it. Thats the same about affirming that the causality chain is infinite; yeah there are causes and effects, but if there are infinite causes and effects when did the causality chain began if does not have a beginning?
@@tonolinus The other issue is that the universe cant be eternal, neither its parts. There is the necessity of something that gave existence not only to particles, but to the space-time too; either the laws of physics are real and there has to be some some explanation about why they are as they are, or either those "laws" are caused by some other "objects" ( so we call them particles, waves, rays, etc) and so on and so on, but there cant be an infinite chain of objects that support each other because of the reasons i gave you on the previous comments.
Then, there must be something that gave that began that chain of causes.
With due respect to Dr. Alexander Pruss and to you, this is really a very bad argument.
In this arrangement of Grim Reapers, they are made to stand exclusive of 11 o'clock , instead if you made then stand inclusive of 11 o'clock this solves the problem at once. The Grim reaper at 11 o'clock will be the first Grim reaper to kill Fred. That's it. Problem solved.
I’m so lost lol isn’t the grim reaper at exactly 11:00 the one who ultimately kills Fred? Like not even a second, millisecond, etc. later, but exactly at 11:00? And every other grim reaper does nothing?
The scenario is set up in such a way that no reaper is at 11:00.
@@ApologeticsSquared Ah I see, that makes more sense. So the paradox is that Fred is dead after 11, but since there are an infinite number of grim reaper’ none of them kill them, and thus he isn’t dead?
@@callmewitness128 Almost. He is definitely dead. The problem is just that no one killed him.
@@ApologeticsSquared That makes sense - thank you for unpacking that for me!
Doesn't your first argument about the blue-maker beg the question? The reason why the ball would appear blue instead of yellow could be because the mereological sum of all blue-makers coloured it blue. Given that there isn't a mereological sum of all yellow-makers that could be the difference. In order to not consider this possibility you should first reject the possibility of the mereological sum of blue-makers colouring the ball blue. So, your argument only works if one accepts that the mereological sum of blue-makers couldn't have coloured the ball, wich is what you were trying to prove. I'm not so sure about this tho, but I would like to hear your thoughts. Btw, I don't believe it makes sence to say the mereological sum of grim reapers killed Fred and I'm a causal finitist, I'm just critizicing your specific argument. I think Pruss' argument about fruits works perfectly.
Didn't he essentially respond to this with his example of the apple givers, where every apple giver still has their apple at the end of the time frame, which brings into question how they could give an apple when each apple giver still has their apple
Wouldn't causal finitism rule out an infinite future though? This seems problematic for theists.
I don’t believe so. At no moment in time t is it the case that an infinite causal chain exists, even though there will be infinite amount of moments.
Have a nice day! :)
@@ApologeticsSquared But just like you can trace an object's causal history to a starting point you can also do that in reverse and trace a future-facing causal chain to its endpoint (otherwise, you'd have to admit that there are infinite causal chains in the future direction)
If you want to say that the future isn't real and these chains don't exist yet then you'd have to assume an A theory of time, which is a minority view among both scientists and philosophers.
@@RandomYTubeuser // (otherwise, you'd have to admit that there are infinite causal chains in the future direction) //
I have no problem with that. The thing that I think is utterly impossible is there being some time t such that at t there exists something with an infinite causal history. But an infinite future does not give rise to such a state of affairs; only an infinite past.
// If you want to say that the future isn't real and these chains don't exist yet then you'd have to assume an A theory of time, which is a minority view among both scientists and philosophers.
//
Well, I happen to be an A-Theorist, but I don't actually think a particular theory of time is relevant. In fact, a causal finitist who embraces the A-Theory has to maintain that an infinite past chain of cause and effect is impossible, despite the fact that the past doesn't exist (anymore)!
Thanks for your questions! Have a nice day! :)
False argument because you are mistaking the time of the reaper for the time of Fred
Clearly it was the first Grim Reaper at 11:00, since he didn't have any other reapers before him. That he was followed by infinite reapers after he already killed Fred is irrelevant. This is stupid!
Let me try to explain this another way.
Take the set of the nonnegative integers: Set A = {0, 1, 2, 3, ...}
What's the biggest number in this set? Infinity? No. Infinity isn't in set A. Only integers are in set A, and infinity isn't integer. So, there isn't a biggest member of this set. If you think n is the biggest number in the set, n+1 is always bigger.
Now, we'll map every number n in this set to 2^n to form a new set: Set B = {2^0, 2^1, 2^2, 2^3, ...} + {1, 2, 4, 8, ...}
What's the biggest number in set B? The same thing is happening. There isn't one. For every 2^n, there is a bigger number, 2^(n+1) which is bigger.
Now, we'll map the every number n in the set of nonnegative integers to 1/(2^n): Set C = {1/(2^0), 1/(2^1), 1/(2^2), 1/(2^3), ...} = {1, 1/2, 1/4, 1/8, ...}
Set C definitely has a biggest member: 1. 1 is bigger than any other number in set C. But, is there a smallest number in set C? Is it zero? No. Zero isn't in set C, because there is no integer n such that 1/(2^n) = 0. Actually, every number in set C is the inverse of a corresponding number in set B. The largeness of the number in set B corresponds to the smallness of the number in set C. And, since there isn't a largest number in set B, there isn't a smallest number in set C.
Now, say that we have infinite reapers, each labelled with a nonnegative integer n, to wait 1/(2^n) hours after 11:00 to kill Fred. Is there a reaper scheduled at 11:00 exactly? No, because such a reaper would be scheduled zero hours after 11:00 to kill Fred, and there is no integer n such that 1/(2^n) = 0. Now, which reaper kills Fred? Well, it will be the one that waited the smallest amount of time to kill Fred. But, there is no reaper which waited the smallest amount of time. So, no reaper killed Fred. But, obviously, Fred has to die. Contradiction! So, this story is impossible.
I'm not that clever because I don't get the paradox. Why don't we just say the Grim Repear at 11:00? The first grim Repear?
The paradox’s construction is based on there not being a “first reaper.” There is no reaper scheduled AT 11:00. There and s a reaper scheduled an hour after 11:00, another half an hour after, another a quarter of an hour after 11:00, and so on. They each get closer and closer, so each one is beaten by another.
Have a nice day! :)
@@ApologeticsSquared
Ok.. I'm still lost. I've listened to Capturing Christianity channel and others. I just don't get it. Thanks for trying to explain it. You saying: "there is no first Repear" helps but why is there no first Repear? How can there not be if he's scheduled at 11?
I know I'm missing something because so many athiest acknowledge the strength of the argument but I can't see it
Okay. Let’s try it like this:
Draw a line on a piece of paper. Label the leftmost point 11:00 and the rightmost point 12:00. Below the line, write every natural number, from 1 to infinity (1,2,3,4,...). Now that you’ve written everything down, you get out a red pen. Make a dot in the middle of the line. This represents scheduling a reaper at 11:30. Since you’ve scheduled 1 reaper, cross out the number 1. Then, halfway in between that red dot and 11:00, make another dot and cross out the number 2. Now you have two reapers: reaper 1 and reaper 2. Continue with this process: you divide the leftmost segment in half and add a red dot, then cross out another number. Notice, once you cross out number 1000, it will be reaper 1000 that is up to kill Fred. Once you cross out 5000, reaper 5000 is first in line to kill Fred. So, if infinite reapers can exist, you can do this infinitely. You can cross out every number and make the corresponding reaper. So, which is in line to kill Fred? Well, reaper number infinity? There is no reaper infinity! The only numbers you wrote down (and later crossed out) were all less than infinity! So, none of them are in line to kill Fred. But Fred can’t escape them, so he must die. Contradiction!
Have a nice day! :)
@@ApologeticsSquared
I think I got it- thanks bro
So, Is Fred still alive?
Nope. Poor him.
Have a nice day! :)
Let me help you out here: it is the *exact* one who is a plank time after 11:00 (or the next one after that). Any infinitely decreasing collection shorter than a Plank time has no meaning in modern physics. This Zeno type of reasoning is hundreds of years out of date, and it's quantum homologous are a hundred years out of date. [This is fun, but it's very stale.]
This is a good point, but the scenario was already known to be physically impossible. The mass of infinite grim reapers would collapse into a black hole and so on. But, if our laws of physics are not metaphysically necessary, and physics could be some way such that reapers like this could exist and be set up in a chain, then the paradox is possible. But it isn't impossible, so we need to pinpoint what's barring it from possibility: the causal finitist argues that it's the infinite causal chains.
The grim reaper paradox ceases to be a paradox when you introduce randomness, which we observe in reality, so I've never found this argument convincing. In short, assume that each grim reaper has some non-zero probability p (
Not quite. First, you haven't answered the question; *which* reaper killed Fred? Secondly, there seems to be no metaphysical contradiction with a reaper having a zero probability of not showing up, which would leave the scenario unchanged. Thirdly, even if you say that randomness is necessary, you need to deal with the following: if something has a nonzero probability of happening, there is a possible world where that thing happens. If every reaper does have some chance of showing up, then there's a possible world where they all show up. But, in that possible world, which reaper kills Fred?
Have a nice day! :)
@@ApologeticsSquared 1) "which reaper killed Fred?" That's not part of the paradox. The paradox resolves if we know Fred is alive or dead. If you want to know which GR killed Fred, then you're appealing to PSR. But, it's sufficient for the weaker (probabilistic) PSR to hold if "some" GR killed Fred (or else QM breaks PSR).
2) Well if a GR has zero probability of not showing up, he has probability 1 of showing up. This just means you think the universe is deterministic (not probabilistic), which is fine, but is a strong position that I do not hold (as well as most physicists etc). I'm simply stating that, if the universe is fundamentally probabilistic (which seems to be the case), then the GR paradox is no longer a paradox. You asserting that the universe is deterministic is just that, an assertion.
3) I don't see why we'd have to get into modal logic. Even so, the probability of all (infinite number of) GRs showing up is zero, so it's not a problem.
I think you have to realize that Pruss' argument hinges on a lot of strong assumptions. His paradoxes can be solved when we introduce randomness, which is why he (unconvincingly imo) argues against randomness (but also walks a thin line between determinism). Sure, he has two PhDs, but so do a lot of people (including yours truly).
@@dr.shousa I *really* want to respond to everything, but I'm going to force myself to focus on your first paragraph, because that's the heart of the issue.
// "which reaper killed Fred?" That's not part of the paradox. The paradox resolves if we know Fred is alive or dead. //
I know of no one who construes that to be the paradox. If Fred is alive, he will become dead because a reaper will kill him. If he is dead, he will stay dead. So Fred is definitely dead!
But fine, whatever. Let's say the Grim Reaper Paradox is about whether Fred is alive or dead. Well, then let's talk about the Grim Reaper Paradox version 2.0! It's exactly like the regular Grim Reaper Paradox, except that the point of *this* paradox is "which reaper killed Fred?" Let's talk about *that*. Am I changing the subject? Nope! The Grim Reaper Paradox version 2.0 is what I EXPLICITLY presented in my video at 3:09. So let's talk about this paradox! :)
// If you want to know which GR killed Fred, then you're appealing to PSR. But, it's sufficient for the weaker (probabilistic) PSR to hold if "some" GR killed Fred (or else QM breaks PSR). //
This isn't actually an appeal to the PSR, but rather the Law of Noncontradiction which (pace Rationality Rules) is uncontroversial. You see, for any reaper scheduled 2^(-n) hours before 11:00, we can know that it was not the reaper which killed Fred, since it would have been beaten by the reaper scheduled 2^(-n-1) hours before 11:00. Thus, ∀r(-F(r)) where r ranges over reapers and F is defined as "being a reaper which kills Fred."
I'm breaking out FOL because you have two PhDs. :)
However, if "some" reaper killed Fred, then ∃r(F(r)). Which is definitionally equivalent to -∀r(-F(r)). Thus, if we maintain that no reaper killed Fred, yet some reaper killed Fred, we have ∀r(-F(r)) and -∀r(-F(r)), which is p and -p. Contradiction! QED.
Have a nice day! :)
@@ApologeticsSquared I mean Pruss himself states "Hence, if p is true, then no Grim Reaper kills you and a Grim Reaper kills you, which is absurd." So I think it's pretty clear that the paradox revolves around Fred being alive and dead at the same time (which I guess we can just call he's in a superposition, just like how physicists avoided breaking PNC for QM, but whatever).
Even if we want to know which GR killed Fred, I can simply state that it's the smallest i that satisfies t(r_i)-t(t_{i-1})>epsilon, where t returns the arrival time and i denotes the order of the reaper that shows up (with some probability).
I think you've forgotten that I had it so GR leaves Fred with some time epsilon, making your contradiction moot. The GR doesn't have to be the first to arrive to kill Fred, GR simply has to appear without another GR being present, which happens with probability 1.
Under my setup, this universe is causally connected (with some randomness) to some first random event, which acts as a causal reset (eg the first random fluctuation that caused the expansion). But we can still have an infinite chain of causality, as long as these casual resets happen at some point.
The bigger point is that we don't know/can't prove that FOL (and it's axioms) is correct. Even if we accept it (which most, but not all, do, and is why it's uncontroversial, at least with philosophers, but not with logicians), there's no way for us to know if it's correct/applicable outside this universe. Most philosophers (I've talked to) accept this limitation, but assume it for the sake of argument. Nonetheless, it makes these arguments, that extend to the metaphysical, quite dubious.
@@dr.shousa // I mean Pruss himself states "Hence, if p is true, then no Grim Reaper kills you and a Grim Reaper kills you, which is absurd." So I think it's pretty clear that the paradox revolves around Fred being alive and dead at the same time... //
But that quote from Pruss didn't mention whether or not Fred is dead; just whether or not Fred is *killed*; the problem seems to be that Fred is dead without being killed by a Grim Reaper, because you can't tell me *which* reaper killed Fred.
// Even if we want to know which GR killed Fred, I can simply state that it's the smallest i that satisfies t(r_i)-t(t_{i-1})>epsilon, where t returns the arrival time and i denotes the order of the reaper that shows up (with some probability).
//
In the setup that I presented in the video, that would be the first reaper who shows up and kills Fred. But there is no first reaper. Contradiction.
// I think you've forgotten that I had it so GR leaves Fred with some time epsilon, making your contradiction moot. //
I haven't forgotten about your setup. It's just that it's not what I care to discuss at the moment. I want to discuss the setup I laid out in the video. Does *it* produce a contradiction?
// Under my setup, this universe is causally connected (with some randomness) to some first random event... //
Again, it's not controversial that we can change the scenario that I presented in the video and get rid of the paradox. But what if we *don't* change the setup I presented in the video? Then which reaper killed Fred?
I'm expecting an answer like, "Well, you don't understand! I believe that the universe has randomness in it, which obliterates the paradox." Okay, maybe in the actual world there is randomness, but in a possible world where there is no randomness, what happens? Surely, even if there are no deterministic reapers and deterministic Freds, these are at least *possible.* So it would be possible to set up the paradox in the video. But the paradox entails a contradiction, and contradictions are not possible. So the paradox cannot happen. So, we have evidence for causal finitism.
// The bigger point is that we don't know/can't prove that FOL (and it's axioms) is correct. //
If my paradox relies on FOL, I'm *really* okay with that. :)
// Even if we accept it (which most, but not all, do, and is why it's uncontroversial, at least with philosophers, but not with logicians) //
That's news to me! Can I have a source on this?
// there's no way for us to know if it's correct/applicable outside this universe. //
What does that mean? Like, if I go to Mars, FOL doesn't change. But somehow, leaving the "universe" causes FOL to change? No theorem of FOL is dependent on a proposition about us being inside the universe! So what do you mean?
Have a nice day! :)
No you can't use the same logic on every reaper. The only reason this certain reaper doesn't kill, is that there is someone before him, either one position or ten or ten billion.
So whoever is first is the killer.
And you're claiming falsely that there's no such thing because there's someone before this first one. You lose this argument the moment you have to give the reapers room in time and actually draw a line saying 11 o clock starts right here. I don't care if it's the PLANK second or something smaller, that is 1 to the minus 915542694596621, I don't care! That second will eventually be history and the first moment will get colors changed.
The first reaper killed Fred.. no matter how many reapers you add the first reaper did it.
This is not a paradox.
There is no "first" reaper, that's the paradox. If one is told to kill Fred at 12, then 1130 (if he wasn't already dead), then the next one at 1115, then the next at half that, then the next at half that, then the next one at half that, for infinity, there is no "first one", however if the stroke of midnight is reached, it is guaranteed that Fred will be dead, because at least one of them would have realized he isn't dead yet and killed him.
This leaves us with Fred being dead but nobody having killed him. If you think it isn't a paradox and the "first one" killed him, can you tell everyone what time that was at, and show us the math for that?
@@godfreydebouillon8807 the reaper paradox as explained here not a paradox. It does matter what time the first reaper kill him. The paradox is not knowing which reaper did it not the time. But we do know. It's the first reaper he comes in contact with. There is no escaping any 1 reaper... it's impossible to know the time but we know the reaper.
The correct explained paradox is that there is world of infinite reapers. Only one reaper is scheduled to kill you at 12am. At 1am you will be dead for sure. If you are still breathing by 12:01 an infinite amount of readers will show to kill you from 12 to 1am only if your still breathing. The requirement for the reapers to appear is Fred still breathing. Not scheduled. So when 1am comes and Fred is dead we have no why of knowing what reaper did it. But if you scheduled all these reapers is the first one you scheduled. But if the reapers only appear if he is still breathing it's impossible to know who did it.
@@jonathanfranklin4448it's not that we don't know which reaper did it: it's impossible that any one reaper would kill you at 11:00
I don’t think either of your solutions to the “unified reapers” idea actually succeed in proving that we shouldn’t use this “unified reapers” idea in response to the grim reaper paradox.
With the red ball scenario, if the blue makers don’t have any reason to not change the red ball into something other than only blue, then no individual blue maker needs to change the red ball into a blue one since there’s another option available.
Thus, no matter if you have the whole group of blue makers or just focus on the individual blue makers, you still end up with a “random” colored ball.
The same reasoning can be applied to the example of the bag and the jolly givers. If the whole group of givers are capable of giving something other than an apple, then each individual giver doesn’t have to give an apple since there’s another option available.
Thus, no matter if you have the whole group of givers or just an individual giver, you’ll still end up with a “random” item in the bag.
I do agree that we shouldn’t look at the whole group of reapers instead of the individual reapers. I’m not sure if I have a solid reason why though. The best I got is that a group of individuals is different from adding numbers. From there it looks like there should be a way to successfully argue that a group of individuals must be evaluated as separate individuals in the paradox.
It seems you have a slight misunderstanding; Blue-Makers have no ability to turn things yellow. They can only turns *red* things into *blue* things. However, it seems there is no reason for the red ball to turn blue, because no Blue-Maker turned the ball blue! But, then, it seems inexplicable why the ball doesn't turn yellow; there seems to be no extra reason why the ball shouldn't turn yellow.
Have a nice day! :)
@@ApologeticsSquared I don't think I'm misunderstanding your response to the presented objection, but I might be misunderstanding that objection. The idea that I had about the objection was that it is kind of like it's acting as if the group of grim reapers is just one grim reaper. If we apply that idea to the arguments against viewing it that way, then the objection seems to still hold fro the reason I gave. If it's possible for the group to have some other result, then one individual could produce a different result since that's how the whole group is being viewed as. Like it's just one individual instead of many.
I think I understand (maybe). The thing is, it's not that the collection of reapers is being treated as one reaper, but the collection of reapers is being treated as a thing itself. It's like saying "the swarm of bees killed him." What I'm really doing is treating the collection as a thing itself, and talking about what that collection did. I'm not treating the swarm of bees like one bee, and swarms of bees can do things that individual bees cannot (like surround people). My point is that if we allow that the collection of Blue-Makers can make things blue, they should also be able to make things yellow.
Have a nice day! :)