The Kalam and Successive Addition | Dr. Wes Morriston
ฝัง
- เผยแพร่เมื่อ 15 มิ.ย. 2021
- Can an actual infinite be formed by successive addition? I'm joined by Wes Morriston to discuss this question and more.
Here's Wes' excellent 2021 paper that we are discussing in the video: www.tandfonline.com/doi/full/...
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RESOURCES
Malpass’ (2021) paper criticizing Craig’s successive addition argument: drive.google.com/file/d/1z07W...
Malpass and Morriston’s (2020) paper criticizing the Hilbert’s Hotel argument: drive.google.com/file/d/15XuA...
Malpass, Hedrick, and Morriston video on the Craig-Malpass debate on @Thoughtology : • Episode 16, Wes Morris...
Malpass’ response to Craig’s five-point reply to Malpass & Morriston: useofreason.wordpress.com/202...
My Kalam playlist: • Some Paradoxes of Infi...
And the usual links:
My book: www.amazon.com/Majesty-Reason...
My website: majestyofreason.wordpress.com/
Small aside: Pace what was said in the discussion, I've come to think that there's nothing inconsistent merely in claiming both (a) if the past were infinite, we would have always already arrived at the present and (b) if the past were infinite, we would never arrive at the present. For one can consistently hold both (a) and (b) and employ them both to argue against (the possibility of) an infinite past. (Even still, Wes argues quite forcefully in his recent AJP paper that the arguments in the literature for (a) and (b) fail.)
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Wes has the rare skill of being able to articulate very difficult and unintuitive things in a remarkably clear and precise way, and I think you too, Joe, share this rare skill. I'm looking forward to witnessing the heights you reach. Wonderful conversation, much appreciated
Glad you're beginning to research more on philosophy of religion.
@@matthieulavagna ^^^
This looks like someone went back in time and got interviewed by his past self.
Kalam: I’m gonna say 3 simple sentences that are easy to infer
Philosophers: is that a challenge?
WL Craig confuses a series with no beginning and a series with a beginning that occurred an infinite time ago.
Yet another wonderful discussion! Thank you Joe and Wes.
Love this channel so much! Excellent content!
Absolutely love the channel and the whole philosophy of religion community online. Really giving me a chance to exercise my philosophy muscle now that I've finished my degree and am moving on to different things!
yessssss so happy to read this comment!!❤️
This was great
I think I would deny that even the forward case of siccessive addition is impossible because of zeno paradoxes. Because its atleast I think not metaphisically impossible that space and time are continuous rather than discreet, and if that is or was the case what we have in a zeno paradox is an infinite series of events being completed in a finite ammount of time
Watching this video while also going through the corresponding paper is really helpful for understanding Morriston's argument. Joe you just need to interview every philosopher of religion on every paper they've ever written and I should be set. lol.
"You can't form an infinite series of events by successive addition" is ambiguous between (i) You cannot turn a series into an infinite series by successive addition (true but irrelevant to the Kalam) and (ii) You cannot have a series which is infinite and which has members constantly added by successive addition (relevant to the Kalam but cannot be shown to be true w/o already assuming the impossibility of an infinite past).
Great video, as always. Would you consider a Q&A video?? You’re a cool guy & I’m sure a lot of us are curious about your own journey & interests & whatnot.
Great idea! I think I will make an AMA/Q&A announcement video this week🙂
@@MajestyofReason let’s goooooooooo
The guy watching the video might try doing it grim reaper style.
Each video frame is indexed by a negative integer -n. He then watches the video frames in reverse at times 1-1/n. He will be finished by time 1 and then does it again for 2-1/n. It’s now his favorite movie.
🚨Kalam counter argument: ☝️anything that is sentient/has need/is rational/can reason/has will to do something/can differentiate between having and not having = needs a cause.
Seems to me that an oscillating universe infinite into the past would never have accumulated an infinity of oscillations in the first place, since any talk of accumulation necessarily suggests a point at which the number of previous oscillations is some natural number. But a universe infinite into the past would have no point in the past in which the number of previous oscillations is anything other than ∞. So the correct sequence then is, arguably, {...∞, ∞ + 1, ∞ +2, ∞ + 3,...}. A slight alternative which tempts me is to assert that (since infinity is not in the set of natural numbers) the number of previous oscillations at any point is 𝐮𝐧𝐝𝐞𝐟𝐢𝐧𝐞𝐝.
I wonder if the problem is solved if we define that in an infinite set -must- include all the elements in the set? Infinity + 1 in a way does not make sense. That is, if you add 1 to infinity then it is included without addition ... it is simply part of the set when it occurs. If there are an infinite number of stars, and we see a new star take shape, then it does not really make sense to say that now there is an infinite + 1 star in the universe. It also means that it does not really make sense to start at 1 and then count to infinity.
I'll be honest. I was never able to get how Craig ever got to the final important part of the argument.
The same way there cannot be a beginning of existence, there cannot be a beginning of motion. Existence doesnt change, change and time are seemingly mind dependent illusions.
Question: Wouldn’t there be an actual infinite for any temporal series that originate from a singularity because of infinite frame dragging (even if spacetime is quantized)? Wouldn’t the limits imposed by quantized spacetime be made inoperable because of the infinite curvature of spacetime attendant to inertial frames near a singularity?
hello Joe, nice video again, thanks a lot. I want to ask you an unrelated question, what do you think about the theory of time, is it theory A or theory B, is it correct, also what do you think about the god time relationship around time theories, do you think divine timeless god or divine temporal god what do you think about it? is it more reasonable?
Is there a difference between the theories such that they can't both be true?
Hy Joe,
I have a question about the discussion at 43:54 (why did he finish it at a specific time). If I understand correctly, the answer was that the shifting of time is necessary for creating the contradiction but shifting of time is incompatible with Craig view of time. I feel like there is a way to pose that problem without any shifting.
- Lets say there are two counters, each counting at exactly the same time every day and they have been counting forever.
- From the supposition that there is a 1-to-1 correspondence between the set of ]-infinty, -1] and ]-infinity, 0] it would follow that its a possible scenario that at the same day one counter arrives at -1 while the other arrives at 0.
- But this can't be true if they both counted at the same moment every day, right?
Or am I misunderstanding something? If I don't, what solves this contradiction? Although to be fair, this seems to be more of a mathematical problem that should equally plague the mathematical usage of the concept of infinity, not just a metaphysical problem that only plagues the concept of infinity in reality.
An infinite future isn't needed for heaven. I'm in heaven now
@@CosmoPhiloPharmaco Heyhey! Long time :)
That was a great topic, I wouldn't say I've done further research, but I have discussed it with my wise old dad a couple of times.
Do you reckon the same problems arise when considering a single universe with an eternal timeline?
@@CosmoPhiloPharmaco My dad and I haven't reached any firm conclusions :)
That sounded solid to me. I was thinking similar conditions should apply as with the variety of infinite multiverse models, and you've phrased them well.
Analogously, maybe there's an infinite multiverse without repetition. There could be infinite possible configurations of the constants of nature, and no repeats among all of those actualized in universes.
Also perhaps, even given the same constants, if each universe has infinite particles there could be infinite possible arrangements of them. But maybe infinite particles implies a spatially infinite model, and all that would be relevant here is any particular observable universe patch.
hmmmmm.... :)
*"the same (or similar)"*
-- Given that infinite particles allows for infinite possible arrangements of a single universe (if I'm right about that), should we think that there must still be only finitely many _non-similar,_ significantly different possible arrangements?
Or could there be infinite significantly different arrangements?
@@CosmoPhiloPharmaco (Part 2) Oh oh! Upon realizing just now that maybe there are an infinite variety of types of particles, I lean towards it being possible that there are infinite significantly different arrangements of matter, even within the horizon of a finite observable universe. I'd been thinking of rearranging a limited set of particle types actualized in infinite quantities, but that assumption can be dropped.
That may also be relevant where you said *"Given eternal time, it seems unavoidable the same (or similar) configurations of matter will be actualized infinitely many times. Right?"*
You gave two ways to avoid that, maybe this is a (3)?
p.s. What can I call you?
I'm sure it was the Greek letter Psi last time, but now you're Lambda :P
@@CosmoPhiloPharmaco Arnaud, alright cool. Lambda is great! I think the story of Einstein's greatest blunder is how physics books first began captivating me at the age of 8.
It was mostly Paul Davies and Michio Kaku books, and another topic they regularly covered was M-theory, the string theory cosmology with universes as membranes floating in a higher dimensional space. As far as I can see, that would allow for multiple coexisting spatially infinite universes, without logical contradiction.
Similarly but without working out the details so rigorously, science fiction explores the idea of parallel universes or other 'dimensions', which inhabit different spaces that don't overlap.
These have basically always been in my mental repertoire, so I don't have much of an intuition that a multiverse of spatially infinite universes seems logically impossible.
To me it only seems to conflict with the Max Tegmark 'level one' multiverse, calling a single spatially infinite universe a multiverse of universe pockets. That whole infinite space is what we are calling 'a universe', so if we try to make it the multiverse too then a single one seems to take up all the space.
Maybe with M-theory one could object that the universes are infinite in 3 spatial dimensions, but not in the fourth where they are thin membranes.
... But I don't think we have any context here needing us to have universes that are infinitely extended in _all_ the spatial dimensions, in the logically consistent model we are searching for. Do we? Just 3 I think.
That does raise an interesting angle though - maybe one or two dimensions of a normal 3D universe are spatially infinite, but not all three.
Then even without M-theory's extra spatial dimension, you could have an infinity of universes that have infinite volume. Stacked or floating parallel to each other M-theory style. An infinitely tall pile of infinitely long sausage universes! :D
This might even resolve that apparent contradiction between a Tegmark level 1 multiverse and what we are considering... but it might be abandoning too much of the idea of a spatially infinite universe for each sausage to count.
It could also be tough to argue these sausages count as distinct universes, but we do manage that one in M-theory so I think it could probably be overcome. :) :)
Hi Majesty, I understand you have compelling reasons for atheism to be true as well as theism. Could I check out any videos from you steelmanning an atheist position?
The Sanskrit word Ananta means without end. Such a concept is not subject to the same objections as infinity.
Is it possible that what William Lane Craig saying is that you can't add anything to infinity like if there were an infinite number of days before yesterday then you can't have today because you can't add anything to yesterday because the number of days is already infinite?
He is saying that infinites cant be formed through successive addition and you cant traverse an infinite.
I think Wes completely destroyed any indexical arguments about traversal that Craig could make by pointing out that if a relational view of time is true, you can't think about time outside the immediate relations between objects.
The only interesting arguments left are causal arguments, and difficulties in describing a present caused by infinite historical events.
Wes Morriston DESTROYS logos
What if all events exist simultaneously i.e. they are time independent. Maybe causality is cyclical. In other words, all events exist necessarily and thus are either mutually dependent (x's cannot exist without y's and vice versa) or the causal chain itself is ontologically independent (expressions such as ‘x is a part of y’ or ‘x is a whole composed of some ys’ convey abstract judgments from a particular limited perspective). Maybe our theories on mereology are riddled with unprobable assumptions.
The point about a beginningless series, as far as I understand it, is that if the present moment would have needed to be preceded by an infinite number of moments, then the cause which created this moment can be pushed infinitely in the past, or in other words, the cause of the present moment will always have something in front of it before it hits this moment, thus never being able to reach it. We could imagine an infinite series of dominos which must knock over the last domino. The force which must have passed and hit the last domino would be told "No im sorry before you hit this domino you will have needed to hit this domino, and before this domino you will have needed to hit this one ad infinitum" if this is the case then there will be an unlimited number of things preceding the last domino and surely one cannot get through an infinite number of things.
@@peterevans1572 I'm familiar with his objection, but this was meant to address it not to fall prey to it. I am not saying one has to somehow count up(or back in this case) to infinity from the first domino and lo and behold one can never reach infinity (because I secretly started at a first member while arguing). I am, instead saying what we know, that there is a last domino and that an infinite amount of things preceded it. If it is correct to say "an infinite amount of things happened before that last domino" then you are left with the same result I mentioned before. Namely, an infinite amount of things preceded this domino, but if the cause of this domino could never reach this domino because an infinite amount of things would need to occur before this domino, then we would never reach this domino. You can always stack something up before it to continue the infinite chain, so to speak. The only way I can see to get around this would be to say something like "an infinite amount of things need not happen as at any point they will have already happened, or in other words, the infinite series never 'happens' in any meaninful way, rather it just 'is'." This reply though seems a little incoherent as 1. the worry that anything which just "is" smacks of irrationality and 2. as a time ordered series we are implying these things happened and occurred, each one having its moment before the next. If we say that there is no way in which it happened but only "is" we seem to be having our cake, by calling it time ordered series, and eating it too, saying it doesnt proceed as a time ordered series does(i.e "happens" and unfolds", but just "is".) Or in other words, its quite strange(and likely more than strange) to suggest that a series which suggests itself to proceed one after another in time should be said not to have really done that but to have always just sort have been there as if appearing all at once in an instant(like an infinite pile of rocks, none having to precede before the other rock). Since however we say this series is one within time, it seemingly only makes sense to apply the characteristic to it that the members are passed through, but this leads us to the problem mentioned above.
Correct, also none of the dominoes fall over because there is no first domino. Not only will you not reach this current event you will fail to reach any event ever, because there is no beginning or first domino. Their literally must be a beginning for any temporal moment to occur.
I'm currently studying mathematics and have always thought Craig and others have been wrong on saying that you can't arrive to today with an infinite universe. But have had trouble articulating why. My reasoning have been (without going into details) comparing the setup with a continuous random variable. In this case getting any specific outcome is probability 0 and yet we get a specific outcome. If we imagine us to be some kind of God outside the timeline of a universe with a infinite past then the probability that the present would be any specific day is again 0 but yet it obviously has to be one specific day.
If you were standing in line and there were an infinite number of people in front of you to order food, would you ever get to order food ever.
I agreed with most the points. I didn't agree with one of the way they answered the question of having had sufficient time to count down from Infinity until now. Craig s objection there has nothing to do with series of events being consistent being equated to time. The fact that Craig's hypothetical question isn't consistent with his own view of time isn't a problem since he's trying to show that same very point: that it's inconceivable. There were other easy answers to this question I believe however.
Hi Joe, I was wondering how can I get your book in paperback? I checked and only kindle edition was available.
Thanks for your message!🥰
Are you in the U.S.? The paperback is not available in every country, unfortunately
@@MajestyofReason
Ah, I am not from.U.S, but India.
Is it possible to make it available here anytime in future?
I'm quite interested in Philosophy and want to learn it from scratch.
@@moviescrew8638 unfortunately, I don’t have control over the countries the Amazon publishing house ships my book to😢.
So I think you might have to go with the kindle version, unfortunately. (If that is also unavailable, just email me at majestyofreason @ gmail . com and I’ll help ya 🥰)
Finally, I think you will really enjoy my “essential reading list” near the end of my video entitled “What is Philosophy?”❤️
@@MajestyofReason
Thanks for your replies and attention.
I'll surely check out the reading list and will look for the kindle edition.
Keep doing the great work.
I have one last question,
What do you think of Transcendental Argument for God and Jay Dyer?
@@moviescrew8638 my response is broadly aligned with Josh Rasmussen’s🙂 th-cam.com/video/Zkcs-31PqFg/w-d-xo.html
(P1) If time is finite, then walking from beginning to the end of the 2D-spiral t*(cos(arctanh(2(t-0.5))),sin(arctanh(2(t-0.5)))) with t∈(0,1) - finite time intervall from 0 to 1 - would be possible.
(P2) Since the 2D-spiral t*(cos(arctanh(2(t-0.5))),sin(arctanh(2(t-0.5)))) with t∈(0,1) crosses the x- and y-axes on the 2D-coordinate system infinitely many times and is infinitely long,
walking from beginning to the end of the 2D-spiral t*(cos(arctanh(2(t-0.5))),sin(arctanh(2(t-0.5)))) with t∈(0,1) is impossible.
(Conclusion from P1 and P2)
Time is not finite.
Hm. I guess then, that space-time topology or topologies in general are a *****.
I think your argument is extremely esoteric as it seems to include alot of mathematical calculations. The ordinary laymen may not be able to grasp the content for your case. I certainly was not able to.
Craig's confusion is that today (the present) is the end of a beginningless series, but he is wrong, tomorrow is. Today is n and n is always finite. Tomorrow is n+1 and continues (tomorrow never comes).
I seem to have the intuition that if a begginingless series of events can be an actual infinite than there is a point in the past that is an actually infinite distance from the present and than we could choose that point as our first member. It seems like Wes is going to say that there is an infinite series of past events each of which is a finite distance from the present. To me that doesnt seem to make sense. Maybe I am misunderstanding something or my intuition is wrong. How do you think Wes would respond?
When we say the series of past events is beginningless, we're supposing that the set of past events has the same cardinality as the set of natural numbers (aleph null). Just as there is no natural number infinitely distant from 1, there need be no event infinitely distant from the present. Yet the cardinality of both sets is actually infinite (aleph null).
I think the clearest reply would indeed come from looking at the Natural numbers. So I would like to ask you, does your intuition tell you that there is Natural number N such that |N-1| or the distance between N and 1 is infinite?
@@rishabwarrier2769
The difference between natural numbers and the infinite series of past events is obvious: temporal becoming.
We do not have the intuition that there is any number after the natural ones because there are no cross-temporal relationships in this set. But we have the intuition that, if today it is true that "X events occurred", then there was a time when it is true that "X events will occur".
Malpass answers this by saying that this equivalence is not always possible, using the example of the beginning of time: it is true today that "the beginning of time has occurred", but it cannot have been true at any time that "the beginning of time will occur". But this argument only serves to show that time can never start or end (which is intuitive a priori), although events need to start or end. This is exactly Swinburne's position.
@@caiomateus4194 I'm sorry it's been a while since this comment I'm a little lost are you saying it's intuitive that temporal history is past infinite? And what exactly does cross temporal relationship mean here?
@@rishabwarrier2769
I meant that it is intuitive that there was a beginning of time, because for every truth about "what happened", there is also a corresponding truth about "what will happen", and vice versa. These propositions about the future and the past are derived from cross-temporal relations, which are not present in the numbers.
An eternal past would involve a moment when it is true that "infinite events have occurred", the present moment. But it would not involve a moment when it is true that "infinite events will occur".
I’ve been thinking about this all day, and it all just seems so unintuitive to me
here’s how i look at the problem:
We have an ending point: the present, and the present is dependent on the succession of all past events. If the past is infinite, then that means the present is dependent on an infinite series of successive past events. If we’re here in the present, and the present is the result
of, or in some sense, dependent on the infinite succession of past events, you should be able to arrive at infinity by counting the successive events into the past, since they are what the present depends on. But as it was said, you can’t ever elapse an infinity going this way. But you can have an infinity going the other way? it just seems unintuitive and odd to me even if I admit there isn’t an explicit contradiction. I want to think about it more, but I really just wanted to let you know you’re driving me crazy with this, haha!
This is why I think that causal arguments against an infinite past are stronger than merely indexical or cardinal arguments. A way I explained it to Tommy on the Discord in a way that he could understand it, went something like this:
Suppose that you're researching the evolutionary mechanism of a certain virus, and knowledge of how the virus is in the present depends on knowing how it came to evolve over generations in the past.
Now if the virus evolved over an infinite number of generations, then the following fact is true: "For every n generations you account for in the evolutionary history of the virus, there's another 10^n you will not have accounted for in the evolutionary history of the virus."
Now what this means is that both are true at the same time.
1. For every natural number, n, there exists some t_n at which n past events is accounted for.
2. For every natural number, n, for the same t_n, there are 10^n past events are not yet accounted for.
This means that it's not good enough to merely say that for every natural number n, there will be a time at which n is accounted for in the past, because it's also true that every time n increases, there are more and more not yet accounted for facts in the past, i.e. the further back you evaluate the past, the more behind you get relative to when you started. But what really gives these facts context is that these are missing generations in the evolution of this virus, which means our lack of knowledge about these generations causes a lack of knowledge of present facts, and the hole in this knowledge isn't going anywhere.
I find arguments like this convincing, and so my view is a hybrid of causal finitism with respect to our (or any individual) past history, but with the possibility that you can have an infinite number of causally independent past histories back through time.
I think, that you conflate *Global and Local Explanation* in infinite regressions ( 3. Regress and Global and Local Explanationfrom plato.stanford.edu/entries/infinite-regress/ ).
If the past is infinite and each event should be accounted for somehow, then each event can be accounted for by the previous event directly _ad infinitum_ .
There is no problem with local explanations of each event, so they are possible.
If the past is infinite and any event should be accounted specifically by the account of the infinite past and events as a whole by _ad infinitum_ local explanations, then any event must be accounted by the first event of the infinite past, which there is none, because you know, the past is here supposed to be infinite - without any first event.
So a global explanation is in that sense not possible, but regardless of that any event can be accounted locally _ad infinitum_ and just because we are not capable of accounting any current event globally by the infinite past, from that doesn't follow, that the infinite past is impossible. Only the global explanation is impossible.
The infinite past in itself with local explanations is possible.
Actually any physical and natural law formulated as a differential equation in time is a local explanation of events. Our past might be infinite or not.
I hope, that this clears up somethings for you.
@@logos8312 I don't find your explanation in any way convincing.
If the virus evolved over an infinite number of generations, then one might also say, that "A generation of virus is accounted if and only if there is a descendant generation of the considered generation of the virus."
My parents are accounted by my existence and my grand parents are accounted by the existence of my parents and so on _ad infinitum_ .
This also goes for the generations of the virus and also for events.
So each generation of the virus and each event of the infinite past can be accounted for in this logical sense.
@@zsoltnagy5654 but I'm not just accounting for each generation of the virus, but how it evolved through time at all stages to reach whatever generation it's at now.
Failing that, we have no complete causal explanation for the evolutionary process of the virus.
@@logos8312 But how do we have no complete causal explanation for the evolutionary process of the virus?
If evolution has been very well understood in a general manner, so that it is very clear how *any* generation comes to be by the previous generation or how *any* generation has been evolving into the next generation, then I think each generation's existence can be accounted for by the existence of the descendant generation.
If we have all the necessary and sufficient intel about the biological *Markov chain* and matrix ( en.wikipedia.org/wiki/Markov_chain ), then I think that from a given generation any other generation can be more or less accounted or determined into the future or into the past (-a lot of physical and natural laws and prozesses are symmetrical in time).
So how exactly is the causal explanation in that sense incomplete?
Even if it might be currently incomplete, couldn't it be then completed?
Jones couldn't have been videotaping himself
from forever because then at what point did he turn on the camera? If he turned on the camera at any point, then he has not been videotaping himself since forever. If he did not turn on the camera at any point, then he has not been videotaping himself since forever. An infinite past of some event always produces a logical contradiction because there's no ultimate explanation of the events. Causal finitism is a first in metaphysics in my opinion. Not affirming it is irrational. It's so basic that no arguments are needed to defend it. It's self-evidently true.
Of course, if he's always been filming himself, he never turned on the camera. That's no justification that something can't be always true.
At what point did casual finitism become true?
@@goldenalt3166 Causal finitism is a concept that never "became" true. It just is true per metaphysical necessity. It's similar to the laws of logic. They never "became" true. Certainly, there's a point at which time began and thus causal finitism was in some sense actualized however that's beside the point. What I am saying, is from the mere existence of time we can infer a beginning.
@@goldenalt3166 I never made the claim that something can't always be true. There are facts about reality that need an explanation like videotaping with a camera.
@@michaelsayad5085 Why does videotaping require as explanation? And casual finitism not require one?
@@goldenalt3166 You don't see the difference between having no further explanation for the law of non-contradiction and having no further explanation for why the camera is on instead of off? I believe causal finitism is more like the first rather than the second.
wes looks like your grandpa
The argument being discussed around 49:00, if taken to be sound, would also have to prove that there is no such thing as infinite space. After all, if the Universe is infinite, why isn't everything shifted over 1 m from where it actually is? No ultimate explanation could ever be given. Just like the time version, this argument fails because space is relative. There is no difference whatsoever between our Universe and a Universe where everything is shifted over by 1 m because they are actually the same Universe, just with a different coordinate system, and our choice of coordinate system is arbitrary. Likewise for time - our choice of what time to treat as t=0 is arbitrary.
The argument also seems to make many implausible metaphysical assumptions anyway, like the A theory of time and the principle of sufficient reason.
Anyone who defends an infinite past is just sticking their head in the ground
Press X to doubt
@@MajestyofReason I cant believe a guy as smart as you thinks this is possible.
@@ceceroxy2227 I never claimed it's possible. What I *do* claim is that the successive addition argument against its possibility fails :)
@@MajestyofReason so you believe that you can have an actually infinite number of things through successive addition.
@@ceceroxy2227 wrong. I believe that an argument against that claim fails.
A beginningless series never started, so no series actual happened.
can you get rid of the Arsenal Stuff and support a proper Team like Birmingham City! KRO (look it up)