New objections to the Kalam still work
ฝัง
- เผยแพร่เมื่อ 15 ก.ค. 2024
- Recently, Tyler McNabb had William Lane Craig respond to new objections to the Kalam. In this video, I explain why Craig's responses fail.
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OUTLINE
0:00 Intro
0:15 Objection 1: Potentially infinite?
27:41 Objection 2: Ad hominem?
32:49 Mathematical induction
55:57 Each vs. all
1:06:46 Objection 3: Transfinite subtraction
1:12:19 Tyler’s addition: seemings
1:23:44 Objection 4: Inexplicable countdown?
1:35:10 Grim Reaper Paradox
1:53:56 Conclusion
NOTES
(1) At 1:19:17, I mention arguments for specifically Platonic views of properties, but standard theistic conceptualist views will also involve actual infinites (namely, infinitely many divine concepts, ideas, etc.).
(2) I accidentally clipped out half a sentence in my editing! At 1:20:49, the sentence should conclude: "...it licenses you to conclude that there's a possible world containing precisely that arrangement of regions."
LINKS
(1) The original video from @furtheringchristendom714: • New Objections to the ...
(2) My Prosblogion post: prosblogion.com/2023/01/10/an...
(3) Video with @guardedacumen: • The Kalam and Endless ...
(4) My Kalam playlist: • Kalam Cosmological Arg...
(5) Morriston, "Craig on the actual infinite" (2002): drive.google.com/file/d/1EDk_...
(6) Malpass and Morriston, "Endless and infinite" (2020): drive.google.com/file/d/15XuA...
(7) @thoughtology7732 video: • Episode 16, Wes Morris...
(8) Morriston, "Infinite time and successive addition" (2021): drive.google.com/file/d/1qUJz...
(9) My video on successive addition with Morriston: • The Kalam and Successi...
(10) My Hilbert's Hotel video: • Hilbert's Hotel: A Com...
(11) Swingrover, "Difficulties with William Lane Craig's Arguments for Finitism" (2012): drive.google.com/file/d/1nQPe...
(12) @Friction's video "Revenge of the Grim Reapers": • Revenge of the Grim Re...
(13) My Springer book: (a) www.amazon.com/Existential-In... (b) link.springer.com/book/10.100...
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Note: I accidentally clipped out half a sentence in my editing! At 1:20:49, the sentence should conclude: "...it licenses you to conclude that there's a possible world containing precisely that arrangement of regions."
I have two friends that have earned PhD's in Philosophy one who earned her PhD from Cambridge and one who earned his PhD from Brown University who is teaching at one of the top Universities in South Africa. A number of years ago I asked them what they thought of William Lane Craig and they stated the William Lane Craig was only taken seriously inside of Christian Apologetic circles and was not taken that way outside of that circle. This was well before Low Bar Bill made an appearance hopefully I will be able to ask them both the same question in the future; I'm thinking WLC has become some what of the butt of some unkind jokes.
The ability of joe to uniformly put soo much effort into each of his responses is incredible.
I really do care about helping people get to truth of these matters❤
It’s legitimately discouraging to hear Craig talk about these objections... props to you for dealing with this without screaming
Well, there wasn’t any screaming in the video at least.
You just have to lower your expectations to William Lane Craig objections to 1 in a million before you lose the desire to scream.
Thanks Low Bar Bill.
@@vestafreyja that got me laughing a little bit.
I don't know how much clearer one can make these points, yet somehow they seem to elude Craig each time he encounters them. He needs to be confronted with these objections in a live debate so he can't evade the reasoning with slippery language and changing the subject.
The person I agree with is right again.
Craig will never agree to debate or even dialogue Joe. He’s probably worried about being tripped up by someone so young.
This isn’t the only issue where Craig avoids sufficient live engagement with critics
Joe setup a debate with malpass and Craig! Or Morriston!
@@TheProdigalMeowMeowMeowReturns well he said he wouldn't engage with Scott Clifton of theoretical bullshit but then they eventually had a discussion so you never know.
That's kind of also the way he debates live. If pressed on it, Craig would fall back to the "why are you so upset about this" stance he uses to evade and dismiss legitimate questions; see his own website's Q&A section, where he does this constantly to portray others as emotionally motivated and "angry" at the obvious conclusions of his points. What you would probably need is a sharp and well-educated moderator who will hold Craig's feet to the fire if he's not actually addressing the point he's supposed to be addressing AND who is neutral enough as to be an acceptable choice by both parties to the debate, and I have no idea where you'd find someone like that.
You are great for my attention span, Joe. I find hours go by without me losing focus on your topics. To be fair, I like what you talk about
seems to me, with this definition, that really the future is either finite; time (space-time) will cease to exist as it does now. Or time is infinite and will have no end. And so, given this definition of potential infinite, the future can't be potentially infinite, we just can't tell if it's finite or infinite.
You can ask Cam to arrange a formal debate with Craig on this new objection. This might be a good idea .
Craig only debates people with a PhD; but if he were to break this rule, I'd accept the debate in a heartbeat! :)
Also, we should keep in mind that he's already had ample opportunities to respond to these sorts of objections; he's tried responding to them in print multiple times over, and he's also done it on TH-cam channels. Each and every time, he falls back into the same mistake: confusing the simple future tense with the future perfect tense. He's enjoyed countless opportunities to defend his view from these objections, and yet he hasn't come close to succeeding in that defense.
@@MajestyofReason ig now just like Fodor you also have to wait for few years and after completing your your PhD. You can finally defeat the great kalamful scholar Craig the potential enjoyer.
Or you could just bring him again for non debate non PhD discussion . Whichever is easier.
Have a kalam day 👀
@@MajestyofReason thanks for the info
I think Craig has had, if not debates, exactly, at least some public dialogues with non-PhDs, such as Alex O'Connor.
@@MajestyofReason I think Craig is just being dishonest here, this mistake has been pointed out too many times. I don't buy the idea that he just doesn't understand the argument.
After watching Craig’s response to objection 1, I’m curious to know this:
Is there any other field in philosophy where one of the most widely known and widely cited figures in that field has known about such a simple and indisputable counter argument to their position in the published literature for 20 years, and still failed to understand and incorporate the criticism?
It’s nice to know that others feel the same frustration that I do about this.
Well, you have to understand: Craig is not *doing* philosophy. He's doing apologetics. His *job* is to ignore all evidence & arguments, and tell his christian audience that their faith is just fine.
@@jursamaj Broadly speaking, I agree with you. I’m not sure I’d want to say it’s his job not to understand, but at the very least I think Craig faces strong incentives to misunderstand and misrepresent in virtue of his job. I think philosophy of religion has this problem more broadly, and there are plenty of philosophers who have said as much.
@@jursamaj exactly. He's using the Kalaam, something that can be applicable to any of the religious gods of history, to argue for a specific religion: Christianity.
That's what apologetics do.
Why should another theistic believer from another religion take him seriously with his own conclusions?
@@mf_hume
philosophy:
the love of wisdom, normally encapsulated within a formal academic discipline. Wisdom is the soundness of an action or decision with regard to the application of experience, knowledge, insight, and good judgment. Wisdom may also be described as the body of knowledge and principles that develops within a specified society or period. E.g. “The wisdom of the Tibetan lamas.”
Unfortunately, in most cases in which this term is used, particularly outside India, it tacitly or implicitly refers to ideas and ideologies that are quite far-removed from genuine wisdom. For instance, the typical academic philosopher, especially in the Western tradition, is not a lover of actual wisdom, but a believer in, or at least a practitioner of, adharma, which is the ANTITHESIS of genuine wisdom. Many Western academic (so-called) “philosophers” are notorious for using laborious sophistry, abstruse semantics, gobbledygook, and pseudo-intellectual word-play, in an attempt to justify their blatantly-immoral ideologies and practices, and in many cases, fooling the ignorant layman into accepting the most horrendous crimes as not only normal and natural, but holy and righteous!
An ideal philosopher, on the other hand, is one who is sufficiently intelligent to understand that morality is, of necessity, based on the law of non-violence (“ahiṃsā”, in Sanskrit), and sufficiently wise to live his or her life in such a harmless manner. Cf. “dharma”.
One of the greatest misconceptions of modern times is the belief that philosophers (and psychologists, especially) are, effectively, the substitutes for the priesthood of old. It is perhaps understandable that this misconception has taken place, because the typical priest/monk/rabbi/mullah seems to be an uneducated buffoon compared with those highly-educated gentlemen who have attained doctorates in philosophy, psychology and psychiatry. However, as mentioned in more than a few places in this book, it is imperative to understand that only an infinitesimal percentage of all those who claim to be spiritual teachers are ACTUAL “brāhmaṇa” (as defined in Chapter 20). Therefore, the wisest philosophers of the present age are still those exceptionally rare members of the Holy Priesthood!
At the very moment these words of mine are being typed on my laptop computer, there are probably hundreds of essay papers, as well as books and articles, being composed by professional philosophers and theologians, both within and without academia. None of these papers, and almost none of the papers written in the past, will have any noticeable impact on human society, at least not in the realm of morals and ethics, which is obviously the most vital component of civilization. And, as mentioned in a previous paragraph, since such “lovers-of-wisdom” are almost exclusively adharmic (irreligious and corrupt) it is indeed FORTUITOUS that this is the case. The only (so-called) philosophers who seem to have any perceptible influence in the public arena are “pop” or “armchair” philosophers, such as Mrs. Alisa “Alice” O’Connor (known more popularly by her pen name, Ayn Rand), almost definitely due to the fact that they have published well-liked books and/or promulgate their ideas in the mass media, especially on the World Wide Web.
Thanks to you, I'm now going to put into my quiver of good practices the strategy of looking for hidden, unstated, or implicit conjuncts.
The old Kalam may not ever be settled as maybe in the future there could be new arguments for the universe beginning to exist (in Craig's complicated sense of beginnings) and for the Kalam's causal principle, but I think you and the other scholars who have responded to it have put up many serious barriers to the argument succeeding that are probably not going to be sufficiently addressed within our lifetimes. Well done! ^w^
Much love❤️❤️
I don’t think I am ever reaching this level of philosophical sophistication
I can help you get there!!
Your list of reasons for thinking that an infinite past is possible at 1:20:10 is very helpful.
Great video, Joe!
Thanks my man. Glad it could serve you :)
Even if God came down from the skies and told Craig the Kalam isn't sound, my bet is that he would still believe it is correct in his heart!
@LuthAMF
So perfect that it is unconvincing to most people.
@LuthAMF
Proving that there isn’t any credible evidence for the core doctrines of Christianity…
@LuthAMF Even Craig has admitted that the Kalam *doesn't* get you to *a* god, let alone the christian God.
In any case, apologetics isn't about proving christianity. It's about telling christians that their faith is just fine, and not to worry about all that evidence against it. And since most christians *want* to believe that, it's not a hard sell. In *that* sense, I suppose it is just about the perfect apologetic.
@LuthAMF Good luck with that, since "apologetic" isn't mentioned in the bible, let alone defined.
@@jursamaj
Exactly, apologetics isn't about convincing non-christians... it's about helping Christians feel less stupid for their beliefs.
Oh my God, What a Kalamity!!!
Beautiful work man. Yep language is often unclear, but that is why we supplement with these structures, these are the structures we are talking about. I don't know how more explicit you can be, there's a sense which this is basic stuff, yet infinity is quite unituitive, one doesn't know when numberness still applies and when it doesn't apply. The structure which is preserved under the mapping and the ones who don't apply any more. Maybe you could shove a category theory graph into in his face and explicitly say this survives and this doesn't, but in normal language.
On the structure of a number:
Well if you ignore the position of the objects in space (undefined or given as arbitrary), give them an equivalence relation kind of and yet they are distinct by "order" even though the order in which you count them is ignored (arbitrary) and such that each object is only mapped one-to-one I don't know how you know that without counting though. In the sequence of counting that includes all the pervious cases or just individually has the index (just the name) of the set and has to be finite... ...sure
It occurs to me that (one of) Craig's problem(s) is that he keeps equivocating "a potentially infinite series of events" with "an infinite series of potential events", which I think are different things, but he seems to think they're interchangeable? If I were inclined to be charitable, maybe he thinks the "potential" or unreality of the events in question make this equivocation valid in some way?
I wouldn't be surprised if Craig ended up doubling down on his claim that the endless future is a potential infinite on his deathbed.
Man this is so mathematically satisfying. It’s a rare treat that something is being: philosophically, mathematically, critically satisfying, and healing my childhood trauma😂
I'm here for philosophical therapy😆
I think Craig should just accept that actual temporality can be defined as an infinite present, and that the measurable collection of what will occur includes an infinity of potential presents. That, to me, seems to be the logical implication of Presentism.
Hey Joe do you think that arguments which challenge the traverability of infinites (like Craig's immortal counter argument) are stronger or more defensible than those that challenge the existence of actual infinites (like Hilberts hotel)?
Great content btw. Love your channel
Much love❤️
Excellent question. Do I think those are stronger? I think they’re both quite weak (though I wouldn’t describe arguments for causal finitism as weak, even though I disagree with them). But yeah, I think the traversibility argument from Craig is less weak than the argument from the impossibility of actual infinites. The latter can be attacked from so many angles - from mathematical realism, realism about propositions, endless future problems, conceivability, and so much more. I give, like, 10 different problems in my Hilbert’s Hotel video (and within those there are sub-problems). By contrast, the traversibility argument doesn’t have *as many* problems, I don’t think.
Great question, tho
@@joelapratt Well the first thing to remember is that there are different kinds of infinite sets, and not all infinite sets lack a first or last member. For example, the set of non decimal negative numbers less than zero is infinite, and yet it has a last member (-1). Likewise, the set of whole numbers greater than zero is infinite, and yet it has a first member (1). Now assuming the past is infinite, it's not necessarily true that we are at the last member of an infinite set of days. If the A theory of time is true then that's probably the case, but if the B theory of time is true then we're probably not at the last member of an infinite set of days.
13:01 it’s not just modeled by the positive x-axis, it is modeled by the whole x-axis, you can be in a negative “year” and just use negative years too. It would be true relative to the moving now, but that’s another reference frame.
There are two independent zeros used for reference.
The parentheses here define what number we are asking if it’s always positive: current-time + (a positive number) is true, but (current-time + a positive number) always falling within positive numbers is false. One zero is just an arbitrary absolute reference point, the other is zero in the relative sense for/at each point. Both are free to be all numbers on an x-axis, but it is only in the relative sense the future needs to be a positive number. The future could have negative numbers in the absolute sense. Formally it needs to be in the set of the ray/interval (0, infinity) in the relative case or (x, infinity) in the absolute case. This is using interval notation where infinity needs to be a valid number, but it is just for the sake of being “up to” that number, since it is excluded. Since this isn’t projective geometry where we have a vanishing point at infinity😅
Btw there are no negative numbers or a year zero in our calendars which leads to one off errors in programming, they also count the fences and not the poles (the gaps and not the ticks on the number line) sometimes. In anniversaries you are in the next year’s awards, we are in the 21st century, but not after/at year 2100. So don’t dismiss inclusion or exclusion problems as obvious and conventional or you might just skip a decade in when planning anniversaries.
Just curious what you think about Friction's counterexample. Doesn't that argument make a similar reductio assumption that such circular casual structures are possible just like the Grim Reaper argument makes a reductio assumption that the past is infinite?
Excellent question. I think Troy may have at least two ways to respond: first, he doesn’t need to assume a circular causal structure is possible; instead, the possibility thereof is simply *guaranteed* by (i) the individual possibility of a bulb with the relevant power/disposition, (ii) Koons’ patchwork principle, and (iii) the fact that there’s a spacetime with enough spatiotemporal room to accommodate circularly-arranged bulbs (our spacetime is one example of this). So the possibility of such a circular structure isn’t assumed; instead, it’s a consequence of (i)-(iii). And Troy will presumably argue that since (i) and (iii) are very plausible, we should reject (ii).
Second, Troy might just say that the bulbs aren’t *causally* sensitive to other bulbs but instead simply co-vary with their states. (That may be weird, but remember that all he needs is the bare *possibility* of such a bulb!) So he needn’t assume that a circular causal structure is possible 🙂
Again, though, this is an *excellent* question.
31:02 Isn’t this blatant question begging? The claim to be supported is that an endless future is possible and the justification is that there are “physically possible, empirically adequate cosmological models on which the future is endless”. The reasoning seems to be as follows…
1. A physical universe with an endless future is physically possible.
2. Therefore, an endless future is possible.
It seems question begging, in the case of premise 1 is asserting the conclusion, that an endless future is possible?
This is a good question, and it affords me a chance to clarify what I meant by ‘physically possible’. At this point in the video, I just meant ‘consistent with the laws of nature’. And it’s not controversial that there are empirically adequate models of physical reality that are (1) compatible with the laws of nature and (2) feature an endless future. And it’s quite plausible that this fact counts as evidence for its metaphysical possibility. (And note that this is not assuming from the get-go that it’s metaphysically possible.)
@@MajestyofReason Thanks for the clarification.
How are numeric symbols of the time periods in which collections of events happen, the same as actualized collections of events that happen and not only in potentia? Craig says "temporal becoming" is a potential infinite and then says that future events go on infinitely. How can we reason from something that is only potential to the claim that its actuality is certain to occur?
The potential future is an actual infinite. An actual infinite doesn’t need to be real
According to Craig, yes. That’s because Craig thinks a beginningless past is an actual infinite even though he thinks only the present moment exists.
@@MajestyofReason and a metric-less time before that. Our past is as arbitrarily long as we can get arbitrarily close to something or far away from something maybe😂
What is called compactness in math I think
@@MajestyofReason I’ve counted all the numbers sounds worse than I can count all the numbers. But it is meant in two different senses. Well unless we can get transfinite… btw could a metric-less past map to transfinite stuff too? Btw transfinite stuff is just for ordinal numbers not cardinal ones. If you do an infinite amount of stuff and then after it is still an infinite amount of stuff. But I would say transfinite stuff becomes real if there is a supertask God had to make in time somewhere. A task in which he had to do an infinite amount of things in a finite amount of time, and we are after that then. Then he really did do it even though the past is finite. Could a past become infinite? God only needs to make something happen afterwards. Imagine having an infinite amount of conscious actions as if you where in an infinite future or subtime and something happening afterwards in order. Would you remember an infinite past? Ok this is getting a bit too exotic now
It is time, potentially or possibly, for Craig to concede.
Or actually
I had the same time reasoning as Joe and I came up with more theistic implications!! As John Locke mentions "endless time and space is possessed by God's eternity and omnipresence". An actual infinity indeed!
At 7:08 I think you slipped by saying that the collection became smaller. No. The collection is still the same kind of infinity, removing members did not make it smaller. It's a minor detail, as you only need to show that it did not get larger, and I appreciate the conter-intuitive nature the mathematical language, but we would probably want to be precise.
I was actually using a different sense of ‘smaller’ than the cardinality sense, namely, the inclusive sense 🙂
But you’re right that this could have been clarified in the video! Excellent catch
(This distinction between cardinally greater/smaller and inclusively greater/smaller is covered in depth in my Hilbert’s hotel video. As I explain therein, there is a legitimate sense in which the set is smaller, and another legitimate sense in which it isn’t❤️)
I don't feel like the first objection to Craig's argument regarding the number of future years hits the mark, but there is a chance I don't understand. My impression is not that Craig objects to the possibility that there are sets which have an infinite number of members, after all I think he acknowledges the existence of integers and real numbers. Instead, he denies that those sets are every actualized. I think he could plausibly claim that past events are actualized because they are causally connected to the present, while denying that future events are actualized because they have no causal impact on the present.
There is a lot I do not understand though, so I welcome correction on this point!
Thanks for the comment! It’s great to see you her🙂
(1) Actually, Craig denies the existence of numbers (in part precisely because they would constitute actually infinite collections, which (by his lights) is absurd).
(2) As I explain in the video, it doesn’t matter whether future events are actual or have been actualized; what matters is that they’re numerable, ie, able to be numbered. If so, then they’ll inherit the alleged absurdities attending actually infinite collections, as explained in the video.
Hope this helps!❤️
@@MajestyofReason Thanks, I obviously screwed up on the first point!
Second, yeah you do explain this. I hadn't watched far enough. I'm still confused though, so I will check out the papers you link to.
Thanks for all the work you do!
@@ChristianBechler No worries at all my man -- it's all a learning process, and I hope my other videos and the papers and whatnot serve you well in your pursuit of truth :)
@Majesty of Reason So I hope you do not feel obliged to respond, but I have finished reading both of the papers and I think I can crystallize my objection to these objections more clearly. [Edit: I added a paragraph elucidating why my objection is still substantive.] [Edit 2: I realize now that I am largely just saying what Alexander Pruss has already said in a better way, so I apologize.]
First, I want to say that I am not convinced by the Kalam Cosmological argument, largely because I do not think that Craig has given sufficient reason to doubt the existence of actual infinities (including in the qualified sense that follows.) That said, I do not feel like the objections actually deal with the weight of the intuitions from the thought experiments that Craig brings up even if they do adequately dispense with the Kalam, and so I am still dissatisfied with the present discussion. This is largely because I am not concerned with these objections as relevant to determining the existence of God, but rather about what they tell us about the nature of the infinite. I think my concern with these objections is most similar to Loke's in section 7 in the Malpass+Morriston paper. I suspect I am misunderstanding something, and hopefully someone can clarify my issues.
It seems to me that Craig's examples point to the problems with having an infinite number of things be causally relevant at a given point in space and time, i.e. having an infinite number of causes. In the case of counting up from negative infinity, these means that to get to 0 you need to have passed through an infinite number of states saying a negative numbers. Likewise when you remove the infinite number of red books and replace them with other books, he is saying it is absurd for this to be possible. I do agree with him that it seems bizarre, but I am not convinced it is possible or impossible.
[Edit: Added Paragraph Mentioned Above] I think this notion of causal relevance makes it clear why symmetry is broken. The notion of causal relevance refers to forgoing things. There is no problem that an infinite number of things will be causally relevant. What is problematic is that there are an infinite number of causally relevant things. I think this is the heart of the disagreement, and I still don't understand why it is contradictory to proclaim this and an infinite future. I realize this seems somewhat similar to the formulation of the point that Malpass and Morriston make in section 7 of their paper, so I will read that portion again.
Therefore, when Malpass and Morriston talk about B(X) always being infinite, I agree. I just don’t think it responds to the force of the intuitions. Yes there will be an infinite number of praises, but at any given point there will only be a finite number of things which are causally relevant. Now one could object that God’s knowledge of the future is causally dependent on future outcomes, and therefore an infinite number of things are causally relevant. If true, I think this is a powerful objection, but I do not see this as necessarily true. One could also say that space is infinitely divisible as Morriston (2002) does. But here, one can argue that only a finite number of “specified way[s] of dividing things up” are causally relevant, so space is not infinitely divisible.
Now, I think my position does have negative consequences for the Kalam supporter. In particular, claiming that only a finite number of things can be causally relevant does not suffice to show that there is no infinite regress. There could be two natural laws, one which starts the universe every trillion years and one which wipes the causal slate clean every .9 trillion years. So obviously this position does not work to support the Kalam. Second, this principle also likely present significant restrictions on God’s knowledge. So I don’t think that WLC or Loke would ever endorse my position. But right now, I do not see why it is false and I hope someone can help me!
A purpose in life is in future but acts like a magnet and causes present actions. I think causality is not limited to past but also to future. The reason we trust future is because of induction and then we set a goal for future which seems like we have future causes and present effects.
Could primary humans who were only obsessed with food think of a time at which people will be obsessed these sophisticated abstract concepts and mutual recriminations over these?!
One problem with an infinite past is, if you assume a tensed theory of time, infinite linear traversal is necessary to reach the present. That is, not just each, but every past event must have occurred in sequence in order for the present moment to exist. I believe the impossibility of this can be demonstrated by attempting to count every positive integer. You can never complete this task, as mentioned in the video, because there are infinitely many positive integers. It seems to me that, if counting from one to infinity is impossible, then so is counting from negative infinity to zero, and hence an infinite past is not possible on a tensed theory of time.
For these reasons, it also appears that continuous space or time are logically impossible. If there are infinitely many n-ths of a second in one second, then every one of them has elapsed sequentially by the end of the second. But this requires something equivalent to counting every positive integer linearly, which is impossible.
To my mind, it is therefore the case that, if the past is eternal, then time is not tensed (B-theory is true), which seems to imply that cause/effect relationships are somehow eternally existent (something that seems absurd to me), and that furthermore, space and time must be quantized at some level, however small. Unless, of course, someone can provide me with a better argument to the contrary.
I would like to add that I am aware special and general relativity point to B-theory being true. I just wonder if somehow a B-theory block of spacetime could be embedded in some larger structure that operates according to A-theory (tensed time).
This debate seems to boil down to different intuitions. Craig sides with the finitists, but should we side with the infinitists? What the finitists call a contradiction, infinitists call a feature. Is this settled philosophy?
The analogy I personally use to illustrate how absolutely nonsensical I see Craig's idea that God 'started out' timeless and then 'chose' to enter into time as being is that it would essentially be the equivalent of a character in a paused movie (and hence paused themselves) choosing to somehow unpause the movie from within. If something is truly timeless in the metaphysical sense of the term, there can be no internal potential to initiate change, because by definition the thing would be absolutely static. So if a timeless entity 'became' temporal, I think it would either need to have been a truly random and inexplicable event, or else ironically in Craig's case it would need to have somehow been caused by something that is already temporal. But the idea that something truly timeless could 'choose' to enter time is just completely incoherent as far as I can tell.
@user-lg8gw3rf7f The what to the what of the what?
@@fanghur islamic theology
@@fanghur he is talking about islamic theology in islamic theology in sunni islam which is the largest sect of islam there are three schools of speculative theology or kalam
ashari,maturidi and athari.
Joe: "We're all moving closer to death." Me: Yaaaaay lol 😂😭
I don't think you're right about the endless future being an actual infinite, because these days have not yet occurred. The days do not yet exist, so its better understood as a potential infinite.
The past however has occurred
Someone in the comments below already highlighted your error:
You are equivocating "a potentially infinite series of events" with "an infinite series of potential events."
Joe is talking about an infinite series of potential events which is why it should be considered an actual infinite; because the set contains infinitely many members. ie: it isn't a finite set that ever increases - it's always an infinite set.
@@christaylor6574 what does an infinite series of potential events mean?
@@msmhao That the set of potential events has a cardinality of infinity.
eg: there's an infinite series of positive numbers.
1, 2, 3 ... etc - the set of positive numbers has a cardinality of infinity.
@Chris Taylor can you give an example that is extra-mental, I don't fully understand in abstract terms, sorry.
1:07:30 Craig says the underdetermination of the cardinality of a difference of sets from the cardinality of the operand sets is contradictory and it follows from the logic of identity. However I believe Craig is simply confused. If one extends the cardinality relation, = from some collection of cardinalities to that collection union the collection of ordered pairs of elements from the first collection, CardUCardXCard in the following way then a lot of subtleties happen
First notate the pair of cardinalities from CardXCard, (A, B) as A - B
Secondly notate the normal cardinality relation (what's normally notated in ways like |A| = |B|) instead as ~ (|A|~|B|) while notating the new extension as =.
1. A - B = C if and only if there are sets A', B', and C' such that |A'| ~ A, |B'l ~ B, |C'| ~ C, and |A'\B'| ~ C
2. C = A - B if and only if the condition in case 1 holds
3. A - B = C - D if and only if there are sets A', B', C', and D' such that |A'| ~ A, |B'l ~ B, |C'| ~ C, |D'| ~ D and |A'\B'| ~ |C'\D'|
4. A=B if and only if A~B
If one defines this new "cardinality difference relation" then the relation ceases to be a true equivalence relation specifically because transitivity fails. This means that it doesn't follow that because A = B-C and B-C = D that A=D. It just doesn't always follow. To use Craig's own example it is the case that both aleph null - aleph null = 3 and aleph null - aleph null = aleph null, but if one examines the statement 3 = aleph null that would be the same as 3~aleph null which would be saying that 3 is the same cardinality as aleph null in the original cardinality equivalence relation without involving subtraction of cardinalities which is clearly false. So the "equivalence like" relation between cardinalities and subtractions of cardinalities when formally constructed is only assumed to be an equivalence relation by Craig when it in fact is not because it isn't transitive.
As someone who believes that the Kalam fails as an argument for God, and as someone who adopts the B-theory of time (which pretty much invalidates the argument almost from the get go), I still empathize with Craig's struggle with the idea of counting "from negative infinity" up till now (from an A-theorist perspective of time at the least).
Maybe it's because of the way Craig usually words his objection to an infinite past, which causes what appears to be both sides talking past each other in this specific case, but I don't think it's relevant whether his objection relies on time being an actual substance or not. Or at least, it's not clear to me at first glance how it's relevant.
I'm not an academic philosopher myself, so I'm not well-trained in writing precise and rigorous formulations of arguments, but let me see if I can capture with some thought-experiment the intuition that people like Craig are coming from in their objection to an infinite past. Maybe then someone here could come up with an even more satisfying counter to the objection.
Suppose I stumble upon an audio cassette, which pretty much plays a voice audibly counting down negative integers all the way to 0, and the cassette ends once 0 is uttered. Suppose also that the cassette is not properly rewound to the very beginning. As such, when you first play the cassette, it starts at a point pretty close to 0.
Now for the weird part. When I have the cassette inserted into the radio, and I hold the Rewind button, it never gets me to the beginning of the cassette but instead it just rewinds forever until I stop holding the Rewind button. When I then click the Play button again, it starts playing at the point where I stopped holding the Rewind button. So, basically, no matter how long I hold the Rewind button, when I then let go of the Rewind button and click the Play button, the cassette will always start the countdown with some finite negative integer.
I rewind multiple times and eventually end up being able to start the countdown from
-1,000,000. I try again and trigger the countdown to start from -5,000,000,000. I try again and again until I hit integers as extreme as the negative version of Graham’s number (we can suppose there is something very weird about me being able to rewind all the way to that point)! Finally, I sit back and ponder what the hell is going on. No matter how far back I go, even going so far as to reach a really extreme negative integer, I just can’t seem to get to the beginning point of the cassette. I then confidently assume there just isn’t any.
But then it hits me. If I start the countdown from any finite negative number (no matter how extreme), the countdown will eventually reach 0. Continually rewinding the tape (to various points) and then playing it makes that quite evident to me. But what if there was no beginning point to the countdown? Would that even make any sense? I can start from any finite negative integer and get to 0 eventually, but it’s incredibly unclear to me how this would work if there was no beginning point whatsoever to the countdown.
I then reason that there must be a beginning point to the countdown played by the cassette. I just wasn’t able to get to it. Perhaps, it’s a really, really, really extreme negative integer (maybe a number close to the negative of TREE(3)). At the end, in resignation, I eject the cassette, drop it carelessly on the floor, and go my way, never giving what just happened any thought ever again.
I guess the takeaway from this story is: how would a countdown with no beginning-point work exactly? How would it reach the number 0, or any number for that matter? Is there a solution (that does not adopt a tenseless theory of time or some other theory of time that Craig disagrees with) that not only satisfactorily addresses the wording of this objection/concern but also the intuition underlying it? Not sure if that thought-experiment had any point to it, but I hope it was a fun short story to read at least.
Hello! I think a countdown could work, if for all of the time past it was decided ahead of time, so to speak, that zero would be reached on a particular date, such as 3/25/23 (today). So for today to be zero, yesterday would have been -1, the day before would have been -2, etc. For each day in the past, each day would be counted as t-n, where t = zero (to represent 3/25/23) and n is each of the natural numbers, counted one by one forever. The tricky part would be that for all days past it would have to be known that the zero-date would be 3/25/23.
What do you think of the scientific arguments for the finitude of the past?
I don’t think they work - see Daniel Linford’s dissertation on Philpapers (and shown in my video) or his dialogue here: th-cam.com/users/livetxG_iVmtgpo?feature=share
Is the past potentially infinite if the future is actually infinite and time started from the big bang?
Question: if the future is not an actual infinite and therefore is finite then that could mean that Christianity is false bc the belief that the future in heaven with god is suppose to be an infinite future would be false then: BUT isn’t the “future” in heaven with god proposed to be “outside” of time or represent an existence with god in some timeless amorphous time? Can the future of metric time be finite and come to an end but amorphous time with god continue infinitely? Or is it that when we run the analysis of the future time line this analysis is comprehensive and includes both types of time? But then isn’t it nonsensical to run an analysis of amorphous time? Because saying things like “the number of future days is x” presupposes a unit of metric time and those dosnt apply to future amorphous time? Bc amorphous time is not divided into discrete subunits of temporal metric time (days, weeks, hours)? Moreover, in light of this does it even make sense to analyze amorphous time in terms of its “future” or “past”? Is there even such a thing as “a future within amorphous time” or is existing in amorphous time similar to a form of forced static presentism where there is no time and this no future and no past at all? If this is the case why do we refer to amorphous time as amorphous time at all? Seems like it isn’t a form of time but is instead a state of existence? And thusly, couldn’t the Christian exist in this state with god infinitely still despite accepting that the future is only potentially infinite and not actually infinite?
It seems to me that most of Dr. Craig's objections regarding infinites all follow the same logic as this example:
I lead you into a room who's floor and ceiling are perfectly circular (that is to say, the room is shaped like a cylinder) then I ask you to go stand in the corner.
Well, definitionally there are no corners in a circular room, so the request makes no sense. I haven't disproven round rooms or shown that they aren't a coherent concept, rather I've just taken what is a "typical" quality of rooms, that doesn't actually apply in this case, and then claim the (expected) absence of this quality is somehow proof that the larger concept can't exist. (In this case, he'd be arguing that because the thought experiment requires a corner, but no corner is present in a circular room, that circular rooms can't exist.)
With most of his infinite thought experiments, he seems to be assuming a beginning or endpoint in an infinite set, where we wouldn't expect to have one. These supposed paradoxes are simply misapplications of intuitive (but definitionally incompatible) concepts.
If we live in a block universe as many physicists think, don't the future and past years actually do exist?
Hey Joe, when you mentioned conceivability vs. possibility, I had a thought: there is no difference. I know this is a controversial take. But any counterexample I have seen requires conceiving of the wrong thing. For instance, if you conceive of a bar of metal floating on top of water, you are either not actually conceiving metal or not actually conceiving water. What do you think?
Excellent question. In brief: first, it’s not clear to me that all such examples involve conceiving or imagining the wrong thing (or misdescribing the contents of our conceivings/imaginings). Second, once we grant that we can be quite seriously wrong about the contents of our conceivings/imaginings, I think that alone will satisfy the mitigated modal skeptic; instead of concluding that we should reject the conceivability-possibility link for cases far remote from ordinary experience, they’ll say that the skepticism is merely re-locate: namely, it’s re-located to the stage of identifying the contents of our conceivings/imaginings.
Great question tho!
@Majesty of Reason Thanks, I agree with everything you said, especially from the second point onward. Just wanted to add that I think that moving the locus of skepticism to having a proper conception is far more productive than doubting the link between conceivability and possibility exists in the first place. However, any conclusions about possibility from conceivability need thorough knowledge of the contents in question. I like this way of thinking as it promotes seeking knowledge
Joe, I understand the frustration over the future and future perfect tense, and I do think Craig fails to address the Malpass/Morriston comments. However, what would you say if Craig just conceded and said "yes, an actual infinite number of events will occur, but the paradoxes arise when we say that an actually infinite number of events *have occurred*"
(to me, the paradoxes all seem to arise when you consider a world with an actually infinite causal chain or temporal chain that has already occurred, precisely because of the temporal direction of causality and time - sorry if my vocab isn't great here, hopefully it's clear enough)
Would you just say "this is a different objection, and is focused on traversing the infinite"?
Excellent question!
Someone else in the comment section asked about essentially the same thing. They said: “The claim to which the past-finitist objects is that an infinite series of past events has elapsed prior to now. It's not just that the geometric arrow pointing back that way has infinitely many points, but rather that each point has already been instantiated/actualized prior to now.”
In response, I said:
This is one thing the past-finitist might object to; but it’s certainly not the thing they object to. Instead, many past-finitists - most relevantly, Craig himself - also explicitly object to collections which have features like: (i) one can remove members from the collection while the collection retains the same number of members after said removal; (ii) one can ‘subtract’ identical quantities from said collections and get divergent quantities as a result; and (iii) the whole collection is equinumerous with proper sub-collections thereof. For Craig, these are manifestly absurd features. And yet they attend any collection which (a) admits of removal of members and (b) can be put in 1-1 correspondence with the naturals, regardless of whether the members of this collection ‘have elapsed prior to now’. Even if the future ‘hasn’t elapsed prior to now’, the collection of future years (which can be put in 1-1 correspondence with the naturals, if the future is endless) is such that we can remove members from that collection (which happens as time progresses) while the collection retains the same number of members (namely, aleph-null). It’s also such that we can ‘subtract’ identical quantities from said collections and get divergent quantities as a result, as explained in the video under objection 1. And it’s also such that the whole collection is equinumerous with proper sub-collections thereof, as explained in the video under objection 1. So it’s mistaken to say that ‘the’ claim to which Craig objects is simply that an infinite series ‘has elapsed prior to now’. He takes issue with much more than that, and what he takes issue with commits him to thinking the future must come to an end.
@@MajestyofReason Thanks for the response, Joe. You've read more of Craig's academic work than me, so this is a genuine question: when you say Craig "object(s) to collections which have features like [i,ii,iii]", what, in your opinion, is he objecting to? My understanding is that he is objecting that these collections "can be instantiated in reality", "can exit their causes", "can have elapsed". Even in the Malpass discussion, when asked "how, on presentism, can you say there's an infinite series of past events", he answers "they are numerable *and* have been instantiated in the real world". Isn't that his symmetry breaker? I mean, Craig wouldn't object that there are aleph-null integers in a fictionalist sense, right? Wouldn't he just reject that aleph-null integers are real in a realist sense? In the same way, can't he say the future events are numerably infinite, but they haven't been instantiated in reality, as an infinite past would have been? Please help me understand :)
I agree he isn't really answering the Malpass/Morriston points, I think it's because he sees this "reality instantiation" as such a symmetry breaker that he keeps flying over the future events and jumping to future perfect, where events have been instantiated. I wish he'd just say "yes, future events are numerably infinite, but they haven't exited their causes, and a past infinite series has exited their causes, which is my objection". That's really what I think he thinks (and I'm inclined to agree with), admittedly it's very poorly communicated. Thoughts?
Do you think Craig's argument makes sense under a growing block view of time? If not, what would your objections be?
Excellent question!
I don't think his argument would work under that view, either; first, growing block theory isn't very popular, as it has serious problems. But set that aside; more fundamentally, and as I explain in the video, all we need to get the problem up-and-running is that future events are *numerable*, not that they *exist*. So even if they don't exist (as per growing block theory), they'll still be numerable and hence will still inherit the allegedly absurd properties attending actually infinite collections :)
If we substract from infinity, do we get a number smaller than infinity? As a complete noob, this feels like a no.
See my Hilbert's Hotel video! It answers this question and gives you the foundational knowledge of set theory to understand the answer :)
@@MajestyofReason Bleedin' 'eck! A 3 hour video, good luck to me
@@macdougdoug The -easy- quick answer is: there's not enough information in the question.
1. What subtraction?
The subtraction you "usually think about", algebraic subtraction, is just not defined between infinite cardinalities.
Instead you need "set theoretic subtraction". Which, leads to:
2. Subtraction of what? For set-theoretic subtraction to work, you need to specify what set you're subtracting.
For some, you get the same cardinality. For some a reduced one.
So the answer depends on those specifications
Craig is correct here. If the future were actually infinite, and one could make an incursion into this infinitude of even a picosecond, he could easily traverse the entirety, rendering the whole scheme finite.
It's not only true that an actualized/realized infinite cannot be formed by successive addition, it is also true that no encroachment is possible, even in small increments. As soon as one demonstrates that he can traverse the tiniest portion, as in the number graph, he immediately swallows the whole.
Not sure I follow your logic here. Could you elaborate further? To me, it's easy to see how one could traverse a finite portion of an actual infinite (at least if we're not assuming continuity here, which is a different debate anyway) while never being able to traverse the whole of the actual infinite (as that would then mean it's not infinite, after all). If I count all the whole numbers up to 100 (for example), that doesn't mean I can therefore eventually count all whole numbers.
Furthermore, it makes less sense to me for the future to be potentially infinite (as opposed to actually infinite). If the future is supposed to be potentially infinite, then it is increasing over time, which isn't very intuitive. Put another way, it makes more sense to think of the future containing ALL moments in time that are after the present, rather than having the future be an arbitrary selection of these moments with more and more moments gradually added over time.
@@georgeel-azar4684 The future is potentially infinite in the sense that the number of moments that move from the category of future, to present to past, are indefinite. The future, so called, isn't growing in any sense.
@@Shimbabwe1 Thanks for making your view a bit clearer for me. I don't think this is how Craig defines potential infinite, but putting that aside: if we're assuming an endless future here, then the number of future moments from the perspective of the present moment would still be aleph-null (infinity), even if we were to consider this as indefinite (to be honest, that term is quite vague to me).
Now sure, as time passes, more and more of what was future move through the present into the past. But for each present moment (if we were to somehow freeze that moment and just contemplate the future from the perspective of that moment), there is nevertheless an actual infinity of future moments (assuming an endless future). They may not yet exist, but there is nevertheless an infinite set of these "yet-to-exist" moments.
@@georgeel-azar4684 That's simply a declaration. A definitional stance, with no bearing on actuality. If the future is both infinite and real, then a hypothetical observer can be situated at a point deemed infinitude. Because there is no such reality, then the future cannot be already always infinite, which is necessary on that view.
Nominalizing "the future" as a set, doesn't get us where we're going. It merely categorizes.
how much fun it must be to have a job title that says you can argue about nothing over and over. the kalam was shown to be a waste of ink five minutes after it was proposed and here we are still wasting our time over it.
Lol.
How can the "number of future years" decrease when the future years are infinite?
So no matter how many you remove from them (because "now" has reached those years, as per the illustration), there's always an infinite amount more to reach.
This would demonstrate that, at least, they're not decreasing, surely.
I think the point of the illustration is to show that the infinite future years can't be a "potential infinite" because it isn't increasing over time.
My brain exploded
I really don't see how the first objection is a problem, since as a presentist Craig doesn't believe the future exists, which (as I understand it) means he is a nominalist with regard to any talk about the future or what will be. It was my impression that his arguments against the existence of actual infinites are aimed at growing block theorists, eternalists, or anyone who thinks the past exists. It simply isn't aimed at presentists.
Saying that we can still ask how many future events there will be (an actual infinite) seems to just dress the same objection in new clothes. Events that *will be* just are future events. A presentist might say that *there are* future events or that *there are* events that will be, but as a presentist, they're not commiting to any new entities in their ontology by saying this. It's just the way they're expressing it.
One might object that saying, "there are future events," should commit you to believing in real events that exist in the future, but this would just be to argue against presentism in general, not this specific argument for p2 of the Kalam
He himself is a presentist and believes that even under presentism, his argument succeeds in showing the past must be finite (because the past would constitute an actual infinite despite not existing or being actual). All that matters is that the members of the collection are *numerable* and that their number is aleph-null. They don't all need to exist. (If they did, he couldn't consistently think that the past is an actual infinite and be a presentist, both of which he thinks.)
@@MajestyofReason Oops, I edited the comment a bit, not sure if that changes how you would respond, if you responded before I made the edits. Thanks for replying by the way.
If he thinks the actual infinite argument against an endless past goes through even under presentism, then I think I agree with you. It seems inconsistent to say that the argument implies you can't have an infinite past, but doesn't also imply you can't have an infinite future.
In that case, I wonder why he thinks the argument implies either conclusion under presentism. If I understand presentism correctly, the number of past/future events is neither potentially infinite nor actually infinite. That's because properly speaking, there are no past/future events. Again, if this itself is a problem, it's a problem for presentism in general, not this specific argument for p2 of the Kalam.
@@MajestyofReason please tell me if I'm radically misunderstanding things
Also Craig should probably switch to contingency at this point
I agree. The thing about the Kalam is that it utilizes contemporary science. Which makes the argument bulkier. But that bulk, if sound, smashes like a sumo mech truck.
The Kalam, if sound, is honestly way more powerful than contingency. But it carries more baggage that can be attacked.
@@rebelresource I think ordinary people can see the points of Kalam easily and it's more intuitive compared to Contingency arguments.
@@Mrfunny663vnb83 yeah that sort of makes sense as well.
I think the contingency arguments first phase is very similar to the Kalam though.
@@rebelresource exactly, the average person on the street is much more likely to understand the kalam than contingency
@@ILoveLuhaidan I think I disagree. The Kalam utilizes complex theories of science and time.
Perhaps Craig should lower the standard of the Kalam's theological implications. I may be reading something wrong here but I think the Kalam works only by arguing that the infinite past as a real piece of metaphysics is impossible. If there are so many fronts to defend, and so many a priori points for the argument to work, it loses the parsimony of its use, something that does not happen, I believe, in the other arguments.
In that sense, Joe, you're right, the future is not potential infinity. And if Craig dedicated himself to defending the key points that make the Kalam a solid argument, there would be no problem in the objection.
ps: I insist that I may be omitting something here but it seems to me that the key in the Kalam is that, as I said before, the past is not infinite in a metaphysically real sense. The future, as I see the topic, if it is infinite or finite, is secondary to the Kalam, I think it enters into the theory of time that ones subscribe to
Joe: this will be 1.25 speed
Me: sighs as I click 0.75 so I can comprehend
Your first problem is you need to define what "cause" means. Aristotle had 4 causes. If you're talking about the efficient cause, you're assuming that the past actually does cause the future (the alternative to that is that the future and the past are both simultaneously caused by the laws of physics).
Hi Joe! Have you read Andrew Like’s new book ‘The Kalam and Teleology Arguments: A Reassessment’? I don’t like Loke’s writing style, but he had some interesting arguments for a causal principle
I read it, yes. More precisely, I read the stuff on the Kalam. I also find the book *very* difficult to read. I don't think his central argument for the causal principle -- his 'modus tollens argument' -- succeeds. Actually, the next video in the Kalam series with Stephen is on that argument. If you want, I can email you the script. Email me :)
OMG, I THOUGHT I WAS THE ONLY ONE WHO COULDN'T STAND ANDREW LOKE'S WRITING STYLE!!!! I find it so freaking annoying, but I can't complain because I have to admit his arguments ARE nevertheless valid at least to me (plus he's obviously smarter than I'll ever be), in fact he convinced me of cosmological arguments and became a theist (at least neoclassical theist for now). I must thank you for being on my side regarding Loke's idiosyncratic style both in writing and speaking.
@@logans.butler285 Yes, his habit of "deductivising" and numbering every other sentence can be very annoying to keep up with! I also found it interesting that I found his teleological argument moderately convincing, yet thought his book on the problem of evil to be one of the worst out there.
@@calebp6114 Ah yes, he has a book on the problem of evil, I forgot about that one. Honestly after the hard time I had reading his book on the Kalām I took a break and decided to stick to psychology (at least until I finish my ba). Is it that bad? From what I understand, he adopts the cosmic conflict theodicy, same as Gregory Boyd or John C. Peckham, is that really the case? And if so, then what makes his book so bad? I mean, it's not like he considers that there really was a historical Adam and a literal fall, or does he? (Pls say no)
@@logans.butler285 He has a lot of completely implausible theodicies which he throws out there to dismiss entire categories of evil. E.g. perhaps we live in a Darwinian world because that makes caring for infants and the elderly harder, and so more virtuous and praiseworthy (as if that possible justifies evolutionary evils?). Another cringeworthy comment was the claim that reality cannot be that bad because suicide rates are not high. Yet obviously some people commit suicide without having net-negative lives, and some people with net-negative lives don't commit suicide, making such comments ridiculous. The whole book came across as highly unemotive (similar deductive analyses to his other works), which whilst would be ok in most circumstances, seemed jarring with regards to a lot of the subject matters.
What Craig says that the number of future moments is potentially infinite, couldn't he mean something like "the number of future moments is finite but it grows as time progresses (so that the present moment never catches up to it)"? I.e., today, God plans to end time 2 millions years from now but tomorrow, he revises that plan to 2 million years plus 2 days, the day after tomorrow, he revises the plan to 2 million years plus 4 days etc.? If that's the case, it would be true that the number of future moments is potentially infinite, right? There might even be some Biblical support for this view since 2 Peter explains that the parousia hasn't happened yet (even though it's been a while) because God postponed to give people more time to repent.
Excellent question! So, this seems to be Josh Rasmussen’s variable domain open future proposal in the comments section of the Prosblogion post! I think this *might* be one way to avoid the argument (although I’m still skeptical, since Craig’s argument requires that it’s genuinely *impossible* for the future to be infinite; and yet it seems obvious to me that God *could*, eg, determine that some particle emits bursts infinitely many times throughout the entire endless future.)
(The reason this view needs to deny that facts about the future are fully determinate is that, if the future *is* fully determinate, then it is already determinately true that God will endlessly revise his plans, and so it’s already determinately true that each of infinitely many days will occur)
24:45 and 27:40 are a big reason why I watch these
The instructions at 26:55 were unclear. I have tasted from the quiver of Joe's back pocket. There is nothing but pain and darkness. My mind breaks, shattering into tiny pieces. As I try to gather what shards I can, I hear a voice cry out, from seemingly nowhere yet from everywhere at once. Its Joe, doing a Žižek impression. As a single tear rolls down my face, I realize that I simply haven't lowered the bar enough for me to accept Christianity like WLC has.
Greatest comment of 2023
@@MajestyofReason I understand the responsibility that comes with this honor, and I accept it. I will make you proud.
I've always found the Kalam to be weak sauce and unnecessary for a theistic case. I don't know why Craig keeps defending it
Didn't expect this from you, CI. Andrew Loke re-strengthened this argument more than ever before and managed to defeat Graham Oppy with it on Capturing Christianity. It’s anything but unnecessary or weak. Have you read Loke's work? Also if you are not fond of the Kalām, what othe arguments would you find convincing? - PLEASE don't tell me you like "design" arguments, please do not 😥😥
@@logans.butler285 see my "Swinburnes Nuke" series
@@logans.butler285 🤦♂️😂
Loke is a sophomore philosopher, he didn't defeat anybody and Kalam is the worst argument.
@@anteodedi8937 Sophomore in what sense? Also LogosTheos referred to Andrew Loke as an "excellent philosopher of religion", plus Suan Sorna from Intellectual Catholicism made an entire video going through Loke's debate against Oppy and pointed out NUMEROUS reasons why Loke ultimately annihilated Oppy there. Dude's got a humoungus fandom plus he speaks multiple languages, writes music, and was even an assisting medical doctor, dude's the new Aquinas.
I think it can be bad form to jump straight to pointing fingers about intent and willful blindness, but having seen Craig's demeanor and approach to objections- do you think it's possible he's simply uninterested in processing objections due to some kind of sunk-cost fallacy? At a point, I feel I run out of other ways to interpret a person's inability to characterize objections in their responses. It's as though there's a popular figure who's life's work requires a rejection of space and time being physical, and even after the entire consensus has moved, they are still responding to phantom objections. At what point has one removed themselves from the dialectic to form a cult of true believers that help them maintain asense of infallibility? Maybe it's childish to appeal to this, but I can't imagine Dr. Craig wasting any time in assuming bad faith if the roles were reversed. Yet, in this example, it's him against a relevant contingent of actual experts. Like, it's flat out disrespectful to talk down to his interlocutors when he can't even repeat their objections in good faith. It feels like logic fighting emotional clinging, same as any argument I observe between a scientist and conspiracy theorist. Albeit, no one in the conversation lacks intelligence here, but the gut feeling is the same. The intellect on both sides actually makes it look more egregious.
Admittedly, I don't fully understand the arguments. I don't have the mathematical background to adjudicate have of this stuff. But the each and all distinction seems clear enough even for a music major like myself.
It's funny almost how Craig keeps pointing at a collection of actual, instantiated events (present and past) to plead his case that the collection of potential events (future) isn't infinite. He doesn't seem to acknowledge this likely accidental sleight of hand. It seems to me that the becoming of futures
is irrelevant just as the counting of the natural numbers is irrelevant.
This was a great video, Joe. But I wonder whether Craig really wants (or needs) to deny that the collection of future events is infinitely large. He has no qualms about infinite mathematical series per se. His claim, unless I've misunderstood something, is simply that the collection of future events will never be actualized (though each member of the collection will). The collection of past events, on the other hand, has been actualized. So the past is an actual infinite, but the future is not. When he says that a potential infinite is a series that is at all times increasing but at no time complete, I think he means, by "increasing," that its members are coming into being, or becoming actual. The function A(x) is not always increasing in that sense. A(x) is just a function with a range of aleph-null, and, again, I don't think Craig has any qualms about that. What he denies, I think, is that any concrete thing could exist that is modeled by A(x).
Anyway, regardless of whether this is Craig's view, isn't it still sound? Doesn't the claim that the past never began imply that an infinite series is actual? And doesn't the claim that the future will never end fail to imply this?
I think Joe may have brought this up in the video when he talks about the 'each' vs 'all' issue? That Joe, Wes and Alex are not arguing that the all of the collection will be actualised, but rather 'each' member will be.
Thanks for the comment, Noah! I didn't see this at the time you made it. But I just saw it! So I shall respond now :)
"But I wonder whether Craig really wants (or needs) to deny that the collection of future events is infinitely large."
He definitely wants to! He has published papers where he very firmly tries to resist it. And there's an underlying reason for that resistance: it's precisely because accepting that the cardinality of the collection of future events is aleph-null implicates him in precisely the absurdities implicated in Hilbert's Hotel. For instance, the whole collection will be equinumerous with proper sub-collections thereof, which Craig (mistakenly) regards as absurd. Moreover, we can perform manipulations on the members of the collection of future events that are isomorphic to those performed on the guests in the Hotel, and we'll then be able to employ precisely Craig's (mistaken) reasoning that aleph-null minus aleph-null is both 3 and aleph-null, which (for Craig) is absurd. These manipulations involve counterfactually removing every even-numbered future event, and we'll have removed identical numbers of members from identical numbers of members and gotten divergent numbers of members, which Craig expressly regards as absurd.
"His claim, unless I've misunderstood something, is simply that the collection of future events will never be actualized (though each member of the collection will)."
This is one claim he makes; but it isn't his only claim. He has said in published work that the number of events that will occur is aleph-null; and he has also attempted to responding to Morriston who made the simple future tense entirely explicit -- namely, asking about the number of events each of which will occur. Craig responded (again in published work) to Morriston's precise statement of the question with *potentially* infinitely many. So I don't think Craig is simply saying that there will never come a time at which the entire collection of future events has been actualized. (Cf. the quotes in my HH video, the quotes in Malpass and Morriston's "Endless and infinite", etc.)
And besides, *even if* this is Craig's claim, it overlooks the crucial fact that if the collection of future events has aleph-null-many members -- *whether or not* there comes a time at which all have been actualized -- then that collection inherits the allegedly absurd features of Hilbert's Hotel. The whole collection is equinumerous with proper sub-collection; it's amenable to funky subtraction; and so on.
"The collection of past events, on the other hand, has been actualized. So the past is an actual infinite, but the future is not."
As explained in my Hilbert's Hotel video, however, this isn't how Craig defines an actual infinite. Craig defines an actual infinite as a collection with aleph-null-many members, i.e., a collection that can be put in 1-1 correspondence with the naturals. There is no condition that all the members 'have been actualized'. (As an aside -- and this is not my main point -- Craig thinks platonism about numbers implies the existence of actual infinites, and yet it is not true that numbers 'have been actualized', since platonic numbers don't exist in time.) And since the collection of future events can be put in 1-1 correspondence with the naturals, it's an actual infinite. I recommend checking out my 3hr (sorry bout the length... hehe...) Hilbert's Hotel video wherein I explain how Craig defines actual infinites!
"When he says that a potential infinite is a series that is at all times increasing but at no time complete, I think he means, by "increasing," that its members are coming into being, or becoming actual."
I don't think this is quite right. Craig is speaking about increase in *number* or *quantity*, as he says in his blackwell companion piece: referring to a potentially infinite collection, he says that "Such a collection would be one in which the
membership is not definite in number but may be increased without limit." Here he's characterizing the increase as *increase in number*. So if a collection doesn't increase in number, it's not a potentially infinite collection. Of course, this increase is *connected* to temporal becoming; it's precisely *because* of temporal becoming that the collection of events that have elapsed as the moving now progresses from 2023 onward increases in number. But increasing in number -- which is what Craig means -- is by no means synonymous with temporal becoming.
"What he denies, I think, is that any concrete thing could exist that is modeled by A(x)."
He does deny that; but he also denies that any collection of abstract objects, e.g., can be actually infinite. This is precisely one of his reasons for rejecting platonism. And he also regards as absurd features that are possessed precisely by any collection equinumerous with the naturals. And the collection of future events is precisely one such collection.
"Anyway, regardless of whether this is Craig's view, isn't it still sound? Doesn't the claim that the past never began imply that an infinite series is actual?"
Lots of tricky issues here.
First, lack of beginning doesn't entail infinite temporal duration. Craig's God lacks a beginning, for instance, but doesn't have infinite temporal duration. Something can lack a beginning by, e.g., existing timelessly sans metric time and temporally since metric time's beginning. Something can also lack a beginning by pre-existing the beginning of metric time in a beginningless non-metric time (which isn't infinite in duration, since it's non-metric -- there's no fact of the matter about how long it is). See again my HH video for more on this point.
Second, if presentism is true -- as Craig thinks it is -- past things aren't actual. They aren't anything, and a fortiori, they aren't actual. (To say 'x is actual' is to say 'there is an x such that x is actual'. But in the case of past events, there are no such things. Hence, past events are not actual.)
"And doesn't the claim that the future will never end fail to imply this?"
Under presentism, future events are just as actual as past events (namely, not actual at all). But even if Craig wishes to gerrymander some notion of 'actuality' that applies only to present and past things (and timeless things) but not future things, this doesn't avoid the fundamental problem: that the allegedly absurd features of Hilbert's Hotel are inherited by the collection of future events if the future is endless. So, either these features aren't absurd (and Craig's case fails), or the future can't be endless (which is both false and disastrous for Craig).
27:42 love the accent 😂
Graham Oppy impersonation?
Well craig is defining the potencial infinite as a set that at any given point is finite but grows (over time) towars infinity (from counting them), and that seems correct about the future, Joe defines the potencial infinite has a collection that the total number of its members increases over time so it doesn't look like the same definitions to me, in this video at least craig hasn't defined potencial infinite as something of which the total number of potencial members increases
It’s the same definition. Craig defines it as growing over time. I defined it as increasing over time. It’s the same thing being expressed. By ‘growing over time’, Craig *just means* increases over time. But as I show in the video, the collection of future days doesn’t increase over time🙂
@@MajestyofReasonI get that, I'm not making a distinction between grow and increase, what I mean is that your definition takes the whole of the future from the get go, and it seems to me that this is not what craig is talking about, but rather counting towards future years (which does not imply advancing the present as shown in the video) that set increases towards infinity, and each one of the members of that collection is a future year, but never get to contains all of the future years.
@@diegonicucs6954 When Craig is asked the size of the future, with the meaning of the question clearly specified to be as MajestyofReason defines it, he doesn't answer the question. He changes the subject and talks about something else, the distinction you are highlighting.
*"this is not what craig is talking about, but rather counting towards future years"*
- When asked how many members are in a set of 10 things, someone can count them up in the process of working out the answer, but the appropriate answer is the total, 10.
@@diegonicucs6954 yes, this is essentially the point I made in the video: craig has simply changed the subject. Craig is correct that the collection of years that have occurred as time progresses from 2023 onward is a potential infinite. But then he has simply changed the subject. The subject is how many years will occur. That’s the simple future tense; it includes the entire future. To then talk about the future perfect tense, and to avoid talking about the entire future, is to simply change the subject and to fail to engage the question of how many years there will be.
@@HeyHeyHarmonicaLuke The set of natural numbers is not the same as the set of counting the natural numbers for the simple reason that when counting you will never get all the natural numbers, since you will never finish counting.
So your example may work with a finite set, but not with an infinite set.
Correct me if I’m wrong, but Craig asserts that time itself is moving in a potentially infinite manner, not that there are a potentially infinite number of years. Is the first objection not the infinite divisions on a line type objection?
The first objection is not about infinite divisibility; that concerns a finite period being infinitely divisible into sub-periods. Instead, the first objection is that the collection of future days is an actual infinite, whereas Craig mistakenly says it's a potential infinite.
@@MajestyofReason But I would argue the first objection is indeed akin to infinite divisibility. The number of “future years” might not increase over time; however, the number of “actual” years does , which is what is relevant.
@@MajestyofReason “Future”years never exist as such (by definition) which ties into Craig’s argument that actual infinites can never be instantiated in the real world. He doesn’t argue that actual infinites are logically impossible but that they cannot be instantiated in the real world which is what is crucial here.
Thanks for replying by the way!
@@danielwoulfe4280 I address this in the video🙂
(1) past years also don’t exist. And yet they constitute an actual infinite.
(2) even if the future years don’t exist, that collection still inherits the alleged absurdities attending actually infinite collections. So the problem remains
@@MajestyofReason good points, would love to see a debate between you and mamotha or classical theist
What Craig avoid and change a question that smash his ridiculous belief….I’m shock
Ok, I have to address the simple future vs. future perfect thing as well. The claim to which the past-finitist objects is that an infinite series of past events _has elapsed_ prior to now. It's not just that the geometric arrow pointing back that way has infinitely many points, but rather that each point has already been instantiated/actualized prior to now. The parallel claim about the future (which no one holds) would be that there will come a time at which an infinite number of those will likewise have been actualized/instantiated. No one thinks that will ever happen (not the Christian hoping for eternal life, not Joe, not Malpass; no one). If I believe in everlasting life, I am not claiming I will ever be infinity-old. But the claim of an infinite past is the claim that the world already is in fact "infinity-old". And not because of an idealized geometric arrow (since time is not a direction at all on Presentism), but because of the actualization of an actually infinite number of events prior to now. For everlasting life, all we need believe is that we will never terminate.
I appreciate Joe mentioning that, for Open Theists, there is the matter that even _which_ future events will actualize is entirely potential and undecided. So, the idea that there "are" infinitely many laid out in a line would be absurd. There is, at best, a branching tree, some of the branches of which go on forever, but none of them is "the future"; they are all mere possibilities. I do wonder if a Molinist like Craig thinks that at least God is totally free (i.e. has no "counterfactuals of freedom", such that there is a fact about what He will do in a situation.... if there were, one would think that the creation of this particular world was inevitable....). If so, then God could easily terminate any branch if He freely chose to, and so the whole thing is mere potentiality. More akin to a hope or a story than to established and unchangeable history. For the Presentist, past events "have happened". Their truth is set and unchangeable, they have exited their cause, they have had their effects, they can play a role in explanations of current states of affairs.... None of this is true for future events. It seems to me that the problem is with "happenings". There cannot ever be an infinite number of happenings, no matter how big the arrows are on which the happenings are strung out.
Anyway, I'll shut up now.
Thanks for the comment my man!
You say: “The claim to which the past-finitist objects is that an infinite series of past events has elapsed prior to now. It's not just that the geometric arrow pointing back that way has infinitely many points, but rather that each point has already been instantiated/actualized prior to now.”
This is *one* thing the past-finitist might object to; but it’s certainly not *the* thing they object to. Instead, many past-finitists - most relevantly, Craig himself - also explicitly object to collections which have features like: (i) one can remove members from the collection while the collection retains the same number of members after said removal; (ii) one can ‘subtract’ identical quantities from said collections and get divergent quantities as a result; and (iii) the whole collection is equinumerous with *proper* sub-collections thereof. For Craig, these are manifestly absurd features. And yet they attend *any* collection which (a) admits of removal of members and (b) can be put in 1-1 correspondence with the naturals, *regardless* of whether the members of this collection ‘have elapsed prior to now’. Even if the future ‘hasn’t elapsed prior to now’, the collection of future years (which can be put in 1-1 correspondence with the naturals, if the future is endless) is such that we can remove members from that collection (which happens as time progresses) while the collection retains the same number of members (namely, aleph-null). It’s also such that we can ‘subtract’ identical quantities from said collections and get divergent quantities as a result, as explained in the video. And it’s also such that the whole collection is equinumerous with *proper* sub-collections thereof, as explained in the video. So it’s mistaken to say that ‘the’ claim to which Craig objects is simply that an infinite series ‘has elapsed prior to now’. He takes issue with *much* more than that, and what he takes issue with commits him to thinking the future must come to an end. [Assuming, along with Craig, that Josh Rasmussen’s variable domain open future proposal is false. Cf. the Prosblogion comment section.]
Notice, also, that Craig rejects mathematical realism in part because of the fact that he thinks infinitely many abstract objects would be absurd - in particular, sets of them would have absurd features like being equinumerous with their proper subsets. So his problem with a beginningless past is not merely that the members ‘have elapsed’. It’s also with these allegedly absurd features attending any actually infinite collection, i.e., any collection which can be put in 1-1 correspondence with the naturals.
These point also address what you say about past events ‘having happened’ and whatnot. Even if future events haven’t happened, and don’t exert influence on the present, etc., it’s still the case that the collection of future events (a) admits of removal of members and (b) can be put in 1-1 correspondence with the naturals. And these alone engender most of the central ‘absurdities’ Craig adverts to. :)
As for open theism, only a very specific brand of open theism potentially avoids this problem. Many open theists grant that there’s a determinate fact of the matter about how many days there will be, even if the precise *content* of those days is currently undetermined (and so indeterminate), since many open theists think that God has promised to us an endless afterlife. (And hence something about the present or the past - like God’s intention, or will, or whatever - currently determines that the number of future years is aleph-null, even if the precise content of those future years is indeterminate.) So open theism by itself won’t help; one has to think God hasn’t promised an endless afterlife for us, and that nothing else about the present or past implies that either (including all of God’s beliefs, intentions, wills, promises, revelations, etc.)
I also say 'potentially avoids' rather than 'avoids', since (1) it's not clear to me how a Christian or Muslim could plausibly and consistently combine this view with Scripture (given that God seems to promise/reveal an endless afterlife, so something about God seems to presently determine that each of infinitely days will occur), and (2) since the features of actual infinites in question are allegedly 'absurd', it follows that they would be *impossible*. And so the open theist response above would have to say the number of future years is *necessarily* indeterminate. And to me, that's very implausible; surely it's at least *possible* for God to determine that each of infinitely many days will occur. It seems very plausible to me that God could easily presently determine that, say, a particle will emit bursts at regular intervals throughout the entire endless future. But f=ti run Craig's argument, one would have to deny this.
@@MajestyofReason
So, just a quick response, and I’ll leave you alone! Lol. But, thanks for engaging with my points.
Let me ask you this: Does Craig claim that the set of future events or moments is an actually infinite set? If it isn’t, then none of these concerns you enumerated would apply. And the promise “you will live without end” is not identical to “there is a set of your future events, and it has infinitely many members”. It could be that there is no such thing as the future, but that you will always be present. You will never cease. That seems to be what Craig thinks. The reason I mention the “elapsing” or “having happened” is because it is “happening” which makes them events at all, such that they might or might not belong to a set.
To be clear, I’m not saying you couldn’t choose to *represent* the promise of everlasting life as an infinite set corresponding to the natural numbers. But all representations break down somewhere. I, for one, think representing time as a line at all is highly problematic. Conceptually, if my “future” states are some way “over there”, then they are actually present states just as much as these “over here”. The difference between what is and is not the case is nothing at all like what is the case here vs. what is the case over there. Those are both “is’s” and therefore both fully present. Anyway, I digress….
Let me use the “marble” analogy from Malpass. The past events are like marbles that have already appeared and been put into the jar. The claim of an infinite past, is that the jar already has an actually infinite number of marbles in it. Craig mentions all the “absurdities” that would obtain. So, in response, Malpass et al. would be essentially asking, “what about the source of marbles, from which they are drawn, moment-by-moment, and put into the jar? Isn’t that an infinite collection, just like the collection in the jar would be?” And the answer is “there is no such source or collection! The marbles come into being; they are not drawn from some preexisting collection.” Likewise, the Presentist acknowledges that past events have come into being already, and been “put into the jar”. So, that is surely a collection. But in what sense is there a collection of future ones to worry about (as to whether they have the “absurdities” of the collected jar of past marbles)? There is no such collection. They just come into being moment-by-moment, and then we jar them.
Thoughts?
@@Mentat1231 Thanks again for the interaction - it’s always wonderful to see engagement like this :)
Regarding your first paragraph here, you ask an excellent and tricky question! What makes this difficult is that Craig is a nominalist; he doesn’t believe in sets. This makes it difficult to say that Craig thinks there is a set of such-and-such and that the number of members in this set is such-and-such. The goal of the talk of ‘collections’ and ‘collections of future events’ is simply to follow Craig’s own usage; in particular, Craig talks of the ‘collection of past events’, even though Craig thinks there are no past events, and also there are no sets/collections. So Craig thinks we can still talk about this stuff without ontologically committing to the members of the collection or even ontologically committing to collections/sets. Given this, we can also talk about the collection of future events without ontologically committing to the members of the collection or even ontologically committing to collections/sets. And once we ask about the number of members in this collection, it has to be aleph-null for the reasons mentioned in the video and in the Prosblogion post.
As for your second paragraph, I don’t find compelling issues with representing the past and future as a number line with ticks, as long as we’re clear that it’s a representation that needn’t ontologically commit us to the reality of past and future events; and, ultimately, the goal of this representation is to help people more intuitively see why the number of events, each of which will occur, is aleph-null if the future is endless [and if we reject that brand of open theism]. This can be seen and shown without the use of the representation, so representing time as a line is dispensable. :)
As for your last paragraph about marbles, if we let 1 marble = one past event, and if we let the jar = the collection of past events, then yes, if the past is beginningless, then the jar has infinitely many marbles. But equally, if we let 1 marble = one future event, and if we let the jar = the collection of future events, then if the future is determinate and endless, then the jar has infinitely many marbles. We could even table them - one is 2023, one is 2024, one is 2025, one is 2026, one is 2027, one is 2028, … one is (2023+n) … for every natural number n. Both jars contain infinitely many marbles. You might retort that my [future-representing] marbles don’t exist; but neither do the [past-representing] marbles in your jar. Both our jars contain non-existent marbles. And yes, yours ‘have existed’; but equally, mine *will* exist, and what matters is simply that we can number the marbles (regardless of whether they have existed) and remove them from the jar. Once we admit this - and it needs to be admitted, since we *can* number future events, and future events *are* removed from the collection of future events as time progresses - we get absurdities attending the endless future [to wit, (i)-(iii) mentioned in my earlier comment].
@@MajestyofReason
Just a super quick remark that seems both inescapable and critical to this discussion: On Presentism, future events are like fictions. They are mere unactualized potential. That's why they do not feature in any explanations or causal relations. Past events did actualize, and do feature in explanatory and causal relations toward the real world. They are not like fictions (to take them as such would be to make the real/present world inexplicable and brute). The marbles in the jar have actualized in the real world (i.e. as of the present moment). Future marbles are as unreal as imaginary ones and cannot have been placed in the jar. The Kalam proponent should (IMHO) concern herself only with how many actualizations there have been. And that number cannot already be infinite (for Hilbert/Bernadette reasons) and can never become infinite (as we all agree).
@@MajestyofReason I just want to thank you for taking the time to explain complicated philosophical concepts! Your channel and engagement in the comments is awesome! I learn something from every video and comment.
Discussion of infinite is always very interesting. Personally I think it appears Craig is being willfully ignorant of your actual question because he doesn’t have an answer.
1:15:01 Nice!
I’m convinced that after decades of publishing papers and having them immediately shot down, Craig has bad dreams about Wes.
If I may just give one correction regarding something that is claimed to be "definitional", and is actually, definitionally wrong: MR claims that "potential infinity" is, by definition, an increasing collection. This is completely mistaken. An increasing collection is *one example* of a potential infinity, and it's an example that Aristotle used... *right along with the example of **_division!_* Infinite dividing is also a potential infinite, and it's obviously not an increasing of anything. Aristotle's definition of the potential infinite is this: "one thing is always being taken after another, and each thing that is taken is always finite, but always different." Again, this is _exemplified_ by an ever-increasing collection (and Aristotle sometimes uses that example), but it is equally well exemplified by an ever-dividing collection (which Aristotle also uses).
Eric Schechter defines the potential infinite, as opposed to the actual, as follows: "a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps. As a result, potential infinity is often formalized using the concept of limit."
The Stanford Encyclopedia of Philosophy, in discussing Aristotle's distinction between potential and actual infinities, specifically says that an endless future is potentially infinite.
As one final point on this, picking up on Schechter's mention of a "limit" concept, just consider the limits used in Calculus. They are paradigm examples of potential infinites, and yet they are obviously not always cases of increase. The limits used in differential calculus are for values that are, in fact, ever _decreasing._
I have much to say about later aspects of this video, but I just really felt like this definitional matter needed to be addressed.
You say it’s definitionally wrong, but it isn’t. ‘Potential infinity’ and ‘actual infinity’ are used *differently* in the Kalam literature than how Aristotle used it. This is a well-known point in the literature, and something Craig has explicitly noted in published work. (This also is why Craig *agreed* with my characterization of the potential infinite in the McNabb video. And it’s also a point I’ve made in other videos, e.g., my video responding to Trent Horn’s response to the Kalam documentary from SkyDivePhil. In fact, I directly quote Craig in my Hilbert’s Hotel video defining ‘potential infinite’ as a collection which increases limitlessly as time progresses but is always finite and 'actual infinite' as a collection which can be put in 1-1 correspondence with the naturals (or reals, or etc.).) This is also shown by the fact that Aristotle explicitly says that a beginningless, infinite past is *also* a potential infinite. For Aristotle, to be an actual infinity, all the members need to exist simultaneously, at one-and-the-same time. If the members are spread out over time - e.g., over infinite past time, or infinite future time - then the collection is a potential infinity. But notice that this clearly isn’t how ‘actual infinity’ is used in contemporary discussions on the Kalam, since an infinite past is an *actual*, rather than *potential*, infinity.
Here's the rub: a sufficient condition for being an actual infinite, as the contemporary Kalam literature understands actual infinites, is being a collection that can be put in 1-1 correspondence with the naturals. (And this 1-1 correspondence, in turn, engenders some of the central "absurdities" Craig thinks attend actual infinites, as explained in the video.) But it's demonstrably true that the collection of future years, if the future is endless, can be put in 1-1 correspondence with the naturals. Hence, the collection of future years, if the future is endless, is an actual infinite.
So I’m not mistaken about definitions; instead, you have mistaken Aristotle’s definition with the definition at play in the Kalam literature.
@@MajestyofReason
I appreciate the response. Just two quick rejoinders, because I think they are important:
1) Craig has repeatedly used the "limit" concept from Calculus as a paradigmatic and definitive example of what he means by "potential infinite". I didn't just appeal to Aristotle, but also to other references and specifically to the "limit" concept that Craig always references.
2) Facts about past happenings do all exist at once, namely they are all true now. Facts about future happenings do not exist, since future events have not happened. There is, for the Presentist (or, more broadly, what Craig calls a believer in temporal becoming) a stark asymmetry between the two. And, in any case, it is the "having happened" that brings all the problems for the past, and we all agree that infinite events will never "have happened". Everlasting beings will never be infinitely old. That would be nonsense. And yet, for the infinitist about the past, the world is already "infinity-old". I submit that this is equally nonsense, wholly apart from geometric idealizations.
@@Mentat1231 I appreciate the interaction my dude :)
Regarding your first point, Craig's illustrations there are precisely that -- illustrations. When he actually gives a precise definition of the terms, he gives them exactly as I defined them. And again, Craig himself agreed with my characterization in the McNabb video (and repeatedly in published work).
Also -- and most importantly -- this doesn't affect the 'rub' I gave in my previous message: all I need to make my broader case is that a sufficient condition for being an actually infinite collection is 1-1 correspondence with the naturals. Since an endless future satisfies this, an endless future counts as an actual infinite [as that's understood in contemporary Kalam literature, of course!]
As for your second point, you say: "Facts about past happenings do all exist at once, namely they are all true now. Facts about future happenings do not exist, since future events have not happened."
The point, however, was that the collection of past days itself doesn't all exist at once, and yet it's still an actually infinite collection as contemporary Kalam proponents use the term. But for Aristotle, since they don't all exist at once, that collection is only a potential infinite. This suffices to establish my point that it's a mistake to say that I've wrongly defined 'potential infinite' by appeal to Aristotle.
Second, facts about the future also exist now, since they're true now -- it's true now that I will east breakfast tomorrow; it's true now that Christ will return; it's true now that I will die; it's true now that I will visit the dentist in a few days; and so on. So just as facts about the past exist now because they're true now, facts about the future exist now because they're true now.
As for the point about 'have happened', I address that in response to your other comment :)
@@MajestyofReason
Well, if Craig agrees to the definition, then you’re quite right to use it when responding to him. I guess I hadn’t seen him as doing so. But, please indulge me for just one more response on each of these issues, if you have a second. First of all, even if Craig accepts it, it seems evident that it leaves out using “potential infinite” in two of the places it is paradigmatically and constantly used, including by Craig himself: namely: limits in math and Zeno-like divisions. So, perhaps Craig has been inconsistent by accepting a definition that doesn’t fit the very examples he uses. It wouldn’t be the first time, and Craig is only human. But my point is that neither of those paradigm examples are an increase or growth.
In any case, I have to ask you: Do you think Craig is really claiming that the cardinality of the set of future events is becoming _larger??_ “That is to say…” that there used to be some number of future events that were coming, and now there are more of them that are coming?? Nothing he’s said makes me think he believes that. Indeed, I don’t even know what it _means_ to believe that. It seems incoherent to me, and totally irrelevant to the Finitism problem. What “gets larger” or “increases” is the _value of the present member within the set._ E.g., it’s 2023 now, which is a higher value than 2022. *That* increases without bound, but the cardinality of the future set obviously doesn’t change.
If any set changes in cardinality, it would be the set of events that _have elapsed._ That makes sense, and it seems to be the proper parallel to the claim that an infinite set of events “has elapsed” prior to now. In both cases, the concern is not with a geometric idealization or “arrow”, but with how many things have actually occurred. Imagine that space is finite and spherical. Upon reaching the boundary, you could idealize further spaces, but there wouldn’t really be any. It’s even worse with temporal becoming, which I would argue is very poorly and sketchily represented using geometry.
My point about Aristotle is not that he was right about everything (e.g. I think he’s wrong about the past infinity being potential), but rather that, from the beginning of this distinction between potential and actual, it has never been thought of as _defined_ in terms of increase. Increase was just one _example._ Division is just as much a case of potential infinity, as we see in the response to Zeno.
I myself don’t think there are facts about the future. To defend Craig’s argument, I should use his assumptions, but consider this: If God is perfectly free, then He may (or may not) prevent you from going to the dentist, from dying, etc. So, there really is no fact of the matter about those either. Even something that we can be certain He won’t prevent (like Christ’s return) is a certainty about the present (God’s unchanging nature, etc.); not really a truth about the future. Let me address the “happenings” in the other comment, and then you can have the last word for both. I don’t mean to take up too much of your time. But I appreciate it!
@@Mentat1231 Hello. For someone who believes in an endless future, as Craig does, there are an infinite number of facts about the future that are true now. There will be a tomorrow (t+1), there will be a day after tomorrow (t+2), there will be a day after that (t+3) - and there will be a day for each t+n, where n is each of the natural numbers.
I want to say the Kalam is True but WLC molinism is in the way?
I would agree with Joe on a infinite pass, I am currently a open theist.
1:24:30 Craig's "counting down the negative numbers from infinity past" is completely nonsensical. What does he even *mean* by finishing an infinite task? And in any case, has Craig ever met somebody claiming to be such a counter?
1:35:35 "… writing a systematic philosophical theology." Theology being supposedly "the study of the nature of God". A god which they can't possibly study (and they admit as much). So… a book of blank pages?
Virtual particles can generate real particles with no cause at al. The quantum disproves the Kalam.
15:33 What does WLC mean by _absurd_ ?
Is this a term that has a common meaning in philosophy?
From WLC's usage my interpretation is:
It does not mean there is a logical contradiction.
It does not mean that it contradicts evidence.
so my conclusion is he thinks:
It contradicts his intuition. So f***ing what?
As a scientist I long ago learned that intuition stinks. It has a use - which is to provoke the inductive phase of hypothesis formation, but it must never be taken seriously.
(BTW: anything that uses the term _theory_ , to mean a non-predictive untested model, is bullshit. String Theory is bullshit).
6:19 The cardinality of those sets is the same.
Correct; which is why I stated my premise in terms of 'not increasing'. Staying the same is not increase :)
I do talk in terms of 'removing events' or 'getting smaller', but that's because there's a perfectly legitimate sense in which the set on the right is smaller than the one on the left; namely, it's a proper subset of the one on the left. We can disambiguate two notions of 'greater/less than' for sets: a cardinal sense, and an inclusive sense. In the cardinal sense, set A is greater (larger, etc.) than set B iff A's cardinality is greater than B's cardinality. Likewise, set A is smaller than set B iff A's cardinality is lower than B's cardinality. In the inclusive sense, set A is greater than set B iff B is a proper subset of A -- A has all of B's members *and then some*. Likewise, A is smaller than B iff A is a proper subset of B.
Also, keep in mind that if the collection is a potential infinite, it must have increased; it couldn't stay the same. So it isn't a potential infinite. This is the point of the argument :)
@@MajestyofReason
Do you have a written version of the argument ? We oldies find it harder to focus on spoken arguments.
*Z* includes elements not in *N* yet they are equipollent. You agree your sets have equal cardinality, yet seem to be suggesting that by having one year fewer in one set than another they become non-equipollent, and as such are not infinite. (If they are non-equipollent they are, by definition, not infinite). Am I right in understanding that its what you mean?
@@frogandspanner I am not saying they become non-equipollent. My point is precisely that the two sets *are* equipollent despite the removal of a member from the first to the second; and hence the second set has not increased compared to the first.
In short, when we compare set A to set B and set B is a proper subset of A, set A is not larger than set B. That's the claim, and it's true :)
The broader significance: In order for the collection of future days to be a potential infinite, this collection would have to increase over time; and yet the collection does not increase over time, since the later collections are mere proper sub-collections of earlier collections. Hence there's no increase int he size of the collections over time.
Then are you saying they are actual infinites?
(As a retired Physicist/Mathematician I find all this philosophy language, such as 'potential infinite' very confusing.)
@@frogandspanner if the future is endless, then yes, the cardinality of these sets is aleph-null🙂
I honestly don't believe Craig unintentionally misinterprets any of this. He can't give ground or he will stop believing.
Well we know the “stop believing” isn’t exactly true haha.
But him giving ground would definitely be very very surprising and might become just the end of his respected career
None of William's arguments amount to a proof of anything, not to anyone who hasn't lowered their epistemic bar so low a slug might step over it, as William has.
On the mathematical induction I think premise 5 is false, since aleph-zero is not a natural number, it is unjustified to say that you can count aleph-zero numbers
As you agree, aleph-null isn't an arbitrarily large natural number (or any natural number for that manner), but from the perpective of "now", if you entertain the scenario proposed in the argument, then every single day in the endless future will be counted. The argument is not saying that this has happened already. After all, we're talking of the future here, not the present or past. The point being made is that an [actual] infinite set of potential moments suffer the same so-called absurdities that Kalamists agree tend to other types of [actual] infinite sets.
@@georgeel-azar4684
That has nothing to do with the objection.
@@diegonicucs6954 Did you not object that it's unjustified to say one can count an infinite number [of future moments]? If so, then my post did have something to say in response to that. If not, then maybe you need to reword your objection because it's not clear what you're getting at then.
@@georgeel-azar4684
Nah you just dont get it
The objection: since aleph-zero is not a natural number, it is unjustified to say that you can count aleph-zero numbers
You response: every single day in the endless future will be counted. The argument is not saying that this has happened already
If I said that A is not justified and the answer is "then A", then you are not addressing the objection.
I can make it more clear if you want: Explain to me why this proposition is true: You can count aleph-zero numbers
@@diegonicucs6954 The problem is that if I say "A is justified", and then you counter with "something similar to A but not identical to A is unjustified", then maybe it's you not getting the argument.
Going back to the argument, if it is true that the future is endless, and I'm some immortal being that can count forever, and I start counting from tomorrow, starting with 1 and then onwards. If you grant me all this, then I will indeed count every single natural number.
But notice what is being said and not being said. I'm NOT saying that there will come a time when I will HAVE finished counting all natural numbers. Rather, I am saying that I WILL count every single natural number (starting tomorrow). Notice the tense being used here.
Remember, infinity is not a natural number, so let's not forget to think of infinity here in the relevant sense. If your objection implicitly assumes some gradual progression to aleph-null here, you're looking at it the wrong way. Think of it, instead, as a cardinal number (which is what it is). Infinity is already the case from the first moment (tomorrow).
To answer your question exactly as you worded it: yes but no. The question, as is, needs to be worded better.
Debate with WLC? Lol tell Cameron to make it happen. Have Koons or Josh be WLC’s tag team partner. You’ll get Mapass or Morriston.
The most disappointing part in this video when you say you've never been to NYC. Next time you think about watching and responding to a Craig video, maybe book a flight instead. You'll be much happier (And if you want you can always watch the video on the plane).
But when it is said time increases over time, and when It's 2023 then 2024,2025,2026 those doesn’t exist in actual sense. So reducing future years don't make any sense to me. When you say reducing future years You're presupposing future years as an actual sense.
For the endless future reaper thought experiment, why is it that the first reaper cant swing its scythe? If none of the other future reapers swing their scythe, thats fine, that the condition for the reaper to swing their scythe. Each reaper is separate from the first, right? I see the paradox as flipped; if 1 swings, 2 cant swing but if 2 cant swing then 3 cant and so forth so 2 could swing but then 1 cant swing because 2 will swing and ig that makes a loop...are you saying that if a reaper swings only 1 reaper in the series can swing? Because if its just that a future reaper cant swing, then the first reaper swings and the paradox is resolved. Imagine i eat a sandwich but only if no other person in the future eats the sandwich. Thats fine because i eat the sandwich and now noone else can eat it. Where is the paradox??
You’re overlooking the biconditional applying to each member of the collection: each member of the collection swings if and only if no future member swings. Suppose #1 swings. Then #2 and above won’t swing. But if #2 and above won’t swing, then #3 and above won’t swing. But if #3 and above won’t swing, it follows that #2 swings, since each member swings if no reaper in its future swings. Hence #2 swings. This contradicts our supposition earlier that #1 swings, since #1 swings only if no future reaper swings, and #2 is a future reaper that swings. So #1 doesn’t swing. That contradicts our assumption that #1 swings. Since #1 was just an arbitrarily chosen #, it follows that none of the reapers swing. But if none of the reapers swing, then none of the reapers in #1’s future swing. Hence, #1 swings, since a reaper swings if no reaper in its future swings. Hence, we’ve concluded that no reaper swings, and a reaper swings. Contradiction.
Ig what I would like clarification on is if there can only be 1 swing.
A is true iff B-Z are false
B is true iff C-Z are false
Lets say C-Z are false (temporarily, obviously this is messy since we know theres a paradox that will arrive later on)
A is true. B is almost also true, but if it is, then A cant be true. Thus paradox. So can only 1 reaper swing (is there only 1 sandwich like in my example?) because if so, then i see the paradox: we dont know if A is true unless we check B and we dont know if B is true unless we check C, etc. But if not, then cant we just check A and stop there? Or is it that we dont know if A is true unless we check B-Z? Are we solving for A or is :A is true a premise"? Im sorry, im not formally trained in logic or philosophy so a lot of this take some extra effort to wrap my head around.
Don't worry if you're struggling with this one; it's fairly complex.
The important point to focus on is the 'rule' being applied to each member in the sequence. ie:
condition 1: there is an endless set of reapers.
condition 2 (rule): each reaper of the set swings if and only if no future member swings.
Let's say reaper 1 swings. Condition 2 tells us that no other reaper after will swing.
So we know from this that reaper 2 won't swing. And further we know reaper 3 won't swing and so on etc.
But wait ...
Condition 2 says a reaper will swing if and only if *no future reapers swing.
So if we know reaper 3 and above don't swing, our condition 2 rule tells us that reaper 2 does swing!
So we now know reaper 2 swings.
But wait ...
Again condition 2 says a reaper will swing if and only if *no future reapers swings.
This contradicts our first assumption that if reaper 1 swings reaper 2 doesn't.
This means reaper 1 doesn't swing either.
But that contradicts our initial assumption. Meaning none of the reapers will swing.
7:30 Where does the definition of _Potentially Infinite_ come from? None of my maths books (including my favourite _The theory of Sets and Transfinite Arithmetic_ , Alexander Abian, W B Saunders 1965 - I'm showing my age) defines it.
You are applying a quantifier ( _If the definition of _Potentially Infinite_ is that the number elements of the set increases in time . . . _ ), which reduces the domain of discourse. If you can get the originator of the argument to agree that this constraint is the same as theirs than all is OK. Do they agree?
8:10 This Craigian argument is that time is like a fluid. Newton thought so. They are/were wrong. Relativity works, and explains what the Newtonian model failed to explain (Arago, Fizeau, Bradley, Airy, Michelson-Morley, lasers, Mossbauer effect, Trouton-Noble, muon lifetime, Bailey, Ives & Stillwell, McGowan, Hafele & Keating, Glashow & Coleman, Stodolsky, perihelion of Mercury, gravitational lensing, gravitational redshift, satnav). RELATIVITY WORKS but only if we discard the Newtonian model of time. Time is a dimension, a backdrop against which we measure differences.
Yet WLC keeps to his discredited model of time.
Great question about 7:30 -- yes, I'm actually taking these definitions from Craig himself. I offer quotations in my Hilbert's Hotel video! :) [And also, Craig agreed with the characterization of a potential infinite in the clip I played]
@@MajestyofReason So within the agreed domain of discourse WLC must agree with the logic, and your conclusion. I wonder if he will.
@@frogandspanner Well, it was pointed out to him over two decades ago, and he still hasn't...
@@MajestyofReason I was on Senate at the University where he got his PhD, but too late to speak out at against his award!
New objections still work
New arguments for the Kalam still work
A eternal discution
That's the point. I think that a better way to be sure that God exists is looking at the lives of the saints. For instance, Padre Pio de Pietrelcina performed many incredible miracles.
@@yonnerzmuller5304 I think inferring God from miracles and personal experiences are probably the worst way to go. Jesus even seems to explicitly motion against it
@@Biblig As a person who spent a lot of time studying apologetics and formulating many new arguments in natural theology, I say that that's the best way to go. There are contemporary miracles that are easy to verify. If you, with an opened heart, look at the life of Saint Padre Pio, I think it's impossible to not believe in God.
@@Biblig Btw, could you explain the reasons you think that any argument from miracle is bad?
@@yonnerzmuller5304 OR exorcisms. Unlike the resurrection, which could only have happened once in the past and therefore difficult to prove, these continue happening to this very day since ancient times and if they really are genuine then it would prove the supernatural. I believe more attention should be drawn to contemporary pieces of evidence for theism and supernaturalism to the same priority as cosmological or teleological arguments.
Craig is incorrigible. Over the years, I have numerous times seen philosophers and physicists correcting Craig on diverse topics. He just keeps regurgitating his old shit on and on.
Or looking for new shit to polish and regurgitate.
First it was Penrose, now BGV, only the Kalaam God knows what he wants to do next.
Objection 2 objection. I don't agree with any of these reasons - perhaps one. It doesn't seem "obviously possible" that there exists something endless at all. So, that might not be imaginable or conceivable. Moreover, there are no successful cosmological models with endless futures. The very idea causes all sorts of problems with relativity and B Theory of time, and the un-relatability of infinitude to those theories.
The principle of modal continuity does not apply to a vase that is infinitely tall, for example, because such a thing could not exist.
Dr. Craig believes that the future will be, as it is realized momentarily in the present. So, this objection 2 is little more than a straw man. Perhaps it does rise to ad hominem, but I think Dr. Craig is being too polite.
By the way, no Christian or Muslim needs to live forever into the future. He merely needs to live one more moment beyond the current one, and one more beyond that. This is the potential infinite.
Where's my .75x playback speed crew at?
How has the collection of future years gotten so much smaller 5:55? the collection at [2024,2025, 2026....] is ℵ0 but the collection at [2026, 2027, 2028...] is also ℵ0 i agree they are the same as you progress but they arnt smaller in size as (ℵ0)-x is still ℵ0 iff x is finite number. But i understand your argument.
Good question - that was really just an imprecise way of saying that the collection of future years, as of a later time, is a mere proper subset of the collection of future years as of an earlier time.
@@MajestyofReason would they not be just a "subset" simpliciter but not a proper set since both sets would be ℵ0.
I.e at each place the set can be link together or what i mean is 2024 could be linked with 2026, 2025 could be linked with 2027, 2026 could be linked with 2027 and so on such as they would be the same/equal. Cardinality would be the same.
@@zemunacnoir5877 X and Y can have the same cardinality even though X is a proper subset of Y. The even numbers are a proper subset of the natural numbers, but they have the same cardinality. 'X is a proper subset of Y' just means that all the members of X are members of Y, but there is at least one member of Y that is not a member of X.
@@MajestyofReason Hey joe ty for the reply :) and yea you are of course right about that.
My first objection from your argument is your definition of a potential infinite i dont see why "time" is necessitated. I mean even craig says at and i qoute "potential infinite is a collection that is at everytime finite but increasing toward infinity as a limit" i mean not only that but just take the standard collection/sequence 1, 2, 3, 4, ..... this collection/sequence is a potential infinite because its "number of members is increasing" simpliciter not that "the number of members is increasing over time" what im saying is time does not have a influence in this collection for wether or not its a potential infinite. If so please explain how. My second objection or question is dont you beg the question when you stipulate "future years" i mean i could think of some theories of time that dont have the notion of future years so by that dont you presuppose those theories to be false? 😆
Once again thanks.