In Metaphysics, "Bizarre" Does Not Mean Impossible - Final Thoughts on the KCA
Note: This is my final post on the Kalam Cosmological Argument and other "laws" aimed at discrediting and disparaging my assumptions.
Kristor has responded to one of my posts about the Kalam Cosmological Argument. In his response, he insists that I am honestly mistaken about KCA and classical theism and that pretty much everything I have said about them is false.
I beg to differ, but I won’t dedicate a post to quibbling.
What I will do instead is address the “battering ram” Kristor considers to be ironclad in his argumentation. The one he has consistently employed against my assumptions; the one he believes sinks my assumptions entirely-- the apparent impossibility of traversing the infinite .
Kristor explained his position quite clearly in a comment on this blog:
Kalam demonstrates that perpetuity – of God, or of other beings – is an incoherent notion : there is no way an infinite temporal series of finite events (in the life of a cosmos or of a being) that had no beginning – i.e., a perpetuity – could ever reach the present moment, or any other. From a point in time infinitely far in the past of any moment, any now, an infinite series of finite events would have to traverse infinitely many finite steps to reach that now. And no number of finite steps can sum to infinity. From the perspective of any such now, the series would always be cooking along infinitely far in its past.
Zeno’s paradoxes of motion anticipate Kalam.
For “finite events” in the foregoing we may substitute “finite causes” and reach the same result: no assemblage of finities can add up to infinity; it cannot be the case that it’s turtles all the way down. So, the real world and its panoply of causes must be finite: they must each have a terminus a quo, a First Cause, an absolute beginning.
Thus, perpetuity can’t be carried into actuality. So, neither God nor any world can be perpetual.
The necessity of an absolute beginning is by the way the basis and reason of creatio ex nihilo. The alternative – creatio ex materia – implicitly presupposes the actuality of an impossible perpetuity.
In his most recent post, Kristor maintains his death grip on this position by doubling down via an external source:
An infinite collection formed by successive addition is impossible: Next, Craig argues that – even if an actual infinite is possible – an actual infinite can never be formed by successive addition. But, if the past is infinite, that is exactly what the past must be. Craig argues that, if the past were infinite, then an infinite number of successive moments have been traversed (i.e., an infinite number of moments have “streamed by” so to speak). But, if “traversing the infinite” were possible, it would lead to a number of absurdities. To illustrate this, he uses the example of the infinite counter:
Imagine that there has always been The Count from Sesame Street. He has always existed, and as long as he has existed, he has been counting down. Today, he is about to reach zero. “Negative two!” he says. “Negative one! Zero!!! Ah ah ah!” … Now, it seems clear that, if I begin counting up (“one, two, three…”), I will never reach infinity. One can never count to infinity. But, why should it be any different in the other direction? How could one ever count from infinity? In this example, it seems like The Count would reach zero today, because (if the past is beginningless) there were an infinite number of moments before today. But, wait …
There were also an infinite number of moments before yesterday. So, it seems like The Count should have finished counting yesterday. But, wait… There were also an infinite number of moments before a year ago, or a billion years ago. In fact, no matter how far back in time we go, it seems like The Count should have always already finished counting (since, no matter how far back in time we go, there was always an infinite amount of time before that). But, that is absurd. Therefore, an infinite succession cannot be traversed.
I could counter Kristor’s selective or limited understanding of infinity in my own words, but I don’t think that would make much of an impression on or difference to Kristor.
So, what I will do instead is refer to Edward Feser, a prominent philosopher firmly within Kristor’s classical theist camp, who offered the following concerning the KCA, infinity, and Craig's notion of time:
A third reservation – the one I will discuss here -- has to do with the question of whether one really can demonstrate that an infinitely old universe is metaphysically impossible, and in particular whether one can demonstrate that an accidentally ordered series of causes (as opposed to an essentially ordered series) cannot be infinite.
(This is, of course, the traditional bone of contention for Thomists.) I am not convinced that this cannot be demonstrated. But I’m not sure that Craig’s metaphysical arguments for that conclusion (e.g. the well-known appeals to Hilbert’s hotel and similar examples) work.
Recall that the basic kalām argument says:
1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. So the universe has a cause.
That’s the easy part, and the main work in defending the argument involves (a) defending the second premise, and (b) showing that the cause of the universe must be a divine cause. It is in defending the second premise that Craig appeals to examples like Hilbert’s hotel.
The basic idea of such arguments is this. We can draw a distinction between an actual infinite and a merely potential infinite. A potential infinite is a collection that is actually only finitely large, but can be added to without limit. For example, suppose there are ten chairs in some particular room. We could always add an eleventh, a twelfth, and so on, and (if we knock out some of the walls and expand the room) can in principle add any number of further chairs ad infinitum. A potential infinite never is actually infinitely large, but can still always be added to in theory, as long as time and resources permit. An actual infinite, by contrast, already is infinitely large. An actually infinite collection of chairs, for example, would be one that already includes an infinite number of chairs, all at once and at the same time.
This is a distinction Craig borrows from Aristotle, even if in other respects his argument is not particularly Aristotelian. The use he makes of it is this. The notion of a potential infinite is unproblematic, but the notion of an actual infinite is fraught with paradox.
For instance, if we imagine a hotel with an infinite number of rooms and an infinite number of guests checking in and checking out, we will, if we work out the implications, find them to be utterly bizarre.
So bizarre, in Craig’s view, that we should conclude that such a hotel could not possibly exist in reality. (Those familiar with Craig’s argument will know how the details of examples like these go – I won’t rehearse them here.) And this shows, Craig argues, that the idea of an actual infinite is in general very fishy. There just can’t be an actually infinite collection of things.
Now, an infinitely old universe would constitute an actual infinite, Craig argues. It would amount to an actually infinitely large collection of hours, days, years, or whatever other unit of time you pick. Hence, since there cannot be an actual infinite of any sort, there cannot be an actual infinite of this particular sort. So, the universe cannot be infinitely old.
Now, one problem here is that it will not do to show merely that an actual infinite like the one described in the Hilbert’s hotel scenario is bizarre . To show that something is bizarre does not suffice to show that it is impossible.
For that, you need to show that it involves some outright contradiction or incoherence. But perhaps that can indeed be shown. That isn’t the issue I’m concerned with here. So, for present purposes let’s concede for the sake of argument that scenarios like Hilbert’s hotel really are strictly metaphysically impossible.
The problem is this: How does this show that an infinitely old universe is impossible?
In particular, how does this show that there could not have been in the past an infinite series of hours, days, or years?
The reason this is a problem is that Craig is a presentist . That is to say, he thinks that it is present things and events alone that exist. Past objects and events don’t exist anymore, and future objects and events don’t yet exist. (This contrasts with theories of time like the “growing block” theory, which holds that past and present things and events exist, with the present being the growing edge of a block universe; and with the eternalist view that all things and events, whether past, present, or future, all equally exist.)
Now, his commitment to presentism is not itself the problem; in fact, I agree with Craig about that. (I will have much more to say about that subject in forthcoming work.) The problem is rather this. If the present alone is real, then how can an infinite series of events in time count as an actual infinite?
Past moments of time are not actual; they no longer exist. Hence an infinite series of past moments is not relevantly analogous to Hilbert’s hotel. In the Hilbert’s hotel scenario, all of the hotel rooms in the infinite collection of rooms, all of the guests in the infinite collection of guests, etc. exist together all at once, at the same time. But (for a presentist) past moments, and past things and events in general, no longer exist. They don’t exist together, all at once and at the same time, because they don’t exist at all .
Hence there really is even prima facie (again, if one is a presentist) no such thing as an infinite collection of past moments of time, as there might at least prima facie be an infinite collection of rooms and guests. So, an infinitely old universe scenario is simply not relevantly analogous to scenarios like Hilbert’s hotel – in which case, it seems Craig’s argument will fail even if it is conceded that an actual infinite is impossible.
For an infinitely old universe just wouldn’t be an actual infinite in the relevant sense.
Kristor can do with that what he will, but I think that pretty much sinks the “you can’t traverse the infinite” mantra. So much for "turtles all the way down." If it doesn’t, I have a whole bag of other goodies that could do so in a far more devastating fashion.
But here’s the thing. I don’t want to pursue this anymore because it is drawing me closer to philosophy than to God.
What Kristor and I have been engaged in since September only demonstrates the futility and limitations of pursuing Christianity via secondary thinking (communication through language and other symbols). We could literally keep this up to infinity and get nowhere with each other.
I would much rather focus on expounding my assumptions and how these relate to my primary thinking and direct knowledge.
I invite Kristor to do the same.
Leave the world of secondary thinking for a while and see what happens.
Note added: The whole spiel about "counting to infinity" in the example Kristor cites is hogwash. It is nothing more than a conflation of actual infinity and potential infinity. Infinity is not a number. It is a property of a number.
Counting to infinity would be akin to counting to primeness or evenness. That actual infinities are logically and metaphysically possible has not been a controversial topic in mathematics for over a century--yet people like Craig and Kristor still consider them to be killshots for metaphysical assumptions that do not complement theirs.
What do the KCA, the necessity of a first cause, and other philosophical arguments have to do with being a Christian or following Jesus? Well, for me, not much, but for guys like Kristor, it seems to be all that matters.
Kristor has responded to one of my posts about the Kalam Cosmological Argument. In his response, he insists that I am honestly mistaken about KCA and classical theism and that pretty much everything I have said about them is false.
I beg to differ, but I won’t dedicate a post to quibbling.
What I will do instead is address the “battering ram” Kristor considers to be ironclad in his argumentation. The one he has consistently employed against my assumptions; the one he believes sinks my assumptions entirely-- the apparent impossibility of traversing the infinite .
Kristor explained his position quite clearly in a comment on this blog:
Kalam demonstrates that perpetuity – of God, or of other beings – is an incoherent notion : there is no way an infinite temporal series of finite events (in the life of a cosmos or of a being) that had no beginning – i.e., a perpetuity – could ever reach the present moment, or any other. From a point in time infinitely far in the past of any moment, any now, an infinite series of finite events would have to traverse infinitely many finite steps to reach that now. And no number of finite steps can sum to infinity. From the perspective of any such now, the series would always be cooking along infinitely far in its past.
Zeno’s paradoxes of motion anticipate Kalam.
For “finite events” in the foregoing we may substitute “finite causes” and reach the same result: no assemblage of finities can add up to infinity; it cannot be the case that it’s turtles all the way down. So, the real world and its panoply of causes must be finite: they must each have a terminus a quo, a First Cause, an absolute beginning.
Thus, perpetuity can’t be carried into actuality. So, neither God nor any world can be perpetual.
The necessity of an absolute beginning is by the way the basis and reason of creatio ex nihilo. The alternative – creatio ex materia – implicitly presupposes the actuality of an impossible perpetuity.
In his most recent post, Kristor maintains his death grip on this position by doubling down via an external source:
An infinite collection formed by successive addition is impossible: Next, Craig argues that – even if an actual infinite is possible – an actual infinite can never be formed by successive addition. But, if the past is infinite, that is exactly what the past must be. Craig argues that, if the past were infinite, then an infinite number of successive moments have been traversed (i.e., an infinite number of moments have “streamed by” so to speak). But, if “traversing the infinite” were possible, it would lead to a number of absurdities. To illustrate this, he uses the example of the infinite counter:
Imagine that there has always been The Count from Sesame Street. He has always existed, and as long as he has existed, he has been counting down. Today, he is about to reach zero. “Negative two!” he says. “Negative one! Zero!!! Ah ah ah!” … Now, it seems clear that, if I begin counting up (“one, two, three…”), I will never reach infinity. One can never count to infinity. But, why should it be any different in the other direction? How could one ever count from infinity? In this example, it seems like The Count would reach zero today, because (if the past is beginningless) there were an infinite number of moments before today. But, wait …
There were also an infinite number of moments before yesterday. So, it seems like The Count should have finished counting yesterday. But, wait… There were also an infinite number of moments before a year ago, or a billion years ago. In fact, no matter how far back in time we go, it seems like The Count should have always already finished counting (since, no matter how far back in time we go, there was always an infinite amount of time before that). But, that is absurd. Therefore, an infinite succession cannot be traversed.
I could counter Kristor’s selective or limited understanding of infinity in my own words, but I don’t think that would make much of an impression on or difference to Kristor.
So, what I will do instead is refer to Edward Feser, a prominent philosopher firmly within Kristor’s classical theist camp, who offered the following concerning the KCA, infinity, and Craig's notion of time:
A third reservation – the one I will discuss here -- has to do with the question of whether one really can demonstrate that an infinitely old universe is metaphysically impossible, and in particular whether one can demonstrate that an accidentally ordered series of causes (as opposed to an essentially ordered series) cannot be infinite.
(This is, of course, the traditional bone of contention for Thomists.) I am not convinced that this cannot be demonstrated. But I’m not sure that Craig’s metaphysical arguments for that conclusion (e.g. the well-known appeals to Hilbert’s hotel and similar examples) work.
Recall that the basic kalām argument says:
1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. So the universe has a cause.
That’s the easy part, and the main work in defending the argument involves (a) defending the second premise, and (b) showing that the cause of the universe must be a divine cause. It is in defending the second premise that Craig appeals to examples like Hilbert’s hotel.
The basic idea of such arguments is this. We can draw a distinction between an actual infinite and a merely potential infinite. A potential infinite is a collection that is actually only finitely large, but can be added to without limit. For example, suppose there are ten chairs in some particular room. We could always add an eleventh, a twelfth, and so on, and (if we knock out some of the walls and expand the room) can in principle add any number of further chairs ad infinitum. A potential infinite never is actually infinitely large, but can still always be added to in theory, as long as time and resources permit. An actual infinite, by contrast, already is infinitely large. An actually infinite collection of chairs, for example, would be one that already includes an infinite number of chairs, all at once and at the same time.
This is a distinction Craig borrows from Aristotle, even if in other respects his argument is not particularly Aristotelian. The use he makes of it is this. The notion of a potential infinite is unproblematic, but the notion of an actual infinite is fraught with paradox.
For instance, if we imagine a hotel with an infinite number of rooms and an infinite number of guests checking in and checking out, we will, if we work out the implications, find them to be utterly bizarre.
So bizarre, in Craig’s view, that we should conclude that such a hotel could not possibly exist in reality. (Those familiar with Craig’s argument will know how the details of examples like these go – I won’t rehearse them here.) And this shows, Craig argues, that the idea of an actual infinite is in general very fishy. There just can’t be an actually infinite collection of things.
Now, an infinitely old universe would constitute an actual infinite, Craig argues. It would amount to an actually infinitely large collection of hours, days, years, or whatever other unit of time you pick. Hence, since there cannot be an actual infinite of any sort, there cannot be an actual infinite of this particular sort. So, the universe cannot be infinitely old.
Now, one problem here is that it will not do to show merely that an actual infinite like the one described in the Hilbert’s hotel scenario is bizarre . To show that something is bizarre does not suffice to show that it is impossible.
For that, you need to show that it involves some outright contradiction or incoherence. But perhaps that can indeed be shown. That isn’t the issue I’m concerned with here. So, for present purposes let’s concede for the sake of argument that scenarios like Hilbert’s hotel really are strictly metaphysically impossible.
The problem is this: How does this show that an infinitely old universe is impossible?
In particular, how does this show that there could not have been in the past an infinite series of hours, days, or years?
The reason this is a problem is that Craig is a presentist . That is to say, he thinks that it is present things and events alone that exist. Past objects and events don’t exist anymore, and future objects and events don’t yet exist. (This contrasts with theories of time like the “growing block” theory, which holds that past and present things and events exist, with the present being the growing edge of a block universe; and with the eternalist view that all things and events, whether past, present, or future, all equally exist.)
Now, his commitment to presentism is not itself the problem; in fact, I agree with Craig about that. (I will have much more to say about that subject in forthcoming work.) The problem is rather this. If the present alone is real, then how can an infinite series of events in time count as an actual infinite?
Past moments of time are not actual; they no longer exist. Hence an infinite series of past moments is not relevantly analogous to Hilbert’s hotel. In the Hilbert’s hotel scenario, all of the hotel rooms in the infinite collection of rooms, all of the guests in the infinite collection of guests, etc. exist together all at once, at the same time. But (for a presentist) past moments, and past things and events in general, no longer exist. They don’t exist together, all at once and at the same time, because they don’t exist at all .
Hence there really is even prima facie (again, if one is a presentist) no such thing as an infinite collection of past moments of time, as there might at least prima facie be an infinite collection of rooms and guests. So, an infinitely old universe scenario is simply not relevantly analogous to scenarios like Hilbert’s hotel – in which case, it seems Craig’s argument will fail even if it is conceded that an actual infinite is impossible.
For an infinitely old universe just wouldn’t be an actual infinite in the relevant sense.
Kristor can do with that what he will, but I think that pretty much sinks the “you can’t traverse the infinite” mantra. So much for "turtles all the way down." If it doesn’t, I have a whole bag of other goodies that could do so in a far more devastating fashion.
But here’s the thing. I don’t want to pursue this anymore because it is drawing me closer to philosophy than to God.
What Kristor and I have been engaged in since September only demonstrates the futility and limitations of pursuing Christianity via secondary thinking (communication through language and other symbols). We could literally keep this up to infinity and get nowhere with each other.
I would much rather focus on expounding my assumptions and how these relate to my primary thinking and direct knowledge.
I invite Kristor to do the same.
Leave the world of secondary thinking for a while and see what happens.
Note added: The whole spiel about "counting to infinity" in the example Kristor cites is hogwash. It is nothing more than a conflation of actual infinity and potential infinity. Infinity is not a number. It is a property of a number.
Counting to infinity would be akin to counting to primeness or evenness. That actual infinities are logically and metaphysically possible has not been a controversial topic in mathematics for over a century--yet people like Craig and Kristor still consider them to be killshots for metaphysical assumptions that do not complement theirs.
What do the KCA, the necessity of a first cause, and other philosophical arguments have to do with being a Christian or following Jesus? Well, for me, not much, but for guys like Kristor, it seems to be all that matters.
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