1. Introduction - Alex reiterates his desire for a symmetry breaker between beginninglessness and endlessness. Craig wants to make the beginningless past an actual infinite and the endless future a potential infinite. Craig argues (and Alex agrees) that the number of events that 'have been' will always be finite. But Alex argues that Craig has missed Morriston's point, which is that the number of yet-to-be events that will eventually be is 'not growing', 'doesn't satisfy Craig's definition of a potential infinite', and hence is an actually infinite transfinite number.
However, that's not where Craig's rebuttal ends; he does have something to say about 'yet-to-be' events: namely, that there are no yet-to-be events. Craig will go on to equate the yet-to-be events with an endless future, rather than an endless series of events (the former's number is 'zero'; the latter will always be finite, and so a potential infinite). And the yet-to-be events are zero not just because they don't exist (the past doesn't exist either); it's because they are not part of the actual world (in the way that the non-existent past is). Alex might retort: there is a transfinite number of unactual, yet-to-be events that will be (in other words, even if the endless future is not actual, an endless future 'will be' actual). But this seems to me to ignore Craig's distinction between an endless series of events (potentially infinite) and an endless future (an actually infinite number of yet-to-be events): the former is a collection of events that is constantly growing and finite (never 'will be' infinite'); the latter is a collection of events that is not growing and will never not be infinite. There is not only what I think to be a distinction with a difference in this case, but there also seems to me to be a substantive distinction between a beginningless past and an endless series of events (as opposed to an endless future). Because of the robustness of the semantic distinctions, I fail to see how Craig is conflating or equivocating regarding the distinction between endless future and an endless series of events on the one hand, and hence the distinction between a beginningless past and an endless series of events on the other hand. I submit that these conceptual distinctions are motivated by broad logical considerations of how Craig applies the idea of tense (considerations that are narrower than the modal scope of Alex's mathematical input/output functions). But I will get to more detail on this on later. Suffice it to say, let me provide a taxonomy, not meant to serve as a proof, but as an aid for the proposed nomenclature.
Semantic Ontological Duration
Tense Claim
a. Have been - Part of the Actual World - Always Finite
b. Will be - Not part of the Actual world - Always Finite
c. Yet to be - Not part of the Actual world - Always Infinite
--------
d. Beginningless Past - The collection of events is not
growing
e. Endless Future - The collection of events is not
growing
f. Beginningless series of events - The collection of events is
growing.
g. Endless series of events - The collection of events is
growing.
Alex flirts with 'f' (which would be a potential infinite) in another blog, which would have the benefit of providing symmetry (as Alex understands it) between 'f' and 'g'. Alex will think that 'd' is an actual infinite, as is 'e'. Craig will deny the actuality of 'e', whereas Alex seems to conflate existence and actuality and thereby try to compel Craig to choose between affirming ('d' and 'e') or ~('d' and 'e'), where Craig thinks he can deny 'e' and affirm 'd'. Craig affirms ('d' and 'g') because of 'tense'. A beginningless collection of events will be an actual infinite in the sense that the number of events in such a collection is a transfinite number and in the sense that the number of events are a part of the actual world (though non-existent). The future, on the other hand, is both non-existent and non-actual, which is another symmetry-breaker between, not a beginningless series and an endless series, but between a beginningless past and an endless future.
***Huge (but interesting) side-thought (I'm developing while sifting through Alex's thoughts on this, not to mention Craig's).
***[Sidebar, involving a thought worth exploring: some theologians speak of the idea of Eternity in contradiction to the idea of endless duration. I first discovered the idea in Peter Kreeft. He says strange things like: "My own death ends my life's time. Whatever eternity is, it is is not time, not even endless time." He doesn't think we'll have a timeless existence in Heaven (though the idea of timelessness gets close); it is not "unending time". Kreeft actually denies that time is like "a line with no last point". He says that Eternity is different dimension orthogonal (my word, but I've seen it geometrically represented this way before) to time (my innovation might involve the temporal implantation of the orthogonal, eternal ontology at some point in the future of real and/or metric time (that'll be distinguished from The Eternal Present and Stump-Kretzmann Eternity). The extra-dimensionality of eternity understood analogically in good Aquinian fashion (also worth diving into more): on analogy to the way quantitative-extra-dimensionality relates to the relation between solids, planes, lines, and points (not to mention temporally extended space/time worms/blocks, perhaps). Kreeft calls it a 'qualitative' extra-dimensionality; it has more, not less, dimensions than space/time (if we keep the geometric analogy, eternity will do to time - duration - what time does to objects, what planes do to lines, what lines do to points - this may sound like the banal point that is already emphasized by relativity spatializing time according to one physical interpretation. But I think the banality of it lies in not analogically extending the spatiality of time. It has got to be analogically extended, not literally extended, which we'll have to do to distinguish relativity from eternity). Kreeft says that 'eternity is not spread out like time'. Admittedly, Kreeft is not a presentist, as I am (but I want to go along with this for a second). Kreeft says: "It is simultaneously present all at once, not piece by piece in passing." He goes on to outline Boethius' view (with non-analytic epigrams like: 'the simultaneous possession of all perfection in a single present.'). Kreeft then endorses something very close to our being space/time worms: "Time is like a floor, and our lives in time are like buckets of water spilled out along that floor." "Eternity is like all the water gathered together in a bucket" (Kreeft). That is distinct from a simple space/time worm view. One wonders what the nature of this 'gathering up' is (and I wonder if I can somehow equate such a gathering with the temporal implantation of the orthogonal, eternal ontology at some point in the future of real and/or metric time, mentioned above). Continuing. Kreeft doesn't want to do what I did above (understanding dimensional extension analogically): Kreeft says: "we need no dimensional analogy, for we can be literal about dimensions: if there are three dimensions of space and time is the fourth dimension, then eternity is the fifth dimension. Eternity includes time as time includes space." Kreeft will correct this by calling Eternity the SIXTH dimension by introducing the Chronos/Kairos distinction. Chronos is the 4th dimension; Kairos is the 5th dimension; Eternity is the 6th dimension. Chronos is like a line; Kairos is like a plane; Eternity is like a solid. The idea of 'endless duration' at issue in the Alex/Craig dispute is, according to Kreeft, talking about a property (duration) that inheres in Chronos only. To switch the geometry a tad, Kreeft says: "Suppose we visualize Kairos as a cone. All its radii come together at its point, eternity." Kreeft: "At one end, the cone of our life-time touches the eternal center, the inner heart of time. At the other end, it is made finite and bounded by its amount of Chronos, the outer skin of time. Our lived time has both an inside and an outside, a heart and a surface skin; our human time (kairos) touches both superhuman time (eternity) and subhuman time (chronos), both the divine and the material, just as our subjective spirit touches both objective spirit (God) and objective matter (the world)." But then Kreeft says something odd; regarding the so-called three levels of reality ("the human, the superhuman, and the subhuman"), Kreeft says that, "Each has its own kind of duration that is natural to it: eternity for God, Kairos for humanity, Chronos for the world." It's odd because Kreeft denies that Eternity involves endless duration and yet all affirms that Eternity involves 'its own kind of duration'. Consider Kreeft's Diagrams:
From the diagrams, I'm trying to find out how Kreeft is understanding 'duration' in Eternity, even though Eternity doesn't involve what Kreeft calls 'endless duration'. I'm wondering whether Craig's notion of an amorphous (or a sort of time without an intrinsic metric) time could loosely qualify as the duration of Eternity. Craig admits that Kalam necessitates the beginning of metric time, not time in any sense. I'll further wonder whether the concept of 'endless duration' is entirely compatible with amorphous time, as Craig seems to think that God's run-up to the creation of the universe (Leibniz's worry) is neutralized if the time is amorphous or if God is timeless. If that's a distinction worth making, I wonder whether we might be able to apply a kind of amorphous beginninglessness to God's run-up to creation; next, you have this metric-Chronos that perhaps has its 'eschaton' (in accordance with Kreeft's Diagram 6, where Kairos is beneath the 'skin' of Chronos toward Eternity as a kind of 'telos', perhaps).]
***Back to the blog!
I would like to focus on the idea that Morriston seems to ignore Craig's distinction between yet-to-be and will-be. Morriston says that 'he was not asking for the number of praises that have been said' [see here for Morriston's thought-experiment involving angels singing praises forever]. Morriston wants to know 'the number of praises yet-to-be-said' . . . 'that is, for the number of praises, each of which will eventually be said.' This response is unsatisfactory to me because Morriston hasn't addressed Craig's purposeful distinction between yet-to-be and will-be (outlined above). But such questions won't be pursued here. In fact, I might not say too much here because Andrew Loke's strategy is a tact I'm not inclined to take.
2. Loke's argument - For a representation of Loke's argument, see Alex's blog. I'll note certain parts I'm having trouble with. First, again, Alex confesses that 'will-be-said' and 'yet-to-be-said' 'sound like synonyms. I don't think they are. I'm not sure I agree with the additional distinction Loke introduces in terms of 'will have been' and 'will be', which seems to mesh together my taxonomy (above) a bit. I disagree with Loke that Craig didn't address the praises yet-to-be-said, per the above. Hence, I have absolutely no good reason to think that Craig is equivocating on yet-to-be and will-be, or that Craig didn't address the yet-to-be, as Alex and Loke seem to indicate.
Loke wants the 'paradoxical implications' of the actual infinite to apply to the 'existence and actualization of an actual infinite number of concrete entities or events'; it shouldn't be directed against an 'actual infinite number of abstract entities'. I will say that I disagree with Loke's appropriation of Moreland's analysis of what it is for an object to be abstract. I do agree that abstract objects can't be persons. The reason for why this is the case will lead to what I think is necessary, and sufficient, for an object to be abstract. Persons have causal powers. Abstract powers are causally effete. They have no causal powers. I'm persuaded by metaphysicians who don't think that spacelessness and timelessness are either necessary or sufficient for an object to abstract. It's not necessary because there are some abstract objects that are in space and time (the center of mass of the solar system, the equator, etc); it isn't sufficient because of the metaphysical possibility of timeless, spaceless persons.
I won't address Loke's point that Hilbert's Hotel is absurd because 'spatially located guests moving about' (since I addressed this in previous blogs). And Loke and Moreland take a tact I myself do not, and so I won't have much to say on it. Loke's Principle is introduced by Alex: Actually infinite collections of abstract objects are passive. This will imply that the yet-to-be praises are actually infinite, even if such praises don't yet exist as concrete entities. Right away we can see why Craig's understanding of yet-to-be praises is perhaps the way it is. Craig is an anti-realist and so he doesn't believe that abstract objects exist. That's why he says that the yet-to-be praises are zero in number (there are no abstract objects); and what Craig denominates as the praises that 'will be' seem to be what Loke is explaining in terms of yet-to-be abstract 'becoming' concrete. The latter would be potentially infinite. Alex considers Loke's idea as 'ambiguous', but I'm not sure I have an issue with it. Loke does hint at a distinction that Alex has broached: that between the number of praises that will never be said and the fact that each of the praises (in the infinite collection) will 'eventually be said'. Loke keeps the problem in the abstract and if it's in the abstract the infinity becomes passive, and so isn't a problem. Alex finds this puzzling. I don't' find it puzzling in the sense of being inexplicable; I find it puzzling as a plausible solution to Morriston's anxieties about symmetry. Assuming it is a plausible solution, are the future praises abstract? I don't think so because I don't think abstract objects exist (neither does Craig). As I said above, Moreland's analysis of what it is for an object to be abstract is (for me as well as Craig) inadequate - it's neither necessary nor sufficient. Alex wonders if there's another category, other than concrete and abstract. I'm not aware of one.
Assuming that Moreland is correct, would the future praises be abstract? Alex's response to Loke is puzzling to me. Alex argues future praises aren't abstract because future praises are future events, and future events are in time. And once the future prayer is said, its 'being said' takes time, and so has duration. This response seems unsatisfactory to me. Recall Loke's distinction between praises that have been said (praises that have become concrete) and yet-to-be praises (praises that will become concrete). Alex's response assumes that Loke is an eternalist about time. I'm not sure that he is. Suppose that he isn't. If he isn't, then such future events don't exist. For example, if there will be a yet-to-be-said praise in the year 4205 A.D., and 4205 A.D. does not exist, in what sense can Loke argue that such a praise exists? It will have to be an abstract existence! And since it's abstract existence is contingent (since it will become concrete, according to Loke), the events temporal existence is also contingent on the praise's indexical instantiating its temporal existence in accordance with time 'becoming'. Once the event is in time, its assumption of temporal existence is simultaneous with its loss of abstract existence. But perhaps I'm not following the full import of Alex's objection to Loke's appropriation of Moreland's criteria as it pertains to future praises. Future praises (per my understanding of Loke) are not concrete; they are abstract (and they will be concrete). Alex wants Loke's distinction to apply to the distinction between 'being currently concrete' and 'not currently existing'. But this also seems unnecessary. Loke will think the future event exists; it exists abstractly. In fact, it is (if future) currently abstract, and it currently exists. It's just not currently concrete. Hence, I'm not inclined to follow Alex in drawing out the implications of this construal of Loke's distinction. In terms of a symmetry breaker, my guess is that Loke will argue that the past is concrete (perhaps he is a growing-block theorist) and the future is wholly abstract (and a potentially infinite quantity of such an abstract future will be concrete). This seems asymmetrical to me.
3. The meaning of 'abstract' and 'concrete' - As I already said above, I reject Moreland's analysis and opt for one that distinguishes between the abstract and the concrete in terms of having causal powers. For me, that is the best analysis. But let me go through the four ways that David Lewis uses to motivate the distinction (as pointed out by Alex).
a. The Way of Example
b. The Way of Conflation
c. The Negative Way
d. The Way of Abstraction
'a' and 'b' seem like an epistemic way. It could work. It's just fallible. For example, this 'way' clashes with Moreland's criterion since many metaphysicians believe that at least some universals are 'in time' even if they're spatially bilocated. 'c' includes 'my' criteria, along with Moreland's: causal interaction and timelessness/spacelessness. 'd' fits the descriptions for some types of abstract objects, but not others (Plato wouldn't think the Forms are merely abstractions from concrete entities). I'm not sure that when Loke thinks that future, abstract events become concrete, Loke would say that that the abstract object 'changed'. It's not that the abstract object ceased to exist once the future, abstract event became concrete. Suppose you're a Platonist and there was a time when there was nothing purple. Once a purple object came into existence, the Form of Being Purple didn't cease to exist and 'become' the purple object; what happened is that a contingent, temporal object contingently came to stand in the exemplification-relation to the Form - the Form can remain immutable, even if its exemplification in a concrete particular was contingently temporal. Hence, I agree with Alex's treatment of 'd': that it's unhelpful here.
I didn't follow why Alex thinks a belief in the potentiality of the future implies open theism (no truths about the future). And actually saying praises forever seems to me to be completely compatible with the series of future praises extending indefinitely as a potential infinite only. Alex's sense in which the future is determinate is quite benign to me. Its determinacy is a soft fact about the future.
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