1. Craig has Morriston being concerned with 'two claims':
a. That "an endless series of events is a merely potential infinite."
b. That "that this establishes a relevant distinction between the beginningless past (which is supposedly impossible) and an endless future (which is clearly possible)."
Craig argues that Morriston needs to demonstrate that even if 'a' is granted, then 'b' hasn't been motivated. Craig believes that Morriston hasn't successfully defended that conditional. Rather than motivate the conditional, Craig claims that Morriston just argues against 'a' (and conditionals can still be true with a false antecedent). I suspect that Alex will help motivate how Morriston argues against 'a': one of Alex's strategy is to lay the burden of proof on Craig to demonstrate why a potential infinite does 'not' imply an actual infinite when it comes to 'time' (but I have addressed this sufficiently for now in a previous blog).
Craig offers an A-theoretic notion of a potential infinite (call it, ANPI):
c. A 'successively ordered' series, that is
d. 'isochronous', and
e. 'later than some denominated event'.
Successive means "following one another or following others." For example, I sat down, then I turned on my computer, then I pulled up my research, then I typed my response, then . . . These are successively ordered series of events. Alex's example of 'counting' the numbers would also qualify. For a series to be isochronous, in this context, it means 'occupying equal time': so, a series of seconds, minutes, hours, and so on. Each second takes a second; each hour takes an hour. 'e' allows you to just pick any even you want to begin your temporal measurement. Pick today. Pick an instant 354,286,348,382 months into the past. Then, progress from that instant, using 'months', forever into the potential, non-actual, non-existent future.
Onto the 2nd section of Craig's essay.
2. I'll skip the way Craig cashes out metaphysical possibility in his second footnote. He does use 'non-trivially true counterfactuals with impossible antecedents', which I like (and which I called counterpossibles in a previous blog). Craig's contention is that Hilbert-type illustrations aren't meant to motivate the mere categorical claim that an actual infinite is metaphysically impossible, but to motivate the truth of a subjunctive, counterfactual conditional, which 'does not depend on the truth of the antecedent' or motivating such a truth. This is a helpful distinction. The logical coherency of people 'checking out of the hotel' wouldn't do anything to take away from the plausibility attaching to the conditional because the mere logical coherency of such people doing such has nothing to do with the compossibility of the antecedent's (in the conditional) metaphysical possibility and the consequent's metaphysical possibility; the antecedent would still be necessarily false in the broad sense.
Craig gets to two ways a series is endless:
f. The series is actually infinite.
g. The series is potentially infinite.
'g' implies an A-theory of time; 'f' implies a B-theory of time.
h. 'will be' is associated with a potential infinite.
Craig alleges that Morriston's examples of 'adding' infinities of praises to infinities of praises involve potential infinities only. I'm inclined to agree. There aren't issues because the number of praises will 'always' be finite anyway, even if God determines that the praises cease at whatever finite number of praises God determines the series to cease (if four, the series stops at four, etc.).
Craig argues that the same doesn't hold for a beginningless series. In a beginningless series, if an A-theory of time is correct, tense is real. If tense is real, tense itself is asymmetric. If tense is asymmetric, then you can't say that the past is potentially infinite in a way that the future would be (that's why it's inaccurate to say that the past is growing in the earlier-than direction). As I suspected, Craig's other arguments against infinity (the impossibility of forming infinite collections via successive addition: I address Alex's concerns in another blog) become relevant. In footnote 3, Craig brings up the old illustration from al-Ghazali involving the orbits of Jupiter and Saturn (Jupiter completes two orbits for every one of Saturn's orbits). It would seem that Saturn would fall more and more behind Jupiter (in terms of the cardinality of orbits). The ideal limit (involving the idea of a potential infinite) would be the potential infinite threshold Saturn would reach in terms of how far behind it would be compared with the orbits of Jupiter: 'they will never arrive at this limit'. But if Saturn/Jupiter have been orbiting from 'eternity past', then the cardinality of their orbits is identical - the idea (it seems to me) is that the intuition attaching to the cardinality would be clashing with the intuition that, if one orbit (of a planet x) happens for every two orbits (of another planet y), then the cardinality of x's orbits will be 1/2 that of the cardinality of y's orbits. Extend this intuition out in terms of Alex's mathematical function, and iron out the logical relations between the orbital transitions, and it seems like arriving at an identical cardinality for the orbits is both absurd and meaningless (and so metaphysically impossible).
Hence, since time is asymmetric, the future and the past would be as well, metaphysically construed. [Again, Alex's mathematical functions seem to be irrelevant because they depend on the begged question of analogically mapping the series of numbers that are a product of the function (a product of narrow logical possibility) onto a metaphysical world involve the ineradicable asymmetry attaching to tense, which, on an A-theory of time, would necessarily attach to a possible world involving tense. Indeed, tense does seem to be of crucial importance, and mathematical functions don't seem to provide the metaphysical bridging principles, according to which the mathematical world can be successfully mapped onto a metaphysical state of affairs involving tense, let alone presentism.]
3. Third Section - Here, Craig alleges that Morriston has switched from denying 'b' (assuming that 'a' is the case, and 'b' follows from 'a') to denying 'a': Morriston will content that an endless series isn't a potential, but an actual, infinite. Craig argues that Morriston can motivate his denial of 'a' at the cost of 'misconstruing' the A-theory of time. This is where we get to the crucial idea of the semantics attaching to the borderline neologisms we're appropriating for the sake of a useful nomenclature. The following is more terminology:
i. 'endless series of events' = 'the actual series of events that have occurred.
j. 'series of events that have not yet happened' = a non-existent, presently unactual series of mere potentialities.
'i' includes the actual world. 'j' is a tenseless determination that isn't part of an actual world exemplifying tense. This tenseless determination involves a collection of 'future praises' that isn't growing. Ontologically speaking, the A-theorist (let alone the presentist) can't affirm 'j'. They can't affirm the semantically/ontological irreducibility of tenseless determinations and remain an A-theorist/presentist. Morriston misconstrues the A-theory (ontologically) because:
k. 'j' constitutes a collection that (1) is not growing, and (2) is not losing members.
The problem is that the ontology of the presentist won't include 'j' as a part of the actual world; 'j' is not just non-existent - it is non-actual, sheer potentiality. It is therefore not on an ontological par with a beginningless past which is 'presently' non-existent and actual since the past-potentialities 'have been' actualized. A presentist ontology won't permit a symmetrical move in terms of presently non-existent future-potentialities because the presently non-existent future-potentialities are not actual.
l. The future is not actual.
m. The past is actual.
From 'l' and 'm' is follows, if there is tense, and tense is asymmetrical, that all of the future 'will never be', whereas all of the past (if beginningless) would 'have been'. There would be no such series as a completed, 'not-growing' collection of presently non-existent future-potentialities. And such a collection isn't denominated in terms of what 'will be' (which is semantically distinct from those tenselessly determined events that are yet-to-be). If we attempt to denominate the number of future events that 'will be', I think Craig is correct that the presentist ontology would only permit us to have a potentially infinite sort of denominations that will 'always' be finite in extent. This confirms what I said in previous blogs about the importance of "the phrases 'an endless series of events' and 'an endless future'" in 'a' and 'a' (above) are a "different series than the series Morriston is envisaging." This is correct, I think.
Morriston's denial that he is talking ontology wasn't persuasive to me. The semantics of tense are attached to a certain ontology. Morriston's move is to switch from an ontological collection of events to a semantic collection of tensed propositions (a collection of 'truths' or 'tensed facts'). Craig is correct that Morriston shouldn't construe such 'truths' ontologically (Platonism), or he has reverted to ontology, something he doesn't think he is doing. Craig denies Platonism and the actual infinity of propositions. Morriston's semantic switch is taken care of by the latter; the ontological position is taken care of by the former denial. [I flesh out God's non-propositional knowledge and God's propositional omniscience in an earlier blog.]
I agree with Craig's conditional as well: if the number of praises will always be finite, an actually infinite number of praises will not be said. Craig uses an analogy that helps: a line (L1) composed of points vs. a line (L2) that is not. If we have L1, we could have an actually infinite number of divisions. And if we were to begin counting all the divisions, we'd never reach a transfinite number of divisions (even though there'd be the tenseless determination of yet-to-be-counted divisions). The presentist ontology would say that the endless future isn't like L2; it's like L1. To conflate the divisions that 'will be' denominated in L1 with the yet-to-be-counted divisions in L2 is just that: a conflation. It's the same with Craig's example with the expanding universe. Craig talks in terms of the universe's volume or space: infinite vs. ever-expanding volume/space.
n. [today, day1, day2, . . . ]
o. [. . . , day~2, day~1, today]
p. [day~n, . . . day~2, day~1, today]
q. [today, day1, day2, . . . dayn]
Craig affirms 'n' without a 'yet-to-be' dayn that ever 'will be'. Hence, Craig denies (but it seems Morriston affirms) 'q'. Craig would deny the metaphysical possibility of 'o' (due to the above reasons) and 'p' (Oppy - for other reasons).
See the blog before this one for Craig's crucial distinction between actuality and existence. Suffice it to say, Craig importantly says: "My claim is that the tenseless existence of the past block of events is not a necessary condition of the past’s actuality."
Footnote iv is Craig's very helpful elucidation of 'limits' when potential infinities involving an approach to infinity as a 'limit concept'. I want to do a separate blog with how I think Craig's elucidation of mathematical functions and the potential infinite could play a role in Alex's decision to utilize his own mathematical functions to elicit actual infinities (in terms of increasing divergence vs. increasing convergence).
I'm inclined to agree with Craig's response to Morriston here. In the next blog, I'll be critiquing Morriston's response to Craig's essay and determining whether the response is persuasive.
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