To read Malpass' blog entries in their entirety, I encourage you to visit the link. I'll be touching on the entries topically and voicing inchoate criticisms as they come. I'll also organize the topics numerically for clarity.
1. Hilbert's Hotel & Pinning down the absurdity - First, a quick comment on Alex's characterization of the hotel. Alex had noted that characterization which involves the accumulation of an actually infinite number of new guests by moving guests around. While this strikes me as absurd, what really brings out the absurdity for me is when you can characterize it in terms of division or subtraction, operations that are prohibited (or meaningless) in transfinite arithmetic. That seems to pump the intuition that worlds in which the guests behave this way are both broadly and mathematically impossible. But I'll leave this point hanging for now. (Much more could be said, however. I just don't want to make these entries too long.)
Alex reads Craig as locating the absurdity of the hotel in terms of the hotel's behavior (this will mean that the hotel - not necessarily an actual infinite - is absurd). Get rid of the behavior, and Craig would have nothing to scratch his head about (albeit, Alex confines this behavioral issue to 'addition', where I think the real rub is regarding the prohibited operations of subtraction). I disagree here, so I don't think it's necessary to consider Alex's distinction between active/passive infinities. I will still consider that distinction, but let me first demonstrate why it's not necessary to depend on the hotel's behavior to flesh out the absurdities. Craig's thoughts here (Excursus on Natural Theology (Part 9), October 14, 2015) are persuasive to me.
I’ve never understood why someone thinks that that is a good objection. We are obviously not talking with regard to Hilbert’s Hotel about a real hotel that is built out of bricks and wood and has people trying to walk down infinite hallways to get out the door. It is a conceptual thought experiment. You imagine the hotel with all the people in the rooms and then, as it were, in thought just eliminate all the people in the odd-numbered rooms. Just vaporize them or something. Then you’ve got all the people left in the even-numbered rooms. You don’t want to get into difficulties about physically moving them about and so forth. Similarly, with respect to the number of past events. If you imagine the number of past days in the history of the universe, it is easy to just mentally annihilate every other day, or all the odd-numbered days, and ask how many are left over. The answer is obvious. There would still be all the even-numbered days, which is the same number. It seems to me that that kind of objection just fails to reckon with the nature of a thought experiment which isn’t based upon real, physical movements and operations.
I think these thoughts indirectly address Alex's concern. Alex wants to make the absurdity of the hotel a function of its behavior; if you eliminate the behavior, you eliminate the absurdity. Alex wants to know what happens if we just don't 'interact' with the hotel. But it seems to me that what elicits the absurdity is not the contingency of not conceptually interacting with the hotel, but the contingency that you can, even if you don't. In other words, the nature of this thought experiment is such that there is such a contingency. Nothing stops the possible 'mental annihilator' from the contingency of engaging in mental annihilation in the context of this thought experiment. This seems to imply that 'even if' one doesn't 'in fact' interact with the hotel (in terms of mental annihilation), the very idea that 'you could' implies that the hotel is absurd 'even if' you don't 'in fact' interact with it. As Craig says, the nature of the experiment doesn't depend on 'real, physical movements and operations.' This implies that the experiment doesn't depend on Alex's notion of 'interaction'. It depends on the contingency of being susceptible to interaction. This distinction belies the relevancy of active/passive infinities (since the distinction is introduced to resolve difficulties with 'actual behavior').
2. The Infinite Universe is Passive - Much of what is said here is resolved by what Craig intimated above. But it also seems to me that Alex's mapping of all the integers onto an eternally existing universe begs the question against the A-theorist in general and the Presentist in particular. If '0' represents The Present, then all the numbers greater than '0' not only don't exist (as I'm sure Alex is aware), but that the indeterminate number of integers that 'will be' is potentially infinite, which isn't a 'number', but a limit concept. Now, this is only the case if (in the context of the analogical mapping) the positive integers represent 'future events that will be'. If I conflate the analogical mapping with the integers themselves, this will give the impression that there already 'is' an actually infinite number of future events that are 'yet to be' (because of the mathematical legitimacy of the actual infinite). This is the motivation for Craig's distinction between 'what will be' and 'what is yet to be', a semantic distinction with a difference, I think [but let's leave this hanging for now - as Alex directly addresses this in our conversation]. Hence, when Alex argues that Craig would characterize 'eternally existing universe' as (partly) having 'infinitely many later moments', this is entirely mistaken and begs the question against tense-theorists that would render the future potentially infinite only [I'll address Alex's arguments regarding particular cases of potential infinites implying actual infinites in later blog entries in the series.]
Regarding the past, however, since Craig thinks the past is actual in a way that the future is not (even though Craig is a presentist who thinks the future neither exists nor subsists), Alex's notion of passive infinity still doesn't apply (due to what was said above). Passive infinites convert to active infinites by virtue of being susceptible to mental annihilation. Still residing in the realm of addition, Alex believes that the 'Hotel of the Past' (so to speak), having as their billboard 'No Vacancy, Guests Welcome', is a 'weak candidate for absurdity. No reason is presented for why it's a weak candidate, but Alex does mention that such a retort is defanged when applied to Alex's analogical mapping of the integers onto the infinite past/future. But such an analogical mapping just seems to me to beg the question at issue. It amounts to saying an actual infinite is metaphysically possible because such an analogical mapping (an actual infinite) is metaphysically possible. But that's the question! Therefore, Alex's dilemma [i.e. 'either the universe is infinite in temporal extension or God doesn't exist'] is a false dilemma. The left disjunct is false and the right disjunct is false. The universe is finite in temporal extension and God exists; so, since both disjuncts are false, the disjunction is false.
3. The Infinite God Objection - Alex links to a video where Craig says that God knows propositional truth. In particular, God knows mathematical truth (6:20). At 1:45, Craig also mentions non-propositional knowledge (including know-how and knowledge-by-acquaintance). Continuing through to 3:00, Craig rightly points out that having that kind of knowledge (in its totality) would be a deficiency (since the indexicality of some of such knowledge would be inappropriate or inapplicable to God qua God): needed is all propositional knowledge and 'appropriate' non-propositional knowledge. Note above that Alex's time-stamp for mathematical truth is 6:20, where Craig mentions God's knowledge of necessary truth. Assuming that such knowledge is necessary (Kripke thought that it was metaphysically possible for such truth to be false in terms of their not being analytically false - but that's a discussion for another time), Alex argues that God would have to know an actually infinite number of mathematical truth: one mathematical truth for every number in the series of natural numbers, say.
But this doesn't necessarily follow at all. Consider Craig's citation of Jody Azzouni (Footnote 33: Jody Azzouni, Deflating Existential Consequence: A Case for Nominalism (Oxford: Oxford University Press, 2004), chaps. 1–2; cf. idem, “Evading Truth Commitments: The Problem Reanalyzed,” Logique & Analyse 206 (2009): 139–176.) in his book God and Abstract Objects (Hardcover: 540 pages, Publisher: Springer; 1st ed. 2017 edition, September 6, 2017):
Consider, for example, neutralist Jody Azzouni’s defense of the claim that empirically indispensable mathematical statements must be taken to be true.33 A deflationist, Azzouni maintains that talk of truth is indispensable because of the need for blind truth ascriptions. Explicit ascriptions of truth to statements are eliminable because the Tarski biconditionals guarantee that we can always replace explicit truth ascriptions with the statements themselves. But in a blind truth ascription the predicate “is true” is preceded by a name or description, as in “The Special Theory of Relativity is true” or “Everything Penrose said is true.” Blind truth ascriptions are required either when one does not know or understand what is asserted to be true or when infinitely many statements are asserted to be true. In either case one cannot substitute explicit truth ascriptions for the blind ascription. (pg. 249)
Further details would lead us into excessive detail. Suffice it to say, Alex's discussion doesn't do justice to the available philosophical options and the entirety of Craig's literary output. Azzouni's neutralism allows us to utilize blind truth ascriptions when preceding names/descriptions. In this case, it'll precede the description of all mathematical truth. And this is permitted because 'infinitely many statements are asserted to be true'. And since 'one cannot substitute explicit truth ascriptions for the blind ascription', it follows that it's no threat to God's omniscience to have, as one of the propositional truths God knows, the 'blind truth ascription' God could 'ascribe' to all the mathematical truths; there wouldn't be a problem because 'infinitely many' mathematical truths are 'asserted to be true', and therefore such ascriptions are 'required'. Alex's insistence that the cardinality of the natural numbers necessitates an infinite cardinality to God's knowledge is undermined (of course, the details of Azzouni's idea are debatable - as is nearly anything in philosophy - but I'm, at least, persuaded). Hence, there can be a 'Craig's List'; the list itself would be a description about the truth of the list as a whole, without the need of discrete quanta of individual propositional truth. But if this is the case, then Alex's 'Infinite God Objection' loses all of its dialectical power. Therefore, I see no good reason to accept its conclusion.
4. God's knowledge is of induction schemas - This is Alex being charitable by offering a possible objection to what he's argued so far. But the reader will discern that blind truth ascriptions are distinct from such induction schemas. I will therefore bypass much of what Alex discusses here, as it's irrelevant to the direction I think the discussion needs to go.
5. God's knowledge is non-propositional - The section is indispensable and, I think, the biggest obstacle to my thesis. For Craig does (at the end of the day) believe God's knowledge is non-propositional. Such a belief seems to stand in marked contrast to what Craig explicitly states in the Youtube video and many instances in Craig's published work (not to mention his website): that God's omniscience is the idea that God knows all true propositions. How is this compatible with affirming that God's knowledge is non-propositional. The answer takes a couple steps.
Consider first the following quotation from Craig (Taking Tense Seriously in Differentiating Past and Future: A Response to Wes Morriston):
The finitist will therefore either deny Platonism with respect to propositions, taking them to be useful fictions perhaps, or deny that there are an infinite number of propositions, since, God’s knowledge being non-propositional, propositions are the byproduct of human intellection and so merely potentially infinite in number, as we come to express propositionally what God knows in a non-propositional way.Four things are being said here.
1. God's knowledge is non-propositional.
2. Propositions are the byproduct of human intellection.
3. If propositions are the byproduct of human intellection, then they are potentially infinite in number.
4. We express propositionally what God knows non-propositionally.
These are four very interesting theses (keep in mind that non-propositional knowledge isn't true or false: something is known, but it's not true or false).
The four theses are reiterated in this from Craig (#197 Does God Know an Actually Infinite Number of Things?):
Alston maintains that God's knowledge is strictly non-propositional, though we represent it to ourselves as knowledge of distinct propositions. Thus, we say, for example, that God knows that Mars has two moons, and He does indeed, know that, but the representation of His knowing this proposition is a merely human way of stating what God knows in a non-propositional manner. Such a conception of divine knowledge has the advantage that it enables us to embrace conceptualism without committing us to an actual infinite of divine cognitions or Divine Ideas.
A nice analogy of God’s cognition on the above view would be your visual field, which you see as an undifferentiated whole, but which could be analyzed as composed of pixels.
So, Gordon, when we say that God knows an infinite number of propositions, we are speaking of the extent of His knowledge, not the mode of His knowledge.
Let's add a fifth thesis:
5. There's a distinction between the extent and the mode of God's omniscience.
This distinction will be clearer when understood in light of the sixth thesis below.
Consider next what Craig says here (#561 Does God Know How a Pineapple Tastes? - January 15, 2018):
God’s non-propositional knowledge is not a function of His omniscience. His omniscience gives Him all propositional knowledge. If He has as well non-propositional knowledge such as you describe, it will be a function of His ability to assume the same mental state as someone having such an experience. Does God have “this knowledge without experience”? Yes and no; He can have the experience of tasting a pineapple but without actually eating a pineapple or having taste buds. Is this because of “His infinite cognitive abilities as compared to our finite abilities?” No, we can imagine a neuroscientist’s stimulating a person’s brain such that the person is put into a mental state of tasting a pineapple. God could do this Himself at will. Of course, to have the unlimited range of non-propositional knowledge you’re thinking of, God’s cognitive abilities must be infinite.This leads to a key sixth thesis:
6. Non-propositional knowledge isn't part of an analysis of God's being omniscient.
This may take many off guard. But it's plausibility gets clearer after noting some distinctions. Non-propositional knowledge (being neither true nor false) involves God's 'ability' to assume mental states involving experiences. Hence, non-propositional knowledge is a function of his omnipotence (since it involves abilities). In light of 5 (above), we can correlate the extent of God's knowledge in terms of an analysis of God's knowledge and understand the mode of God's knowledge in terms of God's non-propositional knowledge, which has to do with omnipotence (or abilities), not omniscience.
Continuing (#197):
On my view there is not a potentially infinite number of numbers. Rather there are no numbers at all! Numbers, if they exist, are abstract objects, and I’m strongly inclined to say that only concrete objects exist. What is true to say and what God knows is that according to standard number theory, there is an actually infinite number of numbers. Moreover, God knows that an actually infinite number of arithmetic truths follow from the axioms of standard arithmetic, like 1+1=2, 2+1=3, 3+1=4, . . . . But, as explained above, He does not know these truths propositionally, as I have just expressed them, but non-propositionally. Therefore, there is literally neither an infinite number of numbers nor an infinite number of propositions.This is in line with what was said above regarding blind truth ascriptions. God doesn't know the contents of Craig's List propositionally; God knows propositionally the blind truth ascriptions regarding the description 'Craig's List'; God knows the contents of the description as an undifferentiated whole, non-propositionally.
With these six theses in mind, let's consider Alex's concerns. First, Alex accuses Craig of contradiction. At first glance, Alex's accusation seems vindicated. But upon further investigation, there seems to be a plausible distinction between God's knowledge being propositional in one sense (in terms of extent and analysis) and non-propositional in another sense (in terms of mode and the content of descriptions in, for example, blind truth ascriptions). Second, Alex objects to Craig's appropriation of Alston (above) on the grounds that Aquinas believed that God knows 'infinite things'. But we saw that there are different ways to cash out that locution. Third, Alex seems to hint at the idea of blind truth ascriptions with God's knowledge of all mathematical truth without believing an 'infinite list', something I think is in the neighborhood. Alex cites Alston's citation of Bradley who construes types of cognition in terms of 'pure immediacy', which seems sufficiently analogous to what Craig says above regarding undifferentiated wholes. I think that's a possible model, but it needn't be required in all its idealistic trappings. However, Alex cites Morriston's objection: the 'richness and articulation of discursive thought' 'must surely involve some sort of distinction and variation and multiplicity in God's mind.' - and so the 'unity' must be 'within a multiplicity', seemingly giving explanatory (or ontological) priority to propositional modes over non-propositional ones. But Alex doesn't emphasize that worry; he emphasizes the allegation that multiplicity utterly disappears. Yet we saw above that it doesn't utterly disappear: the extent of God's knowledge continues to be a multiplicity when given an analysis, where that analysis is the product of human intellection. The domain of extent leaves completely untouched Craig's (and Alston's) notion of the mode of God's knowledge as a function of abilities, rather than omniscience.
Therefore, Alex's 3 reasons are unpersuasive to me, especially when we're sensitive to the 6 theses extracted above.
6. Craig's God is a passive infinity - This section seems to be an exploration of a part of the conclusion I see as a non sequitur. There is the relevant sense in which God's knowledge is a 'closed totality' that involves it being neither a passive nor an active infinity (in terms of either mode or extent, as explained above).
7. Craig's God and Time - Alex points out that Craig believes that God knows tensed facts. That is (if we can borrow from what we've learned above), an aspect of an analysis of God's omniscience will involve God's knowledge of tensed propositional truths that are included in the extent of God's knowledge, an analysis that involves propositions that are the product of human intellection. So far, so consistent.
8. Craig's God is an active actually existing infinity - Alex mentions that God comes to know new things as the tense of future-tense propositions changes to their present-tense counterparts in agreement with the ontological reality of real, temporal becoming. But Alex reverts back to the same notion of God's knowing an infinite number of truths to motivate the apparent absurdity that new truths are being 'added' to an infinity, reminiscent of adding guests to Hilbert's Hotel. This reversion betrays the same lack of analytical nuance noted above: in neither extent nor mode, God's knowledge doesn't involve an infinity of truths. Therefore, Alex's 'growing block problem' doesn't seem to be a problem.
-------------
And those are my thoughts on this blog entry for now. I'm sure Alex will have many helpful comments to make.
No comments:
Post a Comment