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I don't have an explanation as to how noncontingent propositions could enjoy evidential support, but I don't share Peter and Bill's sense that "evidential considerations are simply irrelevant to the probability of noncontingent propositions." Consider Goldbach's conjecture. If true, it is necessarily true. It remains unproven, yet it seems to me that its verification (to date) for integers up to 1.6 x 10^18 is good evidence that it is indeed true (perhaps conjoined with certain basic intuitions about mathematical order and simplicity). In other words, if I were a betting man, I'd bet on its being true. Wouldn't you?
Peter, Thanks for the follow-up comments. I must move on to other things, so I leave you with the last word (for now). As for the book's cover, I believe it depicts a golden egg nestled among ordinary eggs; I guess the black-and-white photo doesn't do it justice. As for what it means, I haven't the foggiest idea. I just signed off on the cover in the absence of anything more fitting. Perhaps the cover designer was offering a sly critique of the book's thesis, by seeing whether I'd be willing to affirm something without having the first notion its meaning. Needless to say, such a critique would be based on an unfortunate misunderstanding of my position. ;)
Thanks again to Peter for these further thoughts. The sort of concerns he raises I address in chapter 7 of the book, although (as I noted even there) more needs to be said. But what I say there goes some of the way, I think, toward alleviating the worry that MACRUEs leave us without the first idea what to believe. Readers can judge for themselves. In the meantime, here are a few brief comments in response to Peter's latest salvo: 1. I agree with Peter that semantic defeat is more serious than epistemic defeat, and that semantic defeaters have "logical priority" over epistemic defeaters. This much is clear. The question is whether the doctrine of the Trinity (if a MACRUE) suffers from semantic defeat. 2. I tentatively grant Peter's notion of a "propositional threshold" for the "evident meaning" of a sentence, although I need to think about this some more. 3. In 3.4) Peter claims that if a sentence S satisfies conditions similar to (ii) and (iii) then the "evident meaning of S is below the propositional threshold". What I don't see, however, is an argument for that claim. Why exactly should I agree with Peter on this point? What am I missing? 4. Furthermore, it's not clear from 3.4) whether it is the truth of (iii) or a person's belief in (iii) that leads to semantic defeat. This is important, because how we understand the problem depends on whether semantic defeat (like epistemic defeat) is person-relative. 5. Consider the Flatlander analogy once again. Suppose the Flatlander accepts the revealed claims "The Cone is circular" and "The Cone is triangular" but soon realizes that they appear (to him and his compatriots) to form an implicit contradiction. Does it immediately become the case that he hasn't the first idea what to believe about the Cone? Does the doctrine of the Cone suddenly suffer semantic defeat? I don't see why that would be. Rather, the Flatlander continues to understand those claims in much the same way as before, but with the further recognition that they constitute a MACRUE and thus his understanding is limited and imprecise in certain respects. We might say that the propositions he actually entertains are approximations to those propositions that represent an 'ideal' (i.e., non-paradoxical) doctrine of the Cone. But his beliefs needn't be thought false on that account. (A theory of vague propositions may prove helpful here.) So the Flatlander continues to think of the Cone as both circular and triangular. I make some suggestions in the book as to how that works out psychologically and inferentially in the case of the doctrine of the Trinity. My only point here is that semantic defeat doesn't seem to be a threat. 6. I reject the comparison with the Sokal affair. In Sokal's paper, the individual sentences didn't express propositions. Such is not the case with the Bible or the Trinitarian creeds. The difficult in the latter case is that the individually meaningful statements form an apparent implicit contradiction. But that's quite a different difficulty than the one faced by the editors of Social Text (whom I'm happy to concede faced semantic defeat!).
Bill, Thanks for the further clarification. Sorry for the delay in replying. My main objection to condition (i) of your rational acceptability is that we can find very plausible cases where a person believes two or more claims that appear to be inconsistent, yet doesn't appear to be irrational in so doing. I give some examples in my article and my book. We've discussed some of these in our exchanges here. I'm not at all opposed to talk of epistemic permissibility and impermissibility. I agree that there are deontological constraints on our believings, acceptings, etc. But like Plantinga, I don't think epistemic justification (construed along deontological lines) is either necessary or sufficient for epistemic warrant (defined as what distinguishes knowledge from mere true belief) or for the kind of rationality that is necessary for knowledge. Certainly a familiarity with Plantinga's theory of warrant will be helpful for understanding how I defend the thesis that it can be rational to accept a paradoxical doctrine (i.e., one that gives the appearance of contradiction). One final comment. The examples I give of the rational acceptance of apparent contradictions don't involve explicit contradictions, i.e., accepting both p and ~p. Rather, they involve accepting a set of claims -- say, p, q, and r -- where those claims seem to involve an implicit contradiction. I think this is a significant difference, both psychologically and epistemically.
Another recent (and relatively brief) defense of the doctrine: Brian Davies, "Simplicity," in C. Taliaferro and C. Meister, eds, The Cambridge Companion to Christian Philosophical Theology (CUP, 2010), 31-45.
Toggle Commented Mar 2, 2010 on Bleg: Divine Simplicity at Maverick Philosopher
Bill, Yes, I was assuming a different understanding of 'rational acceptability', but your clarification is helpful. I was understanding 'rational acceptability' as roughly synonymous with 'rational justification'. If I read you rightly, you take some claim (or set of claims) C to be rationally acceptable just in case you can see that C involves no contradiction. ("If you could show me that there is no contradiction...") Is that correct? Well, if this is a substantive claim about our epistemic duties (and not just a matter of definition) then I disagree, and one of the burdens of my book is to show that there is no good reason to accept it and some good reason to reject it (and not just in theological cases). In chapter 7, I address the objection that it is simply a basic requirement of rationality that we reject all apparent contradictions (even if we grant that some could turn out to be merely apparent, even if we have good grounds for thinking that some are merely apparent). (As an aside, I don't this particular issue selects between internalist and externalist theories of epistemic warrant, so set aside my remarks on that point.) What confuses me, then, is that some of your remarks in our earlier exchanges, and even your subsequent remarks above, indicate that you don't take 'rational acceptability' (as defined above) to be a genuine constraint on our beliefs. For you say, "I grant you that if I have good grounds for believing both limbs of an apparent contradiction, then I have good grounds for thinking that the apparent contradiction is merely apparent." But in this scenario, I cannot see that there is no contradiction -- at least, not by direct reflection on the claims in question -- even if I can know (or at least justifiably believe) on other grounds that there is no genuine contradiction. Your sympathy toward the Flatlander analogy suggests the same. The Flatlander cannot see (prior to 3D heaven) that the conic revelation involves no contradiction, but he can still justifiably believe that the contradiction is merely apparent. The revealed doctrine of the Cone is, in fact, rationally acceptable, in the sense that the Flatlander is not violating any ultima facie epistemic duties (even if, perhaps, he violates one prima facie epistemic duty). You also write, "But the problem for me and Peter is the identity of the Trinitarian proposition that will resolve the apparent contradictoriness of the Trinitarian propositions that we have before our minds here below." Here you apparently distinguish between "the Trinitarian proposition" (singular; label this TPS) and "the Trinitarian propositions" (plural; label these TPP). If I understand your terminology here, the TPS is that proposition which, if grasped, would enable us to see how it is that the apparently contradictory TPP are not really contradictory (presumably by apprising us of some significant metaphysical distinction or refinement). In the case of the Flatlander, the TPS would be equivalent to the proposition that the Cone exists in three spatial dimensions rather than two. But the TPS (or rather its equivalent) cannot be grasped by the Flatlander because of his present conceptual limitations. You then suggest it's a problem that we cannot specify or grasp the TPS. But why think that's a problem for us, if it's not a problem for the Flatlander? Why think that's a problem if (as you've granted) one can have good grounds for believing that an apparent contradiction is merely apparent, even without knowing how the appearance of contradiction can be removed? Why think that's a problem if one has good grounds for think that there is a true TPS even if one can't say what that TPS is?
Sorry about the typos: "rationally acceptability" (twice) should be "rational acceptability", and "psychological impossible" should be "psychologically impossible".
Bill, Please call me James. In this forum, you're the Professor! I'm not saying that the rationally acceptability of the doctrines can be known only by revelation. Consider these two beliefs: B1: The doctrine of the Trinity is paradoxical yet true. B2: I am rational in believing that the doctrine of the Trinity is paradoxical yet true. B1 is a first-level belief, B2 a second-level belief. 'Ordinary' Christian believers rarely form second-level beliefs about their first-level beliefs. My main claim is not that revelation is necessary in order for beliefs like B2 to be rationally justified (although that's probably true) but that it is necessary in order for beliefs like B1 to be rationally justified. In other words, the rational acceptability of the doctrines depends on their actually being epistemically grounded in divine revelation, regardless of whether believers form any second-level beliefs about the rationally acceptability of those doctrines (or their epistemic grounds). It may help to point out here that in the book I defend an externalist theory of rationality and epistemic warrant. I deny that in order for S's belief B to be warranted, S has to know (or have some internal awareness of) just how B is warranted for S. So I argue that a Christian can have warranted beliefs in the component claims of the doctrine of the Trinity without knowing how those beliefs are warranted, provided certain conditions are met (which I discuss in chapters 5 and 6). As for the question of what exactly we're expected to believe when we accept the doctrine of the Trinity -- yes, that's one of the trickier questions. I address it in chapter 7, although no doubt I will have to say more at some point. But I'll make a few brief comments here. In the first place, I don't think we believe a single proposition when we believe the doctrine of the Trinity (which is why talk of "the Trinitarian-proposition" and "the Trinitarian-sentence" can be somewhat misleading). Rather, we believe a number of propositions: to believe in the Trinity is to have a number of beliefs about God. From a psychological standpoint, that's just how our believings generally go. We have many distinct, structurally simple beliefs, rather than a few massively complex conjunctive beliefs. Furthermore, Trinitarians don't believe anything explicitly contradictory (i.e., both a proposition and its negation). Rather, we have a set of beliefs that, on reflection, appear to involve an implicit contradiction. But we withhold the further belief that these involve a genuine contradiction, and thus withhold certain inferences about our beliefs. So far as I can see, there is nothing psychological impossible or infeasible about this. Nor is it necessarily rationally unacceptable, provided one has sufficient epistemic grounds for maintaining this complex belief state (and showing that there could be sufficient epistemic grounds is the burden of my book, of course). The doxastic situation of the Mysterian Trinitarian can be compared again to that of our friend the Flatlander, who ends up holding both the belief that the Cone is triangular and the belief that the Cone is circular, and while unable to reconcile these beliefs and resolve the apparent contradiction, he withholds the inference that one or other must be relinquished. I think scientists sometimes find themselves in an analogous situation, as when they believe that light is simultaneously particular and undular, or they believe that quantum mechanics and special relativity are both true. In each case, they tacitly recognize that there is some unarticulated equivocation or imprecision involved, even though they're presently unable to specify and conceptualize that equivocation/imprecision.
Thanks again to Peter for his stimulating analysis. I hope this won't appear lazy or evasive, but I'm simply going to refer Peter (and other interested readers) to my book, in which I address the sort of epistemological issues he raises. In chapter 5, I offer a defense and extension of Plantinga's epistemology of Christian beliefs, according to which the component claims of central Christian doctrines (such as the Trinity) can be strongly warranted based on biblical revelation. In chapter 6, I argue that if this epistemology is granted along with the Christian doctrines of analogy and divine incomprehensibility, then the recognition that certain Christian doctrines are paradoxical need not function as an epistemic defeater for belief in those doctrines. In chapter 7, I address the objection that the paradoxicality of Christian doctrines is a defeater for the claim that the Bible (understood as the source of those doctrines) is a divine revelation. In other words, I say a lot in the book than in the 2005 article (which inevitably left many important questions unaddressed). Obviously I can't reproduce all that material here, and I'm reluctant to summarize because simplified arguments often end up looking like simplistic arguments. But readers of the book can judge for themselves to what extent Peter's objections have traction. Bill is quite right, though, that Peter's Modus Ponens is my Modus Tollens. It should be understood that my project is a defensive one; specifically, it aims to deflect the objection that if the doctrines of the Trinity and the Incarnation appear to be inconsistent then it can't be rational for Christians to believe them. I'm not attempting to show that the doctrines are true or epistemically warranted; certainly I'm not attempting to make a case for those doctrines that will persuade an atheist like Peter (especially an atheist with preferences like those expressed in Part III above). The argument of the second half of the book, in a nutshell, is that if Christian theism (broadly understood) is actually the case, and if the doctrines of the Trinity and the Incarnation as taught in the Bible are paradoxical, then the model I propose for understanding those doctrines (or something close) is most likely true -- in which case, Christians who believe those doctrines are normally rational to do so. One consequence of this is that the objections Peter raises above beg the question against the Christian Mysterian. Finally, a comment on one of Bill's interpolated comments. Yes, I do indeed believe that everything in the Bible is divinely revealed, including the Old Testament. This shouldn't be so surprising; it's the traditional Christian view. Indeed, it was the view of Jesus himself (Matt. 5:17-18; Luke 16:17; John 10:35; go here for a more detailed argument). I figure what's good enough for Jesus is good enough for me. After all, if anyone would know, he would. :) I'm a little surprised that Bill would endorse the old wrong-value-of-Pi argument against this view. An approximation isn't a falsehood. If it were, every written value of Pi (or measurements implied to be in that ratio) would be false, whether in the Bible or not. Suffice it to say that there are several plausible explanations for the measurements recorded in 1 Kings 7:23 (some of which are listed here). A discussion of whether or not the Old Testament is divinely inspired would take us far afield from the topic at hand, and needlessly so. I'm willing to defend the inerrancy of Scripture, but doing so requires a certain amount of common ground about the nature of God, the teachings of Christ, the basic reliability of the New Testament, and so forth. And in any case, the epistemology of Christian beliefs I defend in the book doesn't require a full-blown doctrine of biblical inerrancy.
I don't have time for a longer response right now, but for the record I want to note that I do not claim, or accept, that the doctrine of the Trinity is "hyper-inscrutable" in the way that Peter has defined the term. This is clear from my book. I realize that Peter thinks this is an implication of my position, but I don't think he has come close to showing that yet. More later, perhaps.
Peter, I reject (A1.4) and (A1.6). Regarding (A1.4), it seems to me as clear a logical principle as any that if P is a proposition and Q is a proposition then P&Q is also a proposition. Furthermore, if P is a proposition then ~P is also a proposition. So if P is a proposition, it follows that P&~P must also be a proposition. The latter is a necessarily false proposition, but it is a proposition nonetheless. Likewise, if some sentence S expresses a proposition, then S conjoined with its negation is also a proposition. Thus it is quite possible for a contradictory sentence to express a proposition. I should emphasize here that I do not claim that the doctrine of the Trinity is necessarily false; indeed, I explicitly deny it. But if (A1.4) is false then your objection fails anyway. Regarding (A1.6), I don't claim that TS is contradictory; I claim that it is apparently contradictory. So even if (A1.4) were true, it still wouldn't follow that TS fails to express a proposition. In my book (and the article that preceded it) I give several non-theological examples of scenarios in which it is plausible to think that a person can intelligibly and rationally believe a set of claims that appears (to them) to be inconsistent, provided they have sufficient epistemic grounds for believing that the contradiction is merely apparent. Perhaps it would be worth interacting with those examples before turning to the more controversial case of the doctrine of the Trinity. If you can show that it can never be rational to believe a set of claims that appear to be inconsistent, regardless of what epistemic grounds one might have for accepting those claims or for believing that the inconsistency is merely apparent, then my proposal is dead in the water. But I think it would be tough to make that case.
Now some comments by way of response. 1. My actual position is less radical than Peter suspects. In terms of his scheme, my claim is that the doctrine of the Trinity is paradoxical because of either epistemic inscrutability (EI) or conceptual inscrutability (CI). I don't know which is the case. I'm quite open to the possibility that some enterprising theologian will come up with a formulation of the doctrine that avoids paradox while preserving orthodoxy. Indeed, I hope that happens. But my argument is that regardless of whether we're facing EI or CI, it can still be rational for Christians to affirm and believe the doctrine in the absence of any satisfactory resolution. (As for what counts as 'rational' here, I discuss that at length in the book.) 2. Peter asserts in 4.1) that any ambiguity or equivocation in the terms used in the Trinitarian-sentence will necessarily infect all sentences in which those terms are used. This is by no means obvious to me. Terms in theological discourse are used with varying meanings all the time (just as in any other field of discourse). Could Peter flesh out his argument here? 3. Peter seems to suggest in 4.2) that if one doesn't understanding precisely how a term is to be understood in some particular context, then one doesn't understand it at all. This strikes me as very implausible. (Bill picks up this point in his comment under 5.) I may well be misreading Peter here, but this seems to be an assumption of his argument. According to the doctrine of analogy (a staple of Christian theology) terms don't have precisely the same meaning when applied to the Creator as they do when applied to creatures. But they're not equivocal either; there is substantial semantic overlap. In my book, I argue that my proposal fits well with this mainstream Christian view of theological language. The terms used in the doctrine of the Trinity are analogical to terms used in ordinary discourse. But we don't need to be able to specify precisely how they differ in order to find those theological statements meaningful. (Compare again the situation of the conceptually-limited Flatlander and his doctrine of the Cone. Surely the Cone isn't hyper-inscrutable to him. He has a partial understanding of the Cone, albeit one that in his conceptual scheme gives rises to some logical perplexities.) It seems to me that Peter's objection is not so much an objection to my proposal as an objection to the doctrine of analogy as such. So if he's right, I'm the least of his targets! 4. Regarding the three questions under point 6: I'm not sure how from our perspective we could distinguish a case of EI from CI. Certainly if someone came up with a non-paradoxical formulation of the doctrine of the Trinity, we would know that it had been EI rather than CI. Other than that, I'm not sure. But since I'm not yet persuaded that either EI or CI is problematic in the way Peter suggests, I'm not too concerned about it. What reasons do we have to believe there are cases of CI? I think there are some theological reasons to think it wouldn't be too surprising to encounter cases of CI. I discuss some in the book. But as I say, I'm not committed to the claim that there are cases of CI. And my answer to question 6.3 is of course: No, we are not. :) 5. My overall sense is that Peter's characterization of linguistic meaning is too restrictive. It's more early-Wittgenstein than late-Wittgenstein, if I can put it that way. I think language (including theological language) is more flexible and complex than his scheme allows. If I'm right, his net probably isn't going to catch my fish.
I have a couple of preliminary questions of clarification. 1. In 1.2) a sentence is S defined as a real contradiction just in case there is no normal model in which S comes out true. But in 2) the notion of apparent contradiction appears to be defined in such a way as to entail real contradiction: "Let S be a sentence expressible in L and suppose S comes out false in every normal model M." In that case S must be a real contradiction, per the prior definition. So on this scheme, one cannot have a merely apparent contradiction. What am I missing? 2. In 2.2) the term "adjusted-normal-model" is defined. But later on, the term "abnormal-model" is introduced. Am I right to take these as synonymous?
I must say it's a real treat to have my proposal stress-tested by two such rigorous thinkers! I wish I had more time to contribute to the discussion, but I will try to make time to post a response tomorrow. I want to be sure I understand Peter's analysis before commenting.
This is a helpful distinction, and one I'm happy to accept (much as Margaret Fuller accepted the universe). It's hard to deny that inconceivability_1 entails impossibility, because impossibility is built into the definition. If I entertain S, and find a contradiction in it, then of course there must exist a contradiction in S to be found. And if S involves a contradiction, it must be impossible. So this is uncontroversial. And the distinction between inconceivability_1 and inconceivability_2 is cogent. No objection there. But I don't see that any of this raises problems for my position, because I don't claim or imply that the Trinity is inconceivable_1. In fact, Bill's distinction is helpful for clarifying what I am proposing. As best I can tell, the following claims form a consistent set. (1) The Trinity is (at least presently) inconceivable_2 to us. (2) The state of affairs seemingly expressed by the conjunction of the claims that constitute the doctrine of the Trinity is inconceivable_1 to us. (3) The claims that constitute the doctrine of the Trinity are non-vacuous optimal approximations to an 'ideal' doctrine of the Trinity (i.e., a set of claims that would describe with maximal precision, and no apparent contradiction, the metaphysical relations between the Persons and the Godhead). (4) The claims that constitute the doctrine of the Trinity are the closest to the precise truth of the matter that we can comprehend and express, given our present cognitive limitations. I'll throw out another analogy for the wolves (and if it's savaged to death, so be it). The doctrine of the Trinity is like the claim that three cities on a plane form a right-angled triangle, such that the sides of the triangle are 50 miles, 100 miles, and 112 miles -- where that claim is cognized by people who cannot grasp or entertain the concept of fractional values.
Bill (if I may), My response, in very brief, is that appeals to mystery such as these can only be funded by divine revelation, for the sort of reason indicated at the end of my comment here. Put crudely, only God is in a position to correct or overrule the inferences we make from our fallible metaphysical intuitions. It's unlikely that the materialist mysterian could avail himself of such an appeal, because either (a) he rules out divine revelation in principle (if he's a materialist about everything) or (b) if he accepts divine revelation he would still find it a pretty tall order to identify a divine revelation that would warrant such an appeal (contrast the case of the doctrine of the Trinity). For example, as best I can tell, the Bible doesn't offer any support for materialism (in any sense of the word!). Obviously this response raises numerous further questions, such as the proper relationship between human reason and divine revelation, but here I'm simply indicating the line of defense I'd take. In sum, there is a relevant difference between theological mysterianism and materialist mysterianism. I do think that there is slightly different parity argument to be had here, namely, that if materialist mysterianism can be rationally justified then so can theological mysterianism (cf. Plantinga's parity argument in God and Other Minds). In essence, I take the view that of the following two propositions, the first is true but the second is false (or at least, not obviously true). (P1) If materialist mysterianism can be rationally justified, then so can theological mysterianism. (P2) If theological mysterianism can be rationally justified, then so can materialist mysterianism. Finally, I'm inclined to reject the final inference in Bill's post. It doesn't seem right to me to say that if some strategy S can be used to defend both P and Q (where P and Q are incompatible) then S can't be effective for defending either P or Q. To see my point, try replacing S with "rational argumentation in general" or "appeals to prephilosophical intuitions" or "appeals to empirical evidence". But perhaps I'm misunderstanding Bill's point.
Toggle Commented Feb 10, 2010 on Materialist Mysterianism at Maverick Philosopher
Sorry for not returning earlier, Dr. Vallicella! I treated myself to a blog-free weekend. Since it's getting rather busy down here, I'll restrict myself to just a few comments following up on your response to my earlier comment. The more I think about it, the less inclined I am to accept that inconceivability entails impossibility. In the first place, I doubt that there is such a thing as inconceivability an sich. Surely inconceivability is always relative to a mind, and thus must be indexed to the particular abilities of that mind. By extension, we can speak of conceivability with respect to a kind or species of mind, e.g., the human mind or the divine mind. But I don't think it's right to speak of inconceivability an sich. I suspect we may actually agree on this point. And we certainly seem to agree that inconceivability to God entails impossibility. But even though we have no direct epistemic access to any other inconceivability than our own, and despite the formidable historical pedigree of the idea, it still strikes me as implausible to maintain that inconceivability to us entails impossibility. (And who precisely counts as the 'us' here? Humans in general? Philosophically sophisticated humans? Humans in this life? Humans in the next life?) For the principle in question is logically equivalent to the principle that possibility entails conceivability. But is it plausible to think that absolutely whatsoever happens to be possible in this mysterious universe and beyond must be conceivable to the human mind, at least in principle? Can this really be right? I want to emphasize that I'm not advocating some form of modal skepticism, i.e., the view that our intuitions as to what is possible or impossible are generally unreliable. On the contrary, I think they're reliable. I just deny that they're infallible. But it doesn't follow that they can't do a great deal of useful philosophical work. (Incidentally, I'd argue that only theism can underwrite the reliability of our modal intuitions.) As to the question of whether my position suffers from ad hocness: I address this in my book, but my short answer is that only divine revelation has the epistemic authority to trump our intuitions on matters of broad logical (i.e., metaphysical) possibility. After all, who else could be in a position to correct, where necessary, our fallible inferences from inconceivability to impossibility but One for whom inconceivability really does entail impossibility?
I'm an avid follower of your blog, Dr. Vallicella, and I wouldn't normally dare to comment on one of your analyses, but in this case I feel something close to a moral obligation to jump in! I don't think my account of theological paradox (which Dale categorizes as "positive mysterianism") commits me to the view that inconceivability doesn't entail impossibility. On my view, the Trinity isn't analogous to a round square. Rather, my proposal is that the set of claims (and beliefs) involved in the doctrine of the Trinity are approximations to the metaphysical truth of the matter, a truth that is (of course) logically consistent. However, due to our cognitive limitations, we aren't able to grasp (and thus express) anything closer to the truth than these approximations. In other words, there are certain metaphysical distinctions or precisifications that we're constitutionally unable to grasp and articulate. This may be an unappealing claim to analytic philosophers, but I don't think it's incoherent or otherwise outrageous. At any rate, it seems to be harmonious with a broadly Christian view of God and human beings. If this is right, it explains why our best formulations of the doctrine of the Trinity still have a residue of paradox (understood as merely apparent contradiction). So my position is that there are certain fine metaphysical distinctions that are inconceivable for us (at least presently) in the sense that we cannot identify or entertain them. But I can't (yet) see how that commits me to the claim that inconceivability doesn't entail impossibility, or that round squares might turn out to be possible after all. What I'm suggesting, then, is that when God reveals his trinitarian nature to us, it has to be in a manner accommodated to our cognitive capacities, and that necessarily involves conceptual approximations. So what we end up with (to adapt your analogy) is a revelation involving the claim that God is both 'round' and 'square'. God in se is not literally 'round' and 'square', but these concepts (which are not compossible as such) are the closest we can get. Now, there could be any number of reasons why this cognitive situation might arise (I explore a few in my book) but unless I'm missing something, I don't think it's vulnerable to your objection. In fact, I use something like your round-square analogy in my book. Imagine a scenario in which Edwin Abbott's Flatlander receives a revelation from a conical being (who exists outside Flatland, of course). Because the Flatlander lacks the capacity to think three-dimensionally, and thus to grasp the idea of a cone, the conical being has to reveal himself to the Flatlander as both 'circular' and 'triangular'. Of course, this revelation appears contradictory to the Flatlander, but one can argue that it isn't necessarily irrational for him to accept it, albeit with some qualification (e.g., on the understanding that the claims involved are merely optimal approximations). Furthermore, it would be wrong to say that the Flatlander's doctrine of the Cone is cognitively vacuous; that it doesn't really say anything informative about its referent. My proposal is that our epistemic situation vis-à-vis the Trinity is somewhat analogous to that of the Flatlander. And, to return to your objection, I don't think any of this requires me to say that inconceivability doesn't entail impossibility. But suppose that it does. Why couldn't we say that inconceivability is a strong but ultimately defeasible indicator of impossibility? Wouldn't this do all (or nearly all) the useful philosophical work the entailment relation does for us? It's surely an option worth exploring. Anyway, I go into more detail about these matters in my book. An earlier incarnation of my proposal appeared in the following paper, which interacts with Dale's critique of modern trinitarian models: As you'd expect, the discussion between Dale and me has advanced somewhat since then! He has been an invaluable interlocutor, and I'm looking forward (with some apprehension) to reading his forthcoming paper in IJPR. Sorry this has turned out to be such a lengthy comment!
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