Monday, May 25, 2015

D. B. Hart and the “terrorism of obscurantism”


Many years ago, Steven Postrel and I interviewed John Searle for Reason magazine.  Commenting on his famous dispute with Jacques Derrida, Searle remarked:

With Derrida, you can hardly misread him, because he's so obscure.  Every time you say, "He says so and so," he always says, "You misunderstood me."  But if you try to figure out the correct interpretation, then that's not so easy.  I once said this to Michel Foucault, who was more hostile to Derrida even than I am, and Foucault said that Derrida practiced the method of obscurantisme terroriste (terrorism of obscurantism).  We were speaking French.  And I said, "What the hell do you mean by that?"  And he said, "He writes so obscurely you can't tell what he's saying, that's the obscurantism part, and then when you criticize him, he can always say, 'You didn't understand me; you're an idiot.'  That's the terrorism part."

Now, David Bentley Hart is hardly as obscure as Derrida, and I would hardly call him a “terrorist.”  (Foucault’s expression here is characteristically over-the-top.)  Still, I can’t help but think of Searle and Foucault’s description of Derrida’s method of dealing with his critics when reflecting on the way Hart tends to respond to his critics.

First example: Take Hart’s now notorious attack on natural law theory of two years ago.  As I showed in my initial reply to Hart, there are a number of serious problems with that piece.  But as I have also by now pointed out many times, the most serious -- indeed, the fatal problem -- is that Hart relentlessly conflates “new natural law” theory and “old natural law” theory.  His central thesis, which he not only presented in his original article but has reiterated in several follow-up pieces, is that natural law theorists both (a) appeal to formal and final causes inherent in nature but also (b) are blithely unaware of the fact (or at least downplay the fact) that most of the modern readers they are trying to convince firmly reject the very idea of formal and final causes.  And the trouble is that there are no natural law theorists of which this is true.  For (a) is not true of “new” natural law theorists, and (b) is not true of “old” natural law theorists.  Hart is thus attacking a straw man. 

Certainly Hart has, in the original piece, in three different follow-up pieces now, and in two further brief references to the debate, failed to offer a single example -- not one -- of a natural law theorist whose work actually fits his description of natural law theory.  Indeed, he has explicitly refused to name any names, even though doing so would instantly defuse the main objection his critics have raised against him.

(For the record, these follow-up pieces are: Hart’s first reply to his critics in his column in the May 2013 First Things, to which I responded at Public Discourse; Hart’s lengthy further response to his critics in the letters page of the same issue, to which I responded here at the blog; and what he characterized as his final response in his August 2013 column in First Things, to which I also responded here at the blog.  Hart then briefly revisited the debate in his column in the March 2015 First Things, to which I responded here; and he briefly referred to it yet again in his June/July 2015 First Things column, to which I recently responded at Public Discourse.)

Even more bizarrely, though Hart has addressed other objections head on, he has, in those three lengthy follow-up pieces and two briefer remarks -- five occasions total -- not even acknowledged, much less directly responded to, the central objection just summarized, even though it has been repeatedly raised against him.  He could very easily say: “I have been accused of conflating new and old natural law theory, but here is why that charge is mistaken…,” or: “Let me give you a specific example of a natural law theorist who is guilty of doing what I say natural law theorists in general are guilty of.”  But he doesn’t.  Why not?  It can’t be because he has judged that answering his critics is somehow not worth his time; again, he has revisited the debate five times now.  So, obviously he does want to try to answer his critics.  And yet he never acknowledges or directly responds to their central criticism.  Why is that?

Then there is the obscurity in what Hart does say in reply to his critics.  If you read my responses, linked to above, to his three lengthier attempts to reply to those critics, you will see that I there show -- documenting my analysis with many quotes from Hart -- how difficult it is to find a clear and consistent position in what he says.  As I demonstrate in those pieces, just when you think you’ve finally nailed down what Hart means, he says something else that conflicts with that reading.  Hart himself confesses in one place to some “obscurity,” and in another that he “may have been guilty of a few cryptic formulations” and “should have been clearer.”

And yet despite admitting himself to being sometimes “obscure” and “cryptic,” and despite failing repeatedly even to acknowledge much less answer the main objection leveled against him -- where, if only he would do so, he might finally clarify things in a single stroke -- Hart claims that it is my criticisms of his remarks on natural law that are “confused,” “simplistic,” and guilty of “fallacies,” and that our dispute over natural law “largely involved Feser furiously thrashing away at what he imagined I was saying” (where the latter remark was embedded in the larger context of ad hominem remarks about my purportedly robotic and dogmatic adherence to “The System” of “Baroque neoscholasticism,” “manualism,” “two-tier Thomism,” etc.).

Now that, I submit, comes pretty close to what Foucault and Searle call “the method of… [the] terrorism of obscurantism.”

Second example: Hart’s March 2015 column in First Things is primarily devoted to the question of the relationship between faith and reason.  As I noted in my March 13 blog post commenting on that column:

Hart objects to the charge that he is a fideist, arguing that both fideism and rationalism of the seventeenth-century sort are errors that would have been rejected by the mainstream of the ancient and medieval traditions with which he sympathizes.  With that much I agree. 

I also noted several other things Hart says in the column with which I agree, and indeed I said that they are “points whose importance cannot be overemphasized.” 

I also noted, however, that certain other things Hart says there seem, whatever his intentions, to imply a kind of fideism.  For example, he says that even reason “arises from an irreducibly fiduciary movement of the will” (emphasis added), and indicates that he rejects the view that reason is “capable of discerning first principles and deducing final conclusions without any surd of the irrational left over” (emphasis added).  That certainly makes it sound as if he thinks that in all our attempts rationally to justify our beliefs, there is always at bottom some “surd of the irrational” and that it is “the will,” in an “irreducibly fiduciary movement,” which decides upon first principles.  And that is a view of the sort that would commonly be regarded as a kind of fideism.  Still, I did not say that Hart is a fideist, full stop.  I said that his position is ambiguous and can be read in different ways. 

Incidentally, you’ll find a similar ambiguity in Hart’s recent book The Experience of God.  On the one hand, he argues (quite rightly in my view), that any materialist account of our rational thought processes can be shown to be self-undermining, and that the very logic of explanation when pushed through consistently leads inevitably to affirming the existence of a divine necessary being as the only possible explanation of why the world of contingent things exists.  That certainly evinces a very optimistic view of what reason can accomplish vis-à-vis the dispute between theists and philosophical naturalists. 

On the other hand, Hart also says in that book that he has “begun to vest less faith in certain forms of argument” (p. 84), and that it is good to “let all complexities of argument fall away as often as one can” in favor of a “moment of wonder, of sheer existential surprise” (p. 150).  He suggests that “our deepest principles often consist in nothing more -- but nothing less -- than a certain way of seeing things” and that “every form of philosophical thought is itself dependent upon a set of irreducible and unprovable assumptions” (p. 294).  He wants to remind us of “the limits of argument, and of the degree to which our most cherished certitudes are inseparable from our own private experiences” (Ibid.).

Does this mean that all attempted rational justifications come down at the end of the day to “private experiences,” “moments of wonder,” or the like?  Is there, after all, no common ground by which the theist might rationally demonstrate to the naturalist that the latter’s position is mistaken?  Are there just irreducibly different possible “movements of the will,” any of which involves a “surd of the irrational”?  If so, why wouldn’t this amount to fideism?  Or is there some other way to read Hart’s remarks here?  The problem is not the way Hart answers these questions.  The problem is that Hart doesn’t even address them, much less answer them, at least not in The Experience of God or in the column on faith and reason.  It just isn’t clear what he would say.

Now, a reader recently called my attention to a recent combox discussion at Eclectic Orthodoxy, to which Hart contributed and in the course of which he made the following remark:

[W]e are all so prone to thinking in the rather arid categories of (for want of a better word) analytic correspondence that we regard the entire tacit dimension of knowledge (which is the foundation of all knowledge) as somehow either merely inchoate or merely emotional. If one is not careful, one ends up with the barren dialectic of “rationalism” or “fideism,” and one ends up like a certain popular Thomist I know of, unable to think in any other terms than that.

Well, I’m sure we’re all wondering who the “popular Thomist” in question is.  But one good reason for thinking that it isn’t me -- or rather, for thinking that it shouldn’t be me -- is that my views simply don’t correspond to those attributed by Hart to this “popular Thomist.”  For one thing, and as I explicitly said in my post on Hart’s faith and reason column, like him I reject what he called, in the column, “the Scylla and Charybdis of ‘rationalism’ and ‘fideism’ [which] seems like such a tarnished relic of the seventeenth century (or thereabouts).”  For another thing, I have written quite a bit, and quite sympathetically, on the “tacit dimension of knowledge.”  (See, for example, my defense of Burke’s and Hayek’s account of the indispensable role that tradition, habit, and inexplicit rules play in moral and social knowledge.)  It’s just that I don’t think that this tacit knowledge has anything to do with “movements of the will,” a “surd of the irrational,” or the like. 

Now, if some man assures us with vehemence that he is not a bachelor, but also denies with equal vehemence that he is or ever has been married, never explains to us how both these things can be true but also dismisses with contempt our suggestion that maybe he really is a bachelor after all (accusing us of applying “arid categories” and a “barren dialectic,” no less)… if someone does all that, then we are hardly the ones being unreasonable.  Nor would it be reasonable for his defenders breathlessly to protest “But he said he’s not a bachelor!  You’re not interpreting him charitably!” 

Similarly, though Hart insists that he is not a fideist, but nevertheless also says things that would normally be taken to be fideistic positions, and does not explain how he can reconcile these claims while at the same time dismissing his critics as being simplistic and misunderstanding him… well, once again, that seems pretty close to what Foucault and Searle call “the method of… [the] terrorism of obscurantism.”

Diagnosis: So, just what is Hart’s deal, anyway?  Why this resort to obscurantisme terroriste?  Let’s consider the following:

Item one: As a stylist and a thinker, Hart’s strengths and predilections lie in rhetoric rather than rigor, and he has a clear animus against writers of the opposite tendency.  Hence his confession that he “delight[s] in casual abuse of Thomists,” and his regular glib dismissals of anything he takes to smack of “neoscholasticism.”  Hence his equally condescending remarks about analytic philosophers in The Experience of God.  Hence his explicit refusal, in the same book, actually to set out and defend in any detail the arguments against materialism and for the existence of God that he endorses.  Explicit, step-by-step arguments, the dispassionate weighing of lists of possible objections and possible replies to those objections, the making of fine distinctions and careful definitions of key terms, and so forth -- the sort of thing typical of a Scholastic or an analytic philosopher -- are not the sort of thing for which Hart seems to have much patience.

What Hart really likes are grandiloquent pronouncements and the big picture.  A sense of his style and interests is given by the titles and subtitles you’ll typically find in a Hart book or article: “Being, Consciousness, Bliss,” “The Veil of the Sublime,” “The Mirror of the Infinite,” “A Glorious Sadness,” “The Practice of the Form,” “The Terrors of Easter,” “The Doors of the Sea,” “The Violence of Metaphysics and the Metaphysics of Violence”… that kind of stuff.  The sort of thing sure to prompt an “Oooh!” or an “Aaaaah!” as you dip into Hart while sipping brandy.  Grand Rhetoric and Grand Themes, and hold the argumentational minutiae please.  That’s Hart’s shtick, and he’s shtickin’ with it.  You can see how an analytical Thomist who posts comic book panels on his blog might get under his skin.

Item two: Whether or not you want to call it “fideism,” the view that what we take to be rational argument always comes down at the end of the day to “movements of the will,” “personal experiences,” “ways of seeing things,” “moments of wonder,” and the like tends inevitably to put the accent on the character of a person giving an argument rather than on the argument itself.  If your conclusions are mistaken, perhaps that’s because you haven’t had a “moment of wonder,” or have had the wrong “personal experiences,” so that your overall “way of seeing things” is off kilter.  Or perhaps the “movements of your will” are simply corrupt. 

Of course, sometimes the problem really is with the character of the person giving an argument.  Sometimes people really are arguing in bad faith.  Furthermore, Hart’s view doesn’t entail that all errors are a consequence of some deficiency of character.  It is consistent with some errors just being a result of mistaken inferences or getting the facts wrong. 

Still, if you are someone who is inclined to emphasize “the limits of argument,” and the role that “movements of the will” and the having of the right “personal experiences” play in ensuring a sound overall “way of seeing things,” then there is bound to be a strong temptation to jump too quickly to the ad hominem, to look straightaway for a deficiency in your critics and not just in their criticisms. 

And Hart does indeed sometimes suggest that deficiencies of background experience or personal motivation underlie his critics’ resistance to his views.  Hence, in his most recent response to me in First Things, Hart laments that “Feser [was not] fortunate enough to be catechized into Orthodoxy rather than The System.”  And rather than focusing on the actual arguments I gave against there being animals in Heaven (which was the subject of our dispute), he put the emphasis on what he alleged were my true motives for taking the view I did (viz. to uphold “The System”). 

Kidding on the square, Hart also suggests in The Experience of God that a preference for analytic philosophy reflects “some peculiarity of temperament or the tragic privations of a misspent youth” (p. 344). 

Furthermore, in one of his replies to critics of his article on natural law, Hart says:

I am in the end quite happy for believers in natural law theory to continue plying their oars, rowing against the current (so long as they do so in keeping with classical metaphysics), but I do not think they are going to get where they are heading; so I shall just watch from the bank for a while and then wander off to the hills (to look for saints and angels).

And in reply to one critic in particular, he says:

As to what “other approach” he should take to “modern moral life,” I encourage Mr. Kainz to pursue classical natural law theory (which was not the topic I addressed), if he likes. The Great Commission also comes to mind. (Do what you think best.)

The insinuation is obvious.  If what motivates you is Christ’s Great Commission and if you value the teachings of saints and angels over those of worldly men, then you’ll agree with Hart.  And if you don’t agree with Hart, well…

(I say more about these two passages in my analysis from two years ago of the piece from which they are quoted.)

So, with this in mind, consider the scenario in which Hart not infrequently finds himself.  A Grand Man makes a Grand Point about a Grand Theme, in Grand Style.  And then some yutz analytic philosopher or neoscholastic comes along logic-chopping and ruining the moment.  The temptation is strong to conclude that there’s got to be something wrong with the critic and not just with whatever his silly criticism is.  He just hasn’t got the character or education to see all the Grandness. 

Conclusion: On the one hand, then, we have a strong predilection for rhetoric and an impatience with rigorous argumentation.  That’s a recipe for the first half of obscurantisme terroriste.  And on the other hand, we have a strong tendency to look for volitional, experiential, moral, and spiritual deficiencies -- personal deficiencies -- in those who have the wrong opinions.  That’s a recipe for the second half of obscurantisme terroriste.  Thus, a temptation to deal with critics via what Searle and Foucault call “the method of… [the] terrorism of obscurantism” is, I would suggest, bound to be an occupational hazard of the Hart style of theology.

And this is an analysis even Hart should love.  “The Terrorism of Obscurantism” sounds just like a Hart chapter title, no?

316 comments:

  1. Scott,

    As you well know there is huge difference between the proofs (or rational demonstrations) of things like “2+2=4” and God’s existence. While the first type has to be true, in the second the proofs, they depart from our knowledge of reality (and here, obviously, there has to be an agreement on what reality is, in order to the argument can be effective in the demonstration).

    As an example the main arguments from new atheists depart from disagreements on the human nature (that question free will and human rationality) and nature of reality (metaphysic principles and the intelligibility of nature). The problem of their arguments is not the lack of rationality in their arguments but their incoherence in what they consider that reality is (bad metaphysics).

    As I see it God made humans free and rational (our free will most surely enables humans either to rationally acknowledge God, or to deny God, or even to replace God by something that is in our self-interest), but it is faith (that is a grace of God) that insures any coherence between our will and the will of God. Rationality by itself allows us to seek God (assisted by faith) as (even more easily) to stray from God.

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  2. Skyliner,

    ...I give you the last word.

    When it comes time for my ticket to be punched, may I have as many last breaths to take as you have last words to give. ;)

    My last word, which isn't mine (heh), is slightly off-topic (double heh). Then again, and in a certain subtle sense, perhaps not entirely so.

    Mountaineering tends to draw men and women not easily deflected from their goals. By this late stage in the expedition [to the summit of Mount Everest] we had all been subjected to levels of misery and peril that would have sent more balanced individuals packing for home long ago. To get this far one had to have an uncommonly obdurate personality.

    Unfortunately, the sort of individual who is programmed to ignore personal distress and keep pushing for the top is frequently programmed to disregard signs of grave and imminent danger as well. This forms the nub of a dilemma that every Everest climber eventually comes up against: in order to succeed, you must be exceedingly driven, but if you're too driven you're likely to die. Above 26,000 feet, moreover, the line between appropriate zeal and reckless summit fever becomes grievously thin. Thus the slopes of Everest are littered with corpses.
    -- Krakauer, Jon, Into Thin Air


    - - - - -

    Thanks for the charitable and insightful exchange.

    I found it interesting and helpful as well, so thank you.

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  3. Scott,

    I wanted to add that in some (slightly awkward) sense, faith may seem to imply a voluntary abdication of freedom. But the thing is that it (the supposed loss of freedom) is quite illusory, we are not able of not being free.

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  4. @Vasco Gama:

    As you well know there is huge difference between the proofs (or rational demonstrations) of things like “2+2=4” and God’s existence. While the first type has to be true, in the second the proofs, they depart from our knowledge of reality[.]

    I'm not sure what it means to say that proofs of God's existence "depart from our knowledge of reality." If it means that they rely on premises that are neither self-evident nor demonstrable, then it also means that the supposed "proofs" are not proofs at all. But that doesn't seem to be what you mean, since you add:

    The problem of [new atheists'] arguments is not the lack of rationality in their arguments but their incoherence in what they consider that reality is (bad metaphysics).

    And surely if their account of reality is incoherent, then it's demonstrably untrue. And if God's existence can be demonstrated using metaphysical principles that can themselves be shown to be correct, then those proofs don't "depart from our knowledge of reality" in any way that I can see.

    But there's another problem here: the distinction you're making also doesn't support your claim that the irrationality of denying God's existence would impinge on our freedom. All you've explained (if that) is why you don't think the proofs of God's existence are as rationally indefeasible as the proofs of arithmetic. You haven't explained why, if they were thus indefeasible, they would make us less free. So I'm still left wondering why the irrationality of denying that 2 + 2 = 4 doesn't mean that we aren't free, when the irrationality of denying God's existence would.

    And on the face of it, that doesn't seem to make sense. You've been quite clear that denying the truth of a proposition of arithmetic doesn't involve any sort of "freedom," and I agree. But I don't see why the same doesn't apply to any rationally demonstrable truth (or perhaps to any truth whatsoever). What sort of "freedom" is involved in the ability to deny something that is, in fact, true? Is reasoned argument a form of coercion? If I outline Aquinas's First Way to someone and he finds it persuasive, have I curtailed his "freedom"?

    Let's recap. You've offered an argument of the following form:

    (1) If it is irrational to deny proposition p, then humans are not free.
    (2) Humans are free.
    ∴ It is not irrational to deny proposition p.

    The argument is of course valid (it's a simple modus tollens), so it's sound iff the premises are true.

    Premise (2) isn't in dispute here. My question is about the range of propositions for which you think premise (1) is true, and why.

    We know there's one such proposition, namely God exists. We also know there's one proposition for which you don't think premise (1) is true, namely 2 + 2 = 4. The question is: what do you think is the significant difference between them?

    So far the only difference you've mentioned is that a proof of God's existence must in some unexplained way "depart from our knowledge of reality." Not only can I not make sense of this, but I also don't have a clue what it has to do with such proofs' allegedly interfering with our "freedom."

    I also don't see that issues of faith are relevant, as we're not talking here about propositions that can be known only through revelation. As you agreed in your first reply to me, according to Church teaching, that God exists is knowable by natural reason alone.

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  5. (By "We know there's one such proposition" I mean, of course, that there's one proposition that we know you think makes premise (1) true. I'm not implying my agreement that it really does.)

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  6. You know, I'm a late comer to this thread of comments, and I see that the conversation has moved on, and I see Dr. Hart doesn't seem to care about the insults or protests. I've heard from my degree director that he likes to be outrageous in print but doesn't actually have any personal malice. My husband knows him and says he's sort of a Henry L. Mencken about these things. So I'm not trying to start the argument again. But I have to cast my vote with those who say that Feser's article here is just way off. I was able to follow Hart's arguments in those articles, and I don't see what's supposedly missing. Just saying over and over that he didn't explain what he meant when he did doesn't make sense to me. And I read The Experience of God, and those sentences Feser quotes out of context aren't about giving up on philosophical argument, but of realizing that it's not enough if you've got a mind that can't even see the obvious because you aren't even able to be astonished by existence. It just seems to me to be like Guardini or Blondel. It's just not true he didn't defend his arguments for God from being and consciousness. I can't think of a step he left out. So what's really going on here? I'm not trying to be belligerent here. But this reads like just a lot of empty accusation supported by snippets of texts, cut out in a way to hide the overall argument.

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  7. "Even our notion of what might constitute a “rational” or “realistic” view of things is largely a product not of a dispassionate attention to facts, but of an ideological legacy."

    Funny how I never see "In fact, I can't even know that notion of ideologically-determined notions itself, since it too is largely a product of an ideological legacy and I also cannot know that I can't know that because it too is merely a product of an ideological legacy...."

    And "even our notion of largely is...."

    The real bonus is that these things are never argued. But then any premises would be largely....

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  8. Scott,

    I am not a philosopher, I am a scientist (chemist) with some fascination about philosophy (and only a limited knowledge). I was educated as a Catholic, loss my faith when I was a teenager and I was myself as an atheist/agnostic for most of my life and just returned to the faith about five years ago. Besides English is not my native language (that is Portuguese). The biographic note is for your convenience (and mine) in order to keep in mind that something may be lost in our dialogue (as my domain of your language is far from perfect.

    While propositions like “2+2=4” are true in any possible and imaginary universe. They are true by definition, as what we mean by 4 is that is the character that represents adding 2 and 2 (or 3 and 1, or …). So one says that “2+2=4” is true “a priori” (i.e. not dependent from verification from experience).



    The proofs of the existence of God are “a posteriori” proofs, which means that the proof depends from the experience (in this case our knowledge of reality).

    There is big difference as while the “a priori” propositions can’t be rationality denied, the ones said “a posteriori” are dependent upon the perceived reality.
    You can imagine an extreme idealist position as the claim that reality doesn´t exist, as it is just a product of an evil magician, or something like that… This is an extreme, but various degrees of skepticism are possible (within rational limits), you can imagine the position of the materialist eliminativists, or the reductionists that deny the PSR, free will, or that conveniently accept levels of reality as brute facts. All that may seem rather incoherent, but as long as it is found possible to deal with those inconsistencies it is not irrational to accept it.

    These two types of knowledge may be compared with me knowing my father and knowing that he loves me, in both cases I know that it is true, but it is not the same, and not in the same way.

    I agree with the church when proclaiming that God exists is knowable by natural reason alone. However I think that faith is absolutely essential to ground that knowledge.

    I can tell about my own experience, upon my departure from Catholicism in my teenage years, it was surely not because I suddenly become irrational, neither I became suddenly more rational, I just ceased to feed my faith, and then it was gone.

    In some sense I think that we are forced to realize that doubting is possible (we possess that freedom) so that we maintain humble in a constant quest, in order not to loose ourselves along the way. I don’t find particularly wise the ignorance of my own weaknesses.

    I hope you understand what I am trying to say.

    Best regards,

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  9. You know, I'm a late comer to this thread of comments, and I see that the conversation has moved on, and I see Dr. Hart doesn't seem to care about the insults or protests. I've heard from my degree director that he likes to be outrageous in print but doesn't actually have any personal malice. My husband knows him and says he's sort of a Henry L. Mencken about these things. So I'm not trying to start the argument again. But I have to cast my vote with those who say that Feser's article here is just way off. I was able to follow Hart's arguments in those articles, and I don't see what's supposedly missing. Just saying over and over that he didn't explain what he meant when he did doesn't make sense to me. And I read The Experience of God, and those sentences Feser quotes out of context aren't about giving up on philosophical argument, but of realizing that it's not enough if you've got a mind that can't even see the obvious because you aren't even able to be astonished by existence. It just seems to me to be like Guardini or Blondel. It's just not true he didn't defend his arguments for God from being and consciousness. I can't think of a step he left out. So what's really going on here? I'm not trying to be belligerent here. But this reads like just a lot of empty accusation supported by snippets of texts, cut out in a way to hide the overall argument.

    The problem, Mrs. Good, is that this isn't actually a very substantive comment. For instance, I really appreciated Skyliner's posts. He was actually trying to advance a point. But all you've done is string a bunch of assertions into a grammatically correct paragraph.

    I mean, Hart himself came on here and told everyone to knock it off and quit writing these types of posts.

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  10. I can't think of a step he left out.

    A step he left out of what? His criticism of natural law theory? His account of reason as based on a fiduciary movement of will? Or something else?

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  11. @Vasco Gama:

    Okay, thanks for clarifying.

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  12. Thanks for the reply, John West.

    The problem I think I'm going to encounter from these sceptical types is that they're not sceptical of principles like the PSR, period, it's just that they consider them to be merely 'rules of thumb', generalizations from experience. Presumably they think that holding the PSR to be universally true without enough 'evidence' would simply be a blithe assumption. (Presumably that's what they think 'Religion' is all about in the first place.) They do indeed seem to think the PSR is 'Everything of which we know has an explanation; hence, probably, everything that exists has an explanation.' For that reason, I don't think I can threaten them with universal scepticism, because they're not universally sceptical of the PSR, just conditionally.

    As it happens, yes, I've even found that that scepticism does extend to the Law of Non-Contradiction. Someone told me that the LNC might be refuted if round squares turned up (say, via Taxicab Geometry). The problem there, as I was able to explain, is that that would only show that round squares aren't a genuine contradiction after all (or at least, not in certain contexts), not that contradictions might be genuinely possible.

    I think that's consistently their mistake. They seem to think that all rational knowledge, including logic, epistemology and whatever else, is merely generalizations from experience (in other words, More Science).

    Now, personally, I think that's a big mistake, but what can I say to convince others that it is? I suspect that they'll just tell me they do believe in the PSR, just not unconditionally. Is there a problem with that, too?

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  13. he problem I think I'm going to encounter from these sceptical types is that they're not sceptical of principles like the PSR, period, it's just that they consider them to be merely 'rules of thumb', generalizations from experience. Presumably they think that holding the PSR to be universally true without enough 'evidence' would simply be a blithe assumption.

    One problem is that people aren't taught deductive reasoning. Yet, if there are truths about reality, there are facts from which we can deduce. So anyone who thinks there are genuine, true facts about reality, accepts that there are facts from which we can deduce. If we can deduce, we can prove.

    In contrast, inductive reasoning[1] has a built-in error bar. So no matter how hard someone that only reasons inductively tries, they literally can't prove anything. Proving is not a function of inductive reasoning.

    Some people claim science doesn't know or need deduction—nonsense. The tower of science is built on the deductive foundations of mathematics, and collapses without them.

    As it happens, yes, I've even found that that scepticism does extend to the Law of Non-Contradiction. Someone told me that the LNC might be refuted if round squares turned up (say, via Taxicab Geometry). The problem there, as I was able to explain, is that that would only show that round squares aren't a genuine contradiction after all (or at least, not in certain contexts), not that contradictions might be genuinely possible.

    There are other problems with this, too. For instance, when most people say a round square is a contradiction, they're tacitly assuming everyone understands they mean a Euclidean round square. Since they're tacitly assuming a Euclidean round square, when their interlocutor switches to taxicab geometry he's changing what's meant by “round square” and equivocating in the rest of his response. At most, all his reply tells us is that people ought to specify “Euclidean round square” to avoid confusion.

    Now, personally, I think that's a big mistake, but what can I say to convince others that it is?

    I'm probably not the best person to ask about persuasion, because I honestly don't care about it.

    But I think it's a mistake to try persuading people with radically different metaphysical foundations right off—with the old one-two-three-four-five-God arguments. Instead, I recommend becoming well-versed in the arguments for each piece of your own metaphysics and arguing those pieces over time.

    For example, it's a very rare scientifically educated naturalist who denies the PSR. It's only when the PSR is looped into an argument for God he doubts it. But all that says is that he doesn't like a conclusion to which a proposition he otherwise thinks true leads. It's dishonest, but how many people operate.

    Give them the metaphysical foundations over time, and hopefully they will reason through the rest themselves. Ed calls the Five Ways metaphysical proofs. Sometimes, with complex proofs, one has to work through the proof oneself before assenting to it.

    And if they still don't assent to it, well, them's the breaks pal. What others believe is not within our power. We cannot—nor should we want to—force people into agreement.

    I suspect that they'll just tell me they do believe in the PSR, just not unconditionally.

    Well, then they don't hold to the PSR.

    Is there a problem with that, too?

    One problem is that it's poorly defined. What do they mean by “not unconditionally”? Not when it's inconvenient? Surely that's not an intellectually honest epistemic practice.


    [1]I'm not sure how many people realize this is what they're doing or suggesting. At least sometimes, I supect it's the only method of reasoning they've been given.

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  14. Thanks again, John.

    I suppose you're right; I'm too concerned here with persuading others. After all, they'll find out for themselves if they actually want to know, right?

    One last question if you have time:
    What I think these 'sceptics' believe is that we should believe in abstract principles so long as they fit 'The Evidence'. By that token, it's okay to believe that the PSR applies in areas where it's already been shown to be reliable, but 'assuming' that it applies in new contexts would be gratuitous. Likewise, it would be okay to think that the laws of Cause & Effect apply in cases where they've been empirically shown to apply, but 'assuming' that they apply everywhere would be gratuitous. What's more, C&E could even be shown demonstrably not to apply in some cases (apparently radioactive decay and Quantum events are often mentioned as examples).

    ...and that's what I think they mean by 'not unconditionally'. At the risk of putting words in a hypothetical opponent's mouth, I think they'll say that they hold to those principles where they've been shown to fit 'the evidence' and doubt them when they're brought in to a new context, particularly contexts that aren't directly observable. You can call that 'not believing in the PSR' if the PSR is understood as a universal principle, sure, but that just means that they hold to some other, very similar principle that we can't call 'the PSR', but can still be used as a watered-down replacement that doesn't involve universal scepticism.

    Like I said, I strongly suspect that there's something seriously wrong with this approach, but I can't put my finger on it. Is there a problem with using the 'watered-down', inductive version of the PSR?

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  15. @John West:

    There are other problems with this, too. For instance, when most people say a round square is a contradiction, they're tacitly assuming everyone understands they mean a Euclidean round square. Since they're tacitly assuming a Euclidean round square, when their interlocutor switches to taxicab geometry he's changing what's meant by “round square” and equivocating in the rest of his response. At most, all his reply tells us is that people ought to specify “Euclidean round square” to avoid confusion.

    Agreed on all of this, and as an additional instance I'll point out what I think is a fundamental logical problem.

    Strictly speaking, the contradiction at issue isn't "round square" but "round non-round thing." And that contradiction doesn't arise unless being square is a way of being non-round.

    The logical problem, basically, is that in the ordinary case, "round" and "square" are contraries, not contradictories. So bringing forward a proposed counterexample (as in the taxicab-geometry case) in which they're not contraries doesn't even begin to address the PNC. Even granting arguendo that, in the taxicab geometry, the same shape can be both round and square (under unequivocal definitions of those terms), it still isn't the case that the same object can be both round and not-round, and the PNC remains untouched.

    I think that's pretty much what Arthur was getting at as well, but it's helpful, I hope, to spell it out in a bit more detail.

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  16. Scott,

    Thanks. I started to write a paragraph on broad vs. narrow contradictions. I should have finished it. This odd reply to the LNC has come up a couple times in recent weeks.

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  17. Arthur,

    Like I said, I strongly suspect that there's something seriously wrong with this approach, but I can't put my finger on it. Is there a problem with using the 'watered-down', inductive version of the PSR?

    The short answer is that your intuitions are working right. I intend to give a longer answer later.

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  18. What's more, C&E could even be shown demonstrably not to apply in some cases (apparently radioactive decay and Quantum events are often mentioned as examples).

    Something can behave determinately, randomly, or indeterminately. Say it behaves determinately if it acts with total, 100% order; say it behaves randomly if it behaves with absolutely no order; say it behaves indeterminately if it behaves not with total, 100% order, but also not with absolutely no order—so with only some order.

    If radioactive decay or quantum-level events were completely random, I think that might, possibly, imply acausality and inexplicability.

    They're not, however, completely random. If either were completely random, one would not be able to give any sort of explanation; they would be random. But, for example, given sufficiently large numbers of cases at the quantum level, one can give arithmetically certain probabilistic explanations of what will happen. So, at most, such events are indeterminate but not random, and operate with at least some order. Since quantum-level events operate indeterminately and not randomly, causation is still a possibility. Since one can give probabilistic explanations[1] of such events, it also seems unlikely that they're inexplicable.

    Oh, and for whatever it's worth, since scientists working in quantum physics spend their work lives trying to explain the quantum world, I suspect they would agree that explanations can be provided for events in the quantum world.

    It may also be worth reading this article. In it, Ed points out that when scientists theorize about radioactive decay or quantum mechanics, they're explaining what happens, not whether or not there are causes for what happens.

    Is there a problem with using the 'watered-down', inductive version of the PSR?

    As for your question, I sort of already replied in my post of May 29, 2015 at 10:08 AM. If—as I argued—it's incoherent to admit brute facts because it would make it such that no one could have any justification for trusting the evidence of our sensory perception or the possibility of rational inquiry, then no matter where the PSR denier wants to admit brute facts (even if it's outside of his or his colleagues' experience), it's still going to be incoherent. So, it doesn't matter how much your interlocutors wave their hands about it, if they were to ever admit brute facts anywhere, in any case, they could never be justified in trusting even their belief that there are brute facts. And if there are no brute facts, the PSR holds.

    Maybe I should push it further. By the same logic as the earlier post, if it's even possible there are brute facts, it undermines any justification the PSR denier could have for trusting the evidence of their sensory perception.


    [1]Not that it's needed, but I think the scholastic can give further detail to the probabilistic or indeterministic explanations in terms of the natures of the fields or particles involved.

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  19. Is there a problem with using the 'watered-down', inductive version of the PSR?

    I should probably be explicit. Since such people would have to be able to hold that they could rationally arrive at the conclusion that the PSR is false (hence the uncertainty), not to mention at the very least hold that it's possibly false: yes, there is a problem.

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  20. @John West:

    If radioactive decay or quantum-level events were completely random, I think that might, possibly, imply acausality and inexplicability.

    This is an interesting question. I think I'll play devil's[?] advocate and suggest that, at least according to A-T, it wouldn't.

    Here's why. On the A-T view, "events" are ultimately (within the order of secondary causation; "penultimately" if we count God) the activity/behavior of substances or entities. In that case every event has a cause (or set of causes); it just may not operate deterministically. And the explanation of the event would lie in the nature of the substances/entities that caused it, even if it were their nature to behave "randomly."

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  21. Of course that raises the question whether the nature of a substance/entity could be such that it would, by that nature, behave "randomly." Could truly random behavior (whatever that might mean) genuinely arise from the "nature" of anything? Or does the very idea of a "nature" rule out (some kinds of) randomness? If something did behave "randomly," would we therefore deny that it was really the "cause" of its behavior?

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  22. Could truly random behavior (whatever that might mean) genuinely arise from the "nature" of anything?

    I'm going to say no. It may be precisely because the natures of quantum particles "constrain" what they can or will do that, given sufficiently large numbers of such particles, we're able to give indeterministic explanations and predictions.

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  23. @John West:

    I'm going to say no.

    And I'm going to tentatively* agree. I have further thoughts but let's see who else wants to weigh in.

    ----

    * The placement of that adverb is deliberate. I don't regard the so-called "split infinitive" as a grammatical error.

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  24. Skyliner (if you're still here (and even if you're not)),

    For my own part, I find an especial degree of affinity with the positions of Nicholas Lombardo (whose summary of Aquinas emphasizes the teleological nature of emotion), Robert C. Roberts (who, within the context of a virtue ethics position, defines emotions as "concern-based construals," with the genuinely virtuous person being the one who construes and feels rightly), and Mark R. Wynn (who, amongst other things, argues that there are certain dimensions of reality that cannot be known apart from emotion).

    Though I haven't looked up either Roberts or Wynn just yet, and may not at all, I have looked up Lombardo, and the following is from his _The Logic of Desire_ (pp 41-2):

    - "Aquinas does not hold that the fundamental orientation of the passions toward human flourishing implies that each and every movement of the sense appetite reliably directs us toward our proper telos."

    Good thing, too.

    - "The passions require the guidance of reason, especially in our fallen condition. Paradoxically, however, even when the passions prompt us to act in ways that we ultimately judge inappropriate, in the essential structure, the passions still serve the attainment of our telos."

    I don't see the paradox to which Lombardo refers. I do see what Lombardo refers to; it's just that I don't see it as involving a paradox.

    Of course, if one thinks of the things involved as occurring on a single level, then I suppose one might be tempted to see something which might look paradoxical. But the things involved are not occurring on a single level. And, in fact, at least two levels are involved.

    To better see what I'm getting at, consider the following from St. Thomas (ST II-I 8.1): "[I]n order that the will tend to anything, it is requisite, not that this be good in very truth, but that it be apprehended as good."

    IOW, the will, on one level, apprehends something as good without regard for whether it actually is good in and of itself.

    Whether that something actually is good in and of itself is another matter, and one for the reason, on another level, to judge.

    And no paradox is involved if it should happen that something which at first seems good to the will, subsequently turns out not to be actually good according to the reason.

    Similar thing regarding the passions in general.

    Given this 'levels' perspective, it seems that the reason is higher and the passions lower. And that the reason seems higher and the passions lower may lead one to think of the reason as being superior and the passions as inferior. But an objection already has been made, in a comment under a prior post, to this view of 'affectivity' in relation to reason. Objection noted.

    However, and though I don't think it is wrong to do so, it isn't absolutely necessary to view the matter in terms of levels, let alone in terms of a superior level and an inferior level. It can, instead, be viewed in terms of 'passes'. (Although, and admittedly, this is a soft way of couching the 'levels' perspective.)

    From the 'passes' perspective, one question is first addressed by the passions, and then another question is next addressed by the reason. Thus the passions, on a first pass, address the more general question: "Does this something seem to be good?" And the reason, on a second pass, answers the more specific question: "Is this something actually good?" The passions might answer the question which is its concern with "Yes," and the reason might answer the question which is its concern with, "No." But that the reason answers, "No," when the passions answer, "Yes," in no way is indicative of something paradoxical going on. The passions address and answer one question, and the reason another.

    (cont)

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  25. - "The passions require the guidance of reason in order to become virtuous, and thus fully conducive to human flourishing, but virtue also requires the passions. Without the passions, we should not respond to sensible objects, and without this first step toward engaging the world, human flourishing would not be possible."

    Yes, of course.

    Figuring as much, however, doesn't first require a perspicacious ferreting out or excavation of arcana from the writings of St. Thomas. Indeed, it follows from something which may be said to come under the heading of 'Aquinas 101':

    "Although the intellect is superior to the senses, nevertheless in a manner it receives from the senses, and its first and principal objects are founded in sensible things." ST I 84.8.1

    - "The function of the passions is not to decide upon a course of action; the function of the passions is to respond to stimuli and prompt the human person to act according to the face value of those stimuli. Then the passions defer to the judgment of reason, because only the rational appetite can command human action, and because the sense appetite naturally tends toward conformity with reason."

    Needless to say, what the sense appetite naturally tends toward and where it actually goes are not necessarily always consonant. St. Thomas has noted (in ST I 49.3.5) that, "[M]ore men seek good in regard to the senses than good according to reason." If he's right about that, then I suggest that it is better to be a human being acting as an actual human being than to be a human being acting as a kind of apocryphal lemming.

    - - - - -

    o [T]rue longing for the world of the objective need not lead away from the world of the personal; rather, it ought to lead into this world. To lose sight of the dignity and nobility of ratio, its classically formative power, and its illuminating fullness, simply because the rationalist intellect of the Enlightenment thinkers was flat and uninspired, would make for a lamentable misunderstanding. -- von Hildebrand, The Struggle for the Person

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  26. Say hey, Glenn,

    Just wanted to acknowledge your post. I largely agree with the substance of it (with regard to "passes," have you read the section in Lombardo yet on reason's "democratic rule" over the passions? I suspect you'd like it.). Also, I loved the Hilderbrand quote.

    That said, I can't right now spend a lot of time interacting on these threads. Today, pretty wifey had to return to work after (a blissful) four months maternity leave, which means I'm playing Mr. Mom during the day and having to dedicate whatever time is left over to my dissertation. Affectivity is a central topic in it; perhaps when I'm done with the chapters dealing with it, I can return and try to find a way to email them to you? I've really found your (and others') comments helpful.

    Also, as a side note, the Wynn guy has a chapter in the book about which Ed just posted--he has, I think, the chapter on faith . . .

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  27. One other thing:

    Can anyone here provide a reference for a place wherein Aquinas (or any major figure in the scholastic tradition from Augustine onward) attempts a definition of 'reason?'

    Many thanks!

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  28. Scott,

    And I'm going to tentatively* agree. I have further thoughts but let's see who else wants to weigh in.

    Well, I'm still interested.

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  29. Scott: And I'm going to tentatively* agree. I have further thoughts but let's see who else wants to weigh in.

    I'd agree with your agreement that "truly random" behaviour couldn't arise from any nature. After all, "random" means "uncorrelated". ("Uncorrelated to what?" you ask. Exactly! Uncorrelated to something. "Random" means "random only with respect to some thing or other".) Having behaviour that is unrelated to some other thing seems uninterestingly possible. So it we are presumably asking whether something could by its nature behave in a way that had nothing to do with its nature.

    (Of course, what physicists mean in that sort of context is whether the behaviour of some particle is correlated to any of the things physicists care about, mainly how to compute precise specific predictions. Deciding that because nature doesn't conveniently act just the way physicists would wish therefore causality is out the window seems a badly overreacting case of tipping over the game board.)

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  30. Skyliner,

    No, haven't yet come across Lombardo's mention of reason's "democratic rule" (over the passions). Re the chapters, I probably could find or make the time to read them, but I can't guaranty the same re commenting on them.

    Best wishes for the new born, and those entrusted with his/her care.

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  31. Skyliner,

    One Scholastic definition of reasoning I've come across is as follows: "the act of the mind by which the convenience or disconvenience of two ideas is inferred by the proportion (conformity / di[s]formity) which they have to a third notion."

    Presumably, then, reason would be the faculty or function of mind with which that act is engaged in.

    Also, I finally got around to cracking open Blanshard's Reason and Analysis. Right there, on the first page of Chapter I:

    "Since this is a book in defence of reason, we may well begin by saying, at least provisionally, what 'reason' means.

    "Unfortunately, it means many things... Reason in the widest sense of all, says Thomas Whittaker, is 'the relational element in intelligence, in distinction from the element of content, sensational or emotional,' and he points out that both the Greek term λογος and the Latin ratio, from which 'reason' has largely drawn its meaning, were sometimes used to denote simply 'relation' or 'order'."

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  32. @John West and Mr. Green:

    Yeah, Mr. Green's comments pretty much capture my own further thoughts on the point. I'll just add that I take a basically subjectivist view of probability myself and regard it as essentially a measure of ignorance.

    @Glenn:

    Ahhh, it does my heart good to know someone is reading Blanshard. I've come to disagree with him on some issues (including, relevantly to the previous point, determinism) but every word he ever wrote is worth reading.

    @Skyliner:

    Me too on the best wishes for the wee one and his/her caretakers.

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  33. Scott (and less directly, Mr. Green),

    Yeah, Mr. Green's comments pretty much capture my own further thoughts on the point. I'll just add that I take a basically subjectivist view of probability myself and regard it as essentially a measure of ignorance.

    This seems the intuitive view of probability to me too, but I've always thought of it in terms of all-causation-as-necessitation. Given contingent causation, I'm wondering if this view works in cases of contingent causes and effects.

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  34. @John West:

    This seems the intuitive view of probability to me too, but I've always thought of it in terms of all-causation-as-necessitation.

    So have I until fairly recently. But I don't see why it would fail for contingent causation. Doesn't it seem at first look that contingency is, if anything, a better fit with "randomness" than necessity is?

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  35. In retrospect I think I should spell that last point out a bit more. What I have in mind is something like this: if there's such a thing as contingent causation (as I've come to think there is), then a cause that contingently brings about its effects would seem to be a better candidate for "randomness" (and for probability as a measure of ignorance) than one that does so by necessity. A cause that operates by necessity should always produce the same result (right?), but a cause that operates contingently might sometimes produce varying results and thereby engender more "ignorance"/doubt about its effect.

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  36. Scott,

    So have I until fairly recently. But I don't see why it would fail for contingent causation. Doesn't it seem at first look that contingency is, if anything, a better fit with "randomness" than necessity is?

    Well, maybe I understand the view wrong.

    A cause that operates by necessity should always produce the same result (right?)

    I take it the view is that a cause that operates by necessity does always produce the same result, and that one uses probabilities as a measure of one's uncertainty concerning what that result will be (when we're ignorant of what it will be). If, in contrast, contingent causes actually are to some degree "random", then it would seem that one's probabilities are no longer measures of uncertainty, but rather genuine attempts to model what might or might not happen.

    I think I do agree that contingent causation is more “random”, but it's just that I'm not sure that what one would be doing when applying probabilities to a contingent cause is the same as what one would be doing when applying probabilities to necessitating causes.

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  37. edit: "... to model [the actual likelihood of] what might or what might not happen."

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  38. @John West:

    I think I do agree that contingent causation is more “random”, but it's just that I'm not sure that what one would be doing when applying probabilities to a contingent cause is the same as what one would be doing when applying probabilities to necessitating causes.

    Hmm, yeah, I see your point. Well, I'll probably have to let that percolate a bit before I know what I think.

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  39. Consider two people bouncing on a trampoline – both get equal energy/bounce just so long as they stay in time. A bit out of synchronization and one gets most of the energy, the other looses much or all of their bounce. While each interaction represents a necessary cause, the complex interactions are tough to keep track of and often appear chaotic. Nuclear decay is likely no different in principal. The ‘strong’ force holding things together falls off quickly with distance so the occasional extra high bounce, resulting from necessary but individually unknown interactions, and that piece flies off as decay.

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  40. Vasco Gama wrote:
    While propositions like “2+2=4” are true in any possible and imaginary universe. They are true by definition, as what we mean by 4 is that is the character that represents adding 2 and 2 (or 3 and 1, or …). So one says that “2+2=4” is true “a priori” (i.e. not dependent from verification from experience).

    The proofs of the existence of God are “a posteriori” proofs, which means that the proof depends from the experience (in this case our knowledge of reality).


    Yes, for example the versions of the first cause argument that I know of depend on the observation that there is a universe, and so they don't show that God is a necessary being that must exist in all logically possible worlds (including the one where there is 'nothing rather than something', at least in the sense that nothing exists physically and there are no non-necessary mental beings, though a mathematical platonist would argue that mathematical propositions would still be true or false in this world). The ontological argument is the only one I know of that tries to show God is a necessary being that must exist in all possible worlds, even one with no physical universe and no non-necessary mental beings--and many, including Aquinas, have not found this argument convincing. There are some variants on Anselm's original argument like Plantinga's modal ontological argument, but I think those thinkers who find fault with one would tend to find similar faults with other variants.

    So those here who think God's existence can be proven rationally, do you think it can be proven rationally that God is a necessary being in the same way the truths of mathematics are necessary a priori, or do you just think his existence can be derived logically from some combination of metaphysical truths and a posteriori empirical observations about our world? I wonder if for example some would apply some variant first cause argument to the necessary truths of mathematics themselves--perhaps some would say the diverse truths of math require a single unified context that they all "come from", even if they do not have an origin in time, and that this unified context must be mind-like to perceive each mathematical truth's relation to the rest of mathematics and to understand each one's meaning. So God would be necessary as the perceiver of mathematics in all its infinite complexity, even though God could not be said to have freely created mathematics (mathematical forms would be more like necessary eternal ideas in the eternal mind of God).

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  46. @John West:
    Concerning proofs for God's necessary existence, you ought to check out PSR cosmological arguments and the First Way. Neither of them require a universe except in the weakest possible sense (ie. even if only oneself exists, they can work; and if one isn't willing to affirm even one's own existence, then there are deeper problems).

    It's not that I'm unwilling to affirm my own existence in the real world, it's that unless it can be proven otherwise, it seems as though there should be a possible world where no physical or contingent mental beings exist, and I want to know if it's possible to prove God's existence in that possible world (anyone who believes God created as an act of free will, and had the ability not to create at all, should agree such a world is possible, although of course there are other views of God which make the existence of a universe inevitable, like the view of Spinoza and I think of the Neo-Platonists). If one can't prove God would exist given the premise of that possible world, I don't see how the proof could demonstrate that God's existence is "necessary", since to say that a proposition is "necessarily true" can be taken to be synonymous with "is true in all possible worlds". A proof that God's existence follows from my own existence might establish that in any world where I (or any other contingent being) exists, God must necessarily exist in that world too, but it wouldn't prove God's existence is necessary in all possible worlds.

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  50. @John West:
    As I wrote, you only need to prove that a necessary being exists given the premises in one possible world (PW).

    Is it possible to prove a necessary truth from a contingent one? I don't have detailed knowledge of modal logic, which formalizes the notion of logical reasoning involving possibility and necessity, but intuitively I would doubt it's possible to come up with any proof that starts from a set of premises that include three of the form 1. "It is possible P is true", 2. "It is possible that P is false", and 3. "P is true", and arrives at some conclusion of the form "it is necessary that Q is true" in such a way that premise 3 played an essential role in reaching that conclusion--i.e. if we kept all the premises except for 3 the same (and there could be others besides those 3, such as premises that formalize certain claims about causality and existence), but changed premise 3 to "P is false", then there would not be any way to prove from this new set of premises that "it is necessary that Q is true". Would you claim the proof of God you're talking about could be put into formal logic terms, and if so that it would in fact work in the way I described above, where a necessary truth is only provable given that a contingent proposition is true rather than false?

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  54. "If you're looking for an example of what I was talking about, I've given a specific argument right above your post (I'm just going to assume you didn't notice it before writing your previous post)."

    Well, I wanted to zoom out and ask what you think about the more general question of mathematical logic I asked, since that's something that could presumably be proved one way or another in a mathematical way that wouldn't require thinking about the commonsense or intuitive meaning of various terms (something like the outline of a formalization of Godel's version of the ontological argument shown at the end of this article). In the case of your specific argument, trying to formalize it might show subtle problems that aren't apparent in the verbal formulation. For example, the verbal formulation doesn't distinguish between relative and absolute notions of contingency whereas modal logic allows for facts to be contingent relative to particular sets of possible worlds that don't exhaust all logically possible worlds (see p. 9 of this pdf). So, you might have a purely mathematical set of possible worlds where every property of the set as a whole followed necessarily from the mathematical definition, but certain facts could be contingent relative to the members of the set (in that they are true in some members but not others).

    I suspect that while the principle of sufficient reason is compatible with this relative notion of contingent facts, it probably would be logically incompatible with the notion that there are any facts which are contingent in the ultimate sense (contingent relative to the set of all logically possible worlds). So I think a modal logic formalized version of the PSR would be found to imply a Spinoza-like view where all truths are ultimately necessary truths--but again that's just a hunch. We can't really settle these questions until one of us learns enough modal logic to prove or disprove them mathematically (or at least learns enough to put them in a form we could ask a logician to assess), but my point is that it's not trivially obvious that they type of proof you're talking about would even be logically coherent, even before we get to philosophical questions about the validity of particular premises like the PSR.

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  59. "Incidentally, since you mentioned Plantinga's argument, letting → be the conditional (if/then), M be the possibility operator and L be the necessity operator, he makes use of the S5 claim that MLp → Lp. So, Plantinga's modal argument actually does argue from possible necessity (in the PW senses) to necessity."

    I don't understand the details, but I've seen the objection that Plantinga uses incompatible systems of modal logic in his proof--see here and here (although I don't understand the technical details about S5 vs. other modal logic systems, the point in the second link about a mathematician who says "it's possible the Goldbach conjecture is necessarily true", and uses a Plantinga-style argument to 'prove' it must therefore be necessarily true, seems like a good one).

    "Look, Jesse, if you want me to formalize the argument and write a derivation or a proof tree to show it's valid, just ask."

    If you'd be willing to do that it'd be much appreciated, and if you came up with a valid proof that would presumably settle the question I asked you earlier by providing a counter-example to my hunch about it not being possible to derive necessary truths from contingent ones that are possibly true and possibly false. I would need to spend some time reading up on modal logic before I would be even potentially able to evaluate it (or at least understand enough to formulate well-defined questions for the folks at the math stack exchange), but that is a subject I'd like to do some self-study on so I could save your proof and use it as a motivation to work on it. Also, do you have any thoughts on the argument against Plantinga's proof above, and if the critique points to even a potential problem with his proof, can you formulate whatever proof you give in a way that avoids such criticisms by specifying the particular system of modal logic you're using, and avoids any assumptions incompatible with that specific system?

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  61. I recommend Rod Girle's Philosophy and Modal Logics for a primer (and don't buy Kenneth Konyndyk's book.) For something more thorough, I recommend Hughes and Cresswell's A New Introduction to Modal Logic.

    Thanks for the recommendations, I'll pick up A New Introduction, and take a look at the first one if I feel like I need a more philosophical introduction.

    I'm not sure why you keep mentioning this. To be clear, no one's claiming that necessary truths are being derived entirely from contingent truths

    I didn't say that either, I just said that at least one contingent truth was essential to the proof. Note where I said "I would doubt it's possible to come up with any proof that starts from a set of premises that include three of the form...", and a little later in the same comment, "there could be others besides those 3"...the other premises 4 through N could be anything, including necessary truths. The idea is just that no matter how many premises we start with, if we can use them to prove a necessary truth, but can no longer prove that same necessary truth if all but one of the N premises are kept the same while a single premise about a contingent truth (premise 3 in my outline) is changed, then that's what I mean by "derive necessary truths from contingent ones", and that's what I am skeptical would be possible. I should add that I was assuming that the complete inference rules for deriving one type of truth from another are given by the modal logic system itself, one isn't allowed to just add an arbitrary premise of the form "if P is possibly true and possibly false, then P true implies the necessary truth of Q". If I'm wrong about that assumption, then obviously my hunch about this type of proof being logically invalid is trivially false, and I would have to criticize not the logic but just the real-world truth of the premises.

    Sure. Should be valid in a predicate logic with T axioms. I'll scratch something out in the morning.

    Great. If I want to contact you about it sometime later when I've had a chance to read up a bit on modal logic, is it OK if I use the google+ link in your name?

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  67. @John West:
    As I wrote once before, I think you're conflating how we know something is true with whether or not it's true. If one can prove a being exists that exists in every possible world (PW) based on premises contingently true in one world, w, then I don't see that it matters whether we're able to prove the same conclusion based on premises contingently true in another world, s (or not, due to the lack thereof).

    I agree with your second sentence, my point was just that I was skeptical that the "If" in "If one can prove a being exists that exists in every possible world (PW) based on premises contingently true in one world" was actually possible in the first place. I suppose this skepticism comes from the fact that, outside of theological arguments, I can't think of any examples where a contingent fact plays an essential role in proving a necessary one--obviously there are no mathematical proofs that require using contingent facts about the world as premises, for example.

    And thanks again for writing out a formal proof. It seems like the possibility that hadn't occurred to me until my last comment, where I wrote the following, does apply in this case:

    I should add that I was assuming that the complete inference rules for deriving one type of truth from another are given by the modal logic system itself, one isn't allowed to just add an arbitrary premise of the form "if P is possibly true and possibly false, then P true implies the necessary truth of Q". If I'm wrong about that assumption, then obviously my hunch about this type of proof being logically invalid is trivially false, and I would have to criticize not the logic but just the real-world truth of the premises.

    Your premise 3 says from the outset that if a certain contingent proposition a has property G, this establishes the existence of a necessary entity. If that's a logically valid move (you expressed some uncertainty about the use of existential qualifiers in modal arguments above, presumably some logic textbook would lay out the complete rules for T and settle whether this is allowed?), then of course my hunch is pretty trivially wrong. In fact one could come up with an even simpler proof that invalidates the hunch, and which doesn't require the existential quantifier, just two arbitrary properties P and Q and two objects a and b, and the following 4 starting premises:

    1. M(Pa)
    2. M(~Pa)
    3. Pa
    4. Pa → L(Qb)

    From these, it's obvious the contingent fact that Pa is true implies the necessary truth of Qb, but if you kept premises 1,2,4 the same but changed 3 to ~Pa, then it would no longer be possible to prove Qb was necessarily true.

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  68. Reply to John West, continued:
    Just a conceptual question about the meaning of the → and L symbols here though--is it possible in T to express each of the following distinct English statements formally using these symbols?

    --"The fact that a has property P in this world necessitates that b has property Q in this world, though there may be other possible worlds where a has property P but b does not have property Q."
    --"In any world where a has property P, it must be true that b has property Q in that world, though there may be other possible worlds where a does not have property P and b does not have property Q."
    --"The fact that a has property P in this world means it is necessarily true in all possible worlds that b has property Q, including worlds where a does not have property P."

    Offhand it seems like Pa → L(Qb) could be interpreted to mean either the second or the third statement, and Pa → Qb could be interpreted to mean either the first or the second, but presumably there is a single generally-accepted interpretation of the meaning of these symbols.

    But assuming Pa → L(Qb) means the third, and that this is definitely an allowable proposition in T, then my hunch was wrong. In this case, my argument against the proof based on the PSR has to be with the truth of your third premise saying that the PSR implies the set of all contingent truths must be explained in terms of a necessary truth. I think my basic problem with this is that it seems to run contrary to how I would naturally interpret the word "explanation" in this context. If we have two propositions Pa and Qb (which could obviously be arbitrarily complicated, for example Pa might tell us the complete physical state of the universe at some time along with the laws of physics governing its time-evolution), it seems to me that in order for Qb to be fully "explained" by Pa, it must be true that an ideal reasoner could deduce Qb with complete certainty from the truth of Pa. If not--if Pa is logically compatible with both Qb and ~Qb--then at best Pa can only count as a partial explanation of Qb (making Qb much more probable than ~Qb, for example). And if that's the case, then if Pa is necessarily true, then isn't anything that an ideal reasoner can deduce with complete certainty from a necessary truth also a necessary truth? This would argument would imply either that the PSR must be false (perhaps there are genuinely random events), or that the PSR is true but is incompatible with the notion that there are any "contingent truths" whatsoever, so in fact all truths are necessary ones (this was Spinoza's view, and I think it would also be the view of those mathematical Platonists like Max Tegmark who believe all mathematical form necessarily exist, and that our universe is just a very complicated Platonic mathematical form).

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  74. @John West:
    I've already replied to this a couple times, so I'm going to leave this part alone.

    As far as I can see your comments on it have been based on misunderstandings of what I was saying (both "no one's claiming that necessary truths are being derived entirely from contingent truths", and "I think you're conflating how we know something is true with whether or not it's true"), to which I responded by clarifying what I had actually meant. You haven't yet told me whether you agree or disagree with what I actually meant when I said I had the hunch that a contingent truth can't play an essential role in proving a necessary truth. I would guess that if you did, your answer would be that this hunch is indeed wrong, and that you would agree the premises 1-4 below are allowable ones in predicate logic + T and together imply the necessary truth L(Qb) (whereas if premise 3 was changed to ~Pa there would be no way to prove L(Qb)), but it would help me feel secure in my understanding if you'd confirm that.

    1. M(Pa)
    2. M(~Pa)
    3. Pa
    4. Pa → L(Qb)

    I don't think so, sorry. These issues concerning existence and modality are still being sorted out, and T doesn't really have anything to say about the matter either way. This is part of the reason I mentioned the unfortunate, ruined state of my modal ontology.

    I would have thought that a logical system could be treated as a formal system, where there is a precise set of rules for which strings of symbols qualify as well-formed formulas (WFFs), and also precise inference rules for generating new WFFs from previous ones, all of which could be evaluated by a computer program with no understanding of what the symbols are supposed to "mean" in conceptual terms. I know that's true of first-order predicate logic since I used such a program when learning about it to evaluate formal proofs, are you saying the same isn't true for the "predicate logic with T axioms" that you referred to?

    Following the usual standards, the correct translation of what I wrote should be “In every possible world there exists some x such that, in every possible world, x is a real being.” Not too sure about what you wrote.

    That seems to be a translation of the part after the implication symbol, but it isn't a translation the full statement Ga → L(∃x)L(Hx). My question in the part you're responding to above was specifically about the meaning of putting a statement about necessity after the "→" symbol. Are you not sure about what I wrote because you found it unclear, or because you understand what I'm asking but don't know what the standard accepted answer would be? If you found it unclear, I can give an example which hopefully will make it more clear--if m is a man, and B is the property of being a bachelor, and N is the property of having no living spouse, then we know that in every possible worlds where Bm is true, by necessity it must also be true that Nm is true. Would it be acceptable to express this as Bm → L(Nm), or would that be saying that if m is a bachelor in one world, m must lack a living spouse in all possible worlds?

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  75. Reply to John West, continued:
    I don't see the purpose of your comment about explanation. I take it an explanation is full (but not ultimate) provided it doesn't let a puzzling aspect of the explanandum disappear, and anything puzzling in the explanandum is either also found in the explanans or explained by the explanans.

    I'm not sure what you mean by "puzzling aspect". Can you tell me if you agree or disagree that for proposition #1 to count as a "full explanation" of proposition #2, an ideal reasoner should be able to be certain of the truth of P2 given P1, i.e. in terms of predicate logic P1 → P2? In the most general sense, the "puzzling aspect" of any observed fact is why it is true rather than false, so if I have a P1 that is compatible with both P2 and ~P2, I don't see how P1 can be said to have explained the puzzle of why P2 is true rather than false.

    If you want to try quibbling with the logic, then you're welcome to continue trying to do so. But it seems to me that, if you're going to do that (if you insist), you would be better served trying to do so after you've actually studied the logic.

    If by "quibbling with the logic" you mean trying to show that the logic is incorrect, I'm not doing that. I granted that my initial hunch about modal logic was probably wrong, and asked you a few questions to make sure I was understanding your argument correctly. If I am, then my only quibble is about whether some of your premises make sense philosophically, a question that is not a matter of logic at all (since logic doesn't tell us whether any premise is true or false in reality, just whether there is a logically valid way to derive a given conclusion from a given set of premises).

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  85. As for the second quote, you responded and then proceeded to make what seems to be the same error.

    How do you figure? My response was to say I agreed with your statement "If one can prove a being exists that exists in every possible world (PW) based on premises contingently true in one world, w, then I don't see that it matters whether we're able to prove the same conclusion based on premises contingently true in another world, s (or not, due to the lack thereof)."

    In other words, if q is a statement asserting the existence of such a being, and p is some contingent statement, I would always have agreed that if p is true in our world, and if the premise p → L(q) is also true, then q must be true in every possible world. My original doubt was just over whether p → L(q) is even an allowable premise in modal logic if p is contingent, since I can't conceive of any non-theological examples where one can use a contingently-true statement to derive a necessary conclusion. But I've since learned that this is an allowable premise in modal logic, so my original idea was mistaken. Nevertheless, it wasn't mistaken for the specific reason you accused me of, that I was "conflating how we know something is true with whether or not it's true", since I would always have agreed that if p → L(q) is allowable in modal logic, then if p is true in our world q must be true in every possible world, even in a possible world where p is not true and therefore inhabitants of that world might have any way to "know" q is true.

    You haven't yet told me whether you agree or disagree with what I actually meant when I said I had the hunch that a contingent truth can't play an essential role in proving a necessary truth. I would guess that if you did, your answer would be that this hunch is indeed wrong, and that you would agree the premises 1-4 below are allowable ones in predicate logic + T and together imply the necessary truth L(Qb) (whereas if premise 3 was changed to ~Pa there would be no way to prove L(Qb)), but it would help me feel secure in my understanding if you'd confirm that.

    I haven't answered your argument because it attacks a straw man.

    It wasn't attacking anything, it was trying to get your opinion on the issue because at the time I had a hunch this wasn't possible, but I was open to correction (I am certainly willing to accept your expertise on modal logic issues, and in fact step 3 of your proof was what convinced me my original hunch must have been wrong, I said so immediately after you posted it). In general I find that discussions go more smoothly if each person assumes the other is a sincere reasoner and answers questions they ask, instead of trying to anticipate the rhetorical strategy behind the question and preemptively cut it off without addressing the original question. If it helps, none of my questions about logic are intended as a lead-in to any attempt to tear down the logic of your proof (though I'll take your word for it if you say there is some issue with the use of the existential quantifier)--the only remaining criticism I have of the PSR argument is an extra-logical one about the philosophical interpretation of what it means for one proposition to count as the "explanation" for another, I'll develop that criticism in another comment.

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  86. I would have thought that a logical system could be treated as a formal system, where there is a precise set of rules for which strings of symbols qualify as well-formed formulas (WFFs), and also precise inference rules for generating new WFFs from previous ones, all of which could be evaluated by a computer program with no understanding of what the symbols are supposed to "mean" in conceptual terms. I know that's true of first-order predicate logic since I used such a program when learning about it to evaluate formal proofs, are you saying the same isn't true for the "predicate logic with T axioms" that you referred to?

    Right (first-order predicate logic even has a decision procedure), and two of the problems with the existential quantifier I mentioned are still problems in first-order logic that seeks to use ∃x as an existential quantifier (Aristotelians would use it as a particular quantifier with no existential import.) So yeah, that's right. I don't think you could use that system to evaluate predicate logic with T axioms that uses ∃x as an existential quantifier.

    Assuming "first-order predicate logic + T axioms" is sufficiently precise to specify a formal system, are you saying that if p is some proposition from first-order predicate logic that uses ∃x, then a proposition q that includes Lp could not be a well-formed formula in this system? If it could be a WFF then one could presumably derive other propositions from q using the rules of inference, in which case I'm not clear on what problem you're pointing to above--maybe that one of the later propositions in your proof couldn't be derived from earlier ones using the axioms/rules of inference? Or are you pointing to an issue not at the level of the formalism but at the level of interpretation?

    That seems to be a translation of the part after the implication symbol, but it isn't a translation the full statement Ga → L(∃x)L(Hx). My question in the part you're responding to above was specifically about the meaning of putting a statement about necessity after the "→" symbol. Are you not sure about what I wrote because you found it unclear, or because you understand what I'm asking but don't know what the standard accepted answer would be?

    Don't poison the well. Is it really difficult for you to read the statement I actually wrote instead of some blatantly misleading straw man

    What straw man? I didn't say anything about your own views in the statement above! Again it seems as if you are trying to anticipate my rhetorical strategy, but I'm not sure what avenue of attack you imagine I was taking just by asking the questions above.

    Yes, “If the BCCF has an explanation, then in every possible world (there exists some x such that, (in every possible world, (x is a real being))).”

    OK, thanks. That's really all I was asking, I just wasn't sure about the interpretation of the → symbol in modal logic in terms of possible worlds.

    If “Ga → L(∃x)L(Hx)” is invalid then you should have no problem using it to derive a contradiction.

    I never suggested it was logically invalid, nor did I ask the question as a lead-in to a future argument suggesting it was.

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  87. Are you not sure about what I wrote because you found it unclear, or because you understand what I'm asking but don't know what the standard accepted answer would be? If you found it unclear, I can give an example which hopefully will make it more clear--if m is a man, and B is the property of being a bachelor, and N is the property of having no living spouse, then we know that in every possible worlds where Bm is true, by necessity it must also be true that Nm is true. Would it be acceptable to express this as Bm → L(Nm),

    But Bm → L(Nm) isn't the statement I'm making (it isn't even logically equivalent to it). That would be (Ga → L(Ha)) and closer to (Ga → L(Hx)), but either way not (Ga → L(∃x)L(Hx)).

    I wasn't asking the question with the intention of suggesting your statement was equivalent to it, again I was just trying to clarify the general question I had about the interpretation of → in modal logic, because it was relevant to making sure I had the correct interpretation of Ga → L(∃x)L(Hx). If it helps in understanding what I was confused about this, a couple days ago I put this as a question on the "philosophy stack exchange" website, and the answer I got in terms of Kripke semantics of possible worlds completely settled it for me--you can see the question and answer here.

    I don't think there is a problem with "4. Pa → L(Qb)" in predicate+T (at least, I can't think of one), but it might also run into further issues with de re modality. For instance, apart from the property "x is a real being", "4. Pa → L(Qb)" one might take a more mundane predicate like "Barrack Obama is a human" as a statement that, in every world where Barrack Obama exists, Barrack Obama is a human.

    Thanks. One of the comments I got on my philosophy stack exchange question was that if you wanted to express the idea that in every world where p was true, q must also be true, you could express it as L(p → q), which has a different meaning than p → Lq.

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  88. OK, now I'll try to develop my critique of the PSR argument based on what seems to me that natural meaning of "explanation". I wrote:

    Can you tell me if you agree or disagree that for proposition #1 to count as a "full explanation" of proposition #2, an ideal reasoner should be able to be certain of the truth of P2 given P1, i.e. in terms of predicate logic P1 → P2?

    You replied:

    If everything in the explanans is true, an ideal reasoner with perfect knowledge of the explanans should be able to know the explanandum from the explanans.

    OK. It also seems to me that since we are referring to an ideal reasoner here, there should be some notion that that the explanandum can be deduced from the explanans in some kind of logical way. Though since it's an "ideal" reasoner, we should expand the notion of logical deduction to include non-computable forms of logical deduction--for example, if an ideal reasoner wanted to deduce the truth of the Goldbach conjecture from the Peano axioms of arithmetic, then even if there is no finite proof of the Golbach conjecture from the Peano axioms (mathematicians haven't found one yet), an ideal reasoner could just check that for every integer, there is a true proposition asserting that this particular integer is the sum of two particular odd primes (and any such proposition about individual integers would be provable with the Peano axioms). Once the idea reasoner had checked all the infinite cases and seen that each one checked out, they could then judge the Goldbach conjecture to be implied logically be the Peano axioms, even if it wasn't provable in a finite way from them.

    So what I'm pointing to here is an expanded notion of logical deduction, which allows for both forms of logical proof that involve evaluating an infinite number of cases direction to check propositions with a "for all" in them, and also allows for individual propositions which are formed out of an infinite set of finite propositions joined by ANDs (which your BCCF, the proposition asserting all contingent truths, might have to be). I think this is just what mathematicians refer to as an infinitary logic. In ordinary finitary logic, the turnstile symbol (which I will write here as |— ) can be used to denote the idea that one proposition can be derived from another in a formal logical system. I'm not sure if the p |— q is also used to denote that there is an infinitary logic proof of q from p, but I'll assume it is here (if it's not, just substitute some new symbol to denote the idea that "q is deducible from p using either finite logic or infinitary logic").

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  89. (argument about "explanation" continued)
    With that issue out of the way, my claim about explanations for an ideal reasoner can be stated this way: "if p is a full explanation of the proposition q for an ideal reasoner, and q is some contingent proposition which is true in our world, it must be the case EITHER that q is deducible from p in some purely logical way, i.e. p |- q, OR that the explanation is relying some unstated background facts which are true in our world, such that if all these background facts were written explicitly and combined into a proposition b, then (p & b) |- q." I'm basing the latter part just on our ordinary understanding of what it means to "explain" something, where if one person wants to explain some fact to another person, it's common to leave out all sorts of background assumptions which both people can be expected to know. For example, if I wanted to explain to someone why Francois, who currently lives in France, is a U.S. citizen, I could say "Francois was born in Missouri in 1970, and he never changed the citizenship he had at birth." This depends on the knowledge that Missouri was a U.S. state in 1970, and that U.S. law in 1970 said anyone born in a U.S. state would be a U.S. citizen (and note that these background assumptions are contingent ones which hold in our world but might not in some other possible worlds, like a world where the Confederacy won independence in the Civil War). But as long as the person I'm talking to can be expected to know these facts about how our world works, my explanation is fine, and if needed all the necessary background could be stated explicitly such that, if combined with a formalized version of my explanation "Francois was born in Missouri in 1970, and he never changed the citizenship he had at birth", it would be possible to logically deduce a formalized version of "Francois is a U.S. citizen".

    If you are willing to grant (at least for the sake of argument) that this is a reasonable gloss on "an ideal reasoner can deduce the explanandum from the explanans with certainty", then I can proceed to lay out another reasonable-seeming condition on explanations (basically one that bans explanations that 'beg the question') which together with the above creates a problem with the PSR argument that the BCCF must have a necessary being as an explanation.

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  97. Or are you pointing to an issue not at the level of the formalism but at the level of interpretation?

    Yes, I think this is correct. But it's also a problem for the logic and using the logic to analyze arguments insofar as we need to interpret what symbols like ∃x mean for the logical statements to be meaningful. The lines of symbols—like sentences, as opposed to statements or propositions—have no meaning on their own; without a speaker or mind assigning them meaning, they're just indeterminate garble.

    Sure, but we can break this down in terms of the traditional distinction between logical validity (which only requires that the premises are well-formed formulas and all the logical inferences follow the syntactical rules, without regard for meaning) and soundness (which depends on the interpretation of the meaning of the statements and rules of inference, and requires that they all be objectively true). So I think you're saying there is no doubt that your argument is logically valid, but we must get into issues of interpretation and ontology if we want to decide whether it is sound.

    OK. It also seems to me that since we are referring to an ideal reasoner here, there should be some notion that that the explanandum can be deduced from the explanans in some kind of logical way.

    Well, to know something it has to be true (truth is included in the notion of knowing). So, if the ideal reasoner (IR) can know the explanandum from the explanans, then he can also deduce the explanandum from the explanans. So, yeah. That was included in my reply.

    Just to be clear, when I said "the explanandum can be deduced from the explanans in some kind of logical way", it's important to my argument that the explanans can be put into formal terms, and any implicit background assumptions needed for the deduction can be made explicit and put into formal terms as well, such that explanans + bkd. assumptions can be used to derive the explanandum in the purely syntactical way I mentioned above, where there is no doubt that the derivation is logically valid (using whatever logical system we are assuming). As above, there might be doubt about the soundness of the argument if we didn't think the explanans or the background assumptions were actually true, or if we had philosophical questions about the rules of inference in the logical system being assumed (for example, you might doubt a system that allowed for inferences from statements that use the existential quantifier). But suppose for the sake of argument that God has told the ideal reasoner that the explanans and background assumptions are true, and that some specific rules of inference are trustworthy--in that case the ideal reasoner can be sure, based on the logical validity of the derivation of the explanandum from explanans + bkd. assumptions, that the explanandum is true as well.

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  98. But since we live in a finite world (ie. the standard model of cosmology, at least, agrees) and true propositions (truthbearers) are true just in case they correspond with something in reality (in virtue of corresponding with something in reality), I would deny that the BCCF (with redundancies removed) is or can be an infinitely long conjunction. I would need some type of argumentation for why the BCCF would be infinitely long before even letting that criticism get off the ground.

    Well, the standard model that's usually used in as a starting point cosmology is the FLRW metric, which simplifies things by assuming that at each moment in cosmological time, matter is distributed with uniform density throughout space, and in this metric the space would only be finite if the density was high enough to curve space positively like a higher-dimensional analogue of the surface of a sphere, whereas space would be infinite in extent if the density is lower so that the spatial curvature is zero (a 'flat' universe--and keep in mind that cosmological observations suggest our observable universe has a curvature indistinguishable from flatness) or negative (a 'hyperbolic' space), though a flat or hyperbolic universe can be made finite if you assume an unusual topology as described in this article. This assumption of uniform density at each moment of cosmological time is thought to be a good approximation on large scales, at least in the observable universe, though on smaller scales matter is obviously distributed in a more lumpy way. Also, inflationary theory differs from the FLRW metric in suggesting our observable universe might be a patch of an inflationary bubble of finite size, and outside this bubble the density might be totally different (inflationary theory also naturally suggest the possibility that the Big Bang was not the true beginning of time, but rather a sudden expansion of a small bit of space in a preexisting universes, with the process of new universes bubbling out from older ones potentially going back forever in time).

    Another reason the BCCF might be infinite is that if we take it to contain all the contingent truths about the universe perceived timelessly by God, so unless God literally causes time to end on Judgment Day, the number of contingent truths about the future might be infinite. And one other reason for allowing the possibility of an infinitary proof, distinct from the possibility of the BCCF being infinite, is that the necessary statement (presumably about God) that is being used as the explanation for the BCCF might itself contain an infinite amount of information. For example, even for those who don't believe God actualized "the best of all possible worlds", God's omniscient knowledge of all the infinite possible worlds, and His evaluation of each one, might have had some role in His choice to actualize this particular world. But if you are willing to grant for the sake of argument that a purely finitary logical derivation of the BCCF is possible from some finite starting premises about God along with any other needed background assumptions, then that actually makes my argument simpler. I didn't bring up infinitary logic because I intended to suggest the "infinitely long contingent explanatory regress " you mentioned, just to cover all the bases, since if the facts about God or the BCCF would require an infinite number of symbols to express, one might object that even though an ideal reasoner (one capable of dealing with infinite propositions) could deduce the explanandum from the explanans, this should not be equated with being able to logically derive the explanandum from the explanans since ordinary logical deduction requires finite symbol-strings.

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  99. I would prefer and appreciate if you lay out the rest of your argument anyway, explicitly and up front. It might also save time.

    Sure. In the previous argument I said that if some proposition p is to serve as the explanation for some other proposition q, it must either be that q is deducible from p in a purely logical way by an ideal reasoner (and thus at least in principle deducible by us), or that there are some implicit background assumptions--label them 'i'--being assumed, such that q is deducible in a purely logical way from the combination of (p & i). To continue the argument, I want to add a non-circularity condition saying it doesn't count as an "explanation" if you just assume q at the outset, meaning that neither p nor i can be identical to q, nor can they contain q if they are "molecular sentences" in the sense described here (for example, p could not be (p1 & p2 & q), since that contains q). Also, if q itself is a molecular sentence containing multiple more basic propositions (q1, q2, … , qn), then neither p nor i can contain any of those more basic propositions either--if for example p contained q2, then the explanation would be circular with regards to q2, though it might not be circular with regards to other parts of q like q1. All of this seems reasonable to me in terms of the usual assumption of what counts as circular reasoning, and the assumption that you haven't really "explained" some fact if you just assumed it at the outset, whether explicitly or implicitly (since that would be begging the question).

    From this non-circularity condition, we must conclude that if our explanandum is the BCCF (which we labeled 'a'), then since it contains all conditional truths about our world, then neither the explanans (label it 'g' for God), nor any implicit background assumptions i, can contain any conditional truths--both g and i must consist solely of necessary truths. But if a can be deduced in a purely logical way from necessary truths g & i, then since g & i are true in all possible worlds, and the logical rules of inference are the same in all possible worlds, then ideal reasoners in all possible worlds should be able to conclude a as well--in other words, a must be a necessary truth! I would imagine that the claim "any statement that can be derived logically from a necessary truth must itself be a necessary truth" is expressed as a theorem in some area of math, perhaps metalogic, but even if it's not, the argument above about ideal reasoners in different possible worlds seems sufficient to establish it. And since the conclusion of my argument contradicts the initial assumption that a was supposed to be contigent, if the argument is sound it shows that some initial premise--either that the PSR applies to the proposition a containing all contingent truths, or that there are any truths that are ultimately contingent rather than necessary in the first place--must be flawed.

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  100. After considering the quoted statement somewhat further, I think I'm going to deny it. Primarily, this is because it at least appears to pointlessly strengthen full explanations to something else with all sorts of provability and deducibility stipulations that seem to ask for them to be something much more like ultimate explanations (in which case, I would have just spoken of ultimate explanations instead).

    I was just using "full" to suggest "more complete and precise than the ordinary colloquial explanations we give in natural language", do "full" and "ultimate" explanations have some more technical meaning in some area of philosophy? And would you accept the initial part of my argument, along with the non-circularity condition I just added above, if I substituted "ultimate explanation" for "full explanation"?

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  106. Insofar as your first premise asks that the q (the explanandum) be deducible from p (the explanans), these stipulations block off your own first premise. Conclusions are always, in some sense, contained in the premises. This might, I think, become clearer to you if you attempt to formalize the argument.

    The specific meaning of "contained" I was using was the one I stated, saying that proposition p "contains" another proposition q if p is identical to q, or if p is a molecular sentence and one of the more basic sentences it's made up of is identical to q. I did not mean for "contained" to be more general than that, and in particular I did not mean for p to "contain" q simply because q is logically deducible from p.

    This is where you lost me earlier. Whether or not an ideal reasoner can deduce the necessary truth “There exists a necessary being” in world w (the actual world) but can't in some other world s should have no impact on whether or not the necessary being exists.

    I'm not assuming that at the outset, but rather deriving it from some other assumptions about what counts as a good "explanation". Even if you don't agree with me about what a good explanation is, the argument at least shows some subtleties that I think should be made explicit so everyone reading it can decide for themselves which side they take. For example, one of the many contingent facts contained in the BCCF is the bare fact that a contingent being exists at all--my argument makes more explicit that if explanations can be expressed as logical deductions, then the only way to "explain" this particular fact is by a deduction which assumes as a starting premise that some contingent being exists, which might not be obvious on first glance at your argument. Some who might have initially been inclined to accept your argument might balk if this point is made explicit, which is why I think it's a good idea to do so, unless you disagree that my if-then statement is implied by your argument.

    The proposition “There exists a necessary being” isn't true in virtue of contingent facts

    My argument isn't about the issue of deducing "there exists a necessary being", since I am allowing that to be assumed as a starting premise without the need for any further justification. I'm pointing out that the necessary properties of this necessary being cannot in themselves be the "full" explanation for any contingent facts including the BCCF (where 'full' means detailed and formal enough that the explanandum can be deduced logically from the explanans). And I'm pointing out that if you use as starting premises both those involving the necessary being (g) and some other premises which we know to be true (i), then for the explanation to work logically i will have to include some contingent facts about the world at the outset. To me this seems to make the explanation a circular one, since we will be using some contingent facts to explain why all contingent facts are true, including the ones we assumed from the start.

    Incidentally (I think I pretty much got the gist anyway), I'm not sure about your contrasting of "conditional" with "necessary" here: "[...] neither [...] can contain any conditional truths--both g and i must consist solely of necessary truths". Are you using "conditional" to mean contingent here?

    Yes, sorry, I mixed up my terms in that comment. In the two sentences in that comment where I said "conditional", "contingent" should be substituted.

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  107. You may be confusing something like L(LFx → Lβ) or (LFx → Lβ) with (Lα L→ β) or (α L→ β). Just a thought.

    My comment "any statement that can be derived logically from a necessary truth must itself be a necessary truth" was not about material implication →, but rather about logical deducibility which can be represented with the turnstile symbol I write as |- ...would you disagree that if we have both L α and α |- β, we should be able to conclude L β ? Material implication and logical implication are obviously distinct, for example if α is "The USA consisted of 55 states in the year 2000" and β is "1+1=3", then it is true in our world that α → β but not true that α |- β.

    You also have modus tollens issues to face.

    Can you point out specifically where you think modus tollens would be a problem for my argument?

    I've at this point given arguments for every single one of my premises, including that the PSR (as well as being eminently self-evident) can't be coherently denied.

    I'm not sure which post you're referring to it when you say you've argued it can't be coherently denied (could you quote a line from that comment so I could find it?), but most arguments for the PSR try to show a problem with the view that there are contingent facts that have no explanation, and that's not my own position. My own view is that there probably is no such thing as a "contingent truth", and that all truths about the world are necessary truths, thus making the PSR not so much wrong as inapplicable (since it's specifically stating all contingent truths have explanations), unless you extend it so that it talks about the explanations for necessary truths (and of course we do sometimes talk of 'explaining' necessary truths in terms of other necessary truths, as in mathematics--the idea is usually to deduce a necessary truth that's less self-evident to us from some other necessary truths that are more self-evident to us, like the Peano axioms of arithmetic).

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