Does Inconceivability Entail Impossibility?

In an earlier thread James Anderson makes some observations that cast doubt on the standard entailment from inconceivability to impossibility.  (I had objected that his  theological mysterianism seems to break the inferential link connecting inconceivability and impossibility.) He writes,

But even though we have no direct epistemic access to any other inconceivability than our own, and despite the formidable historical pedigree of the idea, it still strikes me as implausible to maintain that inconceivability to us entails impossibility.  [. . .] For the principle in question is logically equivalent to the principle that possibility entails conceivability. But is it plausible to think that absolutely whatsoever happens to be possible in this mysterious universe and beyond must be conceivable to the human mind, at least in principle? Can this really be right?

I want to emphasize that I'm not advocating some form of modal skepticism, i.e., the view that our intuitions as to what is possible or impossible are generally unreliable. On the contrary, I think they're reliable. I just deny that they're infallible.

This does indeed give me pause.  Anderson is certainly right that if inconceivability entails impossibility, then, by contraposition, possibility entails conceivability.  These entailments stand or fall together.  But is it plausible to maintain that whatever is possible is conceivable?  Why couldn't there be possible states of affairs that are inconceivable to us?

But there may be an ambiguity here.  I grant that there are, or rather could be, possible states of affairs that we cannot bring before our minds.  These would be states of affairs that we cannot entertain due to our cognitive limitations.  But that is not to say that a state of affairs that I can bring before my mind and in which I find a logical contradiction is a possible state of affairs.  Thus we should distinguish two senses of inconceivable, where S is a state of affairs and A is any well-functioning finite cognitive agent:

S is inconceivable₁ to A =df A entertains S and finds a contradiction in S.

S is inconceivable₂ to A =df A is unable to entertain (bring before his mind) S.

Now it seems clear that inconceivability₂ does not entail impossibility.  But I should think that inconceivability₁ does entail impossibility.  For if S is contradictory, then that very state of affairs as the precise accusative of my thought that it is, cannot obtain.  Its possibility in reality is ruled out by the fact that it cannot be entertained without contradiction.

Now does possibility entail conceivability?  No, in that the possible need not be thinkable by us: there could be possibilities that lie beyond our mental horizon.  But possibility does entail conceivability if what we mean is that possible states of affairs that we can bring before our minds must be free of contradiction.

So, in apparent contradiction to what Anderson is claiming, I urge that we can be infallibly sure that a state of  affairs in which we detect a logical contradiction cannot obtain in reality.  There is more to reality, including the reality of the merely possible,  than what we can think of; but what we can think of must be free of contradiction if it is to be possible.

Conceivability without contradiction is no infallible guide to possibility.  But inconceivability₁ is an infallible guide to impossibility.  Where Anderson apparently sees symmetry, I uphold the traditional asymmetry.

Comments

[Paul]

Dr. Vallicella,

One initial example Anderson gives of the types of paradoxes the Christian doctrines under consideration are, i.e., MACRUES (merely apparent contradictions resulting from unarticulated equivocation) is this: Suppose a little child, Sally, with a basic knowledge of men and women, hears her father, who happens to be a doctor, make this claim: "I inspected Mary today. She is a well developed 14 year old girl, and she has XY chromosomes." Sally, trusting her father, wants to believe this. But it appears contradictory. She is unaware of, and perhaps not sophisticated enough, to grasp the nature of speaking genotypically and phenotypically, say. Suppose Sally, trusting the word of her beloved doctor father, who is the smartest man she knows and has never lied to her, takes the above as a MACRUE? The other option is that it is impossible that Sally is a 14-year-old girl with XY chromosomes, and so her father speaks falsely.

Another example: Knowing that Dr. Vallicella is a very sharp and precise thinker, I overhear him say, "I took a picture today." And a few seconds later I overhear him say, "I told you I did not take a picture today." Now, this appears contradictory. However, I give Dr. Vallicella the benefit of the doubt. I say to myself, "Self, this merely appears to be a contradiction." Indeed, there are even possible resolutions I might offer. Perhaps there is an equivocation on "take?" Perhaps it is on "picture?" Suppose I don't know where the equivocation lies, just some possible ones. Should I reason, given what I know and believe about Dr. Vallicella, that what he said was impossible? Why can't I take it as a MACRUE?

Of course the example Anderson gave of the spacelanders and flatlanders fits here as well. A flatlander may be told, "The object O is circular" and "The object O is triangular." Should the flatlanders believe that a "cone" is impossible? Why can't they take it as a MACRUE?

And so with theological paradox we have God telling us S, and we find what appears to be a contradiction in S. Why can't we take it to be a MACRUE?

Surely there are cases where we are warranted to believe that we have a MACRUE on our hands rather than an actual contradiction. And surely in some of these cases we do not know where, precisely, the equivocation is. So it seems that inconceivable[1] can be further disambiguated. If we have good reason to take the apparent contradiction (and we must grant that actual and merely apparent contradictions are at least both apparent, whereas a paradox is merely apparent and an actual contradiction apparent-but-real) as merely apparent, then it impossibility would not follow from inconceivability[1]. And that we have good reason to view the apparently contradictory doctrines as MACRUES is part of Anderson’s case.

[Pete Wolfendale]

I hate to pick, but how do we distinguish inconceivability1 from "is contradictory". It strikes me that we might as well just say that being contradictory implies impossibility, and that it also implies inconceivability2. I can't see what more there could be to inconceivability1 that would make it a more explanatory notion than the notion of contradiction itself.

[Bill Vallicella]

Pete,

To philosophize is to pick. There is more to inconceivability1 than contradictoriness because the latter is a purely logical notion: there can be contradictions (propositions reducible to the form p & ~p) whether or not there are any minds to contemplate them. There is also the intentional notion that S be brought before the mind: S has to be an intentional object of my thinking. To make a jusgment of inconceivability1, I have to do two things: first, bring S before my mind; second, find a contradiction in S.

Does being contradictory imply inconceivability2? I don't see it. Suppose there is some contradictory states of affairs T. Surely it doesn't follow that T can't be brought before one's mind. There being round squares is a contradictory state of affairs. And yet I have no trouble contemplating that state of affairs.

[Steven]

It's not obvious that inconceivability1 implies impossibility. It could be that the only reason A finds a contradiction in S is because he lacks the proper knowledge to resolve the apparent contradiction.

[Steven]

I think I said the same thing Paul did in the last paragraph of his post. S can appear contradictory to A, but nothing follows about S actually being contradictory, unless A is God, say.

[Account Deleted]

Steven,

The question is not whether there are cases such as the one's you and Paul mention. The question is whether we ought to admit the existence of a gap between the appearance of a contradiction and its reality, a gap that the human mind simply cannot close. I deny that it makes sense to admit this form of radical skepticism regarding contradictions.

[James Anderson]

This is a helpful distinction, and one I'm happy to accept (much as Margaret Fuller accepted the universe).

It's hard to deny that inconceivability_1 entails impossibility, because impossibility is built into the definition. If I entertain S, and find a contradiction in it, then of course there must exist a contradiction in S to be found. And if S involves a contradiction, it must be impossible. So this is uncontroversial. And the distinction between inconceivability_1 and inconceivability_2 is cogent. No objection there.

But I don't see that any of this raises problems for my position, because I don't claim or imply that the Trinity is inconceivable_1. In fact, Bill's distinction is helpful for clarifying what I am proposing. As best I can tell, the following claims form a consistent set.

(1) The Trinity is (at least presently) inconceivable_2 to us.

(2) The state of affairs seemingly expressed by the conjunction of the claims that constitute the doctrine of the Trinity is inconceivable_1 to us.

(3) The claims that constitute the doctrine of the Trinity are non-vacuous optimal approximations to an 'ideal' doctrine of the Trinity (i.e., a set of claims that would describe with maximal precision, and no apparent contradiction, the metaphysical relations between the Persons and the Godhead).

(4) The claims that constitute the doctrine of the Trinity are the closest to the precise truth of the matter that we can comprehend and express, given our present cognitive limitations.

I'll throw out another analogy for the wolves (and if it's savaged to death, so be it). The doctrine of the Trinity is like the claim that three cities on a plane form a right-angled triangle, such that the sides of the triangle are 50 miles, 100 miles, and 112 miles -- where that claim is cognized by people who cannot grasp or entertain the concept of fractional values.

[Bill Vallicella]

Steven,

Let S be the existence of a sphere which is red all over and not red all over at the same time and in the same sense of 'red.' Now without knowing anything further about this sphere (its volume, position, material composition, etc.) we can know a priori and with certainty that it cannot exist, that its existence is impossible in reality, indeed logically impossible. I submit that this is a very clear example of a piece of a priori knowledge. A skeptical wedge can be driven between conceivability and possibility, but I cannot see that such a wedge can be driven between inconceivability and possibility, provided thatone clearly and fdistinctly percieves a logical contradiction in the staste of affairs one is considering.

So I agree with Peter Lupu's comments above.

And please that knowing more cannot remove the contradiction. Nomatter how musch further information I add to the descriptionof the sphere, the contradiction remains. Even if you had an infinite conjunction of truths, except that one of them is contradicted by one false proposition, the whole conjunction would be false and impossible.

With conceivability it is different. A meagerly described S can appear contradiction-free when fully described it is not.

[Bill Vallicella]

James,

Ah yes, Margaret Fuller. I seem to have made this Victorian lady's acquaintance in the pages of William James' magisterial Varieties of Religious Experience.

I liked the wolf allusion. 'Lupu' is Rumanian for wolf. Your analogy is also very interesting. The hypotenuse of the triangle is 111.8034 . . . miles in length. People whose numeracy does not extend to fractions and irrational numbers will be approximately right if they think of the hypotenuse as 112 miles in length. What you are getting at, I suppose, is that it is broadly logically impossible that there be some integer i such that i equals the length of the hypotenuse. What these mathematically challenged folks have before their minds is therefore B-L impossible, and yet they are close to the truth 'for all practical purposes.'

Similarly, we are 'theologically challenged' -- it being reasonable to suppose that Original Sin has noetic consequences -- and so (i) the Trinity must appear to us as impossible when it is not, and (ii) our understnading to the Trinity is nevertheless approximate and good enough for such practical purposes as saving our souls. (As I recall the Athanasian Creed, believing the Trinity is made a condition of salvation.)

Did I understand the thrust of the analogy?

Consider the state of affairs T corresponding to the following contradiction where 'is' has the sense of absolute numerical identity: *The Father is God & The Son is God & The Father is not the Son & There is exactly one God.* What I don't understand is how this contradiction, which is clearly and distinctly seen to be such, can correspond to anything other than an impossible state of affairs. How can this contradiction merely seemingly be a contradiction as per your (2) above? And how can a contradictory proposition "approximate" to a noncontradictory state of affairs? What exactly does 'approximate' mean here? It means something different than in the math and physics cases such as your triangle example.

But I'll think about it some more. Thanks for your excellent comment.

[Bill Vallicella]

A further thought. *Snow is white & Snow is not white* is a contradiction. But there is a sense in which something in reality corresponds to it in that an obtaining state of affairs corresponds to the first limb, but not the second. So there is a sense in which it is false to say that nothing corresponds in reality to a contradiction.

Now consider the following contradiction where 'is' has the sense of absolute numerical identity: *The Father is God & The Son is God & The Father is not the Son & There is exactly one God.* A Muslim might say that that contradiction is an approximation to the noncontradictory truth inasmuch as the fourth and final conjunct is true, while the other three are either false or meaningless.

How does Anderson know that Trinitarian doctrine is not an approximation to a non-Trinitarian reality?

[Account Deleted]

Bill,

Your last proposal is that we may think of a state of affairs that makes one of the conjuncts of a contradiction true as the thing to which a contradiction corresponds.

But that will not work. If there is a state of affairs at all which corresponds to the conjunction (P&Q), assuming it is true, it is a joint state of affairs corresponding to P and Q. We do not say that the state of affairs that corresponds to this conjunction is the state of affairs that corresponds to one of the conjuncts, for then the truth maker for (P&Q) would be the very same truth maker that corresponds to P (or Q) alone.

The "Muslim" solution is of course not an acceptable solution to orthodoxy, for it is tantamount to simply abandoning the Trinitarian doctrine. The trinitarian doctrine plus monotheism does not "approximate" a truth, if it is viewed as meaningless or contradictory. It is simply meaningless or necessarily false.

[Bill Vallicella]

Peter,

I didn't quite say that. What I said in effect was that if you decompose *p & ~p* into p, conjunction, and ~p, then one of those propositions will correspond to something real. I am trying to figure out what Anderson means by "approximate."

[Account Deleted]

Bill,

Ohh, sorry, misunderstood you. Then this is fine.

[Account Deleted]

Prof. Anderson and the Hyper-Inscrutability of the Trinitarian Doctrine,

1). Let us say that a *real* contradiction is a sentence which comes out false according to every possible model (M): i.e., M = language-plus-domain-plus-interpretation, where an ‘interpretation’ is a complete and systematic assignment of extensions to the non-logical terms of the language (L). We assume that L is a well developed natural language such as English and we have a sufficiently rich domain to include whatever entities are required to implement an interpretation that will suffice for theological purposes.

1.1) Note: We are assuming throughout classical logic in two sense: (a) the logical constants are interpreted classically; (b) there are no *real* true contradictions.

1.2) Sentence S is a *real* contradiction just in case there is no *normal model* M in which it comes out true. A normal model in this context is one which features an interpretation that assigns extensions to the non-logical terms in the usual way prior to resolving any potential ambiguities. In a realist conception of truth, S has no truth-maker (T-maker) in a normal model or possible world.

2) Let us now define at least one sense of an *apparent contradiction* in model theoretic terms. Let S be a sentence expressible in L and suppose S comes out false in every normal model M. S appears to be a contradiction. Is it really a contradiction? Prof. Anderson maintains that there are sentences which are contradictory in every normal model, but are non-contradictory in some other models of L. How can that be?

2.1) Well, we can make initial sense of this claim as follows. Suppose that one or more terms in S are equivocal or ambiguous. According to one such meaning of these terms, every normal interpretation assigns these terms an extension that renders S contradictory. But according to the other meaning, there is a normal interpretation of these terms according to which S is non-contradictory: i.e., comes out true in some normal models.

2.2) Cases such as these can be accommodated without a significant conceptual revision of the normal-model picture above. We simply need to assume that L is rich enough to express all the meanings of the infected terms. We then introduce into the language two or more new terms to replace the ambiguous term, each of which is assigned an unequivocal meaning, and make appropriate adjustments throughout. Next we assign suitable extensions to the new terms according to their assigned meanings. We then reinterpret S by introducing new sentences S’ and S* to replace S. The result is that at least one of the new sentences, S’ or S*, has a normal-model and hence is true in such a model. The original sentence S, then, is only *apparently* contradictory. Obviously, similar adjustments will have to be made to all sentences expressible in L in which the affected terms occur. Let us call such models *adjusted-normal-models* of S.

2.3) As we have seen, as long as we assume that L is rich enough to express the equivocation or ambiguity, it is possible to devise an adjusted-normal-model for S so that its apparent contradictoriness is removed.

3) However, I suspect that the above way of removing the apparent contradictoriness of S is not what Prof. Anderson calls MACRUEs and it is not what Prof. Anderson thinks is the case with the apparent contradictoriness of the Trinitarian sentence.

3.1) MACRUEs, according to Prof. Anderson, share with the above cases the fact that MACRUE sentences are only apparently contradictory due to the fact that they include equivocal or ambiguous terms. However, the ambiguity involved may be *inscrutable* to us in the sense that we may not be able to find an adjusted-normal-model for a MACRUE sentence. Let us call such sentences *inscrutable-sentences*.

3.2) Now, I wish here to distinguish two cases of such inscrutability:

(A) Epistemic Inscrutability. Cases of epistemic-inscrutability feature the following properties:

(i) S is apparently contradictory;

(ii) Some term(s) in S is equivocal or ambiguous;

(iii) L is conceptually rich enough to express the equivocation or ambiguity;

(iv) There is an adjusted-normal-model Mi according to which at least one interpretation of S is true;

(v) We are currently or (perhaps) permanently unable to find the adjusted-normal-model Mi for S according to which some version of S comes out true because of our own cognitive limitations to correctly disambiguate the infected terms.

(B) Conceptual Inscrutability. These cases feature the following properties:

(i) S is apparently contradictory;

(ii) Some term(s) in S is equivocal or ambiguous;

(iii) L is not rich enough to express the equivocation or ambiguity;

(iv) There is no adjusted-normal-model Mi for S such that according to it S comes out true;

(v) Nevertheless, there is a language L* in which the affected terms could be disambiguated and there is an abnormal-model Ma for L* according to which a revised version of S would come out true;

(iv) We are currently or permanently unable to have cognitive access to L* and to Ma in order to ascertain that S has a model in which it is true.

3.3) It is important to see that in the case that conceptual-inscrutability holds, then the abnormal-model Ma of S is “invisible” from the point of view of the set of models for L. Whatever abnormal-models make S true, these models cannot even be formulated with respect to L: they are not detectable. If they were, then they would become models of L.

4) I think that Prof. Anderson’s MACRUE’s are more akin to cognitively-inscrutable sentences rather than epistemically inscrutable sentences. And Prof. Anderson maintains, I believe, that the Trinitarian-sentence is conceptually-inscrutable.

4.1) It is important to appreciate some general ramifications of these form of inscrutability. On both forms of inscrutability, the ambiguity or equivocation is contagious in the sense that the ambiguity infects *all* sentences in which the infected term(s) occurs. This means that if one or more terms of the Trinitarian-sentence are alleged to be ambiguous, then all occurrences of the said terms are infected with the said ambiguity throughout all theological discourse. Thus, if one maintains that the apparent contradictoriness of the Trinitarian-sentence is due to an ambiguity in the term ‘person’, the term ‘God’, or the term ‘divine’, or all of them, then whenever these terms occur throughout all theological discourse, they must be viewed as infected with ambiguity.

4.2) Thus, to the extent that we insist that we cannot discern the ambiguity in the case of the Trinitarian-sentence, we are thereby committed to plead ignorance regarding all other cases as well. This means that even in the case of the weaker epistemic-inscrutability, we must admit that we cannot understand the meaning of all the theological sentences in which the infected terms occur, even though ex-hypothesis our language is rich enough to disambiguate the alleged equivocation and, therefore, the contradictoriness is merely apparent. Thus, in the case of epistemic-inscrutability, these sentences do have a clear and distinct meaning in the language, but we are unable to discern this meaning and to that extent fail to understand any of the sentences in which the infected terms occur.

4.3) We cannot underestimate the far-reaching consequences of these results, even in the case of the weaker epistemic-inscrutability. For instance, if one maintains that the apparent contradictoriness of the Trinitarian-sentence is due to an ambiguity of the term ‘God’, for instance, then the sentence ‘God created the world’ becomes an inscrutable sentence. We are committed to maintain that while the theological language contains the resources to assign an unambiguous meaning to this sentence and therefore there is an adjusted-normal-model according to which it is true, we simply do not know what this model is.

4.4) We are now in a position of epistemic-ignorance with respect to every theological sentence in which the infected terms occur. Hence, we fail to understand all of them.

5) The situation becomes intolerably worse if we interpret the situation of the Trinitarian-sentences along the lines of conceptual-inscrutability. For in this case we not only fail to know the actual adjusted-normal-model for the Trinitarian-sentence, but we must admit that there is no such model for our theological language as a whole. The situation is rather that while in our own theological language the alleged ambiguity is inexpressible, there is another language to which we have no cognitive access in which the ambiguity is expressible. The result is that we cannot even conceive of a model for the Trinitarian-sentence, although we hold that such a model exists (albeit it is an abnormal-model relative to our own language). Hence, we cannot claim to even possibly understand the Trinitarian-sentence, for we do not even have the linguistic resources to express its real meaning in our own language.

5.1) Once again the above result becomes contagious. Every sentence in which the infected terms occur becomes completely inscrutable to us. Except this time the inscrutability is so complete that we cannot even hope to approximate the real meaning of these sentences, for their real meaning is beyond the conceptual resources available to us in our own language. I shall call this *hyper-inscrutability*.

5.2) Hyper-inscrutability renders virtually all important sentences of theology completely beyond our comprehension. We are simply unable to tell or claim to understand what they mean. We are even unable to tell whether or not this or that sentence in which some of the infected terms occur is even meaningful. It is difficult to see how one can delineate any criteria for what is orthodoxy and what is not under these sort of conditions.

6) Finally, I wish to draw attention to several questions:

6.1) How do we tell whether a given case is a case of merely epistemic-inscrutability or that it belongs to the more severe case of conceptual-inscrutability, which entails hyper-inscrutability with its completely unacceptable consequences?

6.2) What reasons do we have to believe that there are cases of conceptual-inscrutability?

6.3) Are we willing to accept the consequence that the Trinitarian-sentence and therefore our whole theological language is hyper-inscrutable in order to admit the requisite distinction between apparent and real contradictoriness of the severe kind entailed by conceptual-inscrutability?

[aresh v.]

Bill,
A way to understand the approximation is to grasp in which conditions it occurs.
One conceptual fremework is for some reasons a limit-case of another conceptual framework:
natural numbers is a limit case of fractional numbers
bi-dimensionality is a limit case of tri-dimensionality
newton's physics is a limit case of relativity
mono-inherence ontology is a limit case of multi-inherence ontology (supposita theory)
What holds in the first cases holds (as such or under given circumstances) in the second cases not vice versa
For example: Pythagorean theorem is maintained in the Natural domain and also in the Fractional domain
but with the set of Natural values you can't apply the Pythagorean theorem properly in all cases;
As well as the law of contradiction is maintained both mono-inherence ontology and in multi-inherence ontology
but with the set of mono-inherence property-instances you can't apply the law of contradiction properly in all cases;
While Lukas seems to provide such conceptual framework (but then he distinguishes between comprehension and understanding)
Prof. Anderson just denies that we can formulate this conceptual framework by our own means

Peter,
It seems that the propagation of the ambiguity over the religious statements is not a serious problem. As Lukas suggested:
"God's external operation is common to the three persons, God acts externally as though He were just one hypostasis. Therefore in the creation there is nothing that would causally require plurality of hypostases in God. Hence a philosopher unaided by faith assumes one hypostasis in God and cannot arrive at the cognition of the Trinity."
Therefore, we don't fail to understand God's external actions, just because we "cannot arrive at the cognition of the Trinity.", in fact: whatever he does, nothing "would causally require plurality of hypostases in God"

[Account Deleted]

aresh,

I don't get your reply to me (or to Bill). If there is an inscrutable ambiguity in the word 'God' as it appears in the trinitarian-sentence so that we do not know the real meaning of this term in this case, then the inscrutable ambiguity extends to all occurrences of the term 'God' in every sentence, including 'God created the world'.

Either we do not understand the term in the trinitarian-sentence and hence in any other sentence in which it occurs or we understand the term in in any other sentence in which it occurs and hence in the trinitarian-sentence as well.

What you cannot consistently maintain is that while we cannot understand the term when it occurs in the trinitarian-sentence, we magically gain a perfectly clear understanding when the term occurs in other sentences; this option is not consistently available to you. For if you understand the term in other contexts, then why can't you import this very understanding to the trinitarian-sentence, disambiguate it, and thereby resolve the contradiction?

I have no clue what your quote from Lukas means or how it is supposed to be relevant to my post above.

As for your reply to Bill regarding "approximation", my post above shows that no such approximation is possible in this case. What you fail to see is that the present case differs from all of the examples you site. In all of your examples the notion of 'x approximates y' makes prima facie sense because we understand both x and y. In the trinitarian case, ex hypothesis, we do not understand the trinitarian-sentence (according to Prof. Anderson). Therefore, the relation of 'approximation' makes no sense regarding a pair of sentences or theories one of which we completely fail to understand.

[aresh v.]

Peter,
You are right I fail to see you problem. But thanks for you patience :)

As regards the approximation issue, mine and Anderson's were just analogies on where to get the idea of 'approximation' (Bill was maybe reasoning in terms of results, while I suggested that it could be worth it to focus on the conceptual framework that makes the result intelligible and comparable). Of course we can not provide a way to establish in which sense a conceptual framework A is a limit case of a conceptual Framework B until we possess both of them (and for the trinity doctrine it's not the case). Nevertheless since we can generalize from knowledge development that there are conceptual frameworks (conceived at moment t1) which are limit cases of other conceptual frameworks (conceived at moment t2), we can think by analogy that our current conceptual framework is a limit case of another conceptual framework we don't conceive under the current conditions. Furthermore they add that not only we don't conceive the proper conceptual framework now, but we can't! Why?
According to you, the limiting circumstances have to be definible in terms of model (language+domain+interpretation) or conceptual framework (which I understand as mind-indipendent), while I suppose that these limits are epistemical (which I understand as mind-dipendent). What is an epistemical limit? How can we establish if we have any? Maybe by analogy again, this is another issue of course)

As regards the sentence 'God created the world' they could reply:
'tri-hypostasis in one' called 'God' created the world. Understand it?
If no, interpret it as it said 'one hypostasis' called 'God' created the world, it's fine as well, because as regards his external action (e.g. creation), nothing "would causally require plurality of hypostases in God".

regards

[Account Deleted]

aresh,

I repeat: if you do not understand the meaning of the word 'God' in the trinitarian sentence sufficiently to dissolve the apparent contradiction, then you fail to understand the meaning of this word in *any* other sentence including the ones you sited (with the exception of mention rather than use). And conversely, if you do understand the word in other context (such as the ones you site), then take that understanding and show us how to resolve the contradiction in the trinitarian case.

You must respond directly to these claims, otherwise you are skirting the objection with further unclarity. Show me how you understand the term in the context you site and how this meaning resolves the apparent contradiction of the trinitarian sentence. That is what I am asking.

Now, if you think Prof. Novak's supposit-theory does the trick, then that is fine. Then you at least addressed the problem, although there may be *other* objections against this particular resolution. But at least you addressed my point against Prof. Anderson's view. So you must distinguish between the issues I raised regarding Prof. Anderson's views and Prof. Novak's putative solution to the trinitarian problem. These are two separate issues.

[aresh v.]

Peter,

Sometimes repeating is not enough to convince. And I'm not really convinced about your argument. Probably because I didn't get it right. I must confess I'm not a very smart guy so it's well possible that I can't really understand your point. Does that mean that your point is meaningless in general? Or to me?
Well I don't understand it. But I can say at least it's an argument against Anderson's position, in a philosophical debate, thanks to which you want to demonstrate that mysterian position is not maintenable, I can get the single sentences (they aren't unarticulated sounds) the words and the syntax but no matter how many times you repeat it, I don't get how it can exclude something as possible when this for me is still possible. And that's because I'm not smart enough to understand that your argument is very conclusive: there is a lack of capability in reasoning maybe, in applying some deductive rules or maybe I equivocated some words or maybe I just don't know the exact meaning of some of your words. For me the reason why it's so conclusive, is a real mistery. And nevertheless we keep talking about your argument. Doesn't this sound similar to mysterian case?
Now you could object: of course not! Because at least you can say that you don't see any contradiction in my argument, while in the case of the trinity we do. Perfect! But what if I rebut: yes of course you see the contradiction in the trinity but that's because you bring the wrong conceptual framework before your mind!
In short, in both cases the problem has to do with what conceptual framework you bring before your mind (this is the epistemical issue I was talking about), not with contradiction as such: in my case because I'm not so smart to bring before my mind your argument, in your case because God is above mundane mental capabilities of comprehension to let you bring before your mind the proper conceptual framework

One last point: let's define 'meaning' in terms of extension and intension (like in Carnap). Now let's take the proper name 'God' in 'God created the world'. As a proper name it must pick something singular otherwise we fail to apply the proper name in the way we usually do. But besides its extension role it has also a corresponsing intension ('individual concept') which I don't grasp.
Does this fact really compromise the meaning of a sentence like 'God created the world'? It depends: it compromises the meaning of the whole sentence if you stick on the individual concept of '3 spiritual almighty ethernal omniscient hypostases in 1' but it doesn't compromise the meaning of the sentence if you use the individual concept '1 spiritual almighty ethernal omniscient hypostasis' as a substitute. Can I replace the former individual concept with the latter? Yes! They say I can, because nothing "would causally require plurality of hypostases in God" (sorry, this time it's me who is repeating :))

The line I've cited was taken from Lukas's long post to support mysterianism and it's not his statement: it was a quote from a czech theologian V. Šanda who thinks that "The Holy Trinity is a 'mysterium stricte dictum' (MSD)". So I guess I didn't fail to maintain the distinction.

[David Brightly]

Bill,

I have been puzzling over your definitions of two kinds of inconceivability. By 'state of affairs' I take you to mean the way the world mind-independently is. 'Entertaining' a state of affairs S presumably means capturing (aspects of) S under a set of concepts. So bringing S 'before the mind' results in a proposition, P, say. With this clarification, it seems that no S can be inconceivable2. For surely if my mind is well-functioning I must be able to extract *some* P, however inadequate, when immersed in S. Should we not also define 'inconceivable1' as 'entertains S (resulting in P) and finds a contradiction in *P*'? For surely a state of affairs, *in itself*, cannot be contradictory, if only because contradictoriness is a purely logical term. This suggests that the source of contradiction (and hence inconceivability) lies in the 'adequacy' of our concepts to capture S. I'm thinking here of examples from the history of science: If we think combustion involves the release of the substance phlogiston then the end products of burning should weigh less rather than more. If we think of an electron as a minute particle then it would have to pass through just one slit of a double slit experiment rather than two. These contradictions have been resolved by conceptualising combustion and electrons differently. But under this way of looking at conceivability it would seem that inconceivability1 is no longer a guide to impossibility. For under the classical conception of an electron the two-slit diffraction pattern that we actually see is inconceivable1---the classical prediction would be two overlapping one-slit patterns. This is not the result I expected to reach when I began thinking about this. Where have I gone wrong?

[Bill Vallicella]

Thanks, David. I'll try to respond tomorrow.

[Bill Vallicella]

David,

I could have been clearer. There are abstract and concrete (worldly) states of affairs, and I was using the term in the first way. An abstract state of affairs is very much like a propeosition. E.g., *There being round squares* is inconceivable-1 but not inconceivable-2.