(A guest post by Peter Lupu. Editing and commentary by BV.)
As Bill notes, we are attempting to secure and study a copy of James Anderson’s book, Paradox in Christian Theology. (Publication details here, including links to reviews.) Meanwhile, I will propose here some tentative observations that Anderson’s book may or may not have addressed. These observations are inspired by the following point Bill makes in a post above as well as by some conversations we had about the subject:
“…if I cannot see that a proposition is rationally acceptable (because it appears contradictory to me) then I wouldn't know what proposition I was accepting.”
A similar point is made by Richard Cartwright in On the Logical Problem of the Trinity: "Nor is a mystery supposed to be unintelligible, in the sense that the words in which it is expressed simply cannot be understood. After all, we are asked to believe the propositions expressed by the words, not simply that the words express some true propositions or other, we know not which."
1). Let us agree that a Trinitarian Sentence (TS) is such that
(ii) The surface structure (SS) of TS exhibits the logical form of a contradiction;
(iii) We are not in the position currently and may not be in the position in our present form of existence ever to construct a contradiction free formulation or deep structure (DS) for TS;
1.1) For the purposes of the present post, I wish to avoid debates about whether the Bible alone entails TS or the Bible under some [putatively] authoritative interpretation [such as the one provided by the Roman Catholic magisterium] entails TS.
1.2) In order for TS to be a MACRUE [merely apparent contradiction resting on an unarticulated equivocation] the following additional condition needs to be satisfied:
(iv) There exists a contradiction free DS for TS.
1.3) We know (i) and (ii) simply based upon Biblical study plus a bit of logical acumen. We have very good reasons to believe that (iii) holds currently and in any case Anderson is willing to stipulate that (iii) may in fact be the case regarding TS. How do we know (iv)? Anderson thinks that we know (iv) based upon the belief that the Bible is revelatory and, hence, true together with knowing (i)-(iii).
(P2) Semantic defeaters have logical priority over epistemic defeaters: i.e., if a set of considerations C poses both a semantic as well as an epistemic threat to a belief that P, then the semantic threat must be neutralized before the epistemic threat can be neutralized.
3.1) So let us say that the *evident [manifest] meaning* of a sentence is whatever meaning can be gleaned from a given sentence based upon the known meaning of the sentence parts (and the manner in which they are structured). [Peter here assumes the thesis of the Compositionality of Meaning.] A sentence may or may not have more than the evident meaning and whether it does depends on whether some of the terms occurring in it feature certain meanings of which we may not be aware or know at the time of examining the sentence. Let us call the potential meaning that exceeds evident meaning, if any, *latent meaning*.
3.2) We can now say that if the overt meaning of a sentence is below the propositional threshold, then it is insufficient to determine which proposition the sentence expresses and hence it is *propositionally impoverished*; if it is above the propositional threshold, then it suffices to determine which proposition it expresses and hence it is not a propositionally impoverished sentence. Moreover, if in addition the sentence has no latent meaning over and above its evident meaning and the later is below the propositional threshold, then the sentence expresses no proposition.
3.3) A propositionally impoverished sentence cannot be used for the purpose of belief attributions because it is not clear which proposition, if any, the sentence expresses. And since a belief is a relation between a believer, a proposition, and a time interval, we must be able to tell which proposition a sentence expresses in order to use it in a belief attribution.
3.4) Suppose that a sentence S satisfies conditions similar to (ii) and (iii). Then S is either a real contradiction or merely an apparent one. Now suppose someone declines to believe that S is a real contradiction perhaps because they believe that the appearance of a contradiction is due to some equivocation, metaphorical uses of some terms in S, analogies, or a combination of all of these. However, at the same time this person maintains that currently and perhaps for the rest of our present form of existence we will be unable to formulate a contradiction free version (or DS) for S; i.e., we will be unable to remove the equivocation, metaphorical uses, and analogies so as to render a version of S contradiction free. I maintain that under these conditions the evident meaning of S is below the propositional threshold and therefore we cannot tell which proposition, if any, S expresses. Hence, S cannot be used for the purpose of belief attribution.
3.5) Let us now suppose that a body of sentences T entails S. Clearly, due to the entailment relation between T and S, some of the terms that appear in S must also appear in some sentences of T. Particularly, some of the terms in S that have an evident meaning below the propositional threshold must also appear in some of the sentences in T and suffer the same meaning deficit. Now, either T (or T plus some auxiliary theories of meaning, interpretation, etc.,) contains the resources to eliminate the equivocation as well as metaphorical and analogical uses of the infected terms in S or T fails to contain such resources. If it is the former, then T contains the resources to unveil the latent meaning of S so that the evident meaning of S together with the unveiled latent meaning exceeds the required propositional threshold, thereby, constructing a version of S that is not propositionally impoverished. However, under these conditions, S no longer satisfies condition (iii). It is a MAC [merely apparanet contradiction] in Anderson’s language. On the other hand, if it is the latter, [if the body of sentences T does not contain the resources to unveil the latent meaning of S] then some sentences in T must also be propositionally impoverished and, thus, just like S, they are unsuitable to be used for the purpose of belief attribution. Under these conditions, S is a semantic defeater against T.
3.6) The same considerations hold, mutatis mutandis, regarding truth. Since meaning is a necessary (but not always a sufficient) condition for the sentence to have a truth value, a propositionally impoverished sentence cannot be said to be true or false when its meaning is insufficient to determine a proposition.
3.7) As I have stated in P2 (2.1 above) semantic defeaters have priority over epistemic defeaters because semantic defeaters infect the very meaning of a sentence to the extent that it is not even clear which proposition the sentence expresses. And if it is not clear which proposition a sentence expresses, then it is not clear what kind of considerations would suffice to defend against or defeat a putative epistemic defeater. Therefore, when a sentence such as S is both a semantic as well as an epistemic defeater against T, then it will not do to bypass the semantic defeater property of S and launch a defense against the epistemic defeater property. One must first defend against the semantic defeater and only then address the problem of the epistemic defeater.
4) I maintain that the case of TS and the Bible is the same as the case of S and T above. If this is correct, then a TS [a Trinitarian sentence, example above] constitutes both a semantic as well as an epistemic defeater against the claim that the Bible is revelatory. Hence, the Bible contains many sentences that cannot be used as belief attributions because it is not clear which propositions they express. Thus, it would not do to merely defeat the epistemic defeater unless one first finds a way of defeating the semantic defeater. However, since according to condition (iii) above we cannot construct a contradiction free DST for TS, it follows that TS is propositionally impoverished. But, since the Bible entails TS, it follows that some of the sentences included in the Bible are also propositionally impoverished and they cannot be used in belief attributions. [Does Peter mean sentences other than Trinitarian sentences? The Bible or rather the Bible plus the creeds entails Trinitarian sentences in that it contains them, but this is different from the Trinitarian sentences being entailed by non-Trinitarian ones.] Therefore, Anderson cannot use the claim that the Bible is revelatory in order to establish that a contradiction free DS exists for TS: i.e., that condition (iv) above is satisfied and therefore TS is a MACRUE.
Perhaps Peter's critique can be summarized as follows. The fact, if it is a fact, that the Bible is divine revelation and inerrant throughout can be used as an epistemic defeater of the claim that the doctrines of the Trinity and Incarnation are self-contradictory. This is because, necessarily, whatever is revealed by God is true and hence noncontradictory. But the putative fact in question cannot be used as a semantic defeater of the claim that the sentences expressing the theological doctrines are too meaning-impoverished to function in successful belief-attributions. In other words, one cannot use the Bible's status as divine revelation (or the Bible plus some authoritative ecclesiastical interpretation thereof) to secure the very identity of the propositions that function as the contents of the beliefs one attributes to oneslf and to others when one ascribes to oneself and others such beliefs as that there is one God in three divine persons each of which is God and that the Second Person of the Trinity is the same person as Jesus of Nazareth.
4.1) Anderson might respond as follows. Even if my argument above is correct, it applies only to beliefs and not to the assertibility of sentences. Therefore, it is open to him to develop the right sort of epistemology which shows how *asserting* each sentence in the Bible is warranted. Thus even though we do not know which propositions many of the Biblical sentences express and, therefore, cannot use them for belief attribution, we still can show that each of these sentences has the proper epistemic credentials so as to make asserting it warranted. Thus, it would seem that a retreat from belief to assertibility enables Anderson to bypass the semantic defeater and focus exclusively on the epistemic defeater. [By bypassing Fregean propositions, I presume.] Thus, a person is rational to assert each Biblical sentence despite the presence of a semantic defeater associated with TS because Biblical authorities before him found it epistemically credible to do likewise.
4.2) Consider the case of the Sokal affair. In this case we have a bunch of editors that published a paper that was replete with literally meaningless sentences. Now, we must assume that since they found the paper worthy of publication, they would have been willing to assert many of these very sentences and, moreover, they would have insisted that they are warranted to assert them. Yet it certainly was not rational for them to think that asserting these sentences was warranted, since these sentences are literally meaningless. One is simply not warranted to assert the sentences in the Sokal paper merely because certain prior authorities (i.e., the editors) found it credible to do likewise when a semantic defeater is present. Similarly, I contend, one is not warranted to assert the sentences in the Bible when a semantic defeater is present unscathed. The case of the TS and the Bible could very well be similar to the Sokal case insofar as in both cases we have an intact semantic defeater.
5) It is possible that Anderson’s Book already contains a way of deflecting the semantic defeater problem described above. If so I apologize for once again posing a problem which Anderson’s book already addresses.
Thanks again to Peter for these further thoughts.
The sort of concerns he raises I address in chapter 7 of the book, although (as I noted even there) more needs to be said. But what I say there goes some of the way, I think, toward alleviating the worry that MACRUEs leave us without the first idea what to believe. Readers can judge for themselves.
In the meantime, here are a few brief comments in response to Peter's latest salvo:
1. I agree with Peter that semantic defeat is more serious than epistemic defeat, and that semantic defeaters have "logical priority" over epistemic defeaters. This much is clear. The question is whether the doctrine of the Trinity (if a MACRUE) suffers from semantic defeat.
2. I tentatively grant Peter's notion of a "propositional threshold" for the "evident meaning" of a sentence, although I need to think about this some more.
3. In 3.4) Peter claims that if a sentence S satisfies conditions similar to (ii) and (iii) then the "evident meaning of S is below the propositional threshold". What I don't see, however, is an argument for that claim. Why exactly should I agree with Peter on this point? What am I missing?
4. Furthermore, it's not clear from 3.4) whether it is the truth of (iii) or a person's belief in (iii) that leads to semantic defeat. This is important, because how we understand the problem depends on whether semantic defeat (like epistemic defeat) is person-relative.
5. Consider the Flatlander analogy once again. Suppose the Flatlander accepts the revealed claims "The Cone is circular" and "The Cone is triangular" but soon realizes that they appear (to him and his compatriots) to form an implicit contradiction. Does it immediately become the case that he hasn't the first idea what to believe about the Cone? Does the doctrine of the Cone suddenly suffer semantic defeat? I don't see why that would be. Rather, the Flatlander continues to understand those claims in much the same way as before, but with the further recognition that they constitute a MACRUE and thus his understanding is limited and imprecise in certain respects. We might say that the propositions he actually entertains are approximations to those propositions that represent an 'ideal' (i.e., non-paradoxical) doctrine of the Cone. But his beliefs needn't be thought false on that account. (A theory of vague propositions may prove helpful here.)
So the Flatlander continues to think of the Cone as both circular and triangular. I make some suggestions in the book as to how that works out psychologically and inferentially in the case of the doctrine of the Trinity. My only point here is that semantic defeat doesn't seem to be a threat.
6. I reject the comparison with the Sokal affair. In Sokal's paper, the individual sentences didn't express propositions. Such is not the case with the Bible or the Trinitarian creeds. The difficult in the latter case is that the individually meaningful statements form an apparent implicit contradiction. But that's quite a different difficulty than the one faced by the editors of Social Text (whom I'm happy to concede faced semantic defeat!).
Posted by: James Anderson | Tuesday, March 02, 2010 at 06:48 PM
James,
Thanks for your thoughtful and challenging comments. Your comments raise four points.
C1) Does the truth of (iii) or merely the belief in (iii) that leads to semantic defeat?
I suggest that the truth of (iii) (together with (ii)) determines that a semantic defeater in the form of a contradiction is present. If in addition an agent believes in (iii), then they should be able to conclude, under the circumstances, that a semantic defeater is present.
C2) Do I have an argument on behalf of the claim that if S satisfies conditions similar to (ii) and (iii), then the evident meaning of S is below the propositional threshold and, hence, is insufficient to express a proposition?
I suggest we think about this question in stages.
Stage (A): In this stage we attempt to identify S’s logical form. We may think of this phase as a process in which we map lexical items of S into various categories (logical terms, non-logical terms). The process is accompanied with side-notes. Thus we first identify the logical terms in S, if any, and map them into familiar logical notation (e.g., ‘and’ is mapped into ‘&’, ‘not’ into ‘~’, etc.). Next we identify the non-logical terms and map them into the canonical notation (e.g., ‘John’ is a singular term and, hence, mapped into ‘a’, etc.). All along we enter into the side-notes the grounds for these mappings. We now have the logical form of what I have called previously the “surface structure” of S. Suppose that given this process, the surface structure of S exhibits the logical form of a contradiction. Then S satisfies condition (ii).
Stage (B): We may now wonder whether S is a real contradiction or it is not a real contradiction. Given our mapping in Stage (A), S exhibits the logical form of a contradiction. But perhaps our mapping is incorrect at one or more points. Suppose that reflection on our side-notes uncovers a potential ambiguity in one of the lexical items in S. For instance, suppose S is the following sentence:
(a) Flying airplanes is dangerous and flying airplanes is not dangerous.
One might work out the logical form of (a) in Stage (A) to be the following:
(b) P & ~P.
(b) exhibits the logical form of an explicit contradiction. However, upon reflection we might notice that (b) is obtained by assuming that none of the lexical items in ‘flying airplanes is dangerous’ is ambiguous. This assumption is of course false, for the phrase ‘flying airplanes’ is ambiguous between
(c) Piloting airplanes;
(d) Flying airplanes as a passenger.
Uncovering such an ambiguity sheds new light upon the logical status of S, for now we cannot be certain whether our original mappings at Stage (A) are correct. Four possibilities present themselves (assuming no other ambiguities are present):
(I). Both occurrences of the phrase ‘flying airplanes’ in (a) are meant in sense (c);
(II). Both occurrences of the phrase ‘flying airplanes’ in (a) are meant in sense (d);
(III). The first occurrence of the phrase ‘flying airplanes’ is meant in sense (c) whereas the second occurrence in sense (d).
(IV). The converse of (III).
Possibilities (I)-(IV) represent four different propositions that (a) might express. According to both (I) and (II), (a) expresses two different contradictory proposition. According to possibilities (III) and (IV), (a) expresses two different contradiction free propositions. Thus, according to the former two possibilities, (a) is a real contradiction. On the other hand, according to the later two possibilities, (a) is not a real contradiction.
Stage C: Suppose we are able to determine that one of the later two possibilities holds regarding (a). Then (a) can be construed as expressing one of two contradiction free propositions:
(a*) Piloting airplanes is dangerous and flying airplanes as a passenger is not dangerous.
(a**) Flying airplanes as a passenger is dangerous and piloting airplanes is not dangerous.
Clearly, applying Stage (A) to (a*) and (a**) will show that neither exhibits the logical form of a contradiction. So if (a) is meant in either sense, then it is not a real contradiction. And even if we cannot determine whether (a) is meant in sense (a*) or (a**), we at least know that it is meant in one or another contradiction free senses. Hence, we can determine that (a) is a MAC.
Stage (D): But now suppose that an unfamiliar person walks into a room, asserts (a), and drops dead. Under such circumstances we cannot determine which possibility holds regarding (a). We are even unable to determine whether (a) is a real contradiction or not: i.e., whether possibilities (I) and (II) hold regarding (a) or possibilities (III) or (IV) hold. Under such circumstances, we simply have no clue which proposition among the four possible propositions (a) expresses. The following question arises: does (a) satisfy condition (iii) in the original post? Well, it is not obvious what should be our verdict in such a case. On the one hand, we do know that there are at least two possible versions which render (a) consistent. We might opt to employ the principle of charity in this case and hold that the speaker intended one of these options. On the other hand, in the absence of any information about the speaker, his background, the purpose for the assertion, etc., we simply have no way of telling which proposition from the four possible ones the speaker intended to express. My own intuition in this case is that (a)’s evident meaning is below the propositional threshold and, hence, it is not clear which proposition it expresses. Hence, I lean towards the view that (a) satisfies condition (iii).
TS is in a worst situation than we have seen in the case of (a). Unlike in the case of (a), in the case of TS we cannot proceed beyond Stage (A) and identify a lexical (or structural) ambiguity which might suggest a set of contradiction free propositions one of which TS might express, since we are assuming that TS satisfies conditions (ii) as well as (iii). Moreover, in the absence of an independent proof of (iv), we are not entitled at this stage to simply stipulate that the logical form of a contradiction assigned to TS at Stage (A) is merely the result of an oversight of some lexical or structural ambiguity or some other linguistic deficiency that can be remedied, partially or wholly, like we have seen in the case of (a). Condition (iii) rules such a situation out. Consequently, even if one is unsure whether (a)’s evident meaning is below or above the propositional threshold, it should be clear that under these conditions TS’s evident meaning is below the propositional threshold.
Let me put this a bit differently. If we are not in the position to identify the kind of ambiguity sufficient to remove the apparent contradiction, courtesy of condition (iii), then we are not in the position to offer the sort of amendment to TS that might suggest a neighborhood where a putative proposition expressed by TS might be located. In the case of (a) above, we were able to locate such a neighborhood due to having access to the ambiguity present in the phrase ‘flying airplanes’. Yet even when we are in the position to do so this may not suffice to put the evident meaning of a sentence above the propositional threshold. But in the case of TS we lack the means to even get to this stage, a stage which as we have seen by no means guarantees that the sentence’s evident meaning is above the propositional threshold. Hence, I conclude that when a sentence satisfies (ii) and (iii), its evident meaning is clearly below the propositional threshold.
C3) While I understand in a general way the role your notion of ‘approximation’ among propositions is intended to serve, I am uncertain that it can carry the weight you expect from it. The notion of ‘approximation’ is most suitable when it comes to measurements or things such as maps etc. The reason for this is obvious. When measurements are involved, then we can meaningfully say that a measurement is a “good enough approximation” when its expected numerical deviation from some standard is negligible relative to some purpose at hand. Similarly, for certain navigational purposes a map may provide a sufficient approximation of the terrain, since the degree of its deviation from a complete and full depiction does not hinder the purpose at hand. However, I do not see how these sorts of considerations can be replicated when it comes to a relation between propositions. First, in the above cases the notion of ‘approximation’ requires a measurable scale relative to which it can be defined. I do not see what would correspond to such a scale when we apply the notion of ‘approximation’ to propositions. Second, even if such a scale would have been produced, ‘approximation’ is always relative to a purpose. Thus, whether x is a good enough approximation to y depends upon a purpose: for some purposes it may be, whereas for others it won’t. What is the relevant purpose when it comes to TS? Third, approximation is meaningless unless there is a standard at hand relative to which we can judge whether a given measurement is “good enough”. What is the standard in the case of propositions? Well, if we have the propositions arranged nicely in front of our mind (and have a scale and have a specific purpose), then perhaps we can say that one proposition approximates another proposition that is considered the standard. But in the case of TS we simply do not have the relevant propositions in front of our minds.
The above comments are not intended to imply that your notion of ‘approximation’ cannot work. It may be possible to work out these and other obstacles. I only want to emphasize that at least according to my current understanding, this notion is too thin to carry the weight you demand from it. And it may be possible to develop an alternative notion, such as the notion of a proposition’s “neighborhood”, which can perhaps do the work you expect from ‘approximation’ and avoid the obstacles facing the later. I don’t know!
C4) I introduced the Sokal affair exclusively as an objection against the “assertability” proposal which I entertained as a back-up position you might adopt in the event you find merit in some of my objections. It is not intended to be an objection against the original position regarding beliefs.
Concluding Remarks: A position such as yours extends beyond the particular paradoxes you have focused upon. Therefore, a full assessment of its overall merit depends upon what are its more general consequences. And here matters become somewhat alarming. For if we were to extend the stand you defend regarding TS and other theological paradoxes to all surface contradictions or paradoxes, then what stands in the way of adopting the very same attitude regarding any and all contradictions. I say that this table can be both blue and red all over (at the same time). You say that it is impossible. I respond that it is, but we simply are not in the position now or perhaps ever to comprehend the right metaphysics of colors and surfaces which will resolve the apparent contradiction. And it will not do to say that the theological cases are different than the color case because, unlike in the later, in the former case we have a background body of Biblical knowledge to settle the matter. This will not do because, as I have argued in the original post, you are not entitled to appeal to the revelatory character of the Bible before you show how the semantic defeater is blocked. Appealing to the revelatory character of the Bible prior to defeating the semantic defeater is simply begging the fundamental question that is at stake here.
Posted by: Account Deleted | Saturday, March 06, 2010 at 06:01 AM
I should mention that the "flying airplanes" example is due to Katz who discussed with me this example back in the 90s and I believe it appears also in some of his writings.
Posted by: Account Deleted | Saturday, March 06, 2010 at 06:12 AM
I am happy to report that I have finally secured a copy of James' book, soft cover. Bill and I will share reading the book and so hopefully sometime in the near future we will be more informed about James' position.
The cover of the book depicts an assortment of what appears to be eggs, with one of the eggs has a partially black surface on which a bright white light is reflected. Wonder the meaning?
Posted by: Account Deleted | Sunday, March 07, 2010 at 09:40 AM
Peter,
Thanks for the follow-up comments. I must move on to other things, so I leave you with the last word (for now).
As for the book's cover, I believe it depicts a golden egg nestled among ordinary eggs; I guess the black-and-white photo doesn't do it justice.
As for what it means, I haven't the foggiest idea. I just signed off on the cover in the absence of anything more fitting. Perhaps the cover designer was offering a sly critique of the book's thesis, by seeing whether I'd be willing to affirm something without having the first notion its meaning. Needless to say, such a critique would be based on an unfortunate misunderstanding of my position. ;)
Posted by: James Anderson | Wednesday, March 10, 2010 at 10:32 AM