(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.
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