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Sunday, February 28, 2010

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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!).

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.


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.

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?

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. ;)

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