Category: Mysterianism

MACRUES, Semantic Defeaters, and Epistemic Defeaters (Peter Lupu)

(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

 (i) The Bible entails TS;

(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;

Example of a TS: "The Father is God, the Son is God, the Father is not the Son, and there is exactly one God."  The surface structure of this sentence is contradictory.

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Professor Anderson and the Hyper-Inscrutability of the Trinitarian Doctrine (Peter Lupu)

(This gem is pulled up from the vasty deeps of the ComBox to where it may shine in a more fitting setting.  Minor editing, bolding, and comments in blue by BV.)

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 that includes 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. On a realist conception of truth, S [if contradictory] has no truth-maker (T-maker) in any 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? [Shouldn't Peter have 'false' for contradictory and 'true' for non-contradictory in the preceding sentence?  After all, in (1) we are told in effect that contradictoriness is falsehood in every model, which implies that noncontradictoriness is truth in some model.  'Contradictory in every model' is a pleonastic expression.]

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Materialist Mysterianism

I wonder whether mysterianism in defense of such theological doctrines as the Trinity does not in the end backfire by making possible the philosophical justification of philosophical theses incompatible with it.  To ease our way into this line of inquiry, let us consider materialist mysterianism. 

1.  If mysterianism is an acceptable approach in theology, why can't a materialist make use of it in the philosophy of mind?  The (positive) mysterian maintains that there are true propositions which appear (and presumably must appear given our 'present' cognitive make-up) contradictory.  This is not to be confused with dialetheism, the view that there are some true contradictions.  For the mysterian there are no true contradictions, but there are some truths that must appear to us as contradictory due to our cognitive limitations. 

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