Theological Semantics and the Problem of Interpretation

The sentence 'the cat is on the mat' is meaningless until it has been given an interpretation. We define a function from the sentence to objects within a domain. Standardly, we should say that 'cat' refers to {x: x is a cat}, 'mat' refers to the {x: x is a mat} and 'is on' refers to { (x, y) : x is on y} . Thus, we say that there is some member of the first set a, some member of the second set b, such that is a member of { (x, y) : x is on y}. To give an interpretation is to define a function from relevant linguistic units in the language to things in the world, such that the objects in the world form a functional image f* of the language. Thus, 'the cat is on the mat' is given by f*(cat), f*(mat), and f*(cat, mat) is a member of {(x, y) : x is on y}.

Now imagine providing such an interpretation for Trinitarian discourse. 'God is the Father', 'God is the Son', and 'God is the Holy Spirit', 'the Father generates the Son', and the Holy Spirit proceeds from the Father and the Son'. One could say that f*(Father) is a member of f*(God), f*(Son) is a member of f*(God), f*(Holy Spirit) is a member of f*(God), and that {x : x is God} has one member g. Thus f*(Father) = f*(Son) = f*(Holy Spirit) = g. 'The Father generates the Son' is thus f*(Father, Son) is a member of f*{(x, y) : x generates y}. Accordingly, 'The Holy Spirit proceeds from the Father and Son' is given by f*(Father, Holy Spirit) and f*(Son, Holy Spirit) is a member of {(x, y) : x proceeds y}. What follows, of course, is that it is a member of {(x, y) : x generates y}.

Now, taking 'G' to be "generates", we have that Ggg. Lombard and the Fourth Lateran Council reject Ggg because ascribing the reflexivity of generation to the individual g seems to deny simplicity, for there seems to be no possible world in which something can generate itself without dividing itself. (Notice how one can know oneself or think oneself without dividing oneself - - if one has intuitive, nondiscursive knowledge as has traditionally been thought to be true of God.)

Martin Luther, however, had no problem affirming the propriety of "the divine essence generates the divine essence'. When he said this, he meant that the Father generates the Son. If the Father is the divine essence, and the Son is the divine essence, and the Father generates the Son, then the divine essence generates itself, Ggg. He seems to have no problems with this because if Plato is a man, and Aristotle is a man, and Plato is a teacher of Aristotle, then it is proper to say that man is a teacher of man. Of course, the set M = {x : x is a man} is not a singleton set as is D = {x : x is God}. D has one member g, but M has billions of members.

When thinking the divine essence, one must not only subscribe to it a as a general essence, but one must claim a single instantiation, for if there was more than one instantiation, there would be a compromise of monotheism.

In order to make progress on the various claims in the late medieval period, we must be able to state clearly the ontological situation of the Trinity in the most perspicuous language we possess: first-order predicate logic with identity.