Trinitarian Lives And Validity

Once temporary identities enter the picture, identity-statements are implicitly relativized to times (or something time-like). If so, then if we let "t''s refer to times on Jane's timeline, with the descriptions read non-rigidly, we really have 1b. (ti ! t2)(Jane = the leftmost Rockette), 2b. (t3 (>t2 ! t4)(Jane = the rightmost Rockette), and 3b. (t)(Jane = Jane).

(1b)—(3b) are all true. But what I now argue suggests that the move from them to (4a) is invalid.

Here is an argument philosophers have discussed at length57:

11. Necessarily, 9 is greater than 7.

12. 9 = the number of the planets. So

13. Necessarily, the number of the planets is greater than 7.

The premises are true, yet the conclusion is false, since there could have been just 6 planets. So obviously, something goes wrong here.

(11) asserts of 9 that it has a property, being greater than 7, in all possible worlds. (12) is true, but not in all possible worlds. "9" and "the number of the planets'' actually refer to the same number. But they need not have. Neptune and Pluto might never have formed, or might have formed but never been caught by the Sun's gravity. So it could have been the case that there were just seven planets. If it had, "9" and "the number of the planets'' would not have had the same referent. So it is possible that "9" and "the number of the planets'' do not refer to the same number. (13) asserts in effect that "the number of the planets'' picks out a number larger than 7 in every possible world. But as we have seen, this is not true. So this inference from necessarily Fx and x = y to necessarily Fy is invalid. One moral one might draw from this is that in a modal context (i.e. within the scope of "necessarily"), the fact that two terms "a" and "b" actually refer to the same thing (i.e. that an identity-statement like (12) is true) does not suffice to warrant substituting "b'' for "a." What is required instead to have a valid inference (one which cannot take us from true premises to a false conclusion) is that "a'' and "b" refer to the same thing in every possible world. For consider by contrast

11. Necessarily, 9 is greater than 7. 12a. 9 = 32. So

13a. Necessarily, 32 is greater than 7.

57 Its locus classicus is WV. Quine, From a Logical Point of View (N.Y.: Harper and Row, 1961), 147-8.

"9'' and "32" refer to the same thing in every possible world. And thus both premises and conclusion are true.

Times are like possible worlds—both are items at which propositions can be true—and temporal contexts can be like modal contexts. Consider this argument:

11b. 9 is always greater than 7.

12. 9 = the number of the planets. So

13b. The number of the planets is always greater than 7. Here we go astray as in (11)—(13). For not all the planets formed simultaneously, our sun existed before it had any planets, and the universe existed even before our sun did: (13b) is false. To see why we went astray, let us parse the argument a bit more perspicuously, as involving a temporal operator which quantifies over times as does over possible worlds:

11c. At all times (9 is greater than 7).

12. 9 = the number of the planets. So

13c. At all times (the number of the planets is greater than 7).

The problem is that while (12) is true, it is not true at all times. As the problem parallels that above, one can draw a parallel moral. In a universal-temporal context, even if "a" and "b'' now refer to the same thing, it is valid to substitute "a'' for "b'' only if "a" and "b" always (i.e. at all times) refer to the same thing. This explains the invalidity of the move from (1b)-(3b) to (4a).

I now suggest that the identities in (1) and (2) do not license the universal inter-substitution of terms denoting the one God—that is, that the move from (1), (2) and (5) to (6) is invalid. To move from Jane's case to the Trinity, we need just note that on non-substantival theories of time, times just are sets or mereological fusions of events.58 So if it makes sense to index propositions to times (i.e. treat times as items at which propositions can be true), it can also make sense to index propositions to sets or fusions of events. This (I now submit) is what we must do on the present account of the Trinity. On this account, whether or not God is temporal, there are items like times in God's life—sets or fusions of events in God's life at which propositions are true. These are the sets or fusions of just the events of each Person's life.

The generation argument, again, moves from

5. the Father generates the Son, to

6. God generates God

58 Such theories face a variety of philosophical problems. Many can be treated along lines laid out in Graeme Forbes, "Time, Events and Modality,'' in Robin Le Poidevin and Murray MacBeath, eds., The Philosophy of Time (N.Y.: Oxford University Press, 1993), 80—95, and Jan Cover, "Reference, Modality and Relational Time,'' Philosophical Studies 70 (1993), 251—77.

(5) is true at all Trinitarian lives: it is the Trinitarian equivalent of a necessary or omnitemporal truth. But (1) and (2) are like (12). As (12) is true only at some possible worlds and times, (1) and (2) are each true only at some Trinitarian lives. So though (1) and (2) are true, they do not make it valid to substitute "God" for "the Father'' and "the Son'' in (5), for reasons akin to those operative in the modal and temporal arguments above. The basic point of the Rockette analogy is that one should approach the Trinity by asking in what ways God's life is free from ordinary temporal relations. I suggest that it is free enough from ordinary temporal ordering that we can say that God lives His life in three streams at once, index Trinitarian truths to appropriate sets of events, then use this indexing to block the move to (6). Of course, one can also block the move to (4) this way.

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