## Tuesday, November 15, 2011

### Spinoza and reductionistic determinism

According to some presentist theories of time, facts about the future are grounded in facts about the present and in the laws of nature. What grounds the fact, if it is a fact, that tomorrow the sun will rise is that the present conditions together with the laws of nature entail that the sun will rise tomorrow. Alan Rhoda played with a similar view in regard to the past: facts about the past are grounded in facts about God's present memories.

Suppose determinism holds and there is an initial time t0. Let L be the laws. Then we can imagine a view which we might call initialism in the place of presentism. According to initialism, facts about what happens at a time t>t0 reduce to facts about what the laws are and what the initial conditions are. More precisely, if I is the initial conditions of the world at t0, according to initialism, what it is for a state of affairs to obtain at a time t>t0 is for I and L to jointly entail that it obtains at t. Thus, what it is for there to be humans in the world is for the world to have had initial conditions and laws such as to guarantee the arising of humans.

According to initialism, none of us are substances, because facts about our existence reduce to facts about the initial conditions and laws. In Spinozistic terminology, we are modes of laws and initial conditions or of whatever grounds the laws and initial conditions.

Initialism has some obvious problems. It assumes that determinism holds and that there is an initial time t0. But determinism is in tension with quantum mechanics, and probably the best interpretation of the Big Bang is that although the universe has finite age, there was no initial moment.

There is a strong resemblance between initialism and Spinoza's metaphysics. To make the resemblance closer, we will make some modifications.

Modification 1: Take time to discrete. Thus, there is a finite number of moments of time between t0 and the present. If we do this, we can get a nested view closer to Spinoza's. Instead of reducing the conditions at time tn to the laws and the conditions at t0, we reduce them to the conditions at tn−1 and the laws. Now our present time slices are modes of modes of ... modes of the initial conditions and laws.

The second move we can make is to remove the initial time t0. Instead, there is a doubly infinite sequence of times ...,t−2,t−1,t0,t1,t2,.... How things are at each time reduces to the laws and how they were at the preceding time. Thus, in Spinozistic terminology, we are modes of modes of modes of ....

The third move is to reintroduce something outside of the whole sequence of modes, in which the sequence of events is grounded. After all, the idea of a sequence of modes without any substance seems absurd. One move would be to take that which is outside the sequence to be the lawmaker of L—that entity in virtue of which L is law, the truthmaker of the proposition that L is law. We may perhaps call this entity "Natura Naturans", nature naturing, or if we are pantheistically inclined like Spinoza, "Deus sive Natura" (though the latter identification would be taking a stand on whether Spinoza's Deus is Natura Naturans or the whole shebang of nature, in favor of the former). If we like, we can call the mereological sum of the modes "Natura Naturata", nature natured. The Natura Naturans, then, is the substance of which the temporal modes are ultimately (though with an infinite chain intervening) are modes.

The final move, to make the view be more like Spinoza's, is to take out the reference to times. Instead, we just have a sequence of entities—objects and/or events—that are each reduced to previous ones.

I think one puzzle about this view is how the Natura Naturans is related to the sequence of temporally qualified, "determinate", modes. We could take this relationship to be one of reduction once again: the whole infinite sequence of times reduces to the laws. This fits with much of what Spinoza says. It is, however, in some tension with Spinoza's idea that from the idea of God qua eternal, and it is this which seems to fit best with this eternal lawmaker, temporally determinate facts do not follow.

This exegetical difficulty can perhaps be overcome.

Here is one way. Accept a relationist B-theory of time, and then say that something is determinate insofar as we can delineate the times of its beginning and end. But on a relationist B-theory, sub specie aeternitatis, we just have a doubly infinite sequence without time-as-a-container, and no non-relative, non-arbitrary way of identifying times like "November 15, 2011". Of course, we can stipulate names for beginning and end times of some events, and then with this stipulative delineation in hand, we can delineate temporally when other events will happen. Thus, if a match struck just before noon, it will come on fire just after noon. Thus, to derive facts about when events happen we need facts about when other events happen. We cannot derive when-facts from eternal laws. Spinoza is clear on his view that times are the product of human beings divisions of duration.

If all there was to being a determinate mode was having a beginning and end time, I think that would be a satisfactory answer. But I think temporally determinate modes may be prior on his view to times. Perhaps, though, his thought is this. What we can derive from L is the whole sequence of things, but considered as an undivided sequence, and all divisions and delineations in the sequence are due to us. And from a delineated cause—say, a match's being struck, which is delineated from what comes before (the movement of the match) and what comes after (the fire)—there can be derived a delineated effect. Again, on this reading, the division in the modes is arbitrary.

Actually, I am not sure that Spinoza's mode-to-haver relationship is reductive. But I think it gives an illuminating reading.