Tuesday, January 18, 2005

More on the Trinity and the Triple Point of Water

Pat Hannigan writes:

I certainly am no physicist. However, from what I have read the triple point of water can be demonstrated, thus it is "empirically detectable". Here are two links (L1, L2) to experiments that test the triple point of water.

Note in the first link it states, "When a glass of ice water is covered with plastic, this represents coexistence of three phases, too. In this case, however, air is present. When air is absent, the vapor pressure of water at the triple point is just under 4 mm Hg."

Can one H2O molecule exist in all three states at once? I don't know. Certainly the experiment above shows that a collection can, and does, given certain conditions. At the least, from what I have read, the coexistence of all three phases of H20 is "an empirically detectable phenomenon in nature and not a mere point of intersection on a phase diagram." It is demonstrable.

BV: I don't think we have a useful Trinitarian analogy here. For the analogy to work, one and the same quantity of water would have to be simultaneously (as opposed to successively) in the three states. It is not enough that the three states be present together in the same close vicinity, as in the glass of water example. There what you have is liquid water with ice floating in it, and above it under the plastic, some water vapor. That is not to say that one and the same quantity of H2O is solid, liquid, and gaseous all the way through.

Let me try to put my point in a more rigorous way. Let T be a set of H2O molecules. Suppose S, L, G are disjoint proper subsets of T, and that the union S U L U G = T. In other words, T is partitioned into three proper subsets with no elements in common. We could say, if we like, that T is in all three states simultaneously if all we mean is that S, L, and G are each in exactly one of the states. But then we have no model of the Trinity. If we say that T itself, the union of S, L, and G, is in all three states simultaneously, then we have a model of the Trinity, but not something that occurs in nature.

So I believe I was right in my original water post, and that the Triple Point, though fascinating, is not a counterexample to what I said. What I said is that one and the same quantity of water cannot be simultaneously in all three states. That was a slightly inexact way of putting it. The exact way is the set-theoretical way I just gave.

You raise an interesting side question: Can one water molecule exist in all three states simultaneously? I'd say that one molecule of water cannot exist in even one state! Why? Well, to say that water is in the liquid, solid, or gaseous states is to say something about how a number n of molecules (n >1) are related to one another. To put it in crass phenomenological terms, liquid water flows. When we say that a stream is flowing as opposed to being frozen solid,

we are characterizing the molecules in the aggregate as opposed to one by one: a single molecule can't flow.

It seems to follow that one molecule of H2O is not water. To put it paradoxically, a water molecule is not water! Why? Well, water must exist in one of the three states, but a single water molecule cannot exist in any of the states for the reasons just given. Of course, a molecule of H2O is a molecule of H2O. But a single molecule of H2O is not water.

Back to Thales!

Wm Tanksley writes:

Yes, the triple point is a real thing; it's the temperature and pressure at which a substance exists in all three forms at once. It's used to calibrate our temperature scales, since it's unique. As you say, water at the triple point consists of some molecules in the gaseous state, some in the liquid state, and some in the solid. No single molecule participates in more than one state.

BV: But also: no collection of molecules is in the three states simultaneously and throughout as I explained above. So the triple point on the phase diagram does correspond to something real, namely, the temperature and pressure at which the three states can coexist near each other; but the TP does not correspond to some thing real if we mean a temperature and pressure at which one and the same quantity of water can exist simultaneously and throughout in all three states.

Besides, as you also said, this would be a modal explanation, and thus explicitly ruled out.

BV: Exactly right, which is why all the water analogies fail. The Persons of the Trinity are not states or modes of a substance, but individuals in their own right. Add to that the fact that God is not a substance in the way a stuff like water is a substance.