The other day I listened to this podcast in which a Philosophy Professor called Dr Michael Rea describes what he believes to be a coherent model of the Trinity. It involves the concept of material constitution. The version of this theory that he posits involves a lump of playdough tha has been made into a statue of 'Gumby' (I have no idea who or what Gumby is - Dr Rea is an American). The idea is that although the playdough and the statue occupy the same physical space and are, essentially, the same thing, there is also a clear distinction between the playdough and the statue. For example, one could destroy the statue without destroying the playdough; and if it was you who made the statue, you could say that the playdough was bought from a shop but the statue was not.
Dr Rea even posits a version of this theory that involves three distinct entities which are also the same thing - a lump of marble, which is also a statue, which is also a pillar.
Now, it seems clear to me that if a statue is also being used as a pillar, the difference is merely one of function. There is no intrinsic distinction between the statue and the pillar, and to use this as a trinitarian argument is akin to the oft peddled analogy of someone who is a husband, a father and a brother (this analogy fails, because the husband, father and brother are not three persons but merely one person with three different roles - the husband is the father and the brother - so it is modalistic and thus heretical).
The question of the distinction between the playdough (or marble) and the statue (whether of Gumby or anything else) is a little more complex. It is true that there is a genuine distinction here. There are things that are true of the marble that are not true of the statue and vice versa. However, in a sense, the distinction is als merely functional. The statue is a function of the lump of playdough - if you were to change the shape of it so that it no longer resembled Gumby, it would cease to function as a statue of Gumby. Similarly, if the man in the husband/father/brother analogy were to get divorced, one of his functions (that of husband) would cease to obtain. The playdough/statue is really just one thing with two different functions. If you throw the statue in the air, you are also throwing the lump of playdough in the air. If you paint the lump of playdough red you will also be painting the statue red. This does not serve as an analogy for the Trinity because the distinctions in the trinitarian relations are more than merely functional - the persons perform different actions and have different experiences. For example, the Son 'took on flesh' and underwent crucifixion while the Father and the Spirit did not.
Dr Rea says during the podcast that the lump of playdough represents the divine essence, and that the three Persons of the Trinity are three distinct forms that the essence takes. This is not, in my opinion, a good analogy because (a) it suggests that, rather than possessing or constituting the Divine Essence (or Nature or Being), the Persons are somehow made out of - or constituted by - the Divine Essence almost as if it were a physical substance and (b) even if all three Persons were formed from the same 'lump' of Divine Essence, there would, as a consequence, be no distinction between them as one lump of any given substance cannot assume three distinct forms simultaneously - the same lump of playdough, for example, cannot, at one and the same time, be both cube shaped and spherical.
Incidentally, in the course of the podcast, Dr Rea offers similar criticisms of both C.S. Lewis's cube analogy of the Trinity and William Lane Craig's 'three headed dog'/Trinity Monotheism analogy/model to those that I made in my posts here, here and here.
