Regress, unity, facts, and propositions

Abstract
§1. Here is a familiar regress argument: Take the fact that Ed runs. What is the nature of this fact? If we think ‘runs’ stands for a property, the property of running (call it Running), then, arguably, Ed and this property are constituents of this fact. But the fact cannot simply consist of Ed and Running. For Ed can exist and Running can exist even if Ed doesn’t run. For it to be a fact that Ed runs, Ed must instantiate Running. But adding the talk of instantiation just gets us another constituent of the fact: the relation of instantiation, call it Inst. But Ed can exist, Running can exist, and the relation Inst can exist even if Ed doesn’t run. Trying the same strategy as before we can say that Ed, Running and Inst must stand in the right relation for it to be a fact that Ed runs. But it should be clear that we are off on a vicious regress. As stated, the regress concerns facts, and I will keep referring to as the fact regress. But it is not obvious, at least, that we need to reify facts to get the regress going. All we need is a notion of something’s being the case, and the legitimacy of asking how, or in virtue of what, something is the case: Suppose it is the case that Ed runs. In virtue of what is it so? The existence of Ed and Running are not sufficient for it to be the case that Ed runs. For it to be the case that Ed runs, Ed must instantiate Running. But the existence of Ed, Running, and Inst is not sufficient for it to be the case that Ed runs. Etc. The regress argument given is sometimes called Bradley’s regress. But both because Bradley interpretation is controversial and because there are many different regress arguments bearing family resemblances to each other, I will by and large avoid that label. I think that the regress displayed by this argument brought up clearly is vicious, so some way of blocking the argument must be found. At no stage of the reasoning do we actually find ourselves in a position to say that a fact exists – or that something is the case – but we just add more and more entities, to no avail. Sometimes it is insisted that the regresses established by arguments like the one I have presented are not vicious..
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Jeffrey C. King (2009). XIII-Questions of Unity. Proceedings of the Aristotelian Society 109 (1pt3):257-277.
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