An Issue With Metaphysical Reduction

Take a fact F. In general, what does it mean to say that fact F metaphysically reduces to fact F'? Note I am speaking of metaphysical reduction as opposed to conceptual reduction. First of all, the latter has to do with concepts and propositions rather than facts. For example, when we say that being a bachelor just means being an unmarried male, or when we say the proposition that Alfredo is a grandfather just means that Alfredo is the father of a parent, these count as examples of conceptual reduction. These explications of meanings are just the result of fully specifying the nature of our concepts as they stand. These are very simple examples, but the more complex instances of conceptual reduction in philosophy follow the same general idea as these ones.

Metaphysical reduction on the other hand has to do with facts in the world and how they stand in relation to each other. I take it that the following necessary condition imposes a restriction on the relation of metaphysical reduction:

• (R) If fact F metaphysically reduces to fact F' then (i) fact F holds in virtue of fact F' holding and (ii) the holding of fact F is nothing over and above the holding of fact F'.

As an example, physicalists often say that all mental facts are reducible to physical facts. I take it that this at least means that the mental facts hold in virtue of the physical facts and that they are nothing over and above the physical facts.

Now, (i) and (ii) seem to me to be in tension with each other. In fact, on the most straightforward reading of (ii) their simultaneously holding leads to a contradiction. Hence, we must find some other way to explain (ii), since it does not seem like a primitive relation. This is rather difficult. Let me explain.

By (i), reducibility must be an asymmetrical relation. This means that if F reduces to F' then F' does not reduce to F. For suppose F reduces to F'. Then F holds in virtue of F'. But the 'holding in virtue of' relation is asymmetrical, since otherwise there would be circular chains of ontological dependence. So if F holds in virtue of F', then F' does not hold in virtue of F, and thus by (R), F' is not reducible to F.

The problem is that the most straightforward reading of (ii) is that the holding of fact F is identical with the holding of fact F'. After all, suppose F and F' are not identical and we are dealing with a world of just F and F' (here I'm abbreviating, and I should really be saying the holding of F and the holding of F'). Then there is a perfectly clear sense in which F is something over and above F', viz. there are more things in the world than F! For if F =/= F', then for some x, x =/= F'. So there is something out there in the world which is extra-mentally distinct from F'. That seems to be a legitimate sense in which F is something over and above F'. So if F is not something over and above F' then F = F'.

But of course, if that were the case, then the 'in virtue of' relation here would not be asymmetrical, since if F = F' and F holds in virtue of the holding of F', then by substitution of equals F' holds in virtue of the holding of F. So reducibility would not, in fact, be asymmetrical. And that is a contradiction, since we earlier established it was.

One option is to say that the 'in virtue of' relation is not asymmetrical. But that seems deeply problematic insofar as it doesn't allow us to capture the reducibility we want to pick out. After all, every materialist will accept that all mental facts reduce to physical facts, but no materialist would ever dare say the physical facts reduce to the mental facts! (Personally I find the latter suggestion more plausible than the former, but regardless it is not something the materialist would ever claim.)

Instead, we have to find a sense in which one could say fact F is nothing over and above F' even though F is not identical to F'. And I'm not sure how to explain this. No idea if this works or not, or whether it is at all helpful, but here's a thought: Let us denote by 'a full truthmaker of P' a truthmaker of P which is not a constituent or part of some other truthmaker of P. Let Q be the proposition expressing the holding of F. Maybe we can say F is nothing over and above F' if the set of all full truthmakers of the proposition Q contains only F'. That would make (i) superfluous it seems. Or at least from pretty uncontentious premises (i) would follow as a consequence. This theory is a little weird though, since the question arises as to what, metaphysically speaking, explains why Q would be distinct from the proposition expressing the holding of F'.

With that said, I don't know if that's on the right track. And even if it gets the extension of the relation right it might not even produce a deeper understanding. The point being, I don't myself know how to explain (ii). Like I said though, it doesn't seem like this is a primitive or undefinable relation. I wonder then what we can say about it.

Thoughts on the Grounding Objection to Molinism

So, I want to get a bit more clear on what the grounding objection to Molinism is saying. As far as I can tell at this moment, the grounding objection seems to go something like this.

The anti-Molinist says that some general statement about the relation between grounding and truth such as the following holds:

(A) If some proposition is true then there is an entity which grounds its truth.

It seems in this context 'grounds the truth of p' just means 'is the truthmaker of p'. The objector to Molinism then proposes:

(B) There could be no entity to ground the truth of CCF's.

Of course from A and B it follows that all CCF's, if they are meaningful, are necessarily false. Hopefully this is all a correct representation of the objection.

Essence and Ontological Dependence

This is my term paper from my independent study last quarter on ontological dependence. I will say beforehand that I did not have enough time to make it great, and there is a lot more I could have said. However, I believe it contains a relatively good summary of Kit Fine's position, and I think the stuff toward the end about causation is somewhat original (albeit sketchy). So hopefully someone will find it interesting and useful.

I.  Introduction – Examples and What We Want

In many areas of philosophy, as well as common discourse, it is normal to say that one thing depends on another. Moreoever, one of these uses of the word 'depends' is a distinctly ontological sense, as opposed to, say, a notion of epistemological dependence or logical dependence. I will use the term 'dependence' throughout this essay to stand for this particularly ontological notion, unless otherwise stated. So for instance, we might say that a composite depends on its constituents. Or we might say a smile depends on the mouth of which it is a smile. Or that a hole depends on the thing which it is a hole in. This is a philosophical datum and the only reason one would deny it or feign incomprehension seems to be hard-headedness.

Essences and Truthmakers

After reading David Oderberg's book Real Essentialism I've been concerned with getting a clear understanding of what "essences" are. Essences are not substances in themselves, over and above the entities which have them. On the other hand, they are supposed to provide explanatory power for the objects that have them, and they are supposed to have a specific sort of causal importance, in Aristotle's terms what is called "formal causation". In trying to make sense of these notions I have found truthmaking to be somewhat helpful (provided of course we have a good account of truthmaking). Here's an analysis:

Essence: For any entity X the essence of X is the truthmaker of the proposition that the real definition of X is [such and such].

To begin with, let's be clear about what exactly a truthmaker is. A truthmaker is some fact or aspect of reality in virtue of which a truthbearer, such as a proposition, statement, belief, etc., is true. How exactly is truthmaking helpful here? Well, it describes a real aspect of a thing.

Kit Fine provides a popular neo-Aristotelian definitional account of essences, saying that we can give real definitions of not only words, but entities, in order to explain what they are. These real definitions of objects are their essences. More work needs to be done on getting to the heart of what real definitions are and how we come to know them. (A possible account of what they are, which I am now somewhat doubtful of, is here.) But provided we have a clear understanding of this, Fine's account certainly seems to be on the right track, especially in the face of the failure of some modalist accounts. But according to the classical account, essences not only make things to be what they are; they provide explanations for causal powers. Definitions, which are linguistic entities, obviously do not.

As Kathrin Koslicki puts it in her paper "Essence, Necessity, and Explanation", "A definition, according to Aristotle, is a formula or statement of the essence, i.e. of what it is to be a certain kind of thing." She continues, "On Aristotle’s way of thinking, then, the explanatory power inherent in definitions, in their role as the linguistic correlates of essences, is a direct reflection of the causal power of essences." Since real definitions are the linguistic correlates of essences, truthmaking provides a way to get back to the essence itself.