We’re quite confident that a cake will never show up out of thin air. This is largely based on our past experience. A cake always comes into existence as a result of (a) the mixing of several ingredients, none of which is itself a cake, and (b) the use of kitchen appliances by an intelligent being that intends to make a cake out of the ingredients. The ingredients in (a) are what Aristotle calls a “material cause” of the cake, which is stuff that makes up the cake. The appliances and intelligent being in (b), on the other hand, are what Aristotle calls an “efficient cause” of the cake, which, since the cake has parts, is what builds the cake out of those parts.
It seems that, in order for the existence of the cake to be fully explained, there must be both a material cause and an efficient cause. But more than this, there must be enough things of the right kind constituting the material cause and the efficient cause. A material cause consisting solely of icing and milk would not fully explain the cake’s existence. What about the batter, for instance? That’s kind of important. Further, an efficient cause consisting solely of run-of-the-mill kitchen appliances would not fully explain the cake. Appliances don’t bake cakes all on their own. Similar things can be said about the causes required to fully explain other objects.
There’s a pretty strong tendency, at least among contemporary philosophers, to regard non-full explanations, especially ones like “The cake exists because I mixed icing with milk,” as failing to be explanations at all. Or, if they can be called partial explanations, then they’re no better at explaining facts than no explanation at all. I disagree. Think about it. Person A says a cake popped into existence out of nothingness. Person B says a cake was made from preexisting icing and milk. Who explains the cake better: A or B? Neither? No, I’m pretty sure B explains it better. You might be thinking, “Okay, but Ben, that’s still not a real explanation. The icing and milk simply don’t explain the cake, even though they come closer than nothingness comes to explaining it.” You say “po-tay-toe,” I say “po-tah-toe.” There’s still a relevant difference between showing up out of thin air and being formed from icing and milk.
So let’s get more precise about what it takes for a less-than-full explanation to be a partial explanation rather than no explanation at all. Intuitively, there is some object that my mixing icing with milk does fully explain: milky icing. To be sure, milky icing isn’t a cake, but it’s a lot more like a cake than what nothingness is capable of fully explaining, which is… nothing. Likewise, if I stir icing by itself, I end up with stirred icing. Stirred icing isn’t a cake, but it’s a lot more like a cake than nothingness is. So we can put these explanations on a spectrum of less-than-full explanations: nothingness doesn’t even partially explain a cake, stirred icing partially explains a cake, and milky icing partially but more fully (than mere icing) explains a cake.
What does it mean for what explanation X fully explains to be more similar to a cake than what explanation Y fully explains? Since a cake is an object that occupies space at a certain time, I’ll use a similarity metric similar to the one metaphysician David Lewis uses to compare possible worlds, which are worlds we can imagine but that may not actually exist. He says, roughly, that the more similar the distributions of physical stuff are across space and throughout time in a group of possible worlds, the more similar those possible worlds are. Now, to apply this to cake: Call the distribution of physical stuff across the space occupied by the thing X fully explains “X-dist,” the distribution of physical stuff across the space occupied by the thing Y fully explains “Y-dist,” and the distribution of physical stuff across the space occupied by cake “cake-dist.” What X fully explains is more similar to a cake than what Y fully explains is if X-dist is more similar to cake-dist than Y-dist is.
So, for example, say what X fully explains is milky icing and what Y fully explains is stirred icing. One way of using my metric to compare how similar the two are to cake is, while they’re both partly made of icing like cake is, milky icing differs from stirred icing in that the former contains milk like cake does. In that way, milky icing is more like cake than stirred icing is. However, if I’m not mistaken, the physical parts of a cake are distributed in such a way that the icing is not located where the milk is located. The milk is mixed into the cake sans icing, and then the icing is spread on top of the cake. In that way, stirred icing is more like cake than milky icing is; the milk is misplaced in milky icing, but there is no misplaced milk in stirred icing. So we may be uncertain whether milky icing or stirred icing bears more overall similarity to cake. We can debate such minutiae all we want, but no one should question that milky icing-dist or stirred icing-dist is more similar to cake-dist than nothingness-dist is. Thus, we should agree that what nothingness fully explains, namely more nothingness, is less similar to cake than what mixing icing with milk or stirring icing fully explains. But the closer an explanation gets you to what you’re trying to explain, the more successful it is as an explanation. So a partial explanation is better than no explanation at all.
What if you’re seeking an explanation of something non-physical, like a soul? X more fully explains a soul than Y does if what X fully explains has more properties characteristic of a soul than what Y fully explains has. For instance, suppose it’s characteristic of a soul that it’s able to exist forever. Suppose further that being B1 has the power to create non-physical things that are able to exist forever, whereas being B2 has the power to create only non-physical things that aren’t able to exist forever. Other things being equal, B1 more fully explains the existence of a soul than B2 does.
It’s tempting to think there are cases where a fully explained thing is more similar to cake than nothingness, and yet what fully explains that thing fails to even partially explain cake. After all, it seems any fully explained thing is more similar to a cake than nothingness is. For any thing, whether explained or not, has existence and likely a few other properties in common with cake, but nothingness doesn’t. But there are many fully explained things that apparently bear no meaningful resemblance to cake. Consider a lifeless planet, say a gas giant. This is nothing like a cake, so how does a full explanation of a gas giant even partially explain a cake, even though a gas giant is of course made of atoms like a cake is? It’s important to remember that some partial explanations are fuller than others. So while we’re initially inclined to think fully explaining a gas giant falls short of partially explaining a cake, upon further reflection it’s hard to rule out that fully explaining a gas giant just explains a cake to a ridiculously miniscule extent.
To avoid confusion, however, I must note that the kind of explanation I’m interested in is, as philosophers say, “factive.” That is, to partially explain something is to exist and actually lead to the existence of the thing explained, but without completely answering the question of why it exists. But when a full explanation of a gas giant leads only to that gas giant’s existing, and not a cake’s existing, there is no cake to be explained. So a cake is not partially explained by what fully explains the gas giant in that case. The only conceivable case where a full explanation of a gas giant,** say the formation of a rocky core followed by the accumulation of gas in the atmosphere, partially explains a cake is one where that process does, rather unexpectedly, yield a cake.
Likewise, a cake is only partially explained by my mixing icing with milk, or stirring icing by itself, if a cake happens to result from my doing that.
Of course, if we’re interested in the explanation of a particular cake or soul, we have to consider the context in which the cause acts as well. Someone’s mixing icing with milk, or exercising a power to create a non-physical thing that’s able to survive endlessly, two days ago can’t even partially explain how a cake, or a soul, came to be five minutes ago. Someone’s stirring icing in the backyard (without eventually taking the icing elsewhere) can’t even partially explain how a cake came to be in the kitchen. What can partially explain how a cake came to be in the kitchen five minutes ago is that, immediately prior, someone mixed icing with milk in the kitchen. And what can partially explain how a soul came to be five minutes ago is that, five minutes ago, someone exercised a power to create a non-physical thing that’s able to survive endlessly.
Stay tuned for my application of this line of thought to arguments from contingency!
**Or what would fully explain a gas giant, were a gas giant to result. We can either conceive of both a gas giant and a cake resulting from accretion, or conceive of just a cake resulting from accretion, in which case no gas giant is around to be fully explained.