An A Priori Order
In his Private Notebooks 1914-1916 Wittgenstein writes: “The great question around which everything I write revolves is: Is there an a priori order in the world, and if so, of what does it consist?” The question is a good one (and highly metaphysical). In the Tractatus we read what looks like a reply: “There is no a priori order of things”. (5.634) This appears to imply that the order of things is entirely a posteriori. What we know of the world is derived exclusively from experience; otherwise, our knowledge of the world is a total blank. How this is consistent with the opening propositions of the Tractatus is not explained: “The world is all that is the case” (1), “The world is the totality of facts, not of things” (1.1.), “The world is determined by the facts, and by their being all the facts” (1.11), and so on. For these propositions are presumably intended as a priori necessary truths: it isn’t that we merely empirically discover that the world is all that is the case (etc.), as we discover that it contains hydrogen and walruses; or that it is just contingent that the world is made up of facts, as it is contingent that it contains London and denim jeans. No, the idea is presumably that these are a priorinecessities arrived at by pure reason (perhaps they are even analytic truths, if that’s the way you think of necessity and the a priori). Wittgenstein doesn’t say as much, but it is a natural interpretation of his words. In any case, I wish to discuss Wittgenstein’s question in its own right, not issues of Wittgenstein exegesis. So: is there an a priori order in the world, in things, in reality? Are there things we can know about the world without examining it, without observing it, without living in it? Notice that we are not asking whether there is an a prioriorder in propositions or sentences or in mathematics; we are talking about the world as a whole, including (and especially) what might be called concrete reality—material bodies, biological organisms, the weather. We can readily allow that an a priori order exists in logic, language, and number theory (I don’t think Wittgenstein would disagree—hence his use of “world” and “things”), but it is another question whether an a priori order might hold in the ordinary world of physical and psychological things. The question concerns whether there is such an order in all of reality, including the things we know by ordinary sensory perception. It is surely clear that much of the world is not knowable a priori: most of we know of the world is known empirically. But is any of it knowable (or actually known) a priori, and here we include the world of empirical concrete objects? Imagine standing outside the world, having had no experience of the world: is there anything you can still know about its make-up? We can start with Wittgenstein’s own proclamations: can we know a priori that the world is everything that is the case, the totality of facts not things? These words are not pellucid, despite their resonance. Does the first sentence not mean “everything that is true”, which must then mean “every proposition that is true”? But the world is not made of propositions. The second sentence speaks of a “totality of facts”: but what kind of totality (a set, an aggregate, a list?), and what is a fact? Wittgenstein goes on to introduce the idea of a “combination of objects” as constituting a fact, but that is a faulty conception of facts, and the notion of object here is highly theoretical and abstract. Still, the general drift of Wittgenstein’s words does not seem mistaken: we know a priori that the world must contain certain ontological categories, however difficult it may be to characterize them. We might venture the suggestion that the world consists of particulars and universals, objects and properties, individuals and general characteristics. We don’t know a priori what kinds of entity fall into these categories, but we do know a priori that the world (any world) must divide into them. Thus, there is an a priori order of things, of what there is, of reality. Admittedly, we have to be careful how we formulate the precise nature of what there must be: we don’t want to say that the existence of matter is known a priori, or persisting objects, or even space and time. The world might consist of immaterial stuff, or only of events, or be devoid of space and time: we can’t rule these epistemic possibilities out a priori. Empirically, we know these not to be the case, but they don’t seem like things we could exclude a priori. We can’t just excogitate the existence of matter, enduring objects, and space and time from the concept of a world. So, we should limit ourselves to only the most schematic description of the order we have discerned. I think the best and most convenient way to do this is to say that the world must contain instantiation: any world must have the property that instantiation occurs in it—there must be individual instances of general features or forms or characters or types. This we know a priori—though of course in fact we are confronted with it at every waking moment of our lives (and even in dreams). You can’t make a world without installing instantiation in it. The empty world in which nothing instantiates anything is not a world at all. Nor can particular things exist without instantiation, since every individual must have properties of some kind, as a matter of metaphysical necessity (no individuals without facts about them). But is that all we can know a priori about the world? Not quite, perhaps, because we can add logical laws if we accept that they apply to objects and properties and not just to propositions. We can say that no property can be instantiated and not instantiated in the same object at the same time, and that an object either instantiates a given property or it does not, and that objects and properties are always self-identical. So, any world obeys logical laws; and we know this a priori. We can also say that properties, being general, are shareable (even if not actually shared): this is in the nature of properties (hence the term “universals”). And if they are shareable there ought to be generalizations about them—laws of some sort. More adventurously, if instantiation must be present, then predication cannot be far behind: that is, if language and thought exist in the world, then they must contain predication, because instantiation is just the worldly counterpart to predication. We therefore know something about how the world must be represented in language and thought (if they exist in the world), given its ontological structure of instantiation. We can’t know a priori that they do exist in the world, but if they do they have to contain predication. Still, this is thin gruel compared to the vast number of things that are known a posteriori about the world: it is purely structural rather than substantial. But what is remarkable is that anything can be known a priori about the world: how can we know the form of the world without even looking at it? And isn’t it amazing that the world divides into an a prioripart and an a posteriori part? That is, each object partakes of an a priori order and an a posteriori order. Why should this be—why shouldn’t it all be a posteriori? Not all of an object’s nature has to be known by means of the senses, though most of it is. We have a kind of global cosmic rationalism: everything has a nature that is partially knowable by pure reason. Wittgenstein never asks whether there is an a posteriori order in the world, because it is obvious that there is, but it is not at all obvious that there is also an a priori order—and that these coexist. There is something startling about the fact that the world harbors an a priori order. We don’t learn from experience that instantiation (and associated structures) is a fact about the world; it just follows from being a world of any kind. No doubt this is a rather mysterious type of knowledge (not that a posteriori knowledge is entirely unmysterious), but it evidently exists and is philosophically important.
 Wittgenstein was evidently a metaphysician in the grand style in his Tractatus days (ironically given his influence on the logical positivists), but nothing of this survives in his Investigations years. I have always thought this is a pity because he has a genuine talent for metaphysics. It is really not possible to be interested in logic without straying into metaphysical territory. The Investigations is pretty much devoid of logic.