[Russell] noted that, logically speaking, no set of existential statements can entail a universal statement.
Existential statements are those of the form “there is a bat in the pantry”, or “there are fifty bats in the pantry”. Russell noted, glumly, that no matter how many bats you observe in that pantry, you can never validly conclude that “all bats are in the pantry”. (“The Philosophy of Logical Atomism”, 1956)
This is a serious problem, because we use universal statements all the time, particularly in the case of scientific laws. To take a simplified, somewhat banal example, physicists do not generally say things like”all 6,454,934 objects I have so far observed on planet Earth have fallen to the ground unless impeded by some other object or force”. Rather, they say things like “mass attracts mass”, the idea being that a massive object like the Earth will always pull objects towards its center. This is a universal generalization, a law. The problem of induction revolves around the essential difficulty in deriving such laws from a collection of individual instances. It is a pressing problem because our most successful model of epistemic activity, modern science, requires the articulation of universal generalizations or laws.
Yet, as Russell observed, the problem looks even more threatening in its logical form. Insofar as we are empiricists of any kind, existential statements are all we have. We want to give primacy to (or start with) individual observational experiences, and build our larger theories from on that foundation. It seems like a good foundation: I, for one, cannot really doubt that I have observational experiences of a certain character.
Yet, all such experiences are singular events, referring to a limited class of objects. As such, they must be translated into existential and not universal logical sentences. But these are just two different kinds of statements, and as such universal statements do not entail existential ones, and neither do existential statements entail universal ones.
Nick doesn’t take a stand with respect to the problem, he more enjoys the problems it creates for empiricists. Since Thomists are empiricists too, it’s certainly a problem we have to deal with. If you want the short answer, skip to the last paragraph.
For a longer answer, it helps to start with a point of agreement about universals. Despite all the differences in opinion about them, all sides agree that universals are not given in experience. The differences between the various schools arise from the various ways of diverging from this common point of departure. Plato took the absence of universals in experience as proof that the things we experience participate in some world outside of experience which we knew from our previous life; Hume and Berkeley took this absence as proof that there simply were no universals, even in thought; and Aristotle’s position (at least as St. Thomas develops it) is that the universal is a certain way of understanding things as opposed to a thing understood. This says nothing about the question Russell raises, and if anything it appears to give some confirmation to is point of view, since if all the doctrines about universals admit that they are not given in the things we experience it makes sense to question how in the world can we relate universality to experience. We only set out these various doctrines because they help us narrow the field of possible responses. Since this started as a problem for empiricists, there is no reason to consider Plato’s response; and since it takes no effort to understand the response given by Humean Empiricists (who simply deny the existence of universals altogether, even in thought), the only response that needs to be explained is St. Thomas’s. Here’s what I think he would say:
There is a between what is known and the way it is known. For example, one and the same sense object can be known by different sense powers, whether we consider our own different sense powers (sight and touch) or our powers compared with different animals (our sight vs. a bat’s echolocation or a pit vipers infrared detection.) Just as sensation has its own way of knowing that is to be distinguished from the thing known, so does intellect (whether this happens because intellect just is a sort of sensation, or because it is analogous to it is not important at the moment.) A universal results from, or simply is, a way that something is known. The experience of a universal seems to be nothing but this: when confronted with something in experience, you regard it in such a way that it is not distinguished from the members of some multitude. You walk into an office, say, and see the picture of a child on a desk. For you this is simply “a child” or “a memento” or something of the kind. You see the object as indifferent from any number of other similar things. None of the details much matter – any picture of any child would occasion the same experience as the one you are having now. But how different is the experience of the one who works in that office and at that desk! For him, the experience is certainly not of some generic memento, but of his own child, with all of his unique traits that divide him off from others. And so in one and the same thing experienced, we are capable of seeing the thing in the experience as distinguished or not distinguished from others. The first way of seeing it is the mode of considering a thing as a particular and the second is the mode of considering it as a universal. Each of these different modes of considering has its own unique benefit that the other lacks: the first mode of considering allows for interpersonal relationships, the power and force of art and history, and moral knowledge (since moral truth cannot abstract from particular circumstances); the second mode of considering allows for science and the teaching power of art. Nevertheless, both “universal” and “particular” here speak of modes of understanding not the thing understood.
We can, of course, say that the thing understood is a particular. If we do so, however, then this sense of “particular” is distinguished from the mode of understanding, which means it is distinguished from both the universal and particular. In fact, it is false to say that our experience of things is particular, if we take this as the particular as opposed to the universal. We simply don’t experience every memento as showing us something uniquely set apart from every other memento. It takes a good deal of work to understand the particular in its particularity – only extremely prudent persons and great artists are capable of seeing the concrete particularity of situations well, and extremely prudent people and great artists are hard to come by. There is also a good deal of work in getting the universal exactly right. The vague universality that is oblivious to the distinction in things is also opposed to the reflective and critical universality that a scientist has.
And so to respond to Russell’s claim: what is existential or particular or singular can refer either to the thing understood, or the way of understanding. If the latter, it’s false to say that experience is particular; if the former, then the particular is no more opposed to the universal than it is to the particular.