John N. Deck "Down with 'All'"

Even at this late date, it is possible (indeed necessary) to take a radically fresh look at “universal” statements.

“All trees are plants.” Suppose we take seriously the likelihood that this, or something more primitive upon which it is based, arises originally in an actual knowing of the world. This procedure will at least have the advantage of preserving a certain feature of the statement too often overlooked, namely that it surely seems to be about trees and plants as things-in-the-world. If it is detached from the original knowing, this feature is lost. It then appears—as it often has appeared—as a “relation of ideas,” as “analytic” as “having no existential import,” as a “matter of definition,” in short, as a logical or symbolic vacuity.

Let us take it then, that the person who originally asserts this universal proposition in a living knowledge of the world knows something about trees and plants. But what does he know?

The various formulations “All trees are plants,” “Every tree is a plant,” “The tree is a plant,” “A tree is a plant” seem to express the “same truth,” but which is the truest? Which best expresses this person’s knowledge? Which best renders the world?

Holding, as I do, that logical forms are derived from the world and from talk about the world (that they are not innate mental structures or mindless, reference-empty symbols), I wonder initially at the logicians’ plain preference for “all trees are plants”—or, in its stylized form “For all x, if φ of x then ψ of x.”

There may be people who say, in certain contexts, “all trees are plants.” Let us ask ourselves whether the person who says that could really or does really know anything about “all trees. ”There’s been an objection running around for untold years that he doesn’t know all trees because he knows only the very limited number of trees with which he’s personally acquainted. And that he is generalizing from some necessarily incomplete sample, etc., etc. But that objection has always been answered by the observation that he does know something about all trees because he knows something that’s true of “each” tree or “every” tree, and therefore “in a way” indeed he knows all trees, including the trees with which he has not been acquainted and with which he may never be personally acquainted.

You’ll notice that in this reply there has been a transition from the “all” to the “every” or “each. ”The every has been taken as prior to the all; the all is to be built up from the every. But this is to reverse the priority. “Every” is every out of a plurality. “All” is a plurality. The same with “each. ”The words every and each have the plural as prior to them. They are derived from the plural rather than the other way around. So the person who accepts the priority of the every in a way does both at once: builds up the plurality, here the all, from the every even as he is deriving the every from the all. That shows at least the each and the every are pretty well bound up with the all, and that there’s not much improvement in going from the formulation “All trees are plants” to the formulation “Every tree is a plant.”

Let’s approach the subject afresh: There’s been no apparent gain so far.

We ask again the question: Does the person who says “all trees are plants” really know anything about all trees? Is there an all trees? Obviously, if there isn’t an all trees, then he doesn’t know what he’s talking about.

Is there an “all trees” that ever “were, are, or will be”? First, is this “all trees” a finite number? Now if you adopt an evolutionary perspective and also if you look forward to some end of the universe, end of the planet earth, or end of plant life on the earth, you might be able to say that there’s a limited number of trees, but already you’re involved in certain amount of unsure speculation. At any rate the person who says with happy assurance “all trees are plants” does not necessarily know or think much about these questions.

What if it were said that he knows that “all possible trees are plants”? First, what does he know about possible trees? Only what he has learned from observing actual trees. He knows, at best, the tendency of tree to produce tree and that this tendency is thwartable. Will the interplay of pro-tree and anti-tree tendencies in the world produce a finite number of trees? How could he know this, and is he even thinking of it?

What if the trees or the “possible trees” are infinite? The basic, sound conception of the mathematically infinite is this: that having taken one of the whatever you can take one more, and that having taken this second one you can take one more and so on and on. This conception is perfectly thinkable. It may not be imaginable.)

But the whole point of the infinite is that it is not closed off and so it cannot be totalized, it cannot be alled. If the trees are infinite, there is no “all trees. ”

So we resume the person who says “all trees are plants. ”If the trees are finite he probably doesn’t know this, if the trees are infinite he is wrong in alling them. From this point of view he doesn’t know what he is talking about. All this should alert us to the fact that he probably isn’t even thinking of those questions. What is he thinking about then? Well, he’s thinking about trees: Is he really thinking about “all trees” or is he just thinking about “trees”? Indeed, these so-called A propositions are often expressed in just such a form, “trees are plants,” leaving out the word “all.” “Dogs are carnivores. ”Many, many times there’s no “all” in these statements. So even if this person is determined to say “all trees are plants,” we’d probably do him a favor by encouraging him to adopt the more precise form “trees are plants.”

This does not mean that “all” should be banished from the language or that the ordinary word “all” is always out of order. The proper location of the “all” is in such expressions as “all the books on this table,” or “all the people in this room,” where there often is a definite and known totality. What has happened is that that proper use of “all” has been taken up and misapplied in statements such as “all trees are plants,” “all dogs are animals. ”In the haze in which some semi-ordinary thinking proceeds, a certain form, the “All—is—“ form, which was originally correctly gained from the world and from knowledgeable discourse about the world, has been taken up into other “knowledgeable” discourse where it does not fit.

We have got rid of the totalization but we still have a pluralization. This man is talking about trees. We can be sympathetic with him. There is a natural reason for pluralizing. We do live in a world of natural (and artificial) kinds.

Very soon on in a person’s career he has realized that there are many trees, that there are many chairs, that there are many jujubes. So there’s a natural tendency to express oneself in the plural form.

But let us try to get behind the pluralization. What has this person done here? Has he noticed each tree of his acquaintance and has he then solemnly noticed that it is a plant? “Verified” planthood of it, perhaps? Rather, it seems likely that in his natural process of grasping the world he has noticed something about tree. Tree, the so-called singular. He has noticed that tree has the plant characteristic, the plant quality.

I would hazard that for many people “trees are plants” has been an original discovery, a vital-knowing appreciation of the world. In its guise of elementary-logic-textbook “example,” it represents the embalmment of this original discovery. It can arise as a spontaneous knowing somewhat in this way: someone does not bring tree and plant together at first, perhaps because the tree is much bigger characteristically than other plants and it’s wooden and so on. But then in some stage of his career he does bring the two together. And he notes that the tree, by God, has the plant nature, in fact that it’s nothing more than a big plant!

At any rate, someone notices something essential about tree, but then quite probably expresses it in the plural form because he does live in this world of natural and artificial kinds and has already become aware that there are many trees.

But what he knows doesn’t have too much bearing on the manyness of the trees, the multitude. He is in his words pluralizing, but what he really knows is concerned with tree.

This is the appropriate place to mention that logicians very generally notice, only to dismiss or override, the fact that those “A” propositions are very often spontaneously expressed in the “singular,” both in ordinary life and in scientific discourse. When a biologist wants to tell us something about the amoeba he does not talk stiltedly about “all amoebae. ”He does not talk about all walruses, but about the walrus. And the eggman. But logicians have also noticed that in other instances the singular form does not convey the “all” (really, as we have seen, the nature). “The tree fell on the sleeping dog. ”This is enough for them. They must standardize; they will not pause over the naturalness of these “A” propositions without the “all,” and not only without the “all,” but without even the plural. Logicians deal harshly with “singular” “A” propositions simply because they notice other singular propositions which are not “A. ”They think they have found a certain indefiniteness in common, speech—even in scientific speech—and proceed to “correct” with a heavy-handed fiat.

But it has emerged that what the person we had in mind knows is “the tree is a plant.” He doesn’t know the all. He is not concentrating upon the many. He has not actually taken a plurality and then distilled something out of that plurality. Rather, he has built up the plurality for himself in his own thought or, if you prefer, in his knowing discourse. I’m not saying there isn’t a plurality in nature, but that he for himself has built up the plurality in his own thought by observing not trees but, to start out with tree. And tree, tree, tree. From that has arrived at a secondary notion, trees.

Here we must try to scout an overworked objection. Am I saying that when a person first notices what is, objectively, a tree, he knows the nature of tree? What about a boy’s first tree? When he becomes acquainted with his first tree, not, surely, by “idle contemplation,” but rather by the observation of tree in action, what it does, also by experimenting with it, playing around with it, etc., etc., seeing how it reacts when you kick it, when you climb it, all that sort of thing, all of this taken together—Am I saying that in his first acquaintance with one tree that he “knows tree nature”?

Here we have the problem of how a person builds up a plurality for himself. If I were Kant I would say “What are the conditions of the possibility of his being able to say trees?” More simply and more accurately, how does he come to say trees?

What seems needed is a genetic approach to “trees” as it emerges in this person’s mind. I confess to more than a little difficulty here, but up to now I have not been able to improve on this picture:

First, he must mentally grasp his first tree. No doubt a sensuous grasp leading up to an intellectual grasp. The grasp of the first tree is obviously at first very vague, very incomplete, etc. Proceeding then to the second one. He has to grasp the second one mentally and then “make the comparison” or see the resemblance. It may be supposed that this were all done by comparisons and resemblances, but this is to forget that to make a comparison a person must first know the one, then know the other, and then bring the two together. Probably a person does not look at the two and “see the resemblance” head on. Even if he seemed to do so, seeing the resemblance in this way would clearly involve knowing each individually, and it would be difficult to establish the priority between the “resemblance” and the “individuals.”

We are seeking here for the over-all form of an extremely complicated process. Even if it is true that he must first grasp the first, etc., we must not forget that the initial grasp of the first is really grasping very little about the first. And grasping the second means grasping very little about the second. And the first comparison that one makes doesn’t really amount to much. But then grasping the second will perhaps lead a person back to the first, or may even lead him on to the third, and as this proceeds he probably makes more and more comparisons or sees more resemblances. This means in turn that his grasp of the first, second and third gets more firm, becomes truer.

This is complicated further by the fact that, to have a reasonably adequate grasp of tree, one must see the trees as a “natural race" such that the “singular” tree is not a "self-contained” unit, but contains within it its reference to its parent(s). Part of what it is to be tree is to be related to other trees. So the mental pluralization is not just a noting of a relatively abstract manyness in the world. The mental pluralization must be accomplished to have a satisfactory grasp of the “singular.”

A fresh observation. The end-product of the pluralization (the pluralization for-me, not the manyness in the world, which is so-to-speak “there already”) is often reasonably true, reasonably sure. We don’t often make mistakes when we talk about trees, dogs, knives, cars, etc. We don’t make many mistakes when we “say something about them,” but what I mean is something more basic: We don’t make many mistakes when we allude to trees, dogs, cars, etc., in short there are dogs, trees and cars in the world. We don’t often make that kind of basic mistake.

If we could build up a more fitting account of the generation of these notions of pluralities we would be better off. But let us make the unsatisfactory move of taking these notions of pluralities ties without being perfectly clear about their generation, and try to say what we have when we have them.

Let me present a certain dialectic, the bearings of which will become clearer as we proceed. Suppose someone says that if you’re able to talk as you are about dogs, this shows that each one is dog and nothing but dog, through-and-through dog. Rover is dog, Butch is dog, Sambo is dog, Growler is dog, etc. Then some bright lad will immediately point out: “Oh, you’re saying Rover equals dog and Butch equals dog, therefore, according to a mathematical axiom, Rover equals Butch. Things equal to the same thing are equal to each other!” A rather glib way out of that would be to say that the mathematical “axiom” is valid only for mathematics, that it does not render the structure of the real world and that if in the real world Rover equals dog, Butch equals dog, and yet Rover does not equal Butch, well, that’s the way things are. This easy answer could be bolstered up by some philosophy of mathematics that would show that the mathematical rendering of the world is secondary, abstract, and not very true. And therefore question whether the mathematical “axiom” is properly applied here.

Not bad, but possibly not good enough. It is true that there are many dogs. “That there are many dogs” would be false unless each one or them were dog. Yet we are faced with the fact that each one isn’t “what the others are,” or rather that each one is what the others are in one sense and isn’t what the others are in another sense.

A possible way out of this impasse is to point out that dog is indefinite, that dog itself contains within itself what some would call the possibility of multiplication, which is better called the actuality of multiplication. And, therefore, that dog is not the hard atomic unity that it seems to be at first, and that therefore even in Rover himself there is the reference to the other dogs. This consideration has a certain promise because the dogs are a natural race, and so in Rover himself there is the reference to the other dogs. There is present in him the reference to his parents and ancestors, and through the reference to his parents and ancestors there is the reference to his brothers and cousins. Part of what it is to be a dog is to be referred to the other dogs.

That is perhaps the best we can do on that line, now let’s look at a whole other side. We will go back to the place where we have Rover, Sambo, etc. and the “problem” of how it can be true to say “Rover is (a) dog. Butch is (a) dog, etc.” The apparently easiest way to meet this “problem” is to say that dog is attached to each in a purely external manner. The most primitive form of that would be an extreme nominalism, which would say that “dog” is simply a word which insane mind in its insane way uses to group things which in themselves have no community, no interrelation whatsoever. But that’s only the crudest form. Take a much more sophisticated one. If we omit several in-between stages we can arrive at this formulation: “Rover is a thing which has doghood,” or if you will: “There is a thing such that it has dog quality or dog attributes or dog ‘properties.’”

Here you will notice that a detachment has been made between Rover and dog. Rover is no longer simply and straightforwardly a dog. (1) He is a thing which (2) has dog properties.

But if this is what Rover is, is it true any longer that Rover is a dog? The apparently simple identification made in this common statement seems endangered by the detachment. Rover is not just a dog. He is a thing, etc., etc.

But perhaps “Rover is a dog” is not quite so thorough-going an identification as “Rover is dog.” “Rover is dog” is not true if Rover is really only a thing which has dog properties. But perhaps “Rover is a dog” can be taken to be equivalent to “Rover is a thing, etc.” Maybe the little “a” can bear the burden of this whole translation.

The “a.” It is called the indefinite article, but does it have that definite a meaning? If it has, if it really conveys something like “indefinite member of the ‘class’ of dogs” we would be led on a short detour. Fortunately short. Rover is a dog, Rover is a “member of the class of dogs. ”However, each “member of the class” has for himself the dog characteristics, and therefore it would seem that the detour is at an end, the “class” can drop out of consideration. It is affirmed again that Rover has for himself the dog characteristics and that is enough.

So, let us raise the question again whether, if Rover is properly rendered as a “thing which has the dog characteristics” one could actually make the very ordinary and obviously true identification, “Rover is dog,” or “Rover is a dog. ”It would seem not. But someone might still say that the thing is always lurking in the background: that dog “really means” “thing with the dog characteristics.”

The real question here is whether the thing is in the picture. That isn’t all that easy to solve. It does seem that occasionally something comes before us as the bare thing, or as the almost the bare thing which we call simply “thing,” and then proceed to learn its characteristics. Most of the time, though, it seems that if the thing is there at all it is thing-and-its-characteristics, thing-and-its-nature, pretty firmly welded together. In the cases before us and similar cases, we don’t seem to have very much to the forefront of our consciousness thing-dog or thing-chair, thing which is a dog or thing which is a chair. It seems we’ve got chair, we’ve got dog. Someone might say that these are just shorthand expressions, but we may rightly be suspicious of the “claim” that we customarily speak shorthand,

But what about the constitution of the dog “in himself”? Is he a thing which is a dog? Is there in him a distinction between thing and dog?

There does seem to be, after all, some distinction. He is related at least “logically” to the other things in the world and it seems doubtful that that “logical” relation is completely false, that that logical relation is a totally incorrect rendering of the world. In other words, to say Rover is a thing is not completely false. It’s not a matter of “just our way of looking at the world.” Rover in himself is a thing among other things, and thus his relation to the other things, tables, chairs and cats, is real in him. He’s not cut off. On the other hand this relation in him is almost empty, almost vain, almost nugatory. His relation to the others through just being a thing is almost nothing compared to his causal relations.

His thinghood is pretty well absorbed into his doghood. There is a distinction but it isn’t much of a distinction, and therefore there seems to be great justification in characteristically talking of him and thinking of him as we do, as “dog” rather than as "thing which is a dog.”

The upshot of this whole dialectic is that “Rover is dog” or, if one still insists, “Rover is a dog” (with the identification which is implied) is very true, as true as a detached statement, a detached statement “about a singular” can be. We must allow for certain indefinitenesses. We must allow for this indefiniten-ess in “dog”: that “dog” does convey relation to other dogs. And we must allow for another indefiniteness in dog: We must remember that “Rover is thing” is also true, and that the thinghood and the doghood in Rover are not perfectly coincidental.

All of this must be said to show that “Rover is a dog” is a highly respectable rendering of the world, better than “Rover is a thing which is a dog”, “Rover is a member of the class of dogs” or “Rover is not a dog," because if he were, what could we say about Butch?

What we found wrong with thing-which-is-a-dog we can also find wrong with the symbolic-logic formulation of the A proposition “For all x, if φ of x then ψ of x.” (Often the pretence is made that formulations of this sort don’t mean anything, that (x) φ x ψ x has no necessary translation into ordinary(!) language, but actually the “examples” that always used show in pretty short order that they are really derived from the world and from talk about the world. Or else where would they come from?) So suppose we take seriously “For anything at all, if it is a dog, then it is an animal.” The initial objection to this formula is that it gives too great prominence to the almost empty thing, it’s as though the dog came before you first-hand as a vacuous anything-at-all. Furthermore, “For anything at all, if it is a dog, then it is an animal” is derived from knowing that dogs are animals. You could not say primitively, “if it’s a dog, then it’s an animal.” You must know first that dogs are animals, and then occasionally, when you are actually faced with a bona fide problem of identification, and you’re still not sure, then you might say “Well, one thing is sure: if it’s a dog then it’s an animal.” There is a sort of a gingerly approach in that formulation. You’re not committing yourself about this thing. But still you do not succeed in being totally noncommittal, because in saying “If it’s a dog then it’s an animal,” you are committing yourself to “dogs are animals.”

To recapitulate: First, in the backward order, “Rover is dog” is pretty true, it’s truer than much calling attention to the thinghood of Rover, and therefore it’s practically an identity, with the same for Butch, Sambo, etc., etc.

What we have in the world and what our thought and language renders is dog, dog, dog, dog, —dogs. Singular first, plural second. That seems to be a reasonably good account of the generation of the plurality.

There are these pluralities, and the pluralities are properly rendered by the plural words.

To attach the “all” to the plural word is a mistaken procedure, for the reasons given: Maybe there isn’t any totality. If there is a totality, the speaker perhaps doesn’t know that totality. Even if he does know it, it is probably far from his thought when and if he uses the “all.”

What he is really doing when he uses the “all” is talking about the plurality, and behind the plurality stands the “singularity.”

University of Windsor,

Windsor, Ontario, Canada

Posted October 26, 2006

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Down with "All"