Impossibilities

I. Introduction 24

1. Real impossibility. 25

2. There is no impossibility without intensionality. 30

3. The impossible with content depends upon the actual. 32

(a) Hidden necessities. 34

(b) Unrooted counter-possibilities are nothing at all. 42

II. The Impossible 49

1. Four ways. 49

2. The physically repugnant. 50

3. What about superaddition? 52

4. We cannot refer to kinds that only might have been. 58

5. What about common names? 59

(a) Back to peanut butter and hot dogs. 60

(b) General names and common natures? 61

6. One ought to ask "What about the case of God?" 64

7. Vacuity of overflow conditions is sufficient for impossibility. 65

8. There are no ranges of mere possibility. 65

9. There is no fixed domain of worlds, either. 67

10. Inconceivability does not assure impossibility. 71

Defective and deficient conceptions. 72

11. More about conceivability and possibility. 73

12. Unrooted logical possibility is vacuous. 80

Chapter 2: Outline Page 2

III. Conclusion 82

1. Real impossibility comes down to vacuity of the de re necessities for an intentional object. 82

Chapter 2

Impossibilities

I. Introduction

I am going to explain what real impossibility is, not why what is really impossible is so.

Philosophers have a dismal record explaining impossibility. Either they omit the matter, or they treat impossibilities as if explained by a logical condition that could only have come into being with the recent existence of humans (like a syntactic inconsistency or a semantic or conceptual conflict), or, sometimes, by an eternal opposition of ideal entities (Platonism). But thought and meaning do not explain what could never happen before there began to be minds. Nor could they explain what would not and could not have happened even had there never been animal minds. And there is no reason at all to suppose that any relationship of ideal entities explains real impossibilities because no one has ever found a plausible explanatory relationship between abstract objects and physical things, and because the opposition of ideal entities would only raise the explanatory problem over again.

Although Aristotle [Physics, 1984 ed.] thought what is "due to nature" has a reason because it is necessary, he could not explain what the impossibility of its opposite consists in or is caused by. He obviously thought it more satisfactory to say "such and such has to be" because of "what-it-is," than to say "it just happened" as Democritus did. But, he seems to have had no better account of what cannot be than his opponents had of what just happens to be.

Some recent philosophers, unsatisfied with appeals to convention, to the structure of thought or to meaning exclusions in order to explain impossibility, resorted to parallel possible worlds of abstract objects which are not only supposed to explain the physical objects by exemplification or instantiation, but are supposed, by their opposition to one another, to explain impossibility. The impossible is what is false in all possible worlds. The problem is that these philosophers cannot explain the necessary reality of such abstract objects as worlds, properties and essences, or how such objects could really explain the being and nature of physical things, or how the abstract objects can even be opposed to one another. For to explain the opposition, the notion of impossibility has to be reintroduced and is again unexplained. It hardly explains why Socrates cannot fly to say that there is no possible world in which Socrates exemplifies "flying"; that is at most a logical shadow. Besides it captures only the surface of what we mean when we say something is impossible. So we have to start again.

1. Real impossibility.

First some simple observations and then some supporting considerations:

(i) A verbally consistent description (of non-formal objects) is not enough for real possibility ("talking mice"). The reason here is "hidden necessities": the overflow conditions, scooped up into the conditions of applicability of a predicate or common name by practices of reference.

(ii) Inconceivability does not assure impossibility ("the essence of God," "55 dimensional objects," "special relativity's being false"); neither does unimaginability, ("insensible particles," "no space into which cosmos expands"). Both may be cognitive limitations.

(iii) Local descriptive inconsistency does not assure real impossibility ("infinite force," "parallel lines that cross"). "Sub-atomic particles" for Lucretius, "essentially embodied minds" for Descartes.

(iv) Analyticity, meaning inclusion, does not explain necessity or a priori knowledge or assure truth, but is a product of belief and may survive belief ("birds fly," "aether is the imponderable medium of gravity and light").

(v) There are no mere possibilities not rooted in real things and kinds. Whatever is referentially inaccessible is logically empty ("globons are immeasurable," "ergons are finite").

(vi) Much of what supposedly might have been is unrooted referentially and is inaccessible and empty, not merely because we have no cognitive access but because nothing actual determines whether "it" might have been or not ("There might have been other elements than any there are").

(vii) Impossibility is not "all of a kind," but varies with the subject matter. The reason why there cannot be perfect Euclidean triangles is different from why there cannot be a theoretically "pure" gas, and different from why pigs can't have ceramic insides, and different, again, from why there cannot be silicon-based life.

(viii) What cannot be (involving terms anchored in real kinds or physically grounded predicates), could not have been at all, e.g., "rational reptiles," "wood that thinks" (except for inaccessible and unnameable sorts that may once have been within the capacity of nature and ceased to be, as physical phenomena became determinate one way or another).

The absolutely impossible is empty, beyond causation, beyond reference, beyond reach except indirectly by vague intensionality, because there is no content and there is no subject. The relatively impossible is beyond the ability of the actual, and sometimes, beyond the ability of anything there might have been, not just because of some deficit of ability, but, more often, because of some defect in what we envision. For apart from thought or imagination, there is nothing that is impossible, nothing at all.

Do not conclude that thought or imagination explains impossibility, or that, except for what is impossible in thought or imagination, "anything is possible." All we should conclude, so far, is that (a) no thing or reality is impossible, and (2) the content of impossibility has to come from intensionality. So, before there were intelligent beings, even though garter snakes could not fly, there was no impossibility with the content "garter snakes fly."

Further, we should remind ourselves that there is no thing or reality that is "merely possible," no domains of the possible, because there are not two kinds of being,"esse essentiae," the being of what is merely possible and "esse existentiae," the being of what is actual. In fact there is one thing we can be sure is not possible: for the merely possible to become actual. Yet, notice how easily and grammatically we can talk as if there were subjects or domains of the merely possible, and of the impossible too: we appear to quantify over domains: e.g., "It is impossible that anything impossible can come about." Although those statements have the surface grammar common to talk about domains that have existing elements, there is no existential commitment whatever. For it would be idle to think that there is some state of affairs "the impossible cannot happen" that makes the corresponding statement true. In this case, what is so gets its content from our thinking, just as the impossible does. If you realize the impossible cannot happen, what you think is what is so, but there is no situation, fact or other ontological fixture, independent of thought, that is what you realize.

There are many sorts of relative impossibility: from the impossibility of star-sized tomatoes, to the impossibility of pigs with ceramic insides, to wood that thinks, to rational birds, to my running a three-minute mile, to a 90-foot broad-jump, to my running a live TV program backwards by pressing "reverse" on a remote control or just pointing at the screen, to your talking faster than light, to gold's being soluble in koolade, to our moving backward in time, to your raising the dead at will.

I gather that, among philosophers who think all these situations are impossible, some are considered "harder than others," as if the ones that involve overt or proximate inconsistency are undoable in a way that others are not. That will, on examination, turn out to be false. Still, there is not always the same explanation for the impossibility of what is envisioned. As I said above, sometimes impossibility is from a defect of intensionality, and other times it is from a deficit of ability in something actual or in something that might have been actual, and sometimes it is because the statement requires ens et non ens simul.

Although there is not the same explanation for the impossibility of everything that is relatively impossible, there is an analogous generality that applies to all impossibility: that it involves intentionality along with failures of reference, so as to be relatively to the actual, without referential content, particularly because of indefinite de re necessities. The actual, the potential, and the naturally necessary exhaust referential content.

The impossible involves a deficit. With the absolutely impossible, it is as if blindness extended to every feature of a thing. We cannot even say what is absolutely impossible except for some inconsistencies. For the relatively impossible, a reference-cancelling conflict will do, whether the conflict be within the intensionality (e.g., a contradiction) or whether it be incorporated by reference (picked up by the referring parts of a description or name that amount to causal conflicts) or whether it be by evacuation of definite conditions for being (by failing to scoop up determinate de re necessities) -- later to be called the impossible by vacuity.

The impossible is not what is somehow prevented, as would be only natural to think, like my moving hundreds of miles as I can move a dozen yards. For negative causation just supposes impossibility, and does not explain it. Nor can the impossible be directly caused to be impossible, as a person's being unable to walk might seem to be caused by the loss of his legs. For that supposes that, otherwise, walking is impossible, again not being an explanation. Nor does the conceptual inclusion "walking requires legs" explain the real impossibility either.

A relative impossibility is an intentional content with a reference-cancelling conflict. That means that before there are minds in the universe, there is nothing that is impossible with content; for there is nothing definite that the actual things are not able to do, except everything that supposes being something else or being nothing at all. But there is no relation of "supposing" apart from the understanding.

That may seem unsatisfactory. For from the very natures of things, it seems paths of impossibility stream out like dark shadows: it is impossible that protons loose mass, that particles with mass are not subject to inertia, that mass decays, that galaxies, in a finite time, will not reach a relative recession velocity, where the galactic mass (which is approaching infinity, as the velocity of recession approaches the speed of light) traps all light, making dark galaxies. Those and endless other real and apparent impossibilities seem to have nothing to do with whether anyone ever thinks of them. Still, whatever is impossible has no content apart from what we think.

2. There is no impossibility without intensionality.

There is no reality, no thing with any kind of being, that is impossible. That means that among the ultimate explanatory elements of reality, impossibility will have no place; it only has content by the medium of minds. There is no absolute impossibility with content. What about a square circle? Of course there is no such thing. But there is the idea of a "square circle," namely a "plane figure that is closed, equilateral, rectangular, and has every point equidistant from a given point." Now the idea, the notion caught in the definition, is not impossible; for it exists; I understand it; in fact, I understand it so well I am compelled to judge that no reality fits the definition. Yet not once have I talked about anything that is impossible. Not even ideas can be impossible, except in so far as a recipe for imagining something may require us to go beyond our ability: like imagining a chiliagon plus one, an exact one distinct from every other. It turns out that you cannot imagine anything so definitely that there could not be a pair "exactly" as you imagine (if there can be any at all). Even a rule that cannot be successfully followed is still definable: "take three steps back for every one forward until you gain ten yards, then reverse the steps." It is successfully following it that is impossible, not the rule. Moreover, even a consistent object can be really impossible to exist. Euclid defined a line as "breadthless length." That's consistent as an intentional object but impossible phsycially, just as dimensionless points are.

Even impossibility that is rooted referentially in real things is intentional. We make imaginative, notional, conceptual, pictorial, sensible, arbitrary shadows of things by indefinitely many conventions and systems for projecting intentional objects from real things -- systems ranging from simple perspective for drawing images, to logical, grammatical, geometric, metaphysical, institutional, social, legal, and all other abstractions for making things to think about and talk about, like chess moves, hands of poker, statements, implications, and so forth. The conventions and systems are for making intentional objects, but not all of them have being only dependently on human thought.

Derivative from other intentional objects, including what things might have done, and what they might do but have not, there seem to be paths of impossibility: loci that have to be empty, e.g., the locus of objects satisfying the description of square circles [above], the locus of objects that are wood that thinks, rational reptiles, pigs with ceramic insides. There are, thus, paths of impossibility referentially rooted in what sometime exists. In that sense, the impossible is what lies beyond the ability of anything actual, ever. Still one has to beware of taking the grammar of our expression and contents of imagining to be realities: my car's driving forward in the snow after its wheels lose traction is not reality, it is an imaginary state of real things.

So, giving up some rigor for generality for now, let us say the relatively impossible is what lies beyond the remote capacities of whatever exists; that is, nothing that ever exists, is able to do it. The content of such impossibilities, even when real things and real conditions of things are involved is intentional.

But that is a dead end. It says "nothing is able to do it." Surely, we are not going to explain impossibility with an unanalysed notion of ability? Not beyond getting a kick start by realizing that the relatively impossible is what is beyond the ability of whatever is actual. The idea calls to mind that there is another kind of impossibility. After all, if nothing ever existed, everything would be impossible. Now the question is: what kind of impossibility is that? The answer is: a vantaged impossibility; a description from the vantage of what is actual of what would not have been possible had nothing ever existed. That is, we are not speaking of what is impossible, but of what would have been impossible, referentially anchored in what actually exists.

Similarly, when we ask about whether there might have been something which is not within the ability of any actual thing to be or to cause, there is no thing that we are talking about. Just as possibility not rooted referentially in the actual has no content, so unrooted impossibility is entirely empty.

3. The impossible with content depends upon the actual.

For example star-sized tomatoes, pigs with ceramic insides, rational reptiles, thinking electrons, stones that see, are all impossibilities whose components are real elements of some of our judgements. None of these are cases semantic inconsistency, and even if they were that would not explain why there can't be such things.

Other impossibilities are descriptively embedded in our abstractions. For instance, isosceles triangles where the bisector of the angle of the apex perpendicularly bisects a side that is not the base; squares with unequal diagonals; primes under twenty with 3-cubed roots; imaginary numbers larger than integers; complex numbers with real number factors. In some cases one can detect an inconsistency by "reading it off" the description. And in formalized discourse, given Church's theorem, a contradiction is derivable in a finite number of steps. But the explanation of the impossibility of such objects by the inconsistency of the description, depends upon the fact that the existence of abstract objects depends upon what is true of them. There can indeed be inconsistent abstract objects, at least in the form of intelligible descriptions and rules. Because the existence of abstract objects, as distinct from abstractions in general, is constituted by what is true of them, there can be and are inconsistent abstract objects: for instance, a square circle, an isosceles triangle where the bisector of the apex angle bisects one of the sides, a natural number without a successor by one. There are also inconsistent conceptions that are not verbalized or imagined -- but one has to do that thinking for oneself; we cannot write it out. All are impossible in the sense that no real thing satisfies the conditions, no matter what. Further, there can be impossible intentional objects that are not semantically or syntactically in conflict, but are impossible again in the sense that there can be no such real things, e.g., silicon-based life, or, dimensionless points and length without breadth. But what does "there can be no such real things" come to? As we shall see, it comes to there being no such situation at all because something is missing.

There can be impossible imaginary objects, like, silicon-based persons, because imaginary objects cannot exist anyway, not just because some are inconsistent but because they are all incomplete. Peter Rabbit is neither six feet tall, nor not; neither descended from proto-rabbits nor just rabbits.

(i) Real impossibility, is not assured by local semantic inconsistency. A "velocity that cannot be exceeded" was excluded by Newton's mechanics. The fact that a limiting velocity was locally inconsistent did not disclose a real impossibility. That's the same with "sub-atomic particle" which is inconsistent for Lucretius' cosmology, and within Cartesian discourse it is inconsistent that a human be essentially embodied. That sort of inconsistency does not assure a real impossibility.

Real impossibility, say, that dinosaurs could turn invisible, is obviously antecedent to inconsistency because whatever is impossible is forever impossible but descriptions begin and cease to be, as do whole languages. Nevertheless, there is nowhere for such content to come from but from thought. Formal impossibility, is consequent on inconsistency because there would have been no such intentional objects, even potentially, apart from thought -- although even apart from human thought, it could never have been that 2+2=5. Yet, apart from human thought there would never have been such a purported situation to be impossible.

(ii) Conversely, if a description is verbally consistent, we cannot conclude to real possibility because the "overflow" necessities may conflict or may be indeterminate. In fact, we can conclude to impossibility from any consistent description (thinking birds) that either requires the de re necessities of some sort of thing to have been different or to be replaced or augmented with traits not presently within the capacity of nature, or otherwise to be indeterminate. (I'll consider flying cockroaches later.)

(a) Hidden necessities.

Material things, whether natural or artifacts, all have de re necessities (both indexed and non-indexed) that are not expressed in the meanings of their common names or general predicates, but nevertheless form part of the conditions of applicability for those names and predicates. Typically these are the sorts of things we find out through science about things we are otherwise familiar with: emeralds, tigers, gold, humans, water, electricity, and explosions. Sometimes those overflow conditions have to be the same for each case named, and sometimes not (emeralds are either [Be3Al2Si6O18] or corundum [aluminum oxide]) -- as will be explained. But each case has real overflow conditions without which the name would not apply to the case. How items get to belong to the conditions of applicability is explained as "incorporation by reference," by our referential practices. (More on that later.) That is, when the word "ruby" is applied by expert gem traders, as it has been for thousands of years, the rare stones satisfy a large group of de re necessities, one of which is "being made of (red) corundum (aluminum oxide)," that are conditions of applicability because the paradigms throughout their gemstone practice were made of corundum, even though the traders and artisans didn't know it. Translucent stones of other composition are not regarded as genuine rubies. In passing, notice the notion of "synthetic" gems has split into two related ones: (i) stones of the same composition, but fabricated in a laboratory (though distinguishable to an expert), and (ii) fabricated stones of different composition that at the macro-level look or behave "very much" like real ones (e.g., synthetic diamonds), though easily detected by an expert and even by amateurs. In either case the hidden necessities scooped up by practices of reference are the overflow signification.

Impossibilities are not, in every case, absolute and eternal. What was formerly impossible can later be possible: a human with an artificial heart or a human living with the heart and lungs from a cadaver. Impossibility can be from incapacity that may be transitory; so, the heavy elements were impossible until they were cooked in the light-element stars, and the merely conceptual impossibilities ("sub-atomic particles" for Lucretius, "necessarily embodied reason" for Descartes) assure nothing. Impossibility from natural prevention or indeterminate de re necessity is, however, permanent.

(i) If an empty description (for a material object), "Martians," is verbally consistent, we cannot conclude from that alone that such phenomena are really possible because we cannot assume that there is some consistent and non-repugnant overflow by which the description can be satisfied. That is because we cannot assure ourselves that there is any other pattern of material universals than what is actual. Even less can we be sure that some other pattern of natural laws would allow material objects as we imagine them, say silicon-based life, or an intelligent extra-galactic particle cloud [Hoyle, 1957].

(ii) To say of some empty or physically impossible content, say, formaldehyde-drinking-animals, "but it is logically possible because there is no contradiction" is just a promise: we do not know that whatever involves no contradiction, relatively to our way of thinking, is possible or involves no conflicting overflow. In fact, we know the opposite: that many things that do not involve a contradiction, do involve causal repugnancy or vacuity as to one or more de re necessities. I vividly remember a childhood conviction that an ordinary reel lawn mower turned over and pulled backward would cut dandelions (too tall for the push position); the description was consistent, as far as it went; the image was apparently coherent. A few seconds' experiment revealed the impossibility as well as its reason: the reel blade and its striking plate were in positions opposed to capturing the dandelions. Conviction hemorrhaged into shame.

One can also have absurd convictions that something is impossible, based upon a genuine misunderstanding of what is required; thus, as a child, when I first heard one could transmit pictures through space without wires, I thought it impossible because the pictures would scramble one another. Most people still can't explain how the visible appearances of things from all directions don't scramble one another, as sounds and smells tend to blend (though not as much as one would expect, either; and why not?).

Not seeing how it happens or not being able to imagine something is as bad a guide to impossibility as consistency of conception or some coherent image is to possibility.

We do not even know that "whatever in its complete description involves no contradiction is possible." First, we do not have any complete descriptions that contain all the non-indexed de re necessities for any material thing. And, short of that, "complete description" is a vague notion. Besides when everything relevantly necessary is stated or referred to, say "thinking turkey vulture," the overflow necessities may and probably do causally cancel one another, even when we do not know what they are. Nothing on the surface of a description will tell us that they do not. Because that turns out to be so with many examples to come, we can conclude that not everything which is consistent to think is really possible, and nothing, except God [this Chapter, Part II, Sec. 6], is certain to be really possible just because we can consistently think of it (except for some logically trivial cases).

The richness of a language and the state of scientific knowledge of its speakers will have a lot to do with what is consistent for them to think; for instance, if you don't know about gravity you may think "everything seeks its proper place" is both true and necessary. You may also think weight is inseparable from mass. Yet what is really possible is not likely to vary with the poverty or richness of various languages, or with the belief-content of word meanings (e.g., that "motion" implies "impulse") or with variations in the meaning connections, especially via the belief-elements-of-meaning in various languages. So it should not be surprising that we can conclude very little about real possibility or impossibility from what we can consistently say or deny.

Natural repugnancy, e.g., water and oil will not mix but only emulsify, is independent of our conceptions and certainly neither caused nor explained by them. Repugnancy, causal cancellation of one trait by the conditions that produce another, is typical of physical impossibilities: a nut that is too small for a bolt, threads that do not match, a gasoline engine that will not start for lack of fuel or water in it, or an engine with a broken crankshaft.

Electrons attract one another gravitationally, but repel one another electromagnetically. To suppose the opposite may be semantically consistent, but is, nevertheless to suppose the impossible. That is not explained because the statement "like charges repel" is true; rather "like charges repel" is true because negatively charged particles repel one another and positively charged particles repel one another, etc. The explanation for that, if there is a sub-explanation for it, lies in the world, not in our judgments.

For a long time, and even now, formal truths of arithmetic and geometry were taken to be paradigms of the real necessities and especially of necessities that present their rationale directly to the understanding. The regularities of nature, e.g., "the planets trace out equal areas in equal times," were regarded as derivative, as mathematical or geometrical truths embedded materially, having the same necessity and intelligibility as the pure formal truths, though the rationale was not presented directly to the understanding but by way of the abstracted formal truths. In fact, the mathematizability of the embedded universal laws was thought to explain both the intelligibility of the material world and its absolute regularity.

More recently, as fashions changed, natural regularities, even obvious ones like "we grow old and die or die before that," were deemed contingent and hypothetical because there was "no necessary connection in nature," and even, for a while, conventional. But that positivist line was shaken by Kripke's argument that real identities are necessary and that important ones are discovered through science, e.g., the micro-composition of water and of gold. Note that we don't have to accept such discoveries to be identities in order to recognize the necessity of natural constitution. There are not many now who don't recognize the inexorable necessities of nature and the immense success of science at discovering family after family of them. There are still too many who have not recognized that for each of the necessities of nature, there are no relevant contraries with content.

Once we dismiss simplistic accounts of the necessities and impossibilities, like free divine decrees, exemplification of a world of abstracta, mere relations of thought or meaning or mere convention or centrality in the web of belief, the status and nature of such necessities looks as elusive as it was three centuries ago. The identities of macro-kinds with micro-composition are an exception; they do not seem to need any explanation after being discovered, except in so far as one wants to know how the micro-composition causes the macro-behavior and properties. The question, "Why can't water be made of ammonia atoms" can be disposed of with the reply, "Because water is composed of H2O." And we have had remarkable success at explaining the causation of macro-behavior from micro-composition in terms of very broad natural principles, that are themselves, however, in need of unification and reconciliation. Such explanations are typically either inner-mechanism, "clockwork," explanations, or encompassing generalities at which we have become exceedingly skilled in the last three centuries.

One way we explain impossibilities like the nut that will not fit the bolt is to provide a description of a nut that fits and then indicate, relatively to that description, which conditions are violated. And to the question, "Why are those conditions necessary" we can often go a fair distance explaining in terms of more general features of nature why such conditions are necessary, even to the point, say, of explaining what friction is and why friction both requires energy and changes the parts in contact (encompassing generalities). But at a certain point, when we run out of further "inner mechanisms" or "encompassing generalities," we run out of answers as to why things have to be that way, though we are still prepared to say they have to be. Both "inner mechanisms" and "encompassing generality" explanations have to stop some place, and we don't yet see how natural explanations can stop anywhere but at a question: "Why?" that has the disturbing but ancient consequence that "the final explanation," if any, lies beyond the materiality of things [see S. Weinberg, 1993].

I propose that what the impossibility of natural impossibilities consists in is that a necessity of nature uses up all the possibility relevant to what is actual, leaving the relevant verbal contraries (both as judgments and as intentional objects) referentially empty. Exhausting the potentialities of the actual is what real necessity consists in. In a word, there are no alternative situations involving the same subjects.

Furthermore, despite the logical sound of "exhausts" and of "relevant," real necessity and real impossibility are not logical conditions though they can be partly explicated with logical notions, but not in the ways that have been customary. For the necessities of nature, the iterative principle used by modal logicians in ancient, medieval and recent times, "whatever is necessary is necessarily necessary," is false; not because pigs might fly, but because there needn't have been any pigs at all, or anything else in our cosmos. Natural necessities, being embedded in things, might not have obtained at all. But there are no opposite situations for the same subjects. Similarly, "whatever is possible is necessarily possible" flouts the principle that possibilities involving contingent things have no content absent the existence of such things or the existence of things capable of causing such things.

The polarities among "has to be," "cannot be" and "happen to be" and "happens not to be" as modifiers of "true" and "so" gradually became rigid in philosophical discourse (while retaining their flexibility in other inquiries). So whatever is not something that "cannot be," "might be." This suggests that what is not inconsistent is really possible and fosters the illusion that we can detect real possibility either from our understanding, from our grasping a consistent conception of a thing (as both Aquinas and Descartes thought), or from our imagination of a thing (as Hume and Bill Hart and others, maintained). Those ideas do not survive well. Neither does the related idea that "inconsistency" explains impossibility, even though that too originated in ancient times, was certainly employed by great medieval and modern philosophers, and is the basic explanation one is usually offered. It is a confused form of the ancient and more plausible claim that what is impossible requires ens et non ens simul [Aquinas, Summa Theologica, I, q.25]. The problem with that claim is that the notion "requires" is part of it. Yet that notion can only be explained in terms of logical notions that invoke the idea that the impossible is impossible because it is inconsistent, where we know most natural impossibilities are in no way dependent on thought or language or any inconsistency.

Some said there are formal or logical impossibilities but no real ones. Sometimes they said that was because the denials of formal truths are inconsistent but the denials of regularities of nature are not. Others in a more Humean vein say the same thing but because they acknowledge logical relations among statements but no real necessitation in nature. Even among those who acknowledge that there are necessities of nature, very few think there is any other reason than inconsistency as to why something is impossible, and so they leave us with no account of what real necessity consists in. The implicit claim that there are inconsistent states of affairs (or situations) goes unexamined, even though reflection discloses that genuine inconsistencies have no being except in thought, while real impossibilities overflow thought and are independent except for content from it.

Then there were stories that the impossible is what is false in all possible worlds and the physically impossible is what is false in all relevantly similar (or otherwise related) possible worlds. Before long, it was clear that no explanation was being offered, just another lingo for saying the old things, for instance, that logical impossibilities are inconsistent and formal necessities have contradictory negations, while natural necessities are hypothetical, with no explanation for how the laws of nature came to be that way, or why they are laws or how universal laws are present in and "govern" particular natural events. That's where we are now, looking for a new foothold to explain how it is both true that what is naturally necessary is not necessarily necessary (as "true in all possible worlds" or even "true in all relevantly similar worlds") and that the relevant contraries to what is naturally necessary absolutely cannot happen.

(b) Unrooted counter-possibilities are nothing at all.

Suppose someone says, "there are silicon-based intelligent beings inhabiting one of the planets in the galaxy Cygnis"; none may be possible either because there is no such galaxy, or its stars have no planets or none of them can support silicon-based intelligence or because silicon-based intelligence is naturally repugnant or because the overflow conditions for silicon-based intelligence are not determinate.

For all we know "silicon-based intelligence" may be linguistically coherent but physically repugnant, as Escher's drawings are two-dimensionally coherent but three-dimensionally impossible. Similarly, "Minerva would find the Pieta beautiful" has no content because there exists no such goddess. The expression is formed on the model of those that do have determinate content and thus, determinate truth or falsity, but in this case failure of reference to an existent evacuates enough of the content to defeat any truth-value. We will encounter analogous cases when we consider claims about what might have been.

A counterpossibility is rooted when the referring parts of the description stand for real things or real conditions that are constituents of an actual or potential judgment that such and such might be or might have been so. Having cases is indispensable because the cases fix the overflow conditions the object has to realize. Every real object has real features that overflow our descriptions and predicates, and among them are non-indexed de re necessities. The linguistic meaning of a common name or description only determines conditions of its applicability typically and roughly ("water is a tasteless, odorless, colorless, potable liquid," in effect, distilled water), leaving out an unspecifiably long but determinate set of overflow natural conditions that are de re necessities for the things we refer to with that term, including both the usage of non-specialists and of the craftsmen and scientists concerned with water. So, ice is water, as is steam and as is superheated steam. Yet steam has to expand water volume about 1600 times to fill its container. Steam wets things, as well as heats them, superheated steam does not. The real necessities sometimes even oppose elements of the linguistic meaning: thus "water" applies to necessarily salty tasting ocean and to murky, smelly, foul tasting, poisonous, and non-potable liquids, provided they have a typically high percentage of H2O molecules, and satisfy the molecular bonding laws and the other (including unknown) condition(s) for water. The overflow conditions of applicability are far more extensive, detailed and authoritative as to what the word applies to, than the linguistic meaning. But the order of our knowledge is from pre-scientific practice (and comprehension) to articulate scientific understanding; many diverse de re necessities lie beyond the linguistic meaning yet have to obtain for our words to apply. That's why, in crucial cases, we have to use experts to determine whether we have the real stuff, whether gold, diamonds, jade, TCP, PCP, Vitamin E or DNA.

Supposed possibilities whose full conditions of realization are not fixed (determined) by the actual, fail in content; they are merely verbal, not real. Merely verbal possibilities are, in reality, impossible. To call them "logical" possibilities is just a mistake for there is nothing that settles what the overflow conditions are, and, yet, nothing can exist physically that has indeterminate necessities of nature. Similarly, there are some impossibilities because what it would take to have a case is so indeterminate that nothing could settle that there was one: e.g., my playing Chopin better or worse than everyone else. Now one wants a "proof" that nothing can exist physically that has indeterminate necessities of nature, especially because the claim is not put forward as true on account of a conceptual inclusion; but that will have to wait until some other things become clearer [see pp. 50-52, below].

Without human thought about real things there is nothing to provide the content for impossibilities. That means that before there were humans or other finite intellects, the impossible had no content, even though real physical possibility is exhausted by the necessities of nature. Thought has to determine the content of what cannot be. I am not speaking here of mere contradictory propositions or descriptions, like "the largest number," "the set of all sets," "all numbers" and "all possibilities," but of what cannot be, independently of thought and prior to the existence of all thinking creatures; for example during the age of the dinosaurs, silicon-based life was impossible; but we can only describe that from our vantage, thinking about a putative basis for life, silicon (in opposition to carbon molecules).

Once we recognize that possibility with content, "my being a chef" or "there being imperceptible matter," is not prior to actual being, as if there might have been possibility but no actual being, or as if possibility is not accounted for by actual being (but is either unaccounted for or self-accounting), it is obvious that possibility is somehow derivative from actual being, but not as an accident or incident or something inherent in actual being. Nor can possibility be logically derivative from actual being because logical relations are thought relations, not real as causation is. So it must be, as far as possibility is unactualized, from the ability or potentiality of the actual. Possibility with content certainly cannot be only a consistently thought-of replacement for, extension of, or rearrangement of what is actual. For that is both too narrow and too broad. Not every rearrangement (even consistent) of the actual is really possible, e.g., camels with human heads; and what might have been instead of what is, indeterminately overflows the actual. Yet, the idea of a wholesale alternative to everything that ever or eventually exists is inconsistent.

There is an intermediate step: to show that possibility (and necessity) is not equivalent to, coextensive with, or somehow the same as actual being, with only differences of intention -- a view David Lewis adopted [1986] and one that Henry of Ghent (c. 1300 A.D.) seems vaguely to have anticipated, and that has a more recent indirect antecedent in Spinoza. I will not canvass the many objections here [Ross, 1989], but repeat some that are immediately in point: (a) that Lewis' theory requires that esse possible, esse necessarie and esse actuale be coextensive, differing only in intention, and thus requires that "to be" be homonymous; (b) that no satisfying account can be given of absolute impossibility, since there "are" worlds without "our" laws, or any laws related to our laws, and since notions of semantic inconsistency are all language-relative; (c) that the multiplicity of worlds is causally inert and can only "explain" actual causation and its counterfactuality by an imperialistic revision of what we mean by "careless smoking causes fires" into what Lewis insists we have to be saying about counterparts in suitably related worlds. Interestingly, the whole system seems compatible with a Spinozistic ontological argument: a thinking/material substance -- with infinite other attributes, as well -- that is the one substance, relatively to every physical thing in any world -- that is, a being for which every and any object in any world is a here and now -- is possible. But if possible, it exists because it is metaphysically explanatory relative to every world, and thus exists in every world, or, perhaps better, is the substance of everything in every world.

Lewis cannot fend off this kind of ontological argument by insisting that nothing other than physical things is possible, because, in one attribute, the one substance is physical/material and its material modes in all possible worlds are nothing but its attribute of materiality, taken extensionally. Moreover, it is the one substance of all material things, and of all thinking, and of infinite other kinds of things. Is it inconsistent that there be an infinity of attributes of which thought and matter are just two? I don't think we know. And were Lewis to reply that relative actuality is physical interaction alone, that would implicitly claim that a being whose substance is beyond or more than material is impossible: something that would need a non-circular, independent proof. Such an inspiration from Spinoza would turn Lewis' system into the grand alternative to creationist theism that I consider in Part II of Chapter 3. But Lewis' system, unless further repaired, would still commit what I regard as a deadly offense: telling people they mean, or have to, something other than what they do mean by perfectly ordinary things they say about what they might have done and what might have been, or about causation and natural impossibility. So we can move on to how actual being accounts for possibility.

Possibility is not prior to or equivalent to being. So possibility has to be in some way posterior to being, absolutely, though, with regard to change, possibility has to be prior to what comes to be and posterior to or coincident with something that is. Since no one doubts that what is actual is possible, we have only to consider what is potential and what might have been. What is potential is what is within the ability of what is or comes to be so there is, relatively, the merely possible. Not everything which is within the ability of what is or will come to be also comes to be. So there is, relatively, the merely possible, but anchored referentially in the potentialities of the actual. What might have been, as far as it lies beyond what is or is potential, is empty, in fact, impossible. Thus, that I might have been made of silicon is impossible; that I might have been born on the moon is impossible, even though a time may come when another person may say rightly, "I might have been born on the moon" because it is within the capacity of actual things to have brought it about. (Also we need to distinguish an inherited truth, like "I might have been born on the moon," because of the capacity in nature for that sort of thing to happen, from verbally the same falsity from the lack of capacity for that very thing to have happened to me.)

Given that possibility is not the same as, or equivalent to actual being, and that possibility is not prior to being, then possibility must be derivative from (or otherwise consequent upon) actual being. Clear senses of "derivative from" and "consequent upon" would help, but not at the expense of a petitio over whether logical relations have any reality without minds. So we ought not to say, yet anyway, that the "derivative" and the "consequent" is a kind of logical aura around the actual. There are no logical relations in nature, and, thus, that derivation has to involve real causation or explanation or be made by thought. Real possibility (e.g., that a certain train might have gone off the track) is explained by causal ability whose exercise is subject to external conditions that do not yet obtain, (e.g., a rotted tie), or causation conditioned probabilistically.

The general notion of "the possible" relative to being is only analogous to "the possible" relatively to the logically contradictory and to the physically impossible. It has to be enough for now to say possibility is explanatorily posterior to actual being, and that possibility itself is not explanatory of being or of itself.

The absolutely impossible is not an indeterminate black region surrounding the white region of pure possibility in which there is a gleaming, luminescent center of actuality and around it a hazy halo of bluish white, constantly changing, some parts to luminescence and other parts to plain white, that is "the potential." The impossible is not on a par with the actual or the potential as if it were simply a continuation of the surface with a different color or the absence of color. Even the possible is not a continuation of the surface of the actual. The impossible is as unreal in relation to the actual as is the imaginary "minute before the beginning of time" in relation to physical change.

One could think of all the well-formed arithmetic falsehoods as an outer darkness beyond the white region of well-formed truths. But extending the comparison fails because the content of the anti-theorems is the content of the theorems negated, whereas without a fixed domain of what is possible (like a domain of all consistent propositions) there is nothing to determine the content for impossibility. To block that comparison we have to take note that there is no domain of all consistent propositions or states of affairs, as argued elsewhere [see Ross, 1989 and 1986(b)]. In brief, the lesson is that propositions involving proper names (atomic propositions) are vacuous unless the denotata exist.

There is no "indeterminate empty region" of absolute impossibility, like a shadow, or a night around actual being, any more than there is a black empty space around the universe.

More of another picture. Nothing is impossible with content, except relatively to what is actual, and then via what is possible and via what is thought of. The possible with content lies within the capacity of whatever exists. Unless an intentional object is descriptively and referentially made-up of actual things, it lacks definite content, that is, "content all the way down," because it fails to include "overflow" conditions that can only be included by reference to actual things. Without being determinate "all the way down" an intentional object lacks a sufficient condition for being, by lacking a necessary condition, and thus, is impossible. Thus, for instance, Descartes' sum res cogitans is impossible.

Because imaginary and fictional objects are not rooted in actual things so as to be determinate "all the way down" they, too, are impossible. Of course, one must distinguish imaginary situations involving real objects and real features of things, which we use to rehearse and to predict reality, from fictional and imaginary entities that are indeterminate in ways in which all actual things are determinate, and thus can never be identical with any actual thing. We can imagine fictional or imaginary things in imagined real situations; and still the de re necessities are incomplete: Minnie Mouse in New York; or Zeus at Shea Stadium. Imaginary and fictional things cannot be or become real.

So, possibility, being, and thought are explanatorily prior to impossibility with content: being can explain, derivatively, impossibility, but not the reverse. Thought is required to explain the content, and possibility is required to explain what is exhausted by the actual. Similarly, light can explain dark (as the absence of light), but not the reverse, because light is much more than the absence of dark, just as heat is much more that the absence of cold, for the "overflow" conditions of "light" and "heat" are much more than just "not dark" and "not cold."

II. The Impossible

1. Four ways.

A notion, expressed with a common name, predicate or description, can be impossible in four ways: syntactic, semantic, pragmatic and by vacuity. It can be syntactically inconsistent by requiring something negated, "a largest number," "a set of all sets." It can be semantically inconsistent by a clash of meaning that requires something denied: "insensible water," "a thinking thing that cannot judge," "a vampire." It can be naturally impossible (pragmatically repugnant) by requiring what is causally prevented by something else that is required: "humans with pig snouts," "humans with stag's torsos," "rational reptiles," "being a child-bearing male mammal" or "being a non-mammalian rational animal," or "wood that thinks," or "a mermaid."

Natural impossibility, the most interesting and perplexing sort, typically involves causal cancellation among elements of the overflow signification. It is the sort that many philosophers hold to be merely conditional because it depends upon causal relationships that result from what they consider contingent natural laws. But the resulting indeterminacy of the de re necessities is not contingent. Such causal conflict is a symptom of the underlying explanation: vacuity of de re necessary conditions.

Natural impossibility belongs to notions that are vacuous for one reason or another, "unicorn," "martians," "thinking electrons," "silicon-based rational animals." In fact, natural impossibilities, when we try to adjust the notions to escape the causal conflicts involved, become vacuous either about the overflow necessities, or about what would count as a complete case of the explicit traits, e.g., "thinking wood." No sufficient condition exists because some necessary condition is always either indefinite or absent.

2. The physically repugnant.

Conditions that causally prevent one another are physically repugnant. Typically, what is physically repugnant can be further analyzed into a vacuity because determinate overflow necessities are displaced by the causal conflict. For example, would "wood that thinks" have electrochemical states of the wood fibers that are the medium of thought? Nothing determines that yes or that no. Yet, nothing real can be indeterminate in its non-indexed de re necessities. Suppose you say, "There is some of each," I reply that there is each time another disjunction that nothing determines.

The idea that something has overflow necessities that are not settled by anything at all is a "something comes from nothing" claim: there are overflow necessities for a thing but nothing settles what they are? Then, something required is always missing. Thus there is no sufficient condition for there being such a thing.

We can say that "wood that thinks" is impossible either because of the vacuity of the overflow necessities (say, of the molecular laws required to realize such things), or because of a conflict of the expressed traits (e.g., being wood and thinking) that leaves the overflow necessities undetermined, so that there is no sufficient condition for such a thing. Both are true. In either case the notion is referentially vacuous, but the vacuity is the final explanation, not the conflict.

Some notions that are impossible at one time for lack of determinate conditions we can refer to, can be cured with an increase in knowledge and skill; thus "human living with the heart and lungs of a cadaver," "human walking on the moon," "flying machine," "submarine," "space ship." All these notions lacked determinate de re conditions until the last century or so. Philosophers should resist speculation from "thought experiments" that have cognitively or referentially indeterminate overflow conditions: "that my brain and spine be transplanted into your body," "that I have all my experience, absent the external world." Although many great scientific discoveries result from thought experiments, there are also the cases of the scientists' getting things wrong because the imagined situations were indefinite as to relevant necessities that were not then known. Wisely, the physicist Fineman said he refused to speculate with conditions not already known to be possible. A tight rein on imagination in philosophy is as important as imaginative fertility; think of all the trouble from Descartes' demon and from Putnam's analogue, "brains in a vat"; and from "maybe I could have all my experience exactly as it is, with no external world." The imagination is the master of falsity. Philosophy based on imagined counterpossibility is kiting checks.

The impossibilities we find useful to know about are not typically represented as semantic or syntactic inconsistencies. For instance, it is impossible that there is anything that is just an animal; but "just an animal" is not straightforwardly inconsistent and the impossibility is not because of an inconsistency. That impossibility is particularly interesting because we have found out that there are many different ways in which a natural living thing can be a sentient thing, as if there were many different formulas for many different kinds of organic molecules, each functionally equivalent for making a sentient thing (e.g., a bird, a frog), but not one common formula that can be abstracted and then realized in "just an animal."

"Non-mammalian rational animals" is consistent as far as it goes. But, again, apparently there is no way to abstract a formula for rational animals that can be realized in non-mammalian animals. In general, these cases are like "pigs that fly"; when you imagine the conflicting causal features to be cancelled out, there is nothing to assure that there is a consistent and determinate replacement by a complete de re necessity for what was cancelled.

The principle, "If there are not any (even potentially), there cannot be any" is an application of a general consideration: What is beyond the capacity of nature is impossible by the absence of determinate overflow conditions. That is impossibility from vacuity.

3. What about superaddition?

Could God have made any arbitrary combination of predicates into a real nature, say, "thinking electron"? It has been customary to think the traits denoted by semantically unopposed predicates can be freely combined by an omnipotent being, and might even occur in the cosmos somewhere. That view is sometimes attributed to J. Locke. In fact, it is commonplace among philosophers that logically independent traits combine. For instance, Kripke [1977 and 1980] apparently thinks so because of the contingency of natural laws. So "thinking electrons" should be possible, too, because independent traits can be superadded, as life is to matter, sensation is to life and intelligence is to sensation. In principle "stones that see" would be possible.

But things are not that way at all. Not only can stones not arrange themselves to be able to see, as inorganic matter may have arranged itself into primitive life systems, stones cannot be arranged so as to see; they lack the passive or obediential capacity to see, as well as the active ability. They can't be made able to see any more than a violin, without equivocation, can be made able to play itself.

Natural traits are not independent of one another, however little they may be joined or opposed in our conceptions. To the contrary, much of science indicates that abilities both active and passive, obediential -- what something can be made to do -- are knitted together throughout the cosmos, for instance, so that there is no life without water. Why? Why can't galaxies think? Surely not for lack of parts or communication among parts. Surely not for lack of variety of electrochemical states or functions (fluctuations) among them. We have to find out what nature cannot do and cannot be made to do by experience: experiment, observation, conjecture, and checking, as Leonardo insisted. There is no a priori or external vantage to tell us what nature cannot do; that is because what cannot be done has its content only from what can be done, and the latter is not accessible apart from what nature does, though we improve at projection as we improve at mathematization, modeling and simulation.

To suppose natural laws are replaced so as to allow "thinking electrons," without being fully specific as to how they are replaced, still leaves the overflow necessities indeterminate and the conception vacuous. Whatever in principle lacks a sufficient condition for being is impossible. There are no "traits" apart from laws and no laws except embedded in things. Not just any consistent combination of real features is really possible.

Reconsider, "Could God make thinking electrons?" No. None of the existing electrons, nor anything of the same kind as they, could (consistently) be a thinking thing. But suppose we were talking, as Locke perhaps did, about divine superaddition, the addition of a power to a nature already complete but lacking it? That supposes a conjunction of powers we already know have cases, powers that do not exclude one another by lack of obediential potency in the base power (say, animate matter) but only a lack of active ability in the base power, to which another active ability is added (sensation to life). But not all living things are passively capable of sensation. There is no way to add sensation to most plants. Until we have a case of the combination, or an attempt to make the combination, we do not know what the base power excludes, rather than just lacks: thus, can silicon parts be arranged into an intelligent being? We do not know, but so far it is wise to predict "not." To say "in principle, why not?" is to make ignorance a principle for affirmation. We have to know much more than that we can imagine it or can say it consistently with what we know: after all, 15th century scientists might have said "there are and can be no animacula invisible to the eye that cause disease," consistently with what they knew.

The superaddition hypothesis premises that powers not notionally opposed are physically compatible; but that, in general, is false. You can't have sensation in orchard grass; it lacks the necessary "wiring." There is something like a necessary principle that "there have to be connections in nature"; that's why I can't turn on my television by merely pointing (though someday, perhaps I can). Our general knowledge of micro-matter suggests that there are no mid-range powers of things not connected by at least some common micro-principles among micro-components that restrict their combinations. Compatible verbal descriptions, say, "formaldehyde-drinking animal," may incorporate physical conditions that causally prevent one another.

It is not enough to establish the possibility of what is causally prevented to say "the causal relations of things are contingent and anything might have caused anything else." We do not know that to be so. In fact we have very good reasons to think it is not so because we cannot even state, with determinate overflow conditions, what we suppose, causal relations being different, would then cause what: would shape cause color? It may seem sensible to suppose that anything might have caused anything else, even using an "explanation" notion of "cause." But how could we ever know that, if it were so? The reasoning that because cause and effect are not logically connected, any pair of logically independent events could be related causally, is completely unreliable, for one thing, because it presumes that what is consistently conceivable is possible -- something I have shown to be false. Could a lighted match have caused gasoline vapor to freeze at ambient 100 degrees Fahrenheit?

On reflection, it seems as if things could only have had the causes they do have because supposing otherwise leaves nature full of gaps as to what is really required for things. To suppose shapes cause colors, for instance, is to leave nature with undetermined micro-structuring for such phenomena, with no way to settle how such phenomena would come about or be related to the microstructure for the rest of the world.

Some philosophers have a Humean notion that there is no genuine necessity (apart from relations of ideas) and so no genuine impossibility. For them, nature is all gaps, nothing is really necessary for anything: you could freeze gasoline by breathing on it. Bill Hart [1988] has insisted that whatever is imaginable is possible, with no explanation of how imagination and reality are connected, especially since things were possible before anything was imaginable, there are all sorts of actualities that are not imaginable, and we know some imaginary things are not possible (e.g., three dimensional Escher figures). Because there are no necessary connections, anything can happen, they say. That idea is out of touch with our experience: "Let's go back to yesterday." "Any nut will fit any bolt." "After ten minutes toast untoasts itself." To insist, "But it could happen" is futile. We are not talking about what is extremely unlikely; we are talking about what cannot happen at all, and that, in the end, is because there is no determinate sufficient condition for such things. To say "nothing and everything is sufficient for anything" is to make nonsense out of science and to withdraw from our inquiry.

Description of what-might-have-been is denominative from the actual. That is, it is referentially vantaged from the actual: suppose I had been Asian. A supposition that cancels the anchoring vantage will exhaust its own descriptive force. "Suppose wood could think." Saying that one is only canceling what conflicts with one's description (e.g., "silicon-based life") assumes (1) the contingency of natural laws, (2) their physical independence from one another, (3) that there is only one such combination of overflow necessities for silicon-based life, (otherwise, the overflow necessities are indeterminate), and (4) that our supposition in fact controls what overflow conditions are cancelled. We have no solid reason for any of those presumptions.

"Creating natures" could be called "combining traits whose predicates are semantically independent into bundles bound up with natural necessity." That has to be a metaphor: otherwise, it is plainly self-refuting. Traits do not pre-exist their cases. One cannot recombine the actual cases, because a thing can't become of another sort. Even if traits are semantically independent, they can still be related by hidden or overflow natural necessities and impossibilities: colors cause shapes but not the reverse (to use an example from Aquinas); we can imagine shapes causing colors, e.g., triangles cause primary colors and rectangles cause pastels, etc., but we know it is impossible, even though we can make a computer do it. Even if we cannot explain why such causation is impossible, we know it is because we can make the same shapes of all colors. Do not say "nature is not arranged that way but it could be." Nature could not be so arranged. The proposal is dependent on the contrary of a natural necessity and is vacuous as to its overflow conditions. That is what real impossibility is.

Creation of natures is not at all like "(re)combining independent possibilities," as if they were pieces given in a child's building game. When we synthesize a paint, a dye or a drug, we use the interdependent tendencies of particular batches of matter, not abstract relationships among sorts or kinds, though our descriptions and formulas are expressed in general terms that require anchoring in real cases of the kinds.

Denying that there are real kinds to escape this point is futile, as is supporting the denial with appeals to fuzzy borderlines among natural kinds or to the ways we can synthesize chemical intermediates, and the like. None of that shows there are not real natural kinds; in fact, all such arguments suppose that there really are natural kinds separated by natural necessities, as well as other real kinds (synthetic), and that often enough we are mistaken about them. The deadly fact remains that novocaine, procaine and cocaine, despite their similar molecular rings, are immensely different in their effects on animals and no amount of talk will reduce that to what we think. The same holds for deaths from drugs, toxic wastes, and spent nuclear fuels.

Predicates for concurrent traits can become linguistically linked, as did the notions of "computer" and "machine language"; and predicates for naturally exclusive traits (say "being molecular" and "being massless") can become linguistically opposed, when knowledge becomes commonplace enough [see the discussions of analyticity in Chapter 3, Section 5]. We cannot, then, conclude from the semantic independence of expressions, say "water" and "H20," or "sulfuric acid" and "H2SO4," or "ruby" and "AL2O3," that the realities are separate or contingently linked. Nor can we conclude that the opposition of predicates in any way explains the impossibility of massless electrons.

Linguistic inclusions and exclusions come about in response to our convictions and are missing where conviction is unformed (e.g., "water is made of quarks"). Semantic and conceptual contingency offers no assurance of real contingency, contrary to Descartes' conviction that my being a thinking thing is really distinct from my being an extended thing because the former clear and distinct idea does not include the latter, and, further, that there are features of the latter (divisibility, extension, etc.) that are all excluded by the former. Similarly, S. Kripke reasoned that pain, presenting what-it-is in experience, does not include any brain state and can be thought of and imagined without any particular brain states, and so cannot be the same thing as some sort of brain state. The trouble with such reasoning is that the overflow necessities for a thing may not be presented to observation in what-it-is, especially when we are dealing with a "what" (pain) only by analogy to real substances, or with a "what" known pre-scientifically, e.g., "lion." Necessities may lie below the level at which material systems are made into pain feeling systems, as cats and dogs and mice are. For example, the gravitational requirements for a stream of electrons to amount to an electrical current may not be presented in "what electricity is." An unembodied understanding would be unable to feel pain because bodily states are necessary for pain states, even though it is not clear how to explain that, though Aristotle recognized it long before brain states were understood. So, to suppose there can be pain without brain states is to go beyond what is really possible with only imagination or words as one's warrant. Real necessity and real impossibility are not explained by conceptual inclusions or oppositions, any more than they are explained by the meanings of words.

4. We cannot refer to kinds that only might have been.

We cannot refer to kinds that only might have been, that have no cases at least potentially. One reason -- the one I emphasize here in order to connect up with (a) "no names, no statements," and (b) "no things, no names" -- is that there is nothing to determine the overflow necessities, and thus, the purportedly referring term is vacuous. What about the phoenix, a bird that rises from its ashes, implying whatever else is required? "A bird that rises from its ashes" does not imply whatever else is required. Every real kind, and every thing, has to have determinate overflow necessities. And the overflow necessities are not logically contained in the linguistic meaning. So there cannot be any nameable merely possible kinds that do not share real natures with actual things. A fortiori, there can be no unnameable empty kinds either. As a matter of general principle that is because the kind (as nature) is to the cases as capacity is to realizations; so, "no cases, no natures." [This is explained more fully in Chapter 7.]

5. What about common names?

For common names in general, overflow conditions that are sufficient in one context are much more varied in others than the simple case of emeralds, as mentioned above (beryl or corundum). There may be dozens of things that will do; consider cans: tin, aluminum, plastic, paper. Because cans do not form a single kind, a single overflow signification is not required or incorporated by reference, but rather an indeterminate and changeable range is incorporated. But in each application of the word to a real thing, what the can is composed of has to be complete, the de re necessities of the material have to be settled even though not settled by the meaning or the merely verbal context.

The notion of "incorporation by reference" is broader than its simplest examples because what is incorporated is not determined entirely by what we are referring to. Rather the overflow conditions are determined by the varied referential practices with which we use common names and predicates. So it makes no difference that the largely unknown overflow conditions keep shifting with the particular things we are talking about, say, fabrics, paints, cosmetics, or even that overflow conditions depend on and vary with social practices: e.g., what counts as a book (in the magazine trade a magazine is a book, but an issue is not), or what counts as "a play" or "a long movie." Many of the latter words don't pick out things of more than conventional kinds, with no expectation that the overflow conditions are shared throughout the domain. But with synthetic kinds, medicines, fertilizers, chemicals, type faces and so forth, there is every expectation that individuals and batches will be the same in every relevant respect where "relevant respect" is determined by the demands of the craft involved, analogously to real composition (Baskerville type), and of the surrounding legal structure, and vastly overflows the elements of the meaning.

(a) Back to peanut butter and hot dogs.

The United States Department of Agriculture determines with respect to over forty- thousand different products what their constitution, as a matter of law, is. For instance, the Department determines how much coconut oil there can be in peanut butter and what the amount of pig hairs, skin flecks or hogs lips can be in hot dogs. So there are intermediates among artificial kinds, some being merely conventional, others socially determined, and others determined legally with consideration of public health and fair competition. Real kinds, whether synthetic or natural, in which every case has to share every de re necessity with every other, have many and varied imitators. The basic principle remains that for any pair of things, both of which satisfy some common name or predicate, each must be entirely determinate as to its overflow necessities. But it varies whether the de re necessities in a pair of cases have to be all the same, the same down to the atoms, or the same up to some point, or up to some functional equivalence (lawn-mower blades; razors) or even less.

(b) General names and common natures?

What about terms more general than natural kind terms (species terms whose domains are caused by individuation)? More general names like "living thing," "animal," "dinosaur," "spider," and even "flying thing," have cases that differ in kind, often in many levels of kinds. Some have sub-classes like "mammal," "bats" and "seals"; other common names pick out features, "flying things," that can be satisfied by unrelated things: e.g., insects, planes, birds, squirrels, and some dinosaurs. Many general terms can only have cases whose physical composition is not part of the meaning of the general term. Thus sapphires are transparent blue corundum, though synthetic sapphires are fused aluminum oxide with titanium oxide for color; and emeralds are green beryl, though oriental emeralds are transparent green corundum. But the linguistic meaning of "sapphire" and "emerald" does not include the physical composition. Those are not just peculiarities of language. The composition was unknown when the referential practices became refined and reliable, and nothing in the usual practices of jewel buying and selling needs modification by such additional meaning. The composition of things in the animal kingdom was also unknown when the basic taxonomy was developed. So it is not surprising that the de re necessities for leopards, bears and salmon overflow the meanings of the names, or surprising that some things thought to belong to the same natural kind are later found to differ, sometimes radically.

Nothing can exist that is just a living thing, just an animal, just a dinosaur or just a spider (as it is impossible for anything to be just a thing). The impossibility of "just an animal" or "just a dinosaur" is not just a result of the possibility of distinct kinds of animals or dinosaurs, but part of its explanation. The explanation is not in the potentiality for various species directly, but in the necessity that structures be definite "all the way down" to the atoms and that structures thus definite one way can be made equally definite another way, with the same more general features. An animal has to have a structure that makes it sensitive and cognitive and able to move around, on the whole; but nature is capable of many devices to achieve that, but only in definite sequences ecologically adapted. The large organ structure that finally determines how animality is achieved is the species. The cellular and molecular structures that achieve the large organ species are among the overflow de re necessities.

To be an animal, dinosaur, reptile, bird or spider is notionally incomplete as to the large organ structure by which the general notion is physically accomplished (as well as to the micro-structure involved); that belongs to the overflow signification. As a result, specimens not previously examined can be borderline cases and raise borderline questions. The particular conceptions for kingdom, phylum, order, class, family and genus of individuals are conditions abstracted from particular observed or fossilized physical realizations. The general kind, spider, is prior in evolution to the species, black widow, because, presumably, there was an ancestor species that was a spider but not a black widow. Yet the kind, "spider" was not structurally prior to every species, but just achievable by structures other than whatever were the early species. Individuals are explanatorily first in nature, the more general, like species, genus, family, class and phylum are physically consequential and notionally derivative. The broader terms, while having overflow significations satisfied in nature, have no cases that are the same as what is meant, while specific kinds do. To say of an ant "that's what it is to be an animal" is misleading; even to say "that's what it is to be an ant" is misleading because there are species of ants. But without misdirection we can say of an ant "what it is is an ant" and more generally, "what it is is an animal" (sentient, mobile, reproductive).

The many kinds of things, from shadows to eras to events to substances, along with the inexhaustibility of "being" by kinds, shows that "to be" is not the same as "to be F" where F is some kind-name or group of names; nor is "to be" a what that can be discretely multiplied the way "to be a human" is. Nor is "to be" the same as "to be physical," though that may need argument for some philosophers. Being-as-such is not any kind of what, nor is it a determinable, exhaustible by a range of "whats" [Johnson, 1927]. A material thing does not exist on account of what it is, and is of a kind, of which there can be another case. (I skip immaterial kinds with material cases, ranging from "The First Letter of the Alphabet," to "the diatonic scale," and immaterial species, "The Angel Gabriel," which, strictly, are not individuated.)

"Animal" is not realized in a thing by conceptual addition of one universal to another (like the conjunction of the accidentals, "being a philosopher" with "being a physician"), and certainly not by physical addition (like another coat of paint, another floor to a building, or more complex circuitry), or as the accident and mode "being a pianist" combines with "being a very good pianist," but by the physical necessitation of "being sentiently alive" in "being a rabbit," with the latter physically sufficient for the former, even though the physical structure for a rabbit may be vastly different from that of a clam, which structure is also physically sufficient for "being sentiently alive." In effect, the "circuitry" sufficient for being a rabbit is sufficient for being an animal, as is that of a swallow, but such "circuitry" is different in both.

The apparent logical addition of, say, "rational" to "animal" gives the misleading impression that a real condition "being rational" is conjoined to a real condition "being animal," as a mode or accident of it, when, in fact, "being a rational animal" is a kind of being animal, the way "being yellow" is a kind of being colored. There is no "addition" at all. So, too, being a rabbit is a kind of being an animal. There is not some physical core that is sufficient for being an animal from which modifications are made to get a rabbit rather than a dog. Thus, the superaddition hypothesis is false in its supposition and is really impossible.

Suppose the only rational animals within the capacities of nature are humans, and perhaps dolphins and whales (or their evolutionary descendants). Then "non-mammalian rational animals," say "smart snakes," is a name with naturally repugnant content. It is not just empty; it has to be. The reason lies outside the meaning. It lies in the cancelling causation among the physical conditions. The result is that the overflow de re necessities for "smart snakes" are indeterminate and the expression fails, therefore, to pick out a specific kind, and can at most have the generality of "animal" or "reptile," but without any determinate large organ structure or DNA program for such a thing. It is an imaginary kind, like "the phoenix." For "animal" and "reptile" nature has multiple devices for satisfying such conditions (both at the large organ and DNA level), whereas nature has exhibited no devices for making intelligent snakes, with the consequence that what-there-has-to-be, for there to be one, is indeterminate. Again, this is impossibility of an intentional object by vacuity of the overflow de re necessities for a realization.

6. One ought to ask "What about the case of God?"

If consistency of description is not enough to assure real possibility, won't proofs of the existence of God be in vain? In the case of a divine being we have a meta-condition governing every element of its entitative conditions, namely: each attribute must be a pure perfection. That is, each divine attribute must imply no limitation and exclude no feature that implies no limitation: for instance, being, life, intelligence, will, love, wisdom, power, goodness, etc. No such feature requires a limitation, or excludes any feature that also does not require a limitation. As a result, we can deduce real possibility from the consistency of the description because we have a meta-condition for the overflow necessities that assures that the overflow is consistent, non-repugnant, complete and determinate, even though we can never conceive of all of it, seriatim.

7. Vacuity of overflow conditions is sufficient for impossibility.

If there were never any ergons, say even potentially, no one, even God, could say definitely what there were not but might have been. That is so, even though we might have a linguistic and partially anchored definition, "ergons are the minimal units of energy throughout the cosmos," because the overflow necessities are undetermined (e.g., relationships to space-time).

So, "there is no real possibility that ergons exist" is not the same as "it is impossible that there be atomless water." Ergons are impossible because of the failure of content (and of reference), because of deficient conception; atomless water is impossible because of semantic content that requires conflicting real necessities, because of a defective conception. In neither case is there any reality that is impossible. Rather, purported realities, intentional objects, are not genuine because the conceptions are deficient or defective.

8. There are no ranges of mere possibility.

Now when a general expression, "smallest units of energy," is used, there is no automatic impossibility: rather it depends on the nature of things. Some people suppose there are ranges of mere possibility by imagining "everything else" as maximally consistent rearrangements of and substitutions for what actually exists. As I mentioned, the idea is both too big and too small. Some "rearrangements" are real possibilities, "I might have been an engineer," and others are not, "There might have been formaldehyde-drinking animals." Secondly, possibility is not exhausted by rearrangements of what is actual; there might have been more domestic cats than there are, or other kinds of things than there are, though, for the most part, we cannot say what other kinds there might have been.

Carnapian "state descriptions" and the semantics for quantified modal logic postulated a range of well-formed and logically independent atomic propositions, each of which is determinately true or false, and every permutation of which holds for "some possible world" (with a tier of well-formed assertions true in every world [necessities] and another, false in every world [impossibilities]). That led to an extensional interpretation of intentional logic. It also led to equating impossibility with propositional inconsistency and possibility with propositional consistency without any recognition that there might be necessary conditions for being that lie outside the meanings of general words, hidden in the referents but incorporated into the truth-conditions by the success of the reference, and missing from the conditions when reference fails.

That "what might have been" may exceed rearrangements of the features for actual things seemed only a detail that can be supplied by abstract surrogates (individual essences and empty universals). The implicit platonism for "all" individuals, kinds, and states of affairs and the parallel abstract worlds clash with the intended scientific empiricism and with our natural language notions of causation. How could such abstract surrogates stand in any real explanatory relationship to what actually exists? And what relationship exactly is missing in the case of what never actually exists? Is that a negative relationship between an actual abstraction and a non-existent thing, e.g., my elder brother's not exemplifying an individual essence?

There is no ontological correlate for that neat logical device, "state description." Notation is no guide to ontology. The idea that there is a fixed domain of individuals for all worlds, of all properties and of all kinds, and of all worlds is absurd. It supposes reference on the part of singular terms and kind-terms that we do not have, terms that are empty, and simply makes up surrogates to serve as referents. In particular, since universal propositions decompose into a conjunction of singular propositions and existentials decompose into a disjunction of singular propositions, there have to be proper names for merely possible things or for abstract surrogates for them (individual essences). That violates the principle "no things, no names for them." It also equivocates on the notion of "proper names" because the name "Socrates" is the name of the whole actual individual, not of some abstract "individual essence" or some range of distinct "counterparts," whereas the name "Archibaldus" is either the name of an individual essence or the name of some counterpart (for Lewis), or no name at all. That equivocates on "naming." Abstract objects can't have proper names in the same sense as material individuals. "What is the name of the first letter of the alphabet?" "Answer: 'A'." "Now if that is a proper name then how can each case of the first letter share the name? Similarly for numbers and figures and topological shapes."

9. There is no fixed domain of worlds, either.

So a key feature of quantified modal semantics is incoherent. "Being" cannot be exhausted by logical division into kinds. Imagine lining up things that differ; what would there be about the differences at some certain point that would make no further differences possible? Nothing. Kinds cannot be logically exhausted by individuation, either. If there were enough matter, you could not make the "last possible human" logically by exhausting the differences among humans. That's because which human it is, is not explained by its being human. So, nothing could generate real ranges of kinds or individuals that would be replete (so full that no more can be added).

Besides, the idea that all possibility is encompassed by rearrangements of actual properties (universals), say "at 'all' space time points" recklessly blends what "might have been" globally with the ways actual things might have been -- a fusion that implies that all possible things (and features of things) are somehow actual, either by surrogates (the abstracta of Plantinga, Stalnaker, et. al.) or by the physical occupants of a matrix of space-time points, or by the universal esse possible of D. Lewis. It is obvious what to conclude: the domains of individuals, properties, and kinds are not one for all worlds. There are no real unexemplified properties. There are no real abstracta to allow quantification for such ranges. Neither being nor any real kinds or universals form such a quantifiable magnitude. There is no true ontology for traditional quantified modal logic and, in fact, important axioms, when understood naturally (for example, that whatever is necessary is necessarily necessary, e.g., F = MA) are evidently false.

Possibility with content is equivalent to the actual or potential (in the ability of a cause), not prior to it. The virtually unanimous belief to the contrary, even among materialists, is a platonic illusion, a baleful superstition nourished on the straw of logical notation. The alternatives, like doubling reality with immaterial abstract objects (whether forms, essences, propositions, states of affairs), or making being, possibility and actuality equivalent but intentionally different [D. Lewis, 1986] are ontologically extravagant and intuitively implausible because there is no explanation for the being of such things or of why there should be either abstract objects or physical things at all, and, in particular, no explanation of the "exemplification," "instantiation" or similar relations by which the abstracta are supposed to explain their cases (if any), and no general explanatory ontology at all.

We can say "when there were no humans, it was still (nevertheless) true that humans are animals." But what "was before" is denominated (extrinsically and relationally characterized) by reference to "what came to be." Such a judgment is vantaged in what exists. And so, had "it" not come to be, there would have been no proposition, no state of affairs, and no situation of "its not having been or not having been true." Thus what was never to be and never will be has no content.

When a universal predicate, P, applies in quid (to what natural things are), things that satisfy the predicate have all their other non-indexed de re conditions in common: for instance, all real pigs, assuming that there's only one species, have everything that is required for being a pig in common. Then nothing can bear the predicate (pig, assuming "pig" is an infima species term) and have some other non-indexed de re necessity instead (e.g., "ceramic insides"). The overflow necessities are incorporated by reference into the signification (into the conditions the thing has to satisfy for the name to apply). It follows that there cannot be anything named with real-kind terms in a made-up combination that cancels out necessities required by the component names. In a word, combination-kinds like "thinking electrons," "wood that thinks," etc., with conflicting overflow significations, are impossible. Some impossibilities are due to the absence of determinate overflow conditions and others are due to a conflict of overflow conditions. And the latter is always sufficient for the former.

We cannot say, using expressions already referentially embedded into the necessities of actual things -- already referentially anchored -- what might have been instead, by cutting those predicates loose from their overflow significations, because then nothing definite is indicated by them, and there is no reason at all to think the items in the linguistic meaning (colorless, odorless, tasteless, potable liquid) are physically or counterfactually independent of the overflow necessities, which may be hidden ("being made of H2O, being atomic, being made of quarks"), to which they attach by the reference of "water." In other words, just because you imagine a potable, colorless, odorless, tasteless liquid with a different molecular structure (say, all hydrogen), does not assure that there could be such a thing. Consistency of description or image assures nothing. In fact, we know that liquid hydrogen cannot be a potable liquid.

Syntactical and semantic inconsistencies do not explain real impossibility; they partly record it. But is impossibility from repugnancy or vacuity absolute? Yes it is. It is not just a hypothetical impossibility that birds are mammals, or that voltage should exceed watts divided by amps. There is no relevant contrary situation with any content at all.

But what determines what really conflicts with what? The idea that real impossibility is somehow caused takes us right to "the horizon of being," to being itself, to consider the nature of final explanations. This is the point at which Aristotle's account of real natures stops: he had no explanation of why the opposite of the necessary cannot happen. Others don't even engage the point. My answer is that the opposite of the really necessary has no content. There is nothing else to happen.

Why things are that way has to be answered partly in terms of a producing cause because it is evident that to conform to natural necessities is not the same thing or equivalent to what-it-is-to-be. It is also clear that whatever the cause of the necessities of nature may be, (1) it causes such necessities by causing material being and not by acting according to some regularity among material beings, and (2) it must lie beyond matter, behind the blackboard of physics, to adapt a phrase from S. Weinberg [1993].

What about "things otherwise like those except for origin," that are "smart snakes"? It is the same as with "wood that thinks" or "humans with pig snouts." "Human" is a complete kind, as is "pig" (assuming there is one species only): so, "humans with pig snouts" logically requires clashing causation. Similarly, no animal that is not mammalian has the cortical organization for rationality. The kind of cortical organization for rationality is prevented in snakes by the biological sufficiency of less cognitive ability. You might ask, why do things naturally develop only the cognitive capacity sufficient for biological flourishing in hospitable environments? Natural selection seems like a good answer, though humans seem to be an exception by being "all purpose" animals. We don't need to know so general a truth to know that the cortical organization for snakes prevents the cortical complexity required for rationality; that can be based on pathological examination.

10. Inconceivability does not assure impossibility.

Inconceivability does not even assure that a thing lies beyond the capacity of nature. Nylon was inconceivable a millennium ago because the basic chemical conceptions had yet to be invented. The distance of the fixed stars was inconceivable to persons using only Roman numerals because they would not be able to write it out or say it. Our referential vantage in the cosmos limits the reach of what we can envisage.

Moreover, it worth noting that both Aristotle and Aquinas (and many others besides) thought human conception to be limited by the fact that all conceptions are made by abstraction from material-being known through the senses; there may be realities inconceivable, and thus, cognitively inaccessible to us. If such is the case, the fact that we cannot coherently think of something is not sufficient to assure its impossibility [Abbott, 1884].

Defective and deficient conceptions.

That some thing might change its nature is impossible, as is a human's being immaterial by nature. Those things, though impossible, are not inconceivable, unless one insists on using "inconceivable" in one of its more restricted senses, as philosophers sometimes use "nonsense" to apply to the inconsistent, when others note that it is only if an utterance is not nonsense that it can be inconsistent. It is also impossible for a human to be a vampire or a bat. You might consider these defective concepts that harbor inconsistencies, but the impossibility has to be prior to the inconsistency, where there is one, and is not explained by it, as it is with geometrical impossibilities.

Some inconceivability is only epistemic, the cognitive inaccessibility of enough conditions for us to form a definite conception. That, of course, varies with the person; for some people "aluminum" is as indefinite as "incarnation." We need to distinguish conditions that are inaccessible because we have no access to them, from inaccessibility because there are none. Things without definite conditions for being (e.g., "chronons" or "rabbucks") are, however explicitly we state them, deficient in conception and impossible. "Without sufficient conditions for being" is a way of summarizing my position that there are no contrary situations with content to what is naturally necessary.

"Being red and green all over" seems impossible, even inconsistent to some people. Many take "being one color" to exclude "being another color" at the same place and time and relative to the same color-detecting device. But there are exceptions; for instance, if we take a "thick surface" like the sky, it can be blue all over and at the same time golden where the sun is bright, even for a single observer (who cannot at that time see the blue in the area, of course, while to a person placed differently, that patch will appear blue and another golden, etc.). In the absence of an explicit inconsistency, what explains the impossibility? Like natural necessities, some impossibilities are discovered by experience. It takes no induction to see the dead can't speak. There is nothing else to happen.

But couldn't a creature with two kinds of eyes react to two colors of the same thing at once, ultraviolet and infrared, say? Of course; that's not what was meant. Could two perceivers at different distances find a wall "pink all over" (far away) and dotted red and white (close up)? Of course; that's not what was meant, either. Can something be two colors, say for different angles of vision, like Spanish rouge that is red (looking down on it) and black (looking across its surface)? Of course. But what is at issue is the colors in the visible spectrum, say of primary colors, for the same eyes at the same angle, time, etc. It takes no time to see that, all the qualifications being granted, nothing is more than one color all over for the same viewer at the same time. Yet being two colors at once for the same observer using the same color detection sense does not seem to be impossible for the same reasons that "being the imponderable space-filling medium for the propagation of electro-magnetism" is, or "being a really existing Euclidian right triangle" is. You do not have to know the account in order to know the impossibility.

11. More about conceivability and possibility.

Saying of what is really impossible because of "overflow conflict" or vacuity, it is "logically possible" is just a mistake. We cannot remain definite about what is supposed to be possible while loosening the parts of the description from their overflow necessities. For then there will be no definite conditions for being. That alerts us to something suspicious about "logical possibility." There are real possibilities because what can happen in principle is more than what is actual or within the power of nature or even the remote and the feasible potentialities of things. But what is beyond the remote potentialities of things has no content for us, even if we think of it as being within the absolute power of God, because we cannot think of it more than schematically, that is, without whatever would be its overflow necessities. That's the way Leonardo had to think of a flying machine and Jules Verne of a submarine. That's why Buck Roger's ray gun was not really a laser; such overflow necessities were cognitively and referentially inaccessible. Schematic possibilities are not real possibilities because they lack determinate overflow and so, could not exist as conceived.

That means that frequently what is said to be logically possible is not really possible at all, because what is thought of is deficient by lacking determinate overflow necessities or having conflicting ones. That reminds us that we should not confuse "conjecturally possible," and "possible for all I know," or even "conceptually possible" with claims that something is really possible, claims that have to be grounded in determinate de re necessities all the way down.

Now sometimes we can "get it right" by schematically thinking of something we don't yet know how to produce, say, the way Edison imagined the light bulb before he was able to make a workable filament; that is, we can see that something is structurally within the potentiality of nature before we know how to identify, explain or produce it or have found the parts to make it. To call such things, like the lightbulb, the victrola and the movie camera, logically possible and even really possible seems reasonable, though with a schema, as patents show, conceptual possibility is defeasible by experience. The general and loose talk of any consistent conception's being logically possible, even when we know it is not really possible (such as my being a brain in a vat, or my having all the same experiences without there being any external physical world) is entirely misleading: we have no basis at all for saying "but that could have happened." And the flimsy basis in "there's nothing inconsistent about it" simply dissolves because consistency of conception cannot assure determinate, non-repugnant, overflow necessities.

Philosophers tend to regard anything with a consistent description (and no equivalent inconsistent one) as logically possible. That's because they think any "overflow conflict" is only contingent, along with the laws of nature. There are two mistakes here. The connection of macro-features to micro-structure is very frequently necessary [see next], and the designations of general terms may carry an overflow conflict of de re necessities along "by reference" [see the examples above of how a general term "incorporates real necessities by reference"], or the reference may be evacuated by the supposition that the underlying laws are different [see examples to come].

What is consistent as far as it goes, may have conflicting overflow necessities. That may be the case with "wood that thinks" and "non-mammalian rational animals." We can consistently think of things that cannot be. For example, with Jupiterns (formaldehyde- drinking rational animals, native to Jupiter), the amount of atmospheric ammonia would causally cancel being biotically alive. For you to reply, "not if the laws of nature were different" is a promise without collateral; we have no way of knowing that the laws of nature could be arranged so that there can be what we know to be life, while being otherwise as required by the description (with all that might be required to fill out the overflow conditions to which we have no access).

Whether the necessities of our cosmos are the necessities for any (every) material world, or for every material world with animal life, is not known. To say one can imagine or conceive otherwise provides no assurance at all. Conceivability is not enough for possibility because the overflow conflicts might violate the conditions for material life. And even if cosmic necessities are not necessities for all material worlds, we may not know whether "formaldehyde-drinking animal," made up by reference to two real natures in our world, and incorporating by reference whatever other real natures compose animals and formaldehyde, involves overflow conflicts; but we do know it involves indeterminacy and that indeterminacy of de re necessities is sufficient for impossibility.

There is something odd about speaking of "the conditions for material life." For where would they be, except embedded in living things? How do those conditions control what might have been? The natures of actual things control what might have been (with content) by the fact that what might have been would have to share the natures, and thus, the de re necessities, of what is actual. We have to have a theory of real natures to explain the status of laws and to account for what might have been [see Chapter 3, and the later chapters on abstraction and real natures]. So for someone to say, "But the natures of things might have been different" makes no cognitive advance because we cannot with any solid basis in what actually exists say how the natures of things might have been different. And to attempt to infer such differences from the supposed contingency of natural laws and the possibility of whatever is consistent or imaginable is simply to beg the question, and to do so with what I have shown to be a demonstrably false assumption about the relation of possibility to imaginability and conceivability.

Common names pick out real natures (say "cedar," "pine") only because they designate real cases, cedar trees, pine trees. That is because the signification of a word (the requirements for a bearer) is only partly expressed by the linguistic meaning; the rest of the de re necessities are the overflow. Because no general term contains in its linguistic meaning all the requirements for its bearers, such terms have to be referentially rooted to the real natures of things. So, without naming, common names cannot pick out real possibility. And without real natures, there is nothing to determine what is possible or might have been. But with naming, the overflow necessities are "carried along" and can clash or become indeterminate in various combinations that are linguistically consistent.

We need to caution ourselves about quantified modal logic. It seems to allow us to give proper names to things whose natures are indeterminate, e.g., "there might be chronons." If we are not quantifying over what is real or potentially real, the logic is misleading. Even though quantified principles (say, of S-4 or S-5) have been known and accepted from ancient times, and have been explicitly used by great philosophers, they are on any natural interpretation, false. For instance, why say of whatever is possible "it is possible no matter what" [(p)( p p)]? Most possibilities have content only relatively to a supposed order of nature; the order of nature is contingent from a modal logical point of view, though naturally necessary. Such things would not be possible "no matter what"; for instance had there been nothing at all or no material world, nothing physical would have been possible unless within the power of some agent. Similarly, with "whatever is necessary is necessarily necessary" [(p)( p p)]. Given that the naturally necessary is the actuality of the whole potentiality of the actual, leaving all verbal contraries referentially vacuous, the naturally necessity has its whole content from what is actual. So the only objects classical modal logic applies to strictly are formal objects and God, and even then there remains equivocation on the notion of "proper names" because abstracta do not have proper names as individuals do; nor is "God" a proper name, or God an individual either.

People used to think "invisible light," and "weightless stones," and "pictures transported invisibly on invisible light" were impossible and instantaneous locomotion, points in space-time, temporal instants and extension made of continua of dimensionless points, were possible. Now it seems the other way around. Some are still unsure whether "action at a distance" (without "carrier particles"), is possible. We are not sure what to say about "force not carried by particles," though it seems we need such force-fields to explain particles. We are unsure about paradoxical quantum phenomena, for instance, whether events exceeding the speed of light are possible and whether a particle could be in more than one place "at the same time." But we do know that "transparent metal" is not a negated nature nor a repugnant combination, as it used to seem. Nor is "glass is a liquid" the evident impossibility it might seem to common sense, but rather a natural necessity. We cannot simply reason from what seems apparent, or is imaginable or unimaginable, or coherent or incoherent, to what can be or cannot be. Our imaginations and conceptions and even appearances adapt to reality as experience and reasoning disclose it to us.

In one respect, the real natures of things which determine the potentialities of things are all that is possible; that is, there are no other possibilities with content. There is no universal domain, no treasury of traits from which all possibilities can be concocted. Thus, "Nothing else is possible" is not a denial about candidates with content, but a denial that there are other candidates. That does not exclude our knowing there might have been other species, had certain natural events and accidents occurred, or more or fewer forests and trees or deserts, through our knowledge of the natures of the things that exist. But "there might still be dinosaurs," skipping genetic engineering from fossils, does not seem possible. So not everything we can express in terms of the natures of existent things is on that account really possible [more in Chapter 3].

The impossibilities would have been different, had things been wholly otherwise. That should be no surprise given that what is impossible depends on what there is but has its content entirely from thought. Yet, we cannot, looking at what things there are, tell in general what would have been impossible, except in so far as it is fixed by oppositions of natures we know of (like, "rational reptiles").

Suarez [Metaphysical Disputations, #31] explained the necessity of "all humans are animals" as "it cannot be that a human begins to be unless an animal does," and traced that to the real sameness (he called it "identity") of what it is to be a human with being an animal. That's better than typical possible worlds analyses because it concerns a real nature and sameness. For instance, "All men are mortal" does not cash out as, "take anything, in any world, if it is a human then it is mortal." For, take a world where there are no humans and no mortals: "all men are mortal" is true at that world, just in case, for anything in that world, if it is a human it is mortal. Read that as material implication and it is true of everything in that world. Now what settles that? That each thing is not human? That is what the modal mapping tells us. But it is not what we mean. It is not even true. "All men are mortal" is not true, supposing there are never any humans; it would have no content at all, like "all unicorns are equine." That logical mapping is not what we, non-logicians, mean; that is not what the generality of our judgments consists in. We can only explain the generality of judgments with an account of real natures [which I undertake in Chapter 7]. And we can only explain how our judgments have real natures as constituents by explaining abstraction/dematerialization [see Chapter 5].

W. Lycan offered a mapping onto space-time points, that has the same form and outcome as the one sketched above, where "Humans are mortal" is made true by the falsity of "N is human" at every point N. That does not capture our meaning. It supposes quasi-platonic properties, "being human" and "being mortal," and an infinite domain of all (possible) individuals, things for which no theoretical justification has ever been given and does not rely upon the real natures of existing things at all.

There is nothing to make "humans are mortal" true at a world of empty space-time points, except the falsity of the antecedent ("is a human") for every non-human (for every space-time point), and the made-up rule that a conditional with a false antecedent is true. So, we are served up another "bait and switch" analysis, without even a blush at the presumption (without basis) that there is such a thing as "being human" without any humans, or a blush at the assumption that for every predicate/property, each thing in each world either has it or does not, and there are empty space time points. Why believe any of that? Since that is not what we mean, a fortiori "it is true in all possible worlds that ..." is not what we mean by " 'humans are mortal' is necessarily true", either. We also have to discard the decomposition of quantified statements into singular predications because non-actual things cannot have proper names; and strictly, neither can space-time points or any of the other furniture of non-actual worlds. No explanatory advance is made (except technically, and that involves equivocations that defeat success). It is the generality or shareability of real natures among actual things that needs to be explained [see Chapter 7].

12. Unrooted logical possibility is vacuous.

Modal quantificational analyses of impossibility do not represent our meaning, nor does the extensional generality of quantification represent what we mean by universalization, as I have just indicated. We have no access to unrooted natures. We do not know whether the necessities of the universe are the necessities of all material worlds. We do not even know whether material life is only carbon-based or whether there are other capacities in nature. We cannot even conclude from something's being descriptively inconsistent (semantically, not syntactically), that it is absolutely impossible and, therefore, does not lie within the absolute power of God; Descartes was right on this point, though his examples were unfortunate.

That may be misleading. What is inconsistent is absolutely impossible. The trouble is that surface inconsistency may be relative to contingent and fabricated conceptual alignments, as "subatomic particles exist" would be inconsistent for Lucretius and "humans are essentially embodied" would be for Descartes. But "rational animals fly" (on their own, not on superconductor fields) is impossible. It is wrong to say "but it is logically possible because the notion is not inconsistent." When the conflict lies in the overflow conditions the repugnant overflow is incorporated by reference so that things without the conflict would lie outside the reference and be of a different kind.

Not that all statements that such and such is possible are unwarranted and logically indeterminate, but the ones most often conceded by philosophers are, say, that "there could be wood that thinks" or "we might have had all our same experiences without there being any external world," or "we might have existed unembodied," or "we might have been brains in a vat," or "I might have had your memories."

Rather, there are real counter-possibilities, that I might not have written this today or at all, that I might have been a physician, that I might have been a gymnast. And there are real future possibilities too. Yet they are not "all of a piece." I really could have been a physician in a way I could not have been a gymnast or an F-16 fighter pilot, or even a concert pianist, and I might be a seventy-year-old philosopher in a way that it is not possible that I become U.S. president at 69, as distinct from the impossibility of being elected president at 72. No different genetic or social condition would have been needed for the former, only a different life plan, whereas the physical suppleness and endurance to qualify as a gymnast or pilot or pianist would have had to be produced somehow; and the political future of our nation would have to convulse for me to become president.

A general conclusion is in order. (1) "Really possible" may seem to designate a single ontological status for what might have been or might come to be, when, in fact, there is a family of related kinds of would-have-been-if, and also would-be-if, all based in the real natures of things [see Chapter 7]. (2) Consistent descriptions that require the de re necessities of things to have been different do not express possibilities at all, but impossibilities by repugnance or impossibilities by vacuity.

III. Conclusion

1. Real impossibility comes down to vacuity of the de re necessities for an intentional object.

We seem to have traded what was superficially satisfactory, that the impossible is what is inconsistent, for something nebulous and varied. For example, that there was no impossibility with content before there were human thinkers. But, of course, there were no inconsistencies before there were humans either. So that outcome is not surprising. Secondly, lots of things that are consistent are impossible, that is, cannot be real things: Euclidean figures, natural numbers, and all other purely formal objects, as well as ghosts, imaginary objects and fictions. So the explanation of impossibility cannot lie in inconsistency of the conceptions alone. Lots of things are impossible that are semantically coherent (silicon-based life) but have conflicting overflow necessities (even if we do not know what they are). And lots more of what we can conceive or imagine or conjecture is impossible because nothing determines the overflow necessities, with the result that what seemed to be common names become vacuous by failing to refer determinately (because we, the thinkers, are failing to refer determinately), so that the supposed designata have no determinate overflow necessities: unicorns, rabbucks, satyrs, anti-gravity machines. And, of course, the verbal contraries of necessities of nature do not express contrary situations because these are no contrary situations.

Impossibilities are entia rationis, intentional objects, defective or deficient ones. They are not defective or deficient in intentionality but in the material conditions for there to be such a thing or situation. Before there was thought, there were none. That does not mean that the capacities of nature were not limited or that shapes could cause odors, or that an object could be massless and occupy space (without being a forcefield), but rather that what was beyond the capacities of things had no content. All our sound judgements about what cannot be are vantaged from our references to what actually is, and while it is true that had there ever been nothing at all, nothing would ever have been, what could not have been can only have content from what actually is and the capacities of things in being. Note that if there had been nothing at all -- a situation I think is impossible [Ross, 1969], there would have been no states of affairs, propositions, properties, numbers, or any of the abstracta favored by modal ontologists like Lewis, Stalnaker, Adams, Plantinga and Chisholm. So what would explain that impossibility on any account but this one? Of course, I think there can be no such abstracta anyway, except as fabrications of creative human thought, without any explanatory reality of their own at all. Now the impossibility of such abstracta is not from some syntactic or semantic inconsistency. It is from their vacuity as to what is de re necessary for their being at all. There is nothing about them or any cause that would explain their being at all or how they might continue to be.

Real impossibility, the only kind that counts, except for intellectual book-keeping, is vantaged in the actual, depends on thought for content, and has its impossibility from the eventual failure of the conceptions to determine non-repugnant de re necessities "all the way down" to a sufficient condition for being. And non-repugnancy is entirely founded in what actually is. Things that prevent one another are repugnant. Why things, in the end, prevent one another has no scientific answer. Either there is no further explanation or the causal oppositions of things are co-invented with the things. The latter is the more likely. To talk of a further necessity as explanatory is idle; unless everything is exactly as it has to be, exhausting all possibility, natural necessity explains nothing finally, but instead demands explanation. Impossibility is not the explanation of the necessity of its opposite. Rather, the fact that the necessary fills the potentiality of the actual is the explanation of impossibility, the absence of contrary situations. What explains that some realities complete the potentiality of the actual must again be something actually in being, something that is its own explanation; otherwise, there is no explanation of what plainly demands one.

Next we look at what might have been and the contrary to fact.