James F. Ross


Mistakes about necessity, possibility, counterpossibility and impossibility distort the notions of being and creation.1 Recently such errors cluster in the understanding of quantified modal logic (QML), a device that was for a while thought especially promising for metaphysics.2 Time has told a different story. The underlying modal platonism is gratuitous, without explanatory force and conflicts with the religion it is often used to explain. There are things to consider here that go beyond diagnosing mistakes.3

Even the Notation is Suspect. Discarding the current ontologies for modal logic is not enough. The notation--by that I mean the uninterpreted syntactic systems (QML)--import falsity by what they cannot express and by what they require in outline of any ontology that tracks the "pure" semantics. For instance, the notation cannot be used to express, and thus must treat as the same, predicates that are "of the essence" of a thing and those that apply to it necessarily (propria). It also has to treat as univocal three distinct kinds of existential quantification, over individuals, properties and worlds.4 The "pure" semantics implicitly requires that there be infinite, exhaustive, and replete domains of referents at first order, second order and third orders of quantification (and so, replete domains of individuals, properties and worlds), for there to be an ontology for the systems at all. That feature is what finally makes QML, as formal systems, virtually unusable for metaphysics (see Section IV, below).

The notation--the uninterpreted formal systems--is thus revealed to be suspect, crude and misleading. The crudity is analogous to, but more serious than that of the propositional calculus. Such formal systems are "truth preserving", but not in the sense that we can "carry along through all permitted transformations" all the truth contained in some real statement we start with. We cannot, strictly, start with real statements at all. Formal systems are truth-preserving only for the appropriate formal objects, "propositions" of a certain syntactical form. Rather, adjusting the truth-content to be preserved to the resources of the system, that is, using the fabricated truth-bearers invented just for the logic, no truth-value is lost by the permitted transformations, nor any falsity generated. That is so, but is far less than its consumers expect. Besides, it does not assure against falsehood introduced by the systems in other ways, for instance, by the assumption that truth-bearers (propositions) form an actually infinite array, all interrelated by truth-functional (or other logical, say modal) connectives. (That is absolutely required, even for propostional calculus because there have to be an infinite number of theorems.) The fact is that there is no such domain and that OUR truth-bearers are not so related, nor are they infinite in number.

Nothing is said by philosophers recommending the systems of QML logic about the falsehoods introduced by their understanding of the axioms, or by their interpretation of the naming-commitments of the systems, (say, that there are/are not empty individual names), or by the assumption of S2-S5 that all possibilities are "accessible" from one another by logical transformation (rearrangements of truth values), like getting from one telephone number to another in a "universal" telephone book by systematic changes, a digit at a time. It is simply not true that we can, in principle, generate all the ways things might have been by systematic permutation of the truth-values of "all" propositions. For one thing, there is no such thing as "all" propositions. For another, what might have been the "necessities of nature", like "iron rusts", or any other kind of necessity involving natural kind terms or general names (not made out of names for actual natures), cannot be "reached" by negations of what is so (and affirmations of what is not so), because the natures of what might have been are empty, just as are WHICH things might have been. "They" are not "accessible" from every "possible world."5 Nor are possibilities with content (picked out by names) "possible no matter what."6

Furthermore, the notation, when interpreted, involves ontological claims, like "whatever is possible is necessarily possible", that are treated as "evident", "obvious", and "beyond dispute", while the widely accepted accounts of naming--which all the authors to be mentioned share--require that they be false. To escape inconsistency they invent surrogates (see below).

Besides, there are formal defects in the program of modal semantics. First, there is the maximal set problem. (See II,1 below). Secondly and fatally, the proposed ontologies cannot "match" the pure semantics and, thus, provide a formally exact ontology.7 That is because something required by the pure semantics is inconsistent in the ontology: that the "higher-level" abstractions (say, "worlds") be logically EXHAUSTED by the next lower levels (an array of properties on "all" individuals), and that "every" property be exhausted by "all" possible instantiations of it. That is how the "universal domain" is constituted: completely exhausted by worlds, each of which "contains" all properties and all individuals and every individual either has or has not each property. An ontology is supposed to supply REAL elements, item-by-item, for the three domains of quantification--elements that line up one for one with the "names" generated by the "pure" semantics. None of the ontologies can provide an actual infinity8 of objects that is replete (so full there can't be any more) and logically exhaustive at all three levels of quantification, whose members line up to bear the names that we can generate with the pure semantics,one name to one thing. That is because neither being, nor any nature (kind) can be logically exhausted by kinds or individuation.9 Thus for an expression like "For every world, for every property and for every individual......",the pure semantics provides for a rigorous interpretation, while the applied semantics makes that inconsistent.

When you think "from the top down" of all "worlds" subdivided by any difference of situation into "each world", the scheme might seem coherent, like all arrangements of ten pennies into patterns of heads and tails. But when you think of it from "the bottom up", of every individual of every kind,it becomes evident that there is no such extension. There is no determinate range of all pennies in every pattern of heads and tails. You cannot exhaust a kind by individuation unless every difference makes a difference of thing. Even then,to exhaust 'being' by kinds and kinds by cases there would have to be something that determined when "every" difference had been realized. There is no evading the conclusion that no true ontology can be given that satisfies the formal requirements of QML.10

The above consideration is decisive against the modal actualists.11 They cannot provide a true ontology that matches, formally, the pure semantics. That failure is assured because there is no least difference that makes a difference of kind, or least difference that makes a difference of thing. So it is impossible for any real nature to be exhausted by individuation or any genus to be exhausted by speciation.12 Therefore, there cannot be articulate real domains to "track" the pure semantics of the systems.

We cannot bend the formality to the truth. The notation, under any ontological interpretation (or even with none) cannot be shaped to say what we know modally. It is insensitive to truth-affecting features of what we say, for instance, that there is a difference between necessary and essential attributes and that natural necessity ("iron rusts") does not require a real individual (or any property, nature ,universal or world) that exists "no matter what". Yet the symbolization requires that we talk that way. Real natures come to be and cease to be with the things.13 As a result there is no real nature such that there are "worlds" with the nature but no cases of it. That is, there are no empty natures as the ontologies require, for which they provide "surrogates", nor are there any empty individuals--things that exist only in other possible worlds--for which there are names. Those are fictions of the logic.

Another example: the principle that there cannot be empty proper names (along with the principle that there cannot be empty14 real kind names either) compels us to deny that there is a domain of kinds that will never have cases and of individuals that will never be (because the kind is to the case as capacity to realization). Nor can there be abstract surrogates "for them" either.15 Quantified cases of "whatever is possible is necessarily possible", and the like, are true only if the names and predicates NAME. That, in effect, means that quantified modal principles hold only for the domain of necessarily existing things (like numbers and other formal objects, and God)16, but not for real natures, empty kinds or mere possibilities. It follows that it is not true that "whatever is possible is necessarily possible". On the contrary, possibility is accessible (logically and cognitively) only from the actual.

Thus, whatever might be, not involving any actual individual or universal or kind, is logically and cognitively inaccessible to us. So unless one holds that all universals, or properties, and the like, necessarily exist, or that all individuals necessarily exist17 (and by combinations are the universals), one has to say that it is false that all possibility is accessible by truth-value rearrangements from the actual. You can't get to "It is possible that Greck exists" by truth-value rearrangement of the actual unless "Greck does not exist" is actually so; but when there is no such thing, "Greck" names nothing at all. That is quite different from what modal practitioners pretend.

Thirdly, we cannot make a satisfactory interpretation of quantified modal logic because the formality itself is set-theoretic, bifurcated and assumes "excluded middle"18--all of which seemed quite innocuous for a long time, until it became clear that these are features of made-up objects (propositions), not of real being. Besides, "exists" means different things applied to individuals, properties and worlds.19 The formal systems are thus insensitive to the formality of multiplicity of being, and particularly insensitive to the modality involved in de re necessities of nature, where things that might not have been at all, still could not have been otherwise than as they are; and yet, what could have been entirely otherwise is wholly inaccessible cognitively and logically.

Because there is no true interpretation of the three-storey extensionality of the pure semantics of QML, attempts to use the notation anyway force mistakes about what might have been, and about the other items analysed in terms of possible worlds; for instance, 'being-though-time' (Quinn20), counterfactuality, 'dispositions' and 'law-likeness' (D.Lewis21), 'free will' (Plantinga),' divine power'(Flint-Freddoso), and the attempt to make creation compatible with the platonistic modal metaphysics (T. Morris22).

Obtuse Abstraction. There is a common diagnosis for the points I have been describing, for the inability of the formal systems to capture what we want to say, and for the impossibility of providing a true ontology for the formal systems. It has two parts, (a) the SUBSTITUTIONAL character of applied formal systems, and (b) the reasons platonistic metaphysics cannot explain anything (see the last part of this paper).

What is the matter lies in the kind of abstractions the formal systems involve. Every key element of the systems is an OBTUSE ABSTRACTION.23 The only way to keep the systems, when used to represent the formalities of real possibility and necessity, from turning truth into falsity, is by "double reading" the symbols as short-hand for English.24

We do not have "the true logic" (the formality for 'being as such'). We have only approximations, made by OBTUSE ABSTRACTION. Essentially, obtuse abstractions are idealizations that substitute formally well-behaved features (like truth-functionality) for messier features of reality, to let us achieve formal objectives (like being able to derive proofs rigorously with a few rules, or to prove consistency or completeness of the system). For example, we substitute continuity of dimensionless points in plane geometry for the discontinuity of physical space (and leave out all explanation of length), and we substitute an imaginary actual infinity of truth-functionally related "propositions" (in propositional logic) for the less grainy,and finite, content of our thoughts.25

Such substitutional abstraction is "obtuse". It is orthogonal to reality at the very points about which the formality is exact. Postulating an infinite realm of propositions for which "excluded middle" holds, and an infinite range of individuals for which "bifurcation" of every one of an infinity of properties (represented by an imaginary infinity of predicates) holds, are examples of "made-up features" substituted in our descriptions of things,--obtuse abstractions.26 The very notion, "proposition," is an abstraction from the the assertoric content of judgment expressed verbally. We abstract further into "assertoric truth-value bearers", without reference to language, so we can talk as if there are actual infinities of propositions,arranged according to truth functions, or according to logical implication (or any other logical system we like). We talk as if all propositions are in principle decomposable to units that have singular names completing propositional functions. We thus SUBSTITUTE something WE make as the domain of discourse for truths we construct.27

Moreover, formal truths differ crucially from necessities of nature and contingent truths. There do not have to be "realities" to which the formal truths of arithmetic or geometry or logic "conform". Truth is a matter of being "made right", not a matter of being "matched right".28 Formal being follows formal truth. That holds even for formal objects less rigorous than numbers; for card games and "hands" as well as for money. With nearly everything else, truth follows being. Hence, we can have logical and geometric truths even though there are no such real objects as the general terms designate, and yet that is not because real objects "approximate" such "idealizations."29 Rather, the general terms have designata (ens rationis) as a consequence of formal truth. Formal truths are not made true by some independent compliant reality that they describe, but by the form of understanding they realize.30 And natural necessities are not made true by conforming to eternal states of affairs, either; or by referring to eternal objects or divine ideas.31 (I leave the proof for later.32) The belief to the contrary is the result of (i) not noticing that formal necessities and necessities of nature cannot be "true" and "necessary" in the same sense, and (ii) of overlooking that impossibility is not, in the long run, explicable as inconsistency,33 and (iii) that real universals have to begin to be (be created).

The modal actualists' commitment to abstractions that are like Plato's Forms (because particulars exist by exemplifying them, see below), leaves "Deus, creator omnium visibilium et invisibilium," chiseled away to "the actualizer of a possible world" like a Divine Disney.34

The incoherence of the philosophers is thus from two causes: (1) taking the fabricated features of formal systems, the obtuse abstractions, to be the skeleton of reality, and then (2) constructing an ontology to fit those obtuse abstractions by going to extremes to evade Averroes' principle (in I. Physics, com. 63) that "with the cessation of the things, the names and definitions perish." The actualists tried to avoid "no things, then no names" by inventing "surrogates" for empty kinds and individuals, over which to quantify, so as to explicate such truths as "there might have been things of entirely other kinds than there are " within the notation for QML. The resulting commitments are unbelievable and unorthodox.35

Modalities are not all of a piece. For instance, the opposed truth-conditions for formal necessity and natural necessity preclude a single analysis of "what necessity is".36 Besides, no one assignment of meaning captures what any modality is, anyway. Philosophers have been trying to stuff modal discourse under a single analysis for three decades now, defying the demonstrable semantic contagion that causes modal terms to adapt to context.37

It is, then, a substantive, not a formal or mechanical issue whether a given axiomatization, say S-5, captures the formality of relevant portions of our modal discourse and whether, interpreted for the context at hand, the principles are TRUE (as well as truth-preserving38). It turns out that once we drop the fiction there there is a treasury of necessarily existing real kinds (properties) for which predicates are names, and a treasury of surrogates for all possible individuals of each kind, for which individual constants are names, quantified general principles, like "take anything of any kind whatever, whetever is possible is necessarily possible" are patently false. So too, the quantified versions of "whatever is necessary is necessarily necessary".

No one formalization, sensitive to universalization and instantiation, captures both the modal principles for formal science (like mathematics) and for natural science (for the necessities of nature). Partly, that is because the existential requirements of the two are opposed; formal objects, like natural numbers, "exist" necessarily and on ACCOUNT OF the truth of the formal systems, while necessities of nature ("iron rusts") denote contingent real objects, like iron, from which they earn their truth.

If reality is without empty kinds and without surrogates for non-existing individuals, then no (1) set theoretic (2) quantified modal logic, (3) extensionally interpreted over (4) domains that can be conjunctively and disjunctively exhausted with names--what I mean by "extensive magnitudes"--can capture its modal formality; and no such system can be interpreted so that its axioms come out true. No extant quantified modal logic is appropriate, then, to the formalities of creation.39

II. Interpreting Modal Logic. The first trouble for metaphysics comes from the need to interpret the logic, to say what 'necessary' and 'impossible' mean in terms of some story about real being.40 Thus, one says what "possible worlds" ARE, to explain "what it really means" that "whatever is necessarily true is true in all possible worlds". Plantinga called it giving the "genuine semantics for modal logic" and "saying what necessity really means" (1974:127).41

Some of the assumptions in such thinking are doubtful, even evidently mistaken. Take one not discussed so far. Is 'being possibly true' (or possibly so) itself a matter of necessity? Since Lewis and Langford's Symbolic Logic (1951), everyone seems to think so. Axioms used for propositional modal logic (e.g. "Possibly p entails necessarily possibly p") were generalized into axioms for quantificational possibility (e.g. "possibly there is something that is both a chicken and a Rhode Islander" entails "necessarily it is possible that there is something that is both a chicken and a Rhode Islander"). Then, by postulating things for the "individual","property" and "world" names to name, we get something like the following: "there is a possible world, w, and there is a property, F, 'being a chicken' and a property G, 'being a Rhode Islander', such that "in w there is something that exemplifies both F and G" ENTAILS "in (at) all possible worlds it is true that there is some possible world w such that there is something in w that exemplifies both F and G." All that, without any independent reason why we should think there are such things as worlds and properties and individuals (or surrogates) arranged into permanent domains of reference.

The modal ontologists systematically evaded the principle "no things, no names" by (a) postulating an infinite array of all worlds and of all properties for things, and (b) inventing surrogates (individual essences, haeceities, etc.) to serve as the nominata for otherwise empty names. This is a shell game.

Do you think that among the eternal, necessary companions of God are 'being flamingo pink', 'being the craziest philosopher in New Jersey', 'being identical with Socrates' and ‘Socrates' having known Stalnaker'? Do such abstracta exist? Of course not. Pity the theory that requires that they do.

To the contrary, what is merely possible--unanchored by reference in what there is--and what might have been necessary (say, that antilichts repel chronons) is not accessible42, logically or cognitively, because it is empty. That means that principles like "whatever is possible is necessarily possible", interpreted as they usually are, for a domain of necessarily existing substitutions, are false when applied to real natures. Real natures have being derivatively (in real things) and contingently.

Possible Worlds. A lot of ingenuity went into inventing "applied semantics" for modal logic. Five of the accounts take possible worlds to be REAL.43 They take possibility to be explanatory and prior to actual being (though possibility also requires actual being of the abstractions, the possible worlds). They postulate realities to "match" , to "interpret" the features of the notation, particularly, to supply (i) the three-decker domains of quantification, (ii) the infinity of actual elements in each domain, (iii) the bifurcation [where everything of every lower domain either exemplifies or fails to exemplify every thing of the next higher domain (every predicate), and every exemplification of a predicate either belongs to or does not belong to each of the infinity of worlds.] As I have already pointed out, these features are all obtuse abstractions (See Sect. I,above), made-up features of the logic with no representative character at all. The first mistake was to to fashion the ontology for those features, for something SUBSTITUTED for reality, not for the underlying and basic elements of being. The final mistake was, of course, to pick an ontology that is explanatorily inert and not true.

There are three broad failures in the modal ontologists' enterprise:

(1) Formally, several interpretations of QML are committed to a set of all sets, a maximal set, (of properties, propositions, states of affairs, etc.) that combine set-theoretically to a formally maximal domain that has the traits required for quantification,44 (what I call "an extensive magnitude"). That leads to a demonstrable inconsistency. Efforts to evade that are typically superficial, see note 59,below.

(2) Substantively. The three-decker domains incur liabilities recognized from ancient times: (i) actual infinities are probably incoherent, and (ii) even if not, it is unpersuasive, as Aristotle thought, to appeal to self-explanatory infinite multitudes to explain finite plurality. Plantinga's (Does God Have a Nature?, Milwaukee: Marquette University Press, 1981) late retreat to Augustinean neo-platonism, turning possible worlds and individual essences into divine ideas, makes the problems worse because it makes "exemplification" more obviously equivocal; the "idea", unlike the Platonic Form, is NOT what 'being-f' REALLY is (even though Augustine apparently thought divine ideas are the forms "received in" things). So, to exemplify the divine idea is not "to be a case of it" but "to accord with it". I explain that in IV-5 below, where the explanatory inertness of such ontology shows that it is nothing but streetclothes for the logical notation.

(3) Strategically: the religiously hostile outcome. The modal semantics evacuate the notion of creation. In Lewis' case, see below, there is NOTHING for God to do, because all possibilia are relatively actual. For the other modal semanticists, God is like Plato's demiurge (Timaeus), "making order out of necessity", namely, exemplifying abstractions--working within a given order of objective possibilities, like a child pouring lead into the moulds for toy soldiers. For them, creation is reduced to causing "unique exemplifications", "instantiations" (etc.) of abstracta; or, in Chisholm's parlance, making states of affairs "obtain" (turning them "on"). Not only are possible worlds described as "stuffed" so there is no creation, as D. Lewis does. For the actualists (Plantinga, Adams, Stalnaker and Fine-Prior) God's power over nature is without content. God "actualizes whole worlds." God does not create properties, essences, individual essences, natures or kinds. They are all given to God's nature as the framework of possibility. Creation is not the making of the entire being of a thing (See Aquinas' affirming that it is, at D.P. 6,1c) or making the essence of the thing (See Aquinas,D. P.3, 5 ad 2, saying, "the quiddity itself is said to be created with the thing").45

Furthermore, the difficulties William Lycan mentions in "The Trouble With Possible Worlds" (in Loux, cit. supra. p.274-316) do not lead as he thinks to one's having to make a choice among the ontologies and "put up" with the consequences. The real choice is to recognize that this particular bundle of obtuse abstractions that we call QML is NOT an adequate formalization of our modal discourse, or even of a good part of it, and certainly is not even an approximation of the modal formality of real being, but is deeply misleading and to be replaced with a different basic logic, and further, that no set-theoretic, bifurcated, extensional, higher order quantificational system with the other markings of classical logic (as it is called) is safe to rely on in doing metaphysics. That logic, used to advance the understanding of God, carried commitments that negate central religious teaching. That undermined theology.46

III. The Truth-Defeating Ontologies

1. The Options. For a possible-worlds interpretation of QML, there seem to be two main choices: (1) Modal Monism: one world of universal possibility with "local"actuality (D. Lewis)47, or (2) Dualistic Actualism: two realms of actuality, abstract and concrete (the other theories).

Either we say other possible worlds are made of real things, rocks, people, caves, and stars, that are possibilia48 with viewpointed "local" actuality (that Lewis digested into counterpart theory, 1975, l986). Or we say possible worlds are composed of (necessarily) actual abstract entities that can be "uniquely exemplified", "instantiated" by concrete things. You need abstractions at predicate and individual levels to allow that, for example, 'there might have been more tigers than there are', and also to allow that concrete things are the explanatory outcomes of the actualization,49 exemplification,50 or obtaining51 of constituents of a possible world.

1. Modal Monism, Viewpointed Actualism. D. Lewis' says "everyone knows what sort of thing our actual world is, well, other worlds are more things of that sort, differing not in kind but in what goes on at them." [Lewis.1973:84-91]. Other possible worlds are made of people, rocks, auto accidents, atomic interactions, and, in general, the things that might have been but weren't. The idea was apparently suggested by science fiction [D. Lewis, 1983:28]. Of course, he's right that "other large things" are what are possible. The extremism lies in saying that there are the other large things that are possible. Lewis says there are parallel worlds of equally real possibles, each of which is just as "actual" within its own world as any other in its world. Relative actuality is equivalent to possibility. The possibilia in the worlds have basic (unexplained, self-explaining?) status, though worlds are only arrangements of spatiotemporal connection (1986:71) of their "inhabitants". Everything in every world is actual "from the viewpoint" of everything else in that world, and so on, for all worlds, while everything in every other world is merely possible from the viewpoint of everything in any other world. That's why I call it "viewpointed actualism". (It's as if we had a hotel whose rooms are full of people who think "this is where it's happening" and for whom all other rooms and inhabitants are merely conjectural). Real existence, actuality for things, is world-relative, the way "is happening here and now" depends on when, and where we are. (Cf.Loux,1979:184). From the "viewpoint" of each thing in each world, it exists actually, and its world is the actual world, all others are merely possible.

Lewis persists in The Plurality of Worlds, 1986. Worlds are not made of ghostly things, like states of affairs, propositions, or properties whose instances or exemplifications are the concrete things as the "modal actualists" propose. Other possible worlds are the very alternatives to the solid actual things we know in "the one we inhabit". Other worlds are "large objects," like the cosmos. Every possible world is completely concrete, as ours is but, of course, PHYSICALLY inaccessible from any other.

Consequently, you can only exist in one world, so that what "would have happened to you" is what happens in a similar enough world to your counterpart, and what you would have done, had you chosen differently, is what a counterpart does, in a suitably similar world. Lewis thus robotically parses our counterfactual utterances into what we do not mean. Further, his account equivocates on "there is" because there is the NAMING of possibilia (which involves being) and the EXISTENCE of what is relatively actual (which involves relative being).

Creation has no place at all because all possibilities are equally real and equally actual from their world-restricted viewpoints and every possibility is, viewpointedly, a real being or real situation. So there is no causation of being. There is nothing for a creator to do. That is a notable theological deficit.52

Still, Lewis is right that his competitors are trying to get the utility of modal realism "on the cheap" and all face "bad trouble",cf. Lewis,1986:140 ff. Even so,that does not make Lewis' story believable.

2. Dualistic Actualism. The 'modal actualists'53 disbelieve that absolute possibility and relative actuality are co-extensive. Instead, they opt for double reality, postulating necessary abstracta54 to explain concrete being by "instantiation" and "exemplification". (I think I show that there cannot be any such explanation at IV,below). Further, their understanding of QML commits them to three strata of abstract being: individual-surrogates, universals, and worlds. Different writers have different names for the strata, but all need three domains for first-order (individual), second-order (property), and "world" quantification, so they can say "There is a world, such that there is a property, such that there is a thing that in that world has that property". Two kinds of reality and three-stories of abstracta--all to explain the real modalities of things? And still, God's own being would have to exemplify God's nature and individual essence, unless God were to be another kind of reality they do not explain.

Plantinga, Stalnaker, Cresswell, R. Adams, and Fine-Prior, say possible worlds are made of instantiable, exemplifiable or obtainable abstracts: (maximal) propositions, states of affairs, and the like, other than individual beings, and real kinds, though some (Plantinga, Adams and Stalnaker) allow real properties to be components of possible worlds, as well as to be shared by things in the actual world. Those real properties have to exist necessarily, form a fixed domain for all worlds, and be said to "exist" univocally with their instantiations. That does not seem very likely, does it?55

Plantinga and Adams say worlds are maximal sets, in Plantinga's case, of states of affairs56, and in Adams' case57 of propositions. Stalnaker and Fine do not identify possible worlds with maximal sets, but rather as decomposable wholes, in Stalnaker's case as a decomposable property58 (of which other properties and propositions are decompositions), and in Fine's case as a decomposable proposition that contains (or has the exemplification of) one and only one of every pair of contradictory components.59 [The latter device is supposed to escape the formal paradox of maximal sets.] The actualists don't seem hesitant to identify formal objects (sets) with real things (worlds), any more than some of them are troubled by the formal paradoxes of maximality for sets, or by the questionable legitimacy of such totalities as "all propositions" or by the notion that an infinity of propositions somehow exists and is ordered strictly and only by logical relations apriori (unlike our thoughts and beliefs), so that various maximal consistent sub-portions can be decomposed, etc. The actualists seem to have a con man's gullibility.

All follow the pattern of Carnap's "state-descriptions", postulating ideal lists containing one of every pair of contradictories, like logical Noah's Arks. For the Fine-Prior view60 a world proposition is consistent and, for any contradictory pair of propositions, either entails the one proposition or the other. For Stalnaker, a possible world is a complex property such that for every contradictory exemplification-pair, it either contains (excludes) the one exemplification or the other.61 For Plantinga, a possible world is a maximal domain, containing one or the other of every contradictory propositional pair.62 Consider that there is no such domain as "every" contradictory pair of propositions. Consider that each of the terms underlined above is a modal notion; see #2,below.

The satanic notation, (the triple quantification over worlds properties and individuals) whispered the ontologies. Even the surface grammar of English was given a metaphysical role by Lewis: because we talk about "the ways things might have been" he thought we need some referential status for "them".63 When we look at the modal actualists, in contrast to Lewis, they are all platonists, all committed to the real being of infinities of abstractions that have priority in being and explanatory priority over concrete things which exemplify or instantiate the abstractions. So we should look at the reasons why modal platonism, in any form, fails as an ontology: its hostility to creation, its circularity, its ontological inertness (inability to explain being, quiddity or individuation).

IV The Failure of Modal Platonism

(1). No fit to Religion. The ontologies for QML are incompatible with God's creation of ALL other realities ex nihilo, as I said. The recourse to dependent necessary beings, divine-idea neoplatonism (Plantinga), makes it worse: if the dependent necessary beings are other than God, the simplicity and independence of God are compromised. If they are "parts" of God, simplicity is denied too.64 Not only is creation without content; because the natures, kinds and even individuation of objects is determined a priori, there is no place for creation as entire causation of being. These ontologies "reduce" creation to "actualizing a world" with the peculiar consequence that "actuality" becomes a predicate, a contingent predicate of a world, for which we are offered no explanation,as this kind of predication cannot be exemplification. See the remarks on 'being'and 'predication' below.

(2). Modal Actualism is Circular. All four "actualist" interpretations of logic use modal terms to explain what 'possible worlds" are.65 Plantinga's "being included' in a possible world is analysed as "not possibly obtaining without,"66 Stalnaker's "total ways things might be67 uses "might be" and a modal inclusion relation for less complex properties68 as well. Adams contemplates the possibility69 of the conjunction of every pair of contradictory propositions. Both the totality "every pair" and the notion of contradiction are modal. Besides, Adams' inclusion relation is also modal,70 not material implication alone. Finally, the Fine-Prior world-proposition is explicitly defined in terms of entailing71 one out of every pair of contradictories. So, either the "possible-worlds" analyses of modality are not metaphysically fundamental, or the proposals are circular.

Using modal terms, like "entail", "include", and "all propositions", to explain what possible worlds are, and later defining those and other terms as arrays of truth-values on worlds, is no explanatory gain. And it certainly blocks any pretence at a reductive account that says "what" necessity really is (as we were promised ). It is a typical "bait and switch" analysis (see note 15,above). To say "p entails q" means "in no world, p and not-q" is no advance if "entails" has already been used to explain what a possible world is, e.g., "a world proposition that entails one of every contradictory pair". Besides, the notion of "every contradictory pair" cannot escape a modal explanation, either. [In fact, I doubt that it is a "legitimate totality"]

We can conclude, "being true in all possible worlds" is not what necessity consists in. Even on the actualists' own accounts it can only be a consequence (at most) of what necessity consists in.72

Ontology made-up to the demands of notation, with no other recommendation, and in conflict with what we mean by the expressions it analyses and, for some writers, in conflict with the monotheism it is used to expound, deserves Algazel's reproach for incoherence and self-destruction.73

3. Exemplification of abstracts cannot explain real being. If "exemplification" (and its cognates) is the only way being is acquired, then, just as Plato figured out74, these theories will need "self-exemplification", and "self-participation" to account for the actuality of unactualized possible worlds (or whatever the exemplifiable abstracts are), just as Plato had to do for the Forms. Moreover, God cannot acquire being by a relation to an extrinsic nature, so God has to be self-exemplifying, and the same as his nature.

That requires TWO relations of exemplification. The one relation (of abstracts to one another and of God to his nature) cannot be caused and cannot be contingent and need not be aliorelative, while the other (the relation of concrete things to abstracts) has to be contingent, has to be caused and has to be aliorelative. The "actualists" do no consider that, in consequence, "exemplifies", "instantiates", and so forth, HAS to be equivocal, and so, cannot be an interpretation of THE formal functor/argument relation. There have to be two exemplification relations when the logic provides only for one.75 Yet 'being' cannot be the same as aliorelative participation (exemplification) nor can it be the same as self-exemplification either.

If "exemplification" could explain being, then it would explain the being of the abstractions (the worlds, properties, and individual essences, etc.) by their exemplifying themselves or something else. The actualists offer no such explanation. Concrete things have contingent being. So they have to exemplify their individual essences or thisness (mutatis mutandis for each writer) contingently. Therefore "Socrates is Socrates" cannot be analysed as "Socrates exemplifies Socrateity", as these theories require because Socrates is necessarily Socrates, but on these theories, it is contingent that Socrates exemplifies "Socrateity". Analogous reasoning goes for "Socrates is human". The actualists have conflated 'being' and 'essential predication', implicitly treating 'to have every essential predicate' as THE SAME as 'to be'. That is, BEING is contingent for Socrates [It is contingent that Socrates exists], yet the possible worlds semantics cannot provide an analysis of that because 'contingent being' is not the same as contingent predication [It is wrong to analyze Socrates' contingent being as "it is contingent that Socrates exemplifies Socrateity"].76

What then does exemplification explain? Whatness, perhaps? Maybe individuation? No, (see #4 and 5, next) it cannot. "Exemplification" (and its cognates) is ontologically inert, "a fifth wheel", without explanatory function, serving only to "name" a connection between individual functor and propositional function in the symbolism.

A thing cannot be subject of an inherence relation, or any kind of a "matching" (likeness, or sharing) that determines THAT it exists. "Matching" relations presuppose the being of what is matched. Similarly, the possible worlds (abstractions said to exist actually, and necessarily, to be part of the actual world and of every world), have BEING. How do they have it? By exemplifying still further abstractions to infinity? No. Then, either at some stage, abstractions have being by self-exemplification (and, so, 'being' is one of the shareable abstractions, as Plato thought, Sophist 259), or exemplification does not account for being. But the only self-exemplification that can account for being is exemplification of being-itself. The actualists offer no account of that.77

Now I know a lot of neoplatonist theists wanted to think of God as self-participating being, etc., and everything else as emmanations (decreasing in perfection the way a telescoping antenna decreases in diameter). But it turns out that the logical relationship of 'being' to itself is not exemplification, or any aliorelative match, but sameness.78 Another way to put it is that 'being' is not a universal, it is not "present in and predicable of many things". As I said above, the "actualists" conflate ascriptions of being with predication. Exemplification as a relationship of concrete to abstract (or among abstractions) cannot explain being because it presupposes it.

4. Exemplification of Abstracts (or Possible Worlds) cannot explain whatness. A thing is what-it-is, a human, a dog, a spider, (for the most part)79 inherently and necessarily. A human could not cease to be a human without ceasing to be and could not begin to be, or cease to be, without being human. That seems to hold broadly enough, even of artifacts like radios and airplanes that "do" something on their own. Moreover, no human "becomes" human (except in another sense). A reality, the stuff and structure of things, is the locus of the de re necessity of Socrates' being human, but not the subject of it, as Socrates' nose is the subject of being snub: that-whole object is necessarily human, if it is human at all.

If there were an eternal object or divine idea, 'being human', it would not be identical with Socrates' being human. That comes and goes with Socrates, while such an idea would endure forever. Still, the idea would not, as Plato thought, be WHAT 'being human' IS, but a kind of schema or plan "for-something's being a human". Modal actualists might imagine that the necessary, real and shareable abstract "YELLOW" is what "BEING YELLOW" really is, so that a yellow thing is not really yellow (only the color is), but is 'yellowed', shares in the color, that is, "is made so colored". But they are certainly not going to hold that humans are not really human (as the abstractum is), but just "humaned", "made human", are they? The color inheres in a subject of inherence; but not the humanity.

There are three consequences of these observations. First, the propositional-function/proper-name relationship cannot be just one relation because at least those two different kinds of predication, essential and accidental, are represented with it. Besides, there are other relations of predicate to individual and no one common generic relation for all of them. Secondly, the modal ontologists already confused attributions of being with predication, as I explained above; that continues here and is compounded by their, thirdly, having analysed essential predication on a [partial] model for accidental predication (where 'being F' for a material thing, is "being-F'd" by F, the abstract property or exemplar).

That is, no modern platonist (or theistic neo-platonist I know of) thinks the exemplars ARE the realities of which concrete things are weak copies, and from which they bear the names, but equivocally, the way part of a picture is called "a hat" by likeness, look, even though it is not what a hat really is (a head covering). Or the way the standard motor is the exemplar by resemblance to which other things are motors. I don't suppose they think the world of the abstracta is the world of the "really real", do they? So how could exemplifying the universal explain the WHAT of a thing, when "being a case of that universal" is not the SAME as WHAT it is?

A thing with a real WHAT80 cannot be subject of an inherence relation that makes it what it is, any more than a wood-screw is made to be what-it-is by "exemplifying", or being like, some paradigm, rather than, say, on account of the way its threads grip wood. There is no "The Ideal Wood-screw" to explain whether a particular thing is a wood-screw.

About this I say just two other things now. (1) We do not need real abstractions, THE Letter-'A', to explain the functional equivalence of diverse marks to spell the same words, any more than we need a real abstractum, THE Sound-'AH', to determine a class of allophones, same sounds, say, "Cuba", pronounced ("err") by a Bostonian,and ("ahh") by a Charlestownian. And (2) real abstractions would not help to explain such relations, either.

The relation from concrete thing to abstractum is not explanatory, it is at most conclusory ("exemplifies", "instantiates"). The abstractions are made by us. There are no abstractions in reality, only structures realized in replicable and non-replicable ways.81

We can explain everything the abstraction-talk is supposed explain, better, without postulating any real abstracta at all.82 And to the limited extent that there is extrinsic explanation of the "what" of some things, it is founded in the real "what" of components or stuff (or agents and intentions)--that is not accounted for by convention, ens rationis or language. There is no need for reified abstractions in any case.

Nothing can be "just" a being, neither of a kind nor out-of kinds, anymore than there can be just a bird or animal or dinosaur.83 If there is an instantiation or exemplification by which Socrates is human, then what enters into that relation as its subject? It cannot be "just" a thing or "just" matter (stuff) as subject, because meat and bones (the matter of bodies) is not a human, only a human is.84

Yet we cannot require the subject of alorelative contingent participation (exemplification, instantiation, obtaining, etc.) to BE in order to participate, because for a human to be at all is to be a human. So, no participation would then be required. All that can participate, exemplify or instantiate a WHAT are "bare particulars", "bare nominata" that have no attributes at all. But, of course a subject without attributes cannot "be" the thing that is human. (Nothing without attributes can ever be a thing of a kind; and, as I said,there can be nothing finite that is "just" a being; that is because finitude is not from being-as-such, as Parmenides, Plato and Aristotle knew, but from being a such-and-such (Sophist, 259). In a word, the thing that is human cannot be at all unless it is human and so cannot be extrinsically made human (except by a productive cause). Thus exemplification cannot explain WHAT a human is, anymore than that it is.

Each of the applied semantics for QML attributes necessary and underived being to what cannot have it, and to what cannot explain the being, the whatness or the individuation of concrete things anyway.85

Plantinga says that if Socrates had not existed, we wouldn't have been able to say so (1979:147). Indeed. But he thinks the state of affairs, 'Socrates' not having existed', would have existed, indeed necessarily, and would have obtained. The absence of what would have been individual existence is, apparently, the non-being of 'that very individual'. No. That is incoherent, except as viewpointed in the actual.86 There can be no (imperfect) rigid designation87 of what does not actually (or potentially) exist. "Bleep's never having existed" does not include "Bleep" as a proper name, if "Bleep" never names a person. There are no merely possible individuals. Thus, there is no state of affairs "Bleep's never having existed" except on the supposition that "Bleep" names an actual individual; therefore,"Bleep never existed" could pick out a state of affairs only if it is false. In a word, there are only NEGATIVE states of affairs for things and kinds that actually exist, and they do not obtain. That should tell us that "states of affairs" have to be consequential, to be shadows of real being, not some explanation for real being.

Here is a pragmatic indicator of a pseudo-proposition: a truth-value bearer whose necessary falsity does not entail the necessary truth of its contradictory. (See Kripke,"Truth").88 In fact, to avoid having true singular existentials ("Socrates exists") come out as necessities of nature89 because they are satisfied in all consistent conditions where there is a suitable subject, and thus, not decertified under any consistent condition whatever, we have to consider that simple existentials with proper names are not genuine propositions, not genuine truth-value bearers (in the same sense in which "propositions" of truth-functional logic are truth-valued). Singular existentials are neither predications nor identities [despite those who say that "Socrates exists" means " There is a thing (an x) that is identical with Socrates, Ex(x=S)", oblivious that "Ex(fx)" is theoretically reduced to "Fa.v Fb...," where each disjunct, "Fa", "Fb", involves a name of a thing]. This is another

application of the principle that ascriptions of being cannot be reduced to predication.

So, "Bleep never existed" is, if truth-valued, necessarily false, even though "Bleep exists," if ever true, is contingently true. There is a kind of "sensu composito/sensu diviso" double reading, roughly corresponding to "'Bleep' names", which is contingent, and "There is something identical with the thing "'Bleep' names", which is necessary if it is ever true (i.e., when "Bleep" names), and impossible by vacuity when "Bleep" does not name. Now these connundrums about what to say about empty singular propositions are simply outgrowths of the fabulous abstractions we use for logcal systems, fabrications which turn out to have edges and failures to fit together that we could not anticipate. Anyone who seriously thinks there are propositions for all the things that do not and never will exist is high on logic.

Analogously, if there'd been no tigers, there would be no such state of affairs at all as "there being no tigers". There would have been no such reality as 'being a tiger' for everything that did exist, not to share. Like the singular, the negation "There never were any tigers" is false whenever it has a truth value. So "There are tigers" too, is a pseudoproposition because the name presupposes being. That warns us to look with suspicion at the expansive "states-of-affairs" talk (e.g. R. Chisholm,1983), because some of the things that are supposed to belong to the eternal unchangeable treasury of states-of-affairs are things that have no content except denominatively from what contingently exists. They are "existentially embedded", as are all the necessities of nature. And the only way to get around that (while maintaining that things exist contingently) is to postulate platonic essences, and the like, to be constituents in the states-of-affairs. That's an old scam.

5. No relation of exemplification, instantiation or obtaining could ever account for a thing's being the individual it is. Socrates' exemplifying the property "being-identical-with-Socrates" cannot, for two reasons, constitute, cause or explain his being Socrates. First, in order to instantiate the (supposed) property, "is identical with Socrates", Socrates has to be fully in being, and thus "already" be Socrates. Secondly, Socrates has to be constituted to be a human. But whatever constitutes Socrates to be a human,causes him to be that human. That's because no causes can be sufficient to make something a human but not any particular one. Nor could any human have been any other one. Therefore, satisfying the conditions for individuation is a prerequisite for exemplifying the property "is identical with Socrates". "Exemplifying identity with Socrates" is a consequence of being Socrates, not an explanation of it.

6. Divine Ideas cannot avoid the defects of platonic exemplars. (Plantinga's Augustinean Retreat). Eventually recognizing (1981) that the impacted ontology of necessary beings, God, numbers, sets, states of affairs, properties and propositions he endorsed earlier (See Plantinga, 1974: 169), is not at home with Christian theism, Plantinga assigned the abstracta the place Augustine assigned Plato's Forms: ideas in the mind of God.

The hypothesis, like some others I reject, had its medieval moments. Like the external Forms, it lost its sway because it lacks explanatory force and presupposes the very natures and individuation it purports to explain. Besides, the divine ideas, to serve as an ontology for QML, would require formal traits that cannot be accounted for by the divine understanding that is supposed to emmanate them: in particular, the "logical exhaustion" of perfect being by kinds of "finite imitation", and the exhaustion of kinds by individuation90. As a result, photo-exemplarism is inconsistent; and there can be no such domains of divine ideas as the ontology for QML requires.91

Secondly, if 'being human', say, and individual essences, say 'being Socrates', are ideas in the mind of God, then for them to determine what something is, and which thing it is, say

Socrates (who is not an idea in God's mind), there must be some real relation of Socrates to those ideas, some relation that involves causation of the thing that is Socrates. But as the argument (#3) above shows, exemplification (participation) presupposes sufficient causation of the very things whose being 'exemplification' is supposed to explain.92 So exemplification does not account for the being of a thing, or what it is, or which thing it is. It is a "fifth wheel".

If the divine idea is really a representative idea, it logically presupposes a real kind of which it is an abstraction, (Cf. F. Suarez, D.M. 31.12.40-47). Then it is by the real kind, not the idea, that Socrates is made human. If, however, the divine idea is a photo-exemplar, like a blueprint, a Socrates-picture, that Socrates has to satisfy to be human, the idea is as-it-is because of the Socrates that is to be, not vice-versa. That follows from the fact that there are no empty kind-ideas or individual-ideas. So the divine idea-for-an-F exists only if there is to be an F.93

"Exemplar ideas" cannot account for quiddity and individuation because, stating it comprehensively, the explanation presupposes what it is to explain. There is the special difficulty, too, already mentioned, not among those for pure platonism. For Plato, 'Horse', the Form, is what 'being a horse' really is. Individual horses are horses by sharing the Form, not on their own account, and are, even, derivatively only "called" horses (Parmenides, 130e). On the neo-Augustinean account, God's idea of 'being human' is not WHAT being human is. Thus, we have no account, on that theory, of what the "eternal reality" 'being human' is.

Conclusion: "Possible worlds" metaphysics is bankrupt. No "geniuine semantics" (cf. Plantinga,1974: 127 ff.) for quantified modal logic could be true. Even the formalizations themselves, understood extensionally, and yet taken to be representations of what we mean in modal unbound discourse, in modal discourse about God, or of the modal formality of being, are indefensible and unworkable.

There is, in fact, no one or primary meaning alignment of modal terms to be formalized,(Cf.P.A.). And, more importantly, there is not any meaning alignment of modal terms whose truth is preserved when represented in any ontology that has been offered for quantified modal logic. No classical logic (see the features listed earlier), and in particular, no quantificational classical logic can articulate the formality for plurality of being or even approximate the formal structures for intentional contexts. The whole idea that "necessity" somehow goes beyond "the actual", beyond being, or that possibility is somehow prior to or explanatory of being, is the product of false consciousness.

Furthermore, the ontologies are, on inspection, wholly inadequate to explain how things have being, common natures or individuation. They are overpacked with infinities of abstracts that no one seriously believes to be real, with no more explanatory force than Aristotle found in Plato's Forms, and are, one and all, hostile to God's being the cause of all other being, the creator of the natures of things, of the necessities of nature, and of all possibility and necessity, ad extra, with content.

The simple, profound and enduring error of all these views that treat QML as if there really were a "universal domain" is that being logically decomposes exhaustively into a determinate realm of possibility. It does not. The notion is inconsistent because it supposes that differences of being can exhaust being.94