«Notes on Bergmann's New Ontology and Account of Relations»
Philosophy Research Archives
Vol XII, pp. 220-249.
Bowling Green University, 1986-87
This essay belongs to a series of papers whose aim is to show that some differing accounts of relations in contemporary philosophy (commencing with Frege) are flawed because they resort to what can be labelled `hylomorphism'. Some standard difficulties of Aristotelianism reappear in these analytical approaches. All of them resort to «form» as playing the role of `«ctualizing» a given «matter» (objects taken as arguments, relata, or a relation along with the related terms -- the form then being, e.g., a logical form, as Russell thought when writing his Theory of Knowledge) by making it into another entity. In these accounts the actualizing or structuring form lacks the quality (of actuality or objecthood or whatever) it bestows upon the matter it clings to. The puzzle lies in those forms' baffling slipperiness; for they cannot be meant or intended outside their role of actualizing or informing some matter. But, when we point to (the process or result of) their playing such a role, we cannot mean or intend the form itself, but only the informed matter -- or, if you please, the result of its being thus informed. For some approaches, a problem also arises concerning matter itself, one closely resembling Aristotelian problems with prime matter -- problems which have prompted some interpreters to deny that Aristotle posited any such entityFoot note 1_1. What in these approaches plays the role of Aristotelian matter, when taken «prior to» or outside of its being «informed» by a form, lacks sufficient self-being and endowment with qualities and ontological profile to be an entity directly meant as such. Such a problem e.g. affects Tractarian «objects», which are both form and content, but which can be meant as neither separately. It follows that their ipseity always eludes us and evades being meant or signified. As we are about to see, a similar problem affects Bergmann's new ontology.
After going into Bergmann's ontology in general and especially his account of relations, I'll touch on his most cherished tool, the Ideal Language, and finally show the failure of this grand attempt. A short appendix is devoted to examining Wilson's assay of Bergmann on ineffability.
§1.-- BERGMANN'S NEW ONTOLOGY
In a number of recent papers [Bergmann, 1978, Bergmann, 1981a, Bergmann, 1981b] Gustav Bergmann has developed an ontological account which deserves a careful examination, since in them he has some new ideas about the nature of relational facts. In order to make my presentation crisp, I shall attend only to the account Bergmann has put forward in the three aforementioned papers, giving no attention to his earlier views.
Bergmann's recent account is a new logical atomism, wherein categorial boundaries are absolutely rigid and stern (with just one exception concerning identity statements, as I shall point out shortly). There are two fundamental kinds of entities: (1) determinates, which are independent and separable; and (2) subdeterminates, which are not separable and cannot explicitly be objects (or «intentions», as Bergmann puts it) of intentional acts. Subdeterminates can be intended only implicitly or (so to speak) «slantwise», i.e., in union with other entities forming a complex which is explicitly meant or intended by an intentional act. Determinates are things (which are (non-absolutely) simple), complexes, or classes. None of them is absolutely simple. Absolutely simple entities are subdeterminates. They are of two types: ultimate sorts and items. US (ultimate sorts) might be taken to be of just two types: universals and particulars. Still, as Bergmann [1981b] makes quite clear, if the sort of particulars is just one, there are infinitely many sorts of universals -- one for each Russellian type. To my mind this makes Bergmann's talk about the sort of universals [in Bergmann 1978 and in Bergmann 1981a] problematic. Each item is an individuating principle, a thisness in virtue of which the thing composed by it along with one US is the peculiar entity it happens to be and no other. But neither items nor US can be spoken about or meant; they are too simple for that and so are not separable. This is why they are not existents in their own right, since they lack what I shall call «selfbeing». Bergmann compares the union of an item and a US with an Aristotelico-Thomist union of matter and form [Bergmann, 1978, p. 97]. His claim that Aquinas' materia signata is similar to his own items seems to me less felicitous. As I understand his view, items are much more like Scotistic haecceitates. In Bergmann 1981b [n. 20, p. 209], he credits his Thomist friend, J. Peterson, with prompting him to ontologize the US. (It is, however, the Scotistic connections of this ontology which seem to me most worth exploring.)
On the other hand, there are other non-separable entities whose being consists in somehow either sticking to or seeping into separable entities. Among them are, first, the two modes of actuality and potentiality -- each complex entity being pervaded by one and only one of these two modes. Second, there is exemplification, formerly viewed by Bergmann as a tie gathering a particular and a universal into a complex (a fact), but now regarded as a clinging entity (to be explained shortly). The remaining subdeterminates, such as those signified by connectives or quantifiers, are clinging entities too.
But let me now come to complexes. They are all determinates. First, diads. For any two determinates, x and y, there is a determinate complex which is the diad they both form, Bergmann's notation being either `x≠y' or `(x,y)'. We must repress the temptation to say that difference or otherness is what makes the determinates different or ties them into the complex meant by `x≠y'. Bergmann insists that nothing at all is needed for making them different or for gathering them into their being two rather than one, since they are different in virtue of themselves. Their diversity (i.e., the diad they form together) thus crops up, so to speak, into reality (once they are both admitted). Categorial boundaries between determinates are here (for once) levelled, since any two determinates of whatever category are allowed to form a diad. If g is a (0) (one-place) universal and a a particular, the fact that a exemplifies g is exemplification's clinging to the diad, a≠g. Bergmann introduces ordered pairs Kuratowski-wise, using his diads, rather than classes, for the purpose. The ordered pair (or 2-tuple, as Bergmann is fond of saying) <x,y> is nothing but the diad x≠(x≠y) -- remembering that diads are determinates themselves. Letting r be a two-place relation (i.e., an (0,0) universal), the fact that a bears r to b, where both a and b are particulars, is exemplification's clinging to the diad (r,<a, b>), i.e., to the diversity r≠(a≠(a≠b)). In this way Bergmann has analyzed all atomic facts. Non-atomic facts are generated as follows. For every complex there is a non-atomic fact resulting from a unary operator (negation or a quantifier) clinging to that complex. Next, for any given diad of complexes there is a non-atomic fact resulting from a binary functor (conjunction, disjunction, and so on) clinging to that diad. Notice that diads, complex as they are, are not facts. They are circumstances. Other circumstances are: a particular's belonging to a class and a property's (of mental acts) meaning an «intention». Bergmann introduces classes as entities which are neither simple nor complex. They needn't concern us here (except for a brief remark I shall make shortly), though his class theory is doubtless worth considering.
Bergmann is satisfied that he has in this manner grounded order [Bergmann, 1981a, 146]. We should note the affinity which Bergmann is keen on acknowledging (in order to highlight the relevant divergence) between his way of constructing order and the much more usual set-theoretical move. He says: `I, for one, had I to make a class a constituent of an atomic fact, would rather give up. This is one reason why I think the shift from ordered classes to ordered diads is so important' [Bergmann, 1981a, 147-81. The shift in question is important within Bergmann's ontology in that classes are complexes constituted out of diads, in a fairly mazy way. Thus, as Bergmann remarks, while diads are in a layer closer to the basis, ordered classes are only attained in `a layer at or close to the top' [Ibid., 1471.
The ontological framework is underpinned by three principles:
(1) The exemplification principle: No universal exists unless it is exemplified;
(2) The principle of realism: Whatever is thinkable exists;
(3) The contrast principle: If a complex is sayable, so is the negation thereof, and conversely.
A fourth principle, adherence to which was earlier a badge of Bergmann's peculiar realism, viz., the complexity principle (according to which for two complexes to be different, they must differ in content -- i.e. in at least one of their components, a principle which is a version of a more general content principle) is now either hesitantly and reluctantly given up, or only waveringly and inconsequently hewn to, Finally, Bergmann sketches an Ideal Language (IL) in which there are no variables (since variables stand for nothing), in which quantifiers are dealt with in a way on which I shall have to comment presently, and in which no two signs ever signify one and the same entity (except when both signs signify classes, which are extensional). Another exception is necessitated by his treatment of quantifiers, as we shall see shortly. Moreover, the IL is so devised as to delinearize well-formed phrases, whenever wanted (on which a little more in §4 below).
In this world, all particulars are momentary [Bergmann, 1981b, p. 190 and nn. 6, 20, on pp. 208 and 2811. The rationale for ruling out continuants is that, if a particular, a, can exist at two different times, t, t', then a's being, say, green may be true at t and false at t'; thus, we should need to understand greenness as a two-place relation between a particular of any kind and another particular which must be a time. True, Bergmann acquiesces in talk about series of momentary particulars (e.g. minds are temporal series of states of consciousness), but he seems to suggest that such talk belongs to ontological discourse. Ontological discourse, as he conceives it, is an attempt to say what cannot (literally) be said and so cannot be translated into his IL, unless the series is conceived of as a class. This latter seems somewhat dubious, since Bergmann attempts to keep the resort to classes at a minimum.Foot note 1_2 Momentary entities are not to be mistaken for instantaneous ones; they are `of rather short duration' [Bergmann, 1981b, n.6, 2081. Whether such a view of moments can successfully cope with the problem Bergmann's account is designed to solve is another matter. At any rate, I shall have some comments to make later on Bergmann's ruling out continuants.
Before bringing this Section to a close, let me dwell a moment on quantifiers and negation. Bergmann's IL gets rid of variables by replacing an existential quantification `∃xf(x)' by a formula `∃<a,f(a)>', where `∃' has now become a one-place operator signifying a unary subdeterminate which clings to a diad. The resulting formula can be unpacked as `∃(a≠(a≠f(a)))' [Bergmann, 1981b, pp. 197-81. Bergmann's policy of banning any two signs standing for the same entity is now challenged, since he has either to let `∃(b≠(b≠f(b)))' stand for the same complex entity as the just written formula (by relaxing his ban) or to take appropriate measures, e.g. laying down that only one of the formulas is well formed, thus restricting the field of application of the unary operator ∃ (the existential quantifier) to certain chosen diads. Bergmann [Ibid., 1981 chooses the former alternative (with the usual provisos about `f(a)' and f(b), which needn't concern us here). The same can, of course, be said for the universal quantifier. One result of such treatment is that extensionality for quantifiers is lost: from «p≡q» you can no longer draw «∃xp≡∃xq» (duly rewritten in the above manner). For one thing, when the variable `x' has no free occurrence in `p', the ensuing formula is banned by Bergmann as ill-formed, since, otherwise, what is supposed to be constructed will be one of the materials out of which it is to be constructed. For another, if `p' contains free variables, then Bergmann seems to rule out p≡q as a premise, since it is not a closed formula. Still, such restrictions are far from innocuous, as is well-known.
Let me now come to negation. The effect of negation's clinging to a complex is another complex that is potential iff the former is actual, and vice versa. Therefore, what is meant by `p' is not the same as what is meant by `not not p'. potentiality as conceived by Bergmann has nothing to do with possibility, since impossible (contradictory) complexes are according to him potential. (Bergmann defines contradictory complexes as those whose potential mode is accessible to us.) That means that for any two entities, x, z, both the diad x≠z and its negation, the identity between x and z, exist, except that, while the former is actual, the latter is potential. Nevertheless Bergmann sorts out the meanings of certain sentences hose negation is unthinkable and so nonexistent (in virtue of his «phenomenological» principle identifying to be and to be thinkable). Such unthinkables are, e.g., greenness' being a (0)-universal, or this' being a particular, i.e. those involving true categorial attributions. For a Tractatus-reader all this sounds pretty familiar. What for Wittgenstein is sinnlos represents for Bergmann a complex whose mode is accessible to us, whereas what for Wittgenstein is unsinnig is what for Bergmann is unzayable even if existent. (It remains fairly obscure whether such an existent -- and there is bound to be one, since Bergmann [Bergmann, 1978, p. 98] explicitly says that it is thinkable although unzayable -- is a thing or something else. We could take it that the meaning of `greenness is a (0) universal' is nothing but greenness itself, the subject of our (pseudo) statement, viz., `greenness' there meaning greenness' thisness or `greenness as this peculiar universal it is' [as for Aquinas subjects signify something ut suppositum and for Aristotle they signify something qua its matter].) The absolute simples, items and US, are unspeakable-about. Bergmann also rejects the existence of complexes such as a complex's being pervaded by its mode [Bergmann, 1981b, p. 195], since, should the larger complex exist, its negation would also exist and would be permeated by the opposite mode and so on. All of this would boil down to a gratuitous ontologizing of assertion as actuality. (I hope I have faithfully represented Bergmann's merely hinted-at argument.)Foot note 1_3 Another argument in behalf of the same rejection of over-complexes is [Ibid.,] this one: `A complex's being pervaded by its mode being itself pervaded by one is unthinkable', I think these arguments are unconvincing. (An additional argument is suggested by Bergmann when he denies that pervading should be a tie. See below the fourth objection in §2).
The underlying tractarian arguments are more forceful. One of them is the following. If there is a complex involving another complex, the latter exists non-contingently. In virtue of excluded middle, the former complex is (to put it Bergmann-wise) either potential or actual -- either alternative calling for the existence of the involved complex. Now, for Wittgenstein, no complex exists non-contingently. Things do, although their existence is not necessary.Foot note 1_4 This argument as it stands obviously cannot be accepted by Bergmann. We might try replacing it by one depending upon the principle that whatever is involved in a complex is an actual entity. But that will not do either; for only complexes are actual (or potential), and, what is more, potential complexes, by being clung-to by some subdeterminates, are constituents of other complexes. In spite of that failure, I think that the source of his uneasiness about allowing a complex's being pervaded by a mode to be something (over and above the complex itself) can be pinpointed: If a complex's being pervaded by its mode is something, it is a larger complex. But what are its components? Just the complex and its mode? No, for then the mode would be (exactly like) a clinging entity, since clinging subdeterminates are such that, taken together with a determinate of some kind, they issue in a complex of a peculiar sort. This would in this case mean that, were potentiality and actuality clinging (rather than pervading) subdeterminates, every complex would (separately) be both actual and potential. Since that is impossible, we can safely conclude that, for there to be the envisaged larger complexes, there would be bound to be a further entity -- a pervading tie. Yet, Bergmann's new ontology rules out ties (and to my mind rightly so, since they are nothing else but bashfully recognized relations contrived to escape honest toil, rather like the «non-predicamental relations» of Medieval Aristotelians). Could Bergmann change his new ontology on this issue by holding the modes to be determinates rather than subdeterminates? No, because, in order for the larger complex (that is, for the pervading of the smaller complex by a mode) to differ from a mere diad, a new clinging subdeterminate, pervading, would then be called for. And that would, in turn, entail that any complex was pervaded by both modes -- separately, to be sure -- in virtue of the underlying principle that all possible combinations are in fact realized. This underlying principle can be deduced from the principle of realism: A possible combination is one which can be thought. (This is precisely why Bergmann doesn't view a pervading as a combination.) The difference between a complex's being the case and its failing to be the case would then be nothing but actuality's pervading the complex to be the case. And this would obviously trigger an infinite regress. (See below, my 4th objection in §2.)
A further -- but weaker -- reason for failing to allow a complex's being pervaded by a mode to be something over and above the complex itself is that, were it another entity, it would be a complex one such that necessarily the given complex, p, would be pervaded by actuality iff its being so pervaded were in turn pervaded by actuality -- and so on; which would be the case iff p's being pervaded by potentiality were pervaded by potentiality -- and so on. This would be the case iff p's failing to be pervaded by actuality (another, different complex) were pervaded by potentiality, and so on. All the mutual entailments expressed by the biconditional formulae would be necessary.
According to Bergmann, as put forward in [Bergmann, 1981 b, 189ff], a believing that p is a mental act consisting of the conjunction of two atomic complexes, one of them of the form bel(a), i.e. `a is believing', the other of the form f(a), where f is a thought, i.e., a (0) universal or property of mental particulars such that, analytically, fMp (i.e. f means p or, put a bit more perspicuously, acts exemplifying thought f mean or intend the complex p), while a is a mental particular. Therefore the act is analytically targeted on its meaning or intention. If it is necessarily the case that p iff q, then necessarily an act of believing that p is true iff an act of believing that q is true. I think a proliferation of such mutual necessary entailments would not make Bergmann happy. Granted, Bergmann himself in fact acknowledges some mutual entailments, as e.g. the one between (the truth of) thinking that p and (that of) thinking that p and p, which is different. These cases, though, involve pure logic.
Bergmann's conception of necessity is to my mind purely Leibnizian: there is no other necessity but analyticity: for a sentence to be analytic(ally true) is nothing else but for the complex it stands for to be pervaded by actuality and such that its being so pervaded is accessible to us. (But see below, n. 10.) And I suspect that Bergmann is disinclined to recognize nonlogical analytical truths -- barring just a few exceptions like his sentences of the form `fMp'. Notice that the purported analyticity of that kind of circumstances is not without a number of difficulties. Herbert Hochberg, both in Hochberg, 1978, and in Hochberg, 1981, criticizes Bergmann's contention on the analyticity of such circumstances. Bergmann, 1981a, is in part a reply to Hochberg's criticisms in the earlier paper. Hochberg criticized Bergmann's former use of `«p»Mp'. Bergmann now [1981a, 137] scraps the notation, acknowledging that what is to be found at the left of `M' is the name of a thought, not a structured expression which is implicitly a definite description. Hochberg in  retorts that, on relinquishing the old pseudo-structural notation for thoughts, Bergmann has forsaken the wished-for analyticity of his M-sentences: `all he does is declare, in different words, that `f2Mf1(a)' is analytic' [Ibid., 163]. A related discussion is pursued by Wilson in [Wilson, 1983, 452ff]. Most of all, Bergmann's new notation somewhat obscures the notion of a thought's text. Bergmann has, however, endeavoured to clear it up in [1981b]. He there claims (p. 190) that usually an act is conscious of its intention iff there is, in the conscious state (i.e. collection of simultaneous mental acts) to which it belongs, a further act, consisting of a string of words, which is the text of the former act. But, of course, this is postulation. Bergmann emphasizes that the connection between text and intention is many-many; so he prefers to regard «not-p» and «p is potential» -- if only the latter was sayable in so many words -- as two texts for the same intention. (This notion is made use of below, in the Appendix.)
§2. OBJECTIONS TO BERGMANN'S ONTOLOGICAL VIEW
I turn now to criticism of Bergmann's account. Let me first advance a number of objections to the general framework just sketched, and only then (in the next Section) focus on his way of dealing with relations, which I find far from satisfactory.
The contrast principle wreaks havoc with Bergmann's account, since acceptance of it compels him, on the one hand, to accept tractarian ineffability conclusions and, on the other hand, to countenance as existent such utterly queer «entities» as, for any two determinates, a and b, the identity (or non-diversity, as Bergmann would rather say) between a and b (a=b, or not a≠b), as well as, for any determinate, a, the diversity between a and a itself, i.e. a's self-diversity, a≠a (see [Bergmann, 1981, 140]).Foot note 1_5
The difference between actual and potential complexes is in no way explained, much less grounded or analyzed. We are called upon intuitively to grasp the difference in question. At any rate, potential entities are as real or existent as actual ones; thus, to exist is not the same as to exist actually. False sentences are as corresponding to reality as true ones, except that, while the former denote potential complexes, the latter denote actual ones. All of this runs counter to Russell's reasonable claim that, while there are facts meant by true sentences, false sentences mean nothing. So Bergmann falls back on Aristotle's unanalyzable modes but he does not thereby identify existence tout court with actual existence -- an identification which doubtless gave rise to serious difficulties (actual entailing non-potential), but which proved serviceable all the same. For it blocked the inference from stating an entity's potential existence to stating its existence, period. (Thus Bergmann deems wholly existent or real Locke's being emperor of Japan and even a marsupial for that matter. See below, my criticism of Bergmann's analysis of nonrelational atomic facts.)Foot note 1_6
Bergmann's potentiality has little or nothing to do with what is either in Aristotelian doctrine or usually taken to be potential, i.e., something that is not but can be. potential complexes cannot and could not, according to Bergmann, be actual, nor could actual ones be potential.Foot note 1_7 All that debars us from resorting to usual notions when trying to understand the Bergmannian dichotomy. All Bergmann tells us is that analytic complexes can be known to be actual and that contradictory ones can be known to be potential. As for the remainder, we don't know and shall never know. Yet, what does knowing that a complex is actual (or potential) amount to? I'll have something to say below about the pervading of a complex by its mode. What at present I wish to insist upon is that I see no content at all that I am acquainted with which could be expressed, signified, or what have you, by `potential' and `actual' as Bergmann uses them. Not surprisingly, Bergmann himself bans those two words from his own IL -- for the reasons I outlined at the end of the foregoing section of this paper. It is only in ontological discourse, a kind of discourse which (unsuccessfully?) tries to speak about what is un-speakable about, that we use those words. But then my uneasiness is increased. Those words, as used by Bergmann, are technical, not commonsensical -- a distinction Bergmann's methodology recognizes. But they are banished from the IL. The ground they occupy is most precarious and problematic. What alone seems to me to correspond to our purported grasping a complex's actuality (or potentiality) is that we grasp the complex (or the negation thereof). Could not Bergmann then dispense with modes altogether? Yes, after a fashion. Still, he would then face this result: Not only would true sentences and false ones alike denote existent complexes, but those complexes would be on equal footing, no general feature serving to sort out the former from the latter. What difference would then remain between true and false beliefs? None. Still, whatever difference is acknowledged by Bergmann plays a minor, subdued role in his account. As for analytic or contradictory statements, what alone characterizes them is that their mode is accessible to us. This could be replaced by making a distinction between complexes accessible to us and complexes whose negations are accessible to us. A complex would be accessible to us iff it can be believed with evidence, and we could surely lay down that this happens iff its negation is disbelieved with evidence (see [Bergmann, 1981b, 195]).
As for all other complexes, since their mode remains forever inaccessible to us, who cares? After all we'll never be able to establish that one of those complexes is actual rather than potential. Negation could be defined as the subdeterminate that on clinging to a complex yields another complex whose conjunction with the given one is contradictory and whose disjunction with the given one is analytic. Although such a «solution» is far from satisfactory, it would cope with the same problems Bergmann's account has been devised to deal with and would have the great merit of getting rid of those dark notions of potentiality and actuality. (When trying to meet the coherentist half-way, Bergmann says [Bergmann, 1981b, 205] that, for such believings as are neither analytic nor contradictory, the best we can do is assign and reassign modes to them, blindly as it were, yet systematically, so as to achieve maximum coherence. Let us pass over what assigning a mode to a complex may be. I take that way of speaking to be a mere lapse. At any rate just as much could be secured by a similar quasi-coherentist approach which, while on other matters holding on to Bergmann's views, would waive his modes in the manner just sketched -- except that the coherence ideal would then be grounded in nothing but our own mind's drifts and trends.)
On Bergmann's account a complex is pervaded by the mode of potentiality iff negation's clinging to that complex is pervaded by actuality. It is pervaded by actuality iff negation's clinging thereto is pervaded by potentiality. We have already noticed, however, that no entity's existence grounds a sentence's truth or its negation's falsity; the world contains the same entities whether the sentence is true or false. For a complex to be pervaded by a mode is not a new more complex complex. This is why Bergmann chooses the verb `pervade', meaning that the pervading of a complex by a mode is not a tertium quid, but is the same as the pervaded complex thus pervaded. Otherwise, for the new kind of complex to arise, a tie or bond would be called for, namely pervading. Clearly, Bergmann now dislikes any tying entity, but couldn't he accept a clinging subdeterminate cleaving to a «complex» formed by another complex and a mode? No. For one thing, a mode is a subdeterminate which, if it is glued on a complex, needs no intermediary at all. It would, otherwise, be a determinate, but this is impossible -- as we saw at the end of §1. For another, were pervading a clinging subdeterminate, every complex would be -- separately -- pervaded by both modes, since clinging subdeterminates cling to whatever they can. (Nevertheless see below, §3, how Bergmann seems in the end bound to regard exemplification as such a tie between a complex and a mode.) On the other hand, according to Bergmann, once a complex is there, negation's clinging to it is there too, automatically and without intermediaries. If p is a complex entity, so are not-p, not-not-p, and so on. All of them exist and differ from one another, but, according as to whether the number of «clingings» by negation is even (including zero) or odd, those complexes, as regards the pervading mode, enter two disjoint equivalence classes (so to speak, for Bergmann would of course have nothing of the sort, since classes gather only particulars or perhaps other classes as well). This account of negation seems to me utterly mistaken, especially with the infinity of already existent complexes which are logically equivalent among themselves, and with the incomprehensible pervading of a complex by a mode. If, as I've guessed, that pervading is nothing else but the complex itself «as so pervaded», we get saddled with Aristotelian reduplications or «qua» expressions -- of which there is no available clear logical account and whose historical role has been to serve as a smoke screen to conceal a theory's inferential virtualities or profile.Foot note 1_8
I find it very hard to understand what an entity like a≠a may really be, and, still harder, for blackness to be the same as Somalia's being impoverished by drought. True, any actual diad is necessarily actual, as any potential diad is bound to be potential. (For the only necessity concept Bergmann allows for in his account is analyticity and he reckons all identity or diversity formulae as analytic, since -- barring the two aforementioned exceptions -- in his IL no two expressions ever stand for the same entity.) Still, necessarily potential as they are, the difference between a thing and itself, as well as its identity to anything else are all the same real entities, which, Bergmann contends, exist and can be thought. Now, Bergmann's argument against the existence of words standing for categories or US is that, were there such words, sentences containing them as well as their negations could be said and consequently also thought, whereas a thing of a certain category's not being of that category is unthinkable. But is not a's being the same as each and every entity as unthinkable as greenness' failing to be a universal?Foot note 1_9
Within Bergmann's framework, facts have no properties (they are bare facts) and bear no relationsFoot note 1_10. We cannot say anything about a fact or any other complex -- except of course that it is the same as, or other than, any determinate. Still less can we speak about subdeterminates, such as exemplification, negation, conjunction or existential and universal quantification. They cannot even be sensibly said to be either identical to or different from any entity. (As for such subdeterminates as US and items as well as the two modes of potentiality and actuality, their plight becomes hopelessly bleak. They cannot be either named or meant or otherwise pointed at, as other subdeterminates are, by syncategorematic signs. And, of course, they enter no facts or circumstances. Their failing to do so is, still, nothing at all and accordingly both unthinkable and unsayable. The proposal's main theses are, thus, literally unsayable -- as Bergmann himself outspokenly acknowledges. True, Bergmann Tractatus-wise says that a US and likewise every form is represented by a shape of a sign denoting a thing with that US. Likewise every form is represented by a shape. As regards, e.g., potentiality there surely is some geometrically describable shape shared by all false sentences. We do not know, however, and will never know what it is. In a similar vein, a «Sellarsian realist» could take universals to be unspeakable-about entities which can -- or must -- be represented only by shapes or the like.) Thus, either we face Frege's own troubles, or, still worse (with nothing like correlate or surrogate objects being available within Bergmann's framework) we condemn as unsayable all what we are saying or purporting to say (as Bergmann himself does). The worst fate that can befall a theory is entailing its own ineffability. (Oddly enough, Bergmann's account rules out classes' exemplifying properties and bearing relations, since within his ontological framework classes are not particulars. As I understand Bergmann's doctrine, classes may belong to classes of classes and be the same as themselves as well as different from anything else. Besides that, nothing else can be said about them.)
According to Bergmann, difference is literally nothing, as we saw above. This is why a difference between two things is not a fact, but a mere circumstance, with no constituent other than the two different determinates by themselves, whose existence entails eo ipso the circumstance's own existence. Now Bergmann claims as much about another circumstance, namely a particular's belonging to a class -- the membership sign, he says, standing for nothing. I wonder then what difference, if any, there is between a particular, a's, being a member of a certain class b and the circumstance that a≠b. (Bergmann says that for membership order matters, whereas it does not for diversity. I'm not quite sure he is right on the first score, if we espouse his way of «constructing» classes, which incorporates a Fundierung principle not just for truth but apparently also for sense. Be that as it may, what seems to me most clear is that, membership being literally nothing (since an element's belonging or failing to belong to a certain class requires no tie whatsoever), no order can be achieved through «it».) Nevertheless, a's belonging to b may be potential while a≠b is actual. (And, of course, the converse, if, when `b' stands for a particular, `aεb' is allowed to be well-formed. This is not clearly settled by Bergmann, but, in its behalf, telling considerations can be put forward which would match Bergmann's own case for allowing `c≠d' to be well-formed whenever `c' and `d' stand for determinates). Yet, one and the same complex cannot be pervaded by both potentiality and actuality. Therefore a's belonging to b and a's being other than b are different circumstances, but there is nothing at all, either inside or outside them, which makes them different.
Bergmann's ruling out all but momentary particulars is not, of course, gratuitous. What he thereby achieves is important. However, the price he pays seems to be unbearable. (Bergmann in fact joins P. UngerFoot note 1_11 in upholding that I (or he) do(es) not exist. Or else I am a non-particular, which is what he says. But talk about those non-particulars seems to belong to ontological discourse, which is not, and cannot be, either literally true or subject to an adequate paraphrase.) Are there other alternatives? One of them would be to regard some verbs or predicates as being of variable adicity. Bergmann would retort rightly that, on the ontological side, nothing seems to correspond to any such device. Another alternative would dispense altogether with categorial barriers.Foot note 1_12
In this ontology, existents do exist, but there is nothing by having of which existents exist, since existence is nothing at all. There are two reasons for Bergmann to refrain from positing a property of existing. First, it would straddle categorial boundaries. (But Bergmann is not deterred by similar qualms from taking identity and diversity to straddle categorical borders -- within the range of determinate entities. Were Bergmann to acknowledge a separation principle by dint of which, for any formula «p» and variable `x' with free occurrences in «p», and for any determinate, z, z exemplifies ^xp inasmuch as it is true that p[x/z], then, of course, he would hit a snag. For then all determinates would have to belong to the same category, that of being either identical to or different from any given determinate. This is an excellent reason for Bergmann to stay clear of any such separation principle, either in that strong and unqualified formulation or in any other form.) Second, there cannot even be different properties of existence which are categorially bounded, since, if any such property exists, it is exemplified by every determinate within its range, and thus, for any such determinate, x, that x exemplifies existence (of the relevant category) will be a fact. But for a number of reasons, this cannot be the case. Such atomic facts would be analytic (contrary to a basic tenet of Bergmann's ontology and theory of knowledge). And any such fact's negation might be unthinkable, and therefore nonexistent, since it may seem doubtful whether it makes sense to think of -- or even entertain of -- an entity that it does not exist. (It may seem that we think that it could have failed to exist; but surely Bergmann will reply that, on second thought, we should notice that no such possibility can obtain, since, if for p to be the case is contradictory, so also for p to be able to be the case. And for an entity not to exist is a contradictory state of affairs. That argument, however, might be countered by pointing out that contradictory complexes do exist according to Bergmann. Even so, an existent contradictory complex is, according to him, nonatomic or else a diad.) Furthermore, only simples exemplify properties -- all other determinates being property-less.
Existence is not even a subdeterminate, although the reasons for that are surely more intricate and less plain. At any rate, what I wish to underline is that, should we put up with existents' existing without existence, why not endure black particulars being black without blackness and so on? Admittedly, there are special reasons against accepting existence, but that is beside the point. The point is that, if one turns nominalist as regards existence, he can in exactly the same way turn nominalist as regards properties and relations in general, thus embracing outright Sellarsianism. We can always feign to understand `is black' as a diacritical mark or squiggle in virtue of which `a is black' differs from `a is white', the former statement committing the speaker to (recognizing) black things, the latter to white things -- appropriate measures of paraphrase being taken for the cases of subject-position property terms, in virtue of a reasonable principle of supervenience, which may be accepted by a realist, viz. that a universal cannot have a property without at least some of its «inferiors» (entities that exemplify it) being in some way or other modified or affected thereby. The nominalist thus can conclude that, even though in some cases we don't know what the proper paraphrase is, we do know that there is some such paraphrase. Sharing Bergmann's realist convictions, I reject such a nominalist gambit, but all arguments I have been able to develop for backing up realism would, upon our allowing for a commitment to existents without existence, either crumble altogether or at least lose their strength and become dependent upon contrast-principles which seem to be highly questionable.Foot note 1_13
My final general objection again concerns modes. Since Bergmann's ontology is clearly a form of neo-Aristotelian hylomorphism, let me compare his doctrine about modes with Aristotle's. For Aristotle, there is in every actual thing, barring a pure Actuality like God, a principle of its actuality together with a potentiality principle which receives and contracts the former. So Aristotle can -- in a way which, however, bristles with difficulties -- explain how two things can share one same actuality or form (form always being the actuality principle). That Bergmann cannot do. Both his modes are more like Aristotle's forms (even though, to be sure, Bergmann himself carefully and watchfully remarks that his modes are not Bergmannian forms -- a Bergmannian form being nothing over and above the entity that has it). A mode is shared by several complexes. Now, there is no such entity as the mode's pervading the complex. All this we know. Neither is there any compound made up by both the complex and the mode. How, then, can two complexes share their mode? For, there is nothing in them which can be the mode and which also can be in other complexes.
§3.-- OBJECTIONS TO BERGMANN'S ACCOUNT OF RELATIONS
I shall now consider objections addressed to Bergmann's treatment of relations proper (i.e., difference and identity as well as junctions between complexes and membership which is for now being sidestepped). What strikes me as particularly implausible about this account of relations is that it amounts to saying that a's having r to b is nothing but the 2-tuple's <a,b> exemplifying r, provided that we grant (what is doubtful, as I shall shortly underline) that Bergmann's account of a nonrelational fact is an adequate way of construing a particular's exemplifying a property. For, if a's exemplifying property g is nothing else but the diad's (a,g) being clung to by exemplification (the clinging in question being nothing at all, not even a tie or a subdeterminate -- which, by the way, requires that all our discourse about it is nonsense), then the diad's (<a,b>,r) being clung to by exemplification is bound to be nothing else but <a,b>'s exemplifying r. Now <a,b> is nothing else but (a,(a,b)), i.e., a≠(a≠b). The true subject of the exemplification of r is, on that analysis, the difference between a and a's being different from b. Whatever else can be said for or against this approach, that fact alone seems to me a most unpalatable result. My loving my wife is certainly not the same as love's being exemplified b y my being other than my being different from my wife. It is, instead, I who exemplifies love.
Notice that the usual set-theoretical analysis of relations is much less unbelievable. We can, albeit somewhat artificially, construe love as a property of ordered pairs, if ordered pairs are sets of sets. The set whose only two members are Wittgenstein's singleton and the class comprising just Wittgenstein and Weininger can be said to belong to admiration. (Though unnatural, this at least looks bearable.) After all, that set (to put it in Bergmann's words) exhausts its nature gathering into a single determinate, viz., itself, all and only those determinates which satisfy its enumeration clause [Bergmann, 1981a, p. 142], all of which behave the same way. But nothing of the sort can be said about diads as Bergmann analyses them. The «circumstance» (we'd ordinarily say «fact») that a is different from something else, b (i.e., a's being other than b), is surely something which, at least in a sense, separates a from b or interposes itself between them -- rather than yoking or gathering them.
(Should Bergmann reply that I am mistaking his diads for diversity-facts, for which there is no room in his ontology, I would reply that, although they are not facts in Bergmann's technical sense, they are circumstances which are actual or potential according as their two constituents are different or the same. A sign meaning a diad is true iff the diad is actual, otherwise false. A diad's negation (i.e., negation's clinging to the diad) is the circumstance of both constituents being one and the same. As ordinarily understood by set-theorists a class cannot be asserted or denied. If it could be denied, the negation might mean the class's nonexistence, i.e., the lack of a link uniting or fastening the class's members together into a collection. A Bergmannian diad's negation is, instead, an identity between the two involved terms, something which joins or couples them more closely than the diad. [See Bergmann, 1981b, n.3, p. 207, and n.16, p. 209.])
My second point against Bergmann's analysis of relations is that I do not think his account of nonrelational atomic facts can be subscribed to for a reason similar to that noted above. What Descartes' pride consists in is not exemplification's «clinging to» the difference between Descartes and pride. If that clinging can be something, it surely consists in that for Descartes to be other than pride (or conversely) exemplifies -- period. (According to the accounted hinted at in note 12, that statement can be truthfully made. The difference in question exemplifies, since it exemplifies many properties, e.g., existence, being thought about, and many others. But nothing of the sort can be granted Bergmann. Above all, it must be insisted that this would have but little to do with Descartes' being proud.)
Let me now bring up a more important point concerning Bergmann's analysis of both nonrelational and relational atomic facts. What we have is something like Aristotelian hylomorphism. An entity which lacks selfbeing (ontic separableness and, of course, actuality), i.e., exemplification, by «clinging» to a diad (which, unlike Aristotle's prime matter can be actual by itself) makes the diad into a new complex entity (which, unlike Aristotle's σþνoλoν, can be merely potential). The «clinging tie» is nothing. Once the diad and exemplification are there, the latter's clinging to the former is there too. (That, of course, raises an issue dealt with at the end of objection 2 in §2.) Like Aristotle's substantial form, exemplification needs no intermediary or go-between tying it to its receiving substratum. But then the difference between the diad (Fox, whigness) and the fact of exemplification's clinging to that diad is that the one can be potential and the other actual.
In all facts allowed for within Bergmann's categorial account of facts, the diad clung-to is bound to be actual, while that diad's being clung to by exemplification may be either potential or actual. When it is actual, I see no difference between the diad and the fact. Exemplification fails to play even the Aristotelian role of actualizing its receiving substratum, and, not being conjoined or bound to the diad by any connection at all, lacks moreover any selfbeing or peculiar nature, physiognomy, or what have you. (It is absolutely unclassifiable, falls under no US, and has no feature or property, not even a thisness of its own, since it is not a thing.) I can see no peculiar quality or trait which it can contribute to or bestow on a complex which it enters. If that complex contains, besides it, just another entity which is by itself real (or even actual), I can see no new content of the purportedly new complex. So the only case wherein there may be a difference between the fact and the diad occurs when the fact is potential. Exemplification, then, by clinging to the diad makes it into a potential complex. And then the pervading of the fact by potentiality being nothing at all over and above potentiality and the fact, much the same difficulties can be raised again. What is in and by itself nothing, since it absolutely lacks selfbeing, properties, and so on (even its being other than actuality is nothing -- neither fact nor circumstance) «pervades» a complex, giving it thereby what alone characterizes that fact and makes it different from the diad it contains. If I understand anything of this doctrine, I take it that it amounts to saying that exemplification is a way of potentiality's pervading the diad and nothing else. Exemplification thus becomes a tie between the pervading mode of potentiality and the diad formed by the meanings of the subject and the predicate of the sentence that means the atomic fact. So Bergmann has been unable to dispense with ties. But resorting to ties is a questionable procedure, since a tie is supposed to do the connecting work of a relation without being a relation among relations -- without, that is, its tying two entities being bound to undergo the same kind of analysis which a relational fact must be susceptible to. And that is a unfair device. If such an analysis is avoidable for «tying circumstances», why not for relational facts?
All of the foregoing considerations apply equally well to the Bergmannian analysis of relational facts, since all that sorts those facts out from nonrelational ones is that the involved diad does not consist in a universal's differing from a particular but in its differing from a particular's being other than its being different from another particular. That complication alters nothing concerning what has been said so far.
Bergmann might then just as well acknowledge a tying or fastening bond between a mode and the complex it pervades, since his exemplification is in fact none other than such a bond. The ordering problem is, however, apparently solved. The complex and the mode once given, no alteration of the order with which the mode bears the tying bond (indeed, relation) to the complex can be allowed for in virtue of the categorial restrictions which stem from Bergmann's «canons». Is the price worth it? I don't think so, since it foists upon us the unbearable clog of ineffability. (A difficulty with our reconstructed Bergmannian account is that one and the same diad may be pervaded by a mode through two different «ties»: exemplification, for one, and mere «pervading», for another -- the latter being such that, with regard to the diads we're concerned with in Bergmannian facts, the sole pervading mode is always actuality. The difference between these two pervading links is hard to explain unless we label them as the «exemplificating» and «nonexemplificating» pervading ties -- whatever such a «solution» might be worth. At any rate, a part of the same problem arises even from Bergmann's original account. Since a complex's existence along with a mode's existence doesn't suffice to determine that the complex is pervaded by that mode rather than by the opposite one, something or other must intervene, a pervading tie or, better, some solder by means of which the mode is soldered to the complex or fused into it.)
I want to take exception as well to Bergmann's way of founding order. It seems clear enough that his way suffers from all the problems besetting the usual set-theoretical manner of analyzing away order in relational facts -- most obviously, the failure of the attempt. As much has been cogently argued by Hochberg [Hochberg, 1981]. By analyzing `Booth assassinates Lincoln' as /(<Booth, Lincoln>, assassinating) exemplification/, we are availing ourselves of an implicit ordering operation by means of which we treat the subject or referent (the first term) of the relational fact, Booth, as former and the relatum (the last term) as latter. For the 2-tuple <Booth, Lincoln> is nothing else but Booth≠(Booth≠Lincoln), a diversity wherein one of the terms occurs twice, the other once. Thus one term is taken first and is set over against its own differing from some other term. And then the gap pointed at by the quantifier `some' is filled by the second term. There is, of course, an arbitrariness about the procedure (and that is what has been most often frowned at), inasmuch as we may also take a≠(a≠b) to be a substitution instance of the quantification ∃x(x≠(x≠b)). This is not my present concern, although I agree that the arbitrariness in question has something untoward about it. My point is that we need to take a≠(a≠b) one way or the other -- either as a substitution instance of ∃x(x≠(x≠b)) or as one of ∃x(a≠(a≠x)). The asymmetry of the resulting formula thus evinces an implicit order followed in the process leading to that result. Such an asymmetry is by itself an order.
To see this more clearly, set up the 3-tuple <a,b,c> in accordance with Bergmann's procedure, i.e., as <a,<b,c>>. Then that 3-tuple turns out to be the diad a≠(a≠(b≠(b≠c))). The pattern is clear: first x's difference from x's difference from something, next, that «something» becoming y's difference from y's difference from something. We stop at the last «something» if we have already inserted n-1 terms (each occurring twice), and we are out for an n-tuple. This is how «we» build up the n-tuple expression. (If, alternatively, we choose to identify <a,b,c> with <<a,b>,c>, the 3-tuple turns out to be (a≠(a≠b))≠((a≠(a≠b))≠c). In a way the ordering pattern now becomes clearer, if more intricate. The first element is the one that now occurs four time; the second the one that occurs twice; the third the one that occurs once. Or, if you wish, the other way around, going right to left.) The order emerges not just in the process but in the result. If, as Bergmann's methodology rightly demands, our (grant its being ideal) language must reflect the world in its «structure», I take it that the implicit order in our linguistic pattern reveals or displays the implicit order in the real entity (or «structure») that pattern mirrors. It is then far from being true that order has been grounded in something else.
This is not yet, however, the main point to be highlighted. What seems to me most important and most serious is that, by his so taking as already ordered or structured a whole whose ultimate constituents are the relation's extremes (subject and term or referent and relatum), Bergmann overlooks the fact (rightly emphasized by Russell) that relations have a sense. That is, in any relational fact, the relation proceeds from the referent to the relatum. The signing relation proceeds from King John to the Magna Carta, while on Bergmann's view it is the property of the already structured 2-tuple <King John, the Magna Carta>. Needless to say, that account also bars applying the clipping-off rule. From `Graham Greene writes The Heart of the Matter' we could no longer draw `Graham Greene writes' unless, of course, the conclusion is paraphrased as implicitly quantificational -- a move which, for reasons I cannot deal with here, is highly objectionable.
Failing to account from the clipping-off rule (rxz ∴ rx) is, of course, a common weakness of all available treatments of relations except combinatory ones (which have not as yet been taken seriously enough from a philosophical point of view). Not surprisingly, combinatory approaches also can cope with other difficulties which Bergmann's account (as well as those of Frege, Russell, Hochberg, and -- up to a point -- even Castañeda) fails to handle satisfactorily.Foot note 1_14
§4.-- BERGMANN'S IL
I wish to comment on two points in connection with Bergmann's IL. First, his delinearization [Bergmann, 1981a, pp. 149-50]. The procedure consists in replacing the usual disambiguating symbols (as, in Polish notation, order or, in standard notation, a mix of order and auxiliary symbols, such as parentheses, all in an underlying string structure) with circles. It is understood that, within each circle, the contained signs can be written in any order, left to right or conversely, top to bottom or bottom to top, without a complex sign's being thereby changed. Thus, if we wish to represent a's exemplifying g, we encircle together the signs `g' and `a' and thus represent the diad g≠a. We may then write the exemplification sign near the circle and draw another circle surrounding both the first circle and the exemplification sign. Let us abbreviate as `p' the resulting inscription. If we wish to write `p∧q', we write `p' and `q' in any order and enclose them in a new circle, writing the conjunction sign next to that circle, and finally enclosing all of this within a new circle. By virtue of the ontological canons (and, therefore, by virtue of the well-formedness rules which are their syntactic counterparts) all ambiguity is dispelled. The second and fourth circles cannot represent diads, since exemplification and conjunction are not determinates. For the first and third circles are diacritical marks for being-diverse-from, whereas the other two are disambiguating auxiliary symbols like couples of mating parentheses. The remaining details can be safely ignored here.
Let me now briefly comment on all of the above. As far as I know, the first to have pointed out the linearity of language (or, more exactly, the linearity of linguistic messages) was Ferdinand de Saussure in his Cours de Linguistique générale. And that doctrine has been taken over by all structuralists [see Martinet, 1970, I-10, pp. 16-7]. That linearity is a function of our human natural language's being a vocal rather than, say, a gesture language, since vocality requires a temporal output and thus (as usually conceived) one dimensionality. Written language structures have thus tended to imitate (as far as possible) and tightly fit vocal language structures. Natural language's linearity is, however, far from perfect. For one thing, along with segmental signs, there are suprasegmental signs, such as prosodic factors of tone, stress, and the like, whose role is important in some languages and which add further dimensions. (Linguists have been prone to soft-pedal such suprasegmental signs, since they are less easy to scan and verify and since semantically they play only marginally distinctive roles in languages like English. In other languages, for example, Italian, they play much more systematically distinctive roles.) For another thing, some written representations of vocal language also (if in a restricted way) resort to suprasegmental diacritical marks like accents, etc.
Some conceptographic notations, like Frege's, are partially non-linear in character. But what most of all needs emphasizing is that linear order is often immaterial (though it is certainly there). Many languages allow a great many strings which differ among themselves in the order of the combined signs occurring in them to stand for the same meaning and so to be `felt' by language speakers as all being the same string under different forms and variations. Consider the Latin `Romam condidere troiani', `Condidere troiani Romam', etc., with six strictly equivalent strings, all permutations of one another. But even in these languages linear order matters. At any rate, this is how many or most linguists think, since they take `Romam' to be a syntagmatic phrase made up of two morphemes which cannot be separated. But, of course, other analyzes are available (e.g., the WP approachFoot note 1_15 or transformational accounts). These alternative analyzes would stress the irrelevancy of linear order in such cases.
It would seem that the two procedures by which natural language breaks partially loose from the sway of linear order are quite different and ought not to be run together. Therefore, Hochberg's reply to Bergmann's delinearization program [Hochberg, 1981, pp. 161-2] might be thought to be unconvincing, since all Hochberg accomplishes with it is partially superseding the importance of linear order via resort to inflectional marks. `aRb' could be written, say, as `a¡Rb', with `¡' a desinence of the subject or referent, like a «nominative», so as to make the latter formula strictly equivalent to `Rba¡', `ba¡R', Ra¡b', and so on (six in all again -- with lack of `¡' being a zero-morpheme indicating the role of relatum or term, i.e., a sort of «accusative»).
What I want to underline is that Bergmann's own delinearization is not unlike that one. True, sign combinations are now allowed along two dimensions rather than just one, thus making it possible to align two combined symbols in infinitely many ways, not just in two as in the case of a one dimensional language. These infinitely many ways, however, might be regarded as falling into just eight «canonical» combinations, disregarding smaller differences as many such differences are neglected in the usual one-linear notation. That does not mean, however, that linear order has been done away with. It is still there, though it has become a merely partial order. Besides the formerly existing linear order, another linear order has been added along a second dimension. Do these orders matter? It devolves upon the system's axioms and inference rules to settle the issue. But such is the case for one-linear languages too.
The case of prosodic or suprasegmental signs is similar, since it can be represented as adding either just one or several further dimensions. In some cases the differences thus achieved are semantically irrelevant (although they can and often do matter from a pragmatic viewpoint),
My final comment on Bergmann's delinearization is that we ought to conceive written language signs as writing acts rather than written inscriptions. So the linear order for that language is a temporal one. Likewise, we had better look upon verbal language signs as speech acts, not as sounds. In fact, phonologists have always tended to conceive of phonemes and signifying combinations thereof in just this way, preferring an articulatory account to an acoustic one. What means Paris is an act of saying `Paris'. That changes the entire outlook concerning a sign's having occurrences within another. Literally it isn't true that a(n act of) saying `Peter is here' occurs in or is part of a(n act of) saying `Peter is here or there'. Likewise, the relation between saying `aRb' and saying `a', `R', and `b' is not accurately styled a whole-parts relation.Foot note 1_16
The second point I wish to make about Bergmann's IL concerns diacritical marks. According to Bergmann, diacritical marks stand for nothing but, nevertheless, discharge a disambiguating task. So, e.g., `ε(a,b)' (or `ε<a,b>', as Bergmann claims his class theory requires) stands for the circumstance of a's belonging to b, whereas `ε' itself stands for nothing. What is worth emphasizing is that whether something is a sign or a mere diacritical marks is for the syntacticist to decide as a function of his semantic (and, in last resort, ontological) convictions. A Sellarsian (or Tractarian-Sellarsian) theorist can reconstrue any given language by calling many drawn lines or ink traces mere diacritical marks, i.e., mere features of a certain complex sign's shape -- not signs in their own right. And, of course, certain such ink-traces of a nominalistically devised language, which were designed to serve as diacritical marks, may be reconstrued as denoting-signs by a realist «decipherer». (Even Sellarsian blanks can be so construed, as shown by Wilkin [Wilkin, 1979].) That detracts from the plausibility of the Tractarian claim that needless or dispensable signs are not signs (i.e., they do not denote). The claim gets trivialized by a cunning and skilful «deciphering». In a similar way and via artful «translations», Quine's ontological commitment criterion can be relativized -- as Quine, above all others, is apt to admit, since this is in fact a consequence of his ontological relativity thesis. Therefore, Bergmann's IL doesn't support, as he apparently expects, his own ontological views. But please note that these comments are not designed to support ontological relativity or anything of that sort, but rather to show that, even though a certain way of looking at language (syntactically as well as semantically) goes hand in hand with a certain way of viewing the world, still (using a) language by itself neither commits us to any particular ontology nor relieves us from any such commitment. It commits us to some ontology or other only depending upon such methodological principles as we may espouse This is why the very enterprise of constructing an IL seems to me futile. A symbolic notation, used along with schematic letters, is of utmost usefulness for representing (some features of) spoken language perspicuously, in a catching-the-eye sort of way. Thus conceived of, a symbolic notation is, however, not a language. Furthermore, if an ontological doctrine can be said and made sense of, either it is said in natural language which we (hope we) understand, or else it is set forth in an artificial language which, if it can be understood at all, is to be translated into natural language. (This remark is not a denial that worthwhile insights can be gained through artificial notations -- if they are taken in the way I have just pointed out.)
APPENDIX: WILSON'S ASSESSMENT OF THE INEFFABILITY ISSUE
The issue of ineffability, discussed above in the 1st object of §2, has been taken up at length by Fred Wilson [Wilson, 1983, esp. pp. 441-50]. Wilson focuses on the problem surrounding the US of particularity. I don't think that Wilson has gotten Bergmann right. Following is how Wilson presents Bergmann's argument for the ineffability of `a is a particular'. If a is a particular, we cannot believe that it isn't. (This lemma is proved by Wilson by an amazingly complicated argument, one which Bergmann couldn't accept in Wilson's terms, for reasons I shall leave unsaid here.) Therefore `a is not a particular' must be ill-formed. (Wilson literally says that such a formula `in belief-stating contexts must be considered as ill-formed', p. 449. But surely, if a formula is to be «considered» as ill-formed in certain contexts, it must be so «considered» in any other context whatsoever. Infringement of this rule would hugely complicate syntax and offer no worthwhile return for that complication.) Now, if `particular' were an acceptable term in the language, then `a is a particular' would be a formula (even if an ill-formed one). And every formula `p' is such that «p»Mp (see above, end of §1). Now there is, of course, no complex consisting of a's failing to be a particular. Hence `a is not a particular' means nothing at all. If follows that `particular' is not an acceptable term.
To that line of argument Wilson replies by waiving Bergmann's interpretation of the formula `«p»Mp'. For Wilson this formula says that the-thought-that-p causes one to utter the sentence `p' -- under certain circumstances of course. According to Wilson an ill-formed formula can be uttered, and therefore «it» can be meant. «p»Mp in no way calls for `p' to be well-formed. All that reconstruction and Wilson's own point are at odds with Bergmann's viewpoint and also with what seems reasonable to the present writer. (That does not mean that I look upon Wilson's idea about accepting ill-formed formulae as indefensible. No, that idea makes sense. See, e,g. [Tabakov, 1983].)
First and foremost, according to Bergmann, a complex's being such that its negation cannot be believed in no way entails that the negation of the formula denoting that complex is ill-formed. On the contrary, Bergmann takes all contradictions to be well-formed formulae. Therefore Wilson's argument cannot be Bergmann's. No, what Bergmann is attempting to convey is that, were `a is a particular' to be sayable, its negation would also be sayable (in virtue of the contrast principle). Were such a negation sayable; then the thought whose text it is would mean something, namely, the complex consisting of a's failing to be a particular. But can any such complex entity exist? No, for it would consist in negation's clinging to a's being a particular. Since negation clings to nothing but complexes, a's being a particular would then be, not a two-in-one, which Bergmann takes it to be, but a genuinely complex entity. But it cannot be, since an infinite regress would be triggered. For in that case a's being a particular would be made up of two entities, a and particularity (to say nothing of exemplification, i.e., supposing a's being a particular to be a circumstance rather than a fact). a itself could no longer be something constituted by particularity plus a bare individuating item. (For, in that case, a itself would within itself have to possess whatever complexity could be ascribed to a's being a particular, that is to say, a's being a particular would be nothing else but a itself, within which we'd find the item plus particularity.) Or it could no longer be a bare individuating item -- a determinant, to use Bergmann's former technical term. If it were a determinant, it would be just this determinant, which, by the same token, would require its being made up of both some individuating thisness and determinanthood. And so on. (Wilson's own reconstruction of Bergmann's account is in fact liable to such a regress -- p. 460. He vainly tries to escape the regress `by defining a determinant to be any entity which has either the property of particularity or the property of universality'. I feel unable to see how this suggestion can facilitate any way out. It's not a question about sameness, as Wilson says on p. 461.) Therefore, if `a is a particular' could be said, a's being pervaded by particularity would be a genuinely complex entity, and thus an infinite regress would be triggered. Since Bergmann rejects infinite regresses, he concludes that `a is a particular' cannot be said. On the other hand, application of the contrast principle to tautologies yields, on the ground of Bergmann's assumptions, recognizing real complexes denoted by contradictions.
Wilson is, however, quite right in saying that Bergmann's case for realism (his claim against Sellars that it doesn't suffice to posit green things, but for each green thing you need to posit greenness, on the one hand, and, on the other, some particular entity or substratum) can rightly be likened to a similar case for viewing a thing's particularity as a complex comprising both the universal, particularity, and the thing itself.
I have for years held Bergmann to be one of our age's (few) metaphysicians. I am confident he both deserves and will obtain an honoured position in the history of philosophy. He has the merit of having come to grips with fundamental ontological questions, taking the bull by the horns. If his grand attempt comes out unsuccessful in the end, that is the mark of a need for a radical alternative, leagues away from the beaten track (an alternative such as the sketchy remarks in nn. 12, 14, and 16 aim at).
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[Foot Note 1_1]
I'm thereby referring to Hugh R. King and William Charlton. See [Charlton, 1983]. Charlton's main mistake is his failing to take account of Aristotle's conceiving of prime matter as pure potency. Aristotelian potency encounters to my mind insurmountable difficulties which may be a good reason for disposing of prime matter altogether -- as well as any other individuating principle conceived as «barely» particular,
[Foot Note 1_2]
An anonymous referee invites me to compare Bergmann's view on continuants to Hume's and to make it clear why construing physical things as series of momentary particulars is supposed to be illegitimate. Hume's views are on their own sufficiently difficult to grasp. The discussion in [Bennett, 1971], pp. 333 ff., far from being able to solve Hume's problems, fails even to grasp the heart of Hume's problem, a problem which invokes a Tractarian theme: To say that two things are identical is false, while to say that a thing is the same as itself is meaningless. In other words, if identity is a relation, it needs to relate two things, which is impossible. Notice that Bergmann somehow `solves' this problem by bestowing existence both on the identity between a and b, whatever they may be, and on the difference between a and a itself. (A more accurate examination of Hume's approach is to be found in [Hirsch, 1983]. Even so, Hirsh seems not to have grasped completely Hume's point about identity either.) Be that as it may, Hume himself regarded his reducing continuants to series of momentary entities as resorting to a mere fiction inasmuch as nothing in his ontology is a series over and above the series' members. Whatever we purportedly say about the series is to be understood as somehow or other (under adequate paraphrases, to be sure) applying instead to the members thereof. Withal, Bergmann wisely refrains from viewing continuants as real series of momentary entities. No such series can be a simple, so it ought to be a complex. And, if it is complex, it must be a circumstance, a fact, or a class. It can be neither a circumstance nor a fact, since (1) it can be neither potential nor actual (You can neither assert nor deny the Taj Mahal); (2) no circumstance or fact, as understood by Bergmann, could seriously be identified with a continuant body; (3) talk about any such circumstance or fact would be quite removed from talk about an individual. Then it must needs be a class. But Bergmann rightly dislikes resorting to his classes beyond strict necessity, since classes are in his ontology derived complexes of an inconspicuous nature. Moreover, Bergmann's classes seem to be non-spatial, non-temporal entities. If the Taj Mahal is a class, it cannot have been built in the 17th century. Furthermore, since the category of classes is different from the category of particulars, it would then be senseless to assign to the Taj Mahal anything we usually say about it, e.g., that it is in India -- if to be in India is, as it seems, a property of particulars, e.g., the-Taj-Mahal-now. (Notice that this last problem about categorial boundaries would also afflict any identification of a series of (momentary) particulars with any Bergmannian complex whatever.)
[Foot Note 1_3]
The larger complex in question (the one consisting of another complex being pervaded by a mode) might be supposed to exist while the negation thereof failed to exist. But then the complex would be unsayable. Unsayable complexes are, according to Bergmann, alone in being such that their negations do not exist. Yet no such entity is a complex proper, since negation is a clinging subdeterminate which clings to any complex whatever, thus bringing about a new and existent complex -- whether potential or actual, according as the clung-to complex is actual or potential.
[Foot Note 1_4]
It is, of course, very hard to pinpoint the locus of an argument in the Tractatus. The argument under consideration emerges in 2.02 ff. and in a somewhat different way in 3.23-3.24 (about which see [Pears, 1981], especially the discussion of H. Ishiguro's interpretation, pp. 77-8). I have analyzed that argument at length in Chapter 13 of Section I of [Peña, 1985b], pp. 288-95, and in [Peña, 1985c]. Indirectly the same point can be buttressed by ascertaining that in the Tractatus every speakable-about entity is perforce a simple one (see 3.21 ff, 2.03, 2.072, 2.01). Furthermore, Wittgenstein's criticism of Russell's theory of judgment (in 5.541) also adds to that general line of argument. For a different view of 2.02I1 see [White, 1976].
[Foot Note 1_5]
See the Appendix of this paper where I go into Wilson's discussion of Bergmann's tenets about ineffability.
[Foot Note 1_6]
It has been suggested to me that Bergmann could make use of Meinong's moves, which he examined earlier in his book, Realism. Now, resorting to a Meinongian view of possibility or the like is to my mind at odds with Bergmann's strong realism. For, as I have pointed out in Chapter 11.4 of Section I of [Peña, 1985b], devoted to Meinong, Meinong's thought is to be regarded as a mingling of two kinds of essentialism (`Essentialism' here being taken in this non-Quinean sense: a doctrine according to which some truths are about no existent entity at all): alethic essentialism (which was started by Aristotle) and ontic essentialism (which was started by the Stoics). Routley and the «free logicians» have consequently developed Meinong's thought in the former direction (each in his own way). Grossmann, Castañeda, and Rapaport have rather tended to set up Meinongian ontic-essentialist theories. (The relevant references are to be found in [Peña, 1985b].) Bergmann rightly (to my mind) rejects any essentialism whatsoever. On the other hand, (part of) what Meinong has to say about possibility points towards a kind of acceptance of degrees of being. I myself find this line of thought congenial, but I cannot imagine how it could be reconciled with Bergmann's philosophy. Let me summarize the grounds of my rejection of Bergmann's modes. What I find distasteful is the difference between actuality and existence as regards complexes. (Bergmann is there in the company of philosophers like A. Plantinga with the distinction between existing and obtaining. See [Plantinga, 1974].) But, of course, I'm far from oblivious to the consequences of identifying them (which the logical atomists did). Yet my own enterprise is keen on taking up such identification and then avoiding unacceptable results through appropriate measures (thanks to the recognition of degrees and aspects of truth or existence. See below, n. 12.). On Bergmann's plight in consequence of acceptance of (fully) existing and yet (merely) potential entities, see my objection 3 in §2 of this paper.
[Foot Note 1_7]
Except, of course, in a devaluated sense of `can' or `could', i.e., the Leibnizian one point out above at the end of §1. We may say that a complex which is actual could be potential inasmuch as we thereby are saying nothing else but that it is contingently true that the complex is actual, where `contingently' means just `synthetically' (i.e., in such a way that the complex's mode is inaccessible to us). We have no evidence for which mode pervades the complex, but this does not hinder us from feeling sure that in fact the complex is pervaded by the mode of actuality or by the mode of potentiality, according as we feel sure that the complex is the case of not (as we would commonly put it).
[Foot Note 1_8]
What I mean is that any logically incoherent theory can be patched up so as to hide its logical flaws by means of inserting a number of reduplication clauses. Aristotle himself more than once [mis]uses `þ' clauses. Such a [mis]use is the Achilles heel of Medieval Aristotelians. On facing the incompatibility between God's unchangeableness and necessity on the one hand and the contingency of the created universe, they, e.g., used to say that one and the same entity, God's decision to create, is, as God's decision, necessary and unchangeable but, as decision of creating this or that, contingent. (See my book [Peña, 1981], passim. Sundry references will be found there to Aquinas, Suárez, and other Aristotelian metaphysicians concerning their approach to problems in philosophical theology. In [Peña, 1985b] I've gone into the misuse of reduplicative clauses in ontology proper by all of the Aristotelian lineage, from the Stagirite himself onwards.) The reduplicative device has rightly been jettisoned by contemporary (analytical) philosophers, though it still emerges sometimes in the bloated prose of non-analytic philosophers. I am aware of attempts at bestowing logical respectability on reduplicative clauses. Late Medieval and Post-Renaissance Scholastics endeavoured to whet the tool by positing a number of different senses of reduplicative clauses, i.e., clauses starting with one of the particles `qua', `quatenus', `in-quantum', `ut', `utpote', `prout', `secundum', and so on: the reduplicative sense proper, the specificative sense either proprius or minus proprius, either per se or per accidens, and so on. See Aristotle, Prior Analytics I, ch. 38 (49a12-b3). Also Joannes a S. Thoma (1948), Ars Logica, Prima Pars Summularum l.2c.24, p. 57. For recent accounts of reduplication see P. Geach, `Nominalism', in [Geach, 1972]; [Angelelli, 1978]; [Fine, 1982]; [Back, 1985]. However much ingenuity may be displayed by its friends, I remain firmly convinced that reduplication has had its day. See [Wiggins, 1980], p. 89.
[Foot Note 1_9]
As I shall point out below, in the Appendix, Bergmann can avail himself of an argument against words standing for US which wouldn't tell against the thinkability of contradictions. What my contention in the 5th Objections intends to convey is that, so far as unthinkability goes, I find a≠a no less unthinkable than a's utterly failing to be a particular.
[Foot Note 1_10]
Bergmann is, of course, widely known and quoted as positing bare particulars. As far as his later work is concerned, however, we need to make a distinction: Items and US are bare, propertyless; but particulars proper, i.e., such two-in-one's as are each made up of both an item and a US, are not bare. The notion of bareness may be understood in different ways. Some people say that for a thing to have properties it needs to be in and of itself bare, propertyless. This is how many people view the Tractarian objects (see, e.g., [Goddard and Judge, 1981]). Nevertheless, it's one thing to say that, underneath its having or exemplifying a property, a thing in itself is without properties and accordingly bare (and in that sense it's true to say that Tractarian things are bare -- their ipseity, thing-as-content, having no features). It's quite another thing to say that an entity (of sorts) lacks any properties whatever, whether `in itself' or in any other way (though in fact there is no `any other way' in such cases). The latter, stronger sense is the one that applies to Bergmann's bare entities, viz., items, US, all other subdeterminates, complexes. As for the former, weaker sense, it arises from worrying about what a thing is aside from its entering into relations with other things. Even if Tractarian internal relations, combinabilities, are constitutive of the things, Wittgenstein feels that, even so, the thing itself must be a substratum which as such is bare. Such, at least, is my interpretation -- and apparently it is Goddard and Judge's too. To be sure, Wittgenstein would be right, if, as he believes, the identity of indiscernibles were false, two different things being thus able to share, in the same degree, all their properties and relations, even their internal ones (i.e., their respective forms). The worry is not unjustified in itself, but I think there is a far better solution to the problem than positing bare things in any sense (see below, the end of n. 12). As for Bergmann's own bare entities, some of them, viz., complexes, i.e., facts and circumstances, although propertyless, still have a `feature'. They are either analytic or synthetic. (Recall, however, as was pointed out above, at the end of §1, for a complex to be analytic (ally true or false) is nothing else but for its being pervaded by its mode (actually or potentiality, respectively) to be accessible to us.) I take it that those features are not properties. How could they be properties within the framework of Bergmann's ontology, unless that framework were either shattered or through and through made over? But then what are they? Some odd kind of `over-US' or the like which `pervade' complexes as modes do or as US pervade items in such a way that any such pervading is nothing over and above the pervaded and pervading entities? Withal (but not unrelatedly, of course), complexes enter a [pseudo]relation of sorts, since they are meant (by thoughts). F. Wilson in [Wilson, 1983] criticizes Bergmann on this account, showing the difficulties the Bergmannian `relation' of meaning bristles with. I think that those who know the Aristotelian-Scholastic tradition will recognize here, as elsewhere in Bergmann, some time-honoured devices: relations of reason, connotations which are not really relations, non-predicamental relations. My own attempt at finding a solution to the issues which prompt resort to such devices will consist in avoiding what seem to me subterfuges. But I feel in honesty bound to admit that the task is far from easy. Otherwise, there would be no need to cavil about people's falling back on such procedures, once a clear, unproblematic alternative was found. The solution I myself have to offer is not either easy or problematic.
[Foot Note 1_11]
See [Unger, 1979a], [Unger, 1979b], [Unger, 1980]. Unger's sorites constitute the most relevant challenge to classical logic put forward of late (although he himself doesn't view things in that way. Quine has cleverly made it out). See [Quine, 1981]. Taking up that challenge is going to be one of the two main grounds justifying my own approach, the other ground being the need for an account of relations free of the two Aristotelian liabilities, viz., categorial boundaries and the assumption of something such as prime matter or the like. (These are flaws, since they, each and both, entail ineffability.)
[Foot Note 1_13]
Wilfrid Sellars developed his nominalistic account in a number of papers. See, e.g., [Sellars, 1949], [Sellars, 1963a], [Sellars, 1963b], [Sellars, 1963c]. A thorough implementation of Sellars' ideas is to be found in [Sicha, 1974]. The most in-depth discussion of Sellars' ideas to date are to be found in [Hochberg, 1978] and [Hochberg, l 984] -- which, among other essays, includes the by now famous `Mapping, Meaning and Metaphysics'. See, however, Sellars's reply to that essay in [Sellars, 1977]. A very interesting discussion of Sellars' purported way of avoiding even the linguistic temptation to raise Bradley's paradox is [Wilkin, 1979].
[Foot Note 1_14]
As I have said, the clipping-off rule can be formalized like this. From `rxa' to conclude `rx': If someone eats something, he eats; if he loves s.o., he loves. In English there are but few verbs which can with the same meaning be used both as active and intransitive verbs. Other languages (Greek, Latin, Romance languages) can virtually always delete the direct object of a sentence with the verb in the resulting sentence having the same meaning as in the given one. Yet that linguistic evidence doesn't amount to a proof of the correctness of the clipping-off rule. A number of philosophers (e.g., Frege) and linguists contend that a sentence like `Brian loves' is to be viewed as an elliptical one, the direct object, `someone', having to be understood. Many linguists (among them Lyons, in [Lyons, 1968], pp. 350 ff.) think that (at least many) transitive verbs hide a deep structure causative form. Those linguists implicitly acknowledge just one transitive verb, `to cause', whose direct object is always a nominalized sentence or something of that ilk. My treatment instead takes `to love' as primitive in the active sense, but as an intransitive verb, i.e., as a one-place predicate. For Robin to be loved by Brian is for Brian's love to determine (i.e., be truly attributed to) Robin. Accordingly, all relational verbal phrases are in deep structure one-place VV.PP. But then you no longer can ignore the question of how `Brian loves Robin' is related to `Brian loves'. Understanding in the latter sentence an elided existential quantifier can be justified within the ergative treatment, but the move is, otherwise, for from obvious. What is more, if `Brian loves Robin' results from adjoining `Robin' to `Brian loves', it is clear that the latter cannot be a mere abbreviation of `Brian loves someone'. Obviously, if Brian loves, he loves someone or something, but those are two different facts and needn't be equally true or real, even if they are both real. The latter may be much more existent. The first philosopher to have exploited the clipping-off rule was Plato. (In a more general way any `complement' can be excised without the sentence therefrom resulting being utterly false when the given sentence was, to some extent or other, true. See [Peña, forthcoming].) Notice, finally, that, if you agree that `Brian loves' is an elliptical way of saying `Brian loves someone or something', which I don't, you are also bound to accept my clipping-off rule, although then in a trivialized way. On the other hand, you may spurn my countenancing a one-place predicate, `love', and then say that the rule makes no sense. The few English cases apparently bearing that rule out will be explained away through paraphrase (i.e., through catalysis, the converse procedure to ellipsis). But then, for those cases at least, you accept my rule in the aforementioned trivialized way. And you ought to face up to the fact that in other languages such verbs are not exceptional, but in fact include all active verbs. Ellipsis is thus to be fallen back on more widely -- too widely indeed, since it seems reasonably to keep deep structure as close to surface structure as possible. On the ontological side of the issue, notice that for Brian to love is for love to determine him, i.e. (see note 12 again), for existence to be passing from love into Brian, which may happen in a smaller degree than love's passing from Brian into, say, Robin -- or anyone else for that matter.
[Foot Note 1_15]
Problems faced by linguists are not unlike our own Philosophical problems. Thus for inflected languages a number of alternatives are canvassed, each fraught with its own difficulties. One of those syntactic alternatives is the WP approach (from `Word Paradigm'), according to which a word like the Latin, `hostium', is to be taken as a noncomposite whole, instead of being regarded as a string of morphemes meaning `enemy', `plural', `genitive', then somehow amalgamated or blurred. Among linguists having developed the WP approach, I can mention R.H. Robins. See an introductory account in [Matthews, 1970], pp. 107-10. The problem with WP is that the whole segment `hostium' needs to be regarded as a partless unit and yet also appears somehow to result from two or more adjoined segments even if these segments are `then' fused or welded in some way.
[Foot Note 1_16]
It has not been light-heartedly or with airy insouciance that I've chosen to regard written language signs as acts of writing. All I have been taught ran counter to such a move. My main ground is the one reported in this paper. So long as you regard the sentence `ba' as a whole made up of two Parts, `b' and `a', you face the following trilemma. Either (i) you regard `b' and `a' as signs of different categories, which raises the question of whether the entities respectively denoted are of different ontological categories (an unsayable claim, as is well-know, and one giving rise to such difficulties as the predicament of Frege's concept-correlates); or (ii) you regard them as signs of different syntactic category bearing different semantic relations to the entities they respectively `stand for' (each in its own way of `standing for'), which raises the difficulty that two signs standing for the same entity, say subject b and predicable B, will have nothing at all in common, with no systematic way of obtaining one of those symbols out of the other; or else (iii) you regard them as belonging to the same category and saying that what marks the subject-role of `a' is just the place it occupies, which in turn gives rise to this difficulty: marking a syntactic role (or `function') by a position is a syntactic procedure equivalent to other means used in other languages, like affixing some kind of functional morpheme to the expression to which the position in question has been assigned. (See, e.g., [Martinet, 1970], sections 4-10, pp. 109 ff.) All of this amounts to resorting implicitly to a third sign. My problem with this is not exactly a Bradley regress, but the fact that, if we resort to a third (elliptical) component, we need then to explain something similar to what we had initially tried to explain. If the elliptical functional morpheme is some kind of `desinence', say `:', to be attached to the `subject', i.e., in our case to `a', then the sentence `ba' now becomes `ba:' (equivalent, of course to `a:b'), which, in fact, means that we have a sentence one of whose components is `b', the other component being `a:'. We now need to analyze the inner structure of `a:' (since `:' must stand for something or other), i.e., to explain what is the `subject' therein and how its role is marked. Thus we may apparently conclude that `ba' is an incomposite, riftless atomic whole. But, of course, that conclusion can be refuted. What then? I suggest that a sensible way out is to regard the sentence `ba' as a process, a passing from writing `b' to writing `a', without ever being a mere writing `b' or a mere writing `a'. As the travelling body can be viewed as being at no place and yet also at each place included in the whole stretch of its travelling (see my contradictorial treatment of Zeno's paradox of the arrow in [Peña, 1983c]), likewise during writing -- which is movement after all -- the writer or the writing hand or pen is never at the starting position, never at the final one, never in any part of the whole course, and yet also during each part of the whole interval it is at all the parts of the whole course. Writing `ba' is not writing `b' and then `a'. It is a single movement, a continuous passing from writing `b' to writing `a' (yes, an act may be a passage from another act into a third one).