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nternational Phenomenological SocietyPhilosophy and Phenomenological Research

Ontology in the TractatusAuthor(s): David WeissmanSource: Philosophy and Phenomenological Research , Vol. 27, No. 4 (Jun., 1967), pp. 475-501Published by: International Phenomenological SocietyStable URL: http://www.jstor.org/stable/2105792Accessed: 21-05-2016 19:49 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at

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ONTOLOGY IN THE TRACTATUS

1

'Existing state of affairs' and 'possible state of affairs' are normally regarded as incompatible translations of Sachverhalt (and Tatsache) as they appear in Wittgenstein's Tractatus. I shall argue that these translations are not incompatible, for the reason that each is important to a different part of the two-stage ontological analysis whose outlines appear in the Tractatus. As I understand him, Wittgenstein would have us begin our metaphysics with the analysis of possible states of affairs, and, more fundamentally, with a survey of the categorial features shared by all possible worlds. This, I think, is the heart of his metaphysics, and yet this cannot be all of metaphysics proper, because its first concern is the ontology of our actual world. The description of possible worlds

must justify itself by illuminating the study of our world. There appears to be a single way that Wittgenstein's theory can be

made to do this; the list of categorial features which he adduces and imputes to all possible worlds must be used as a kind of ontological map. If we know that certain categories prevail in every possible world, and hence in our own, we will begin the analysis of states of affairs existing in our world with an assured foreknowledge of the categorial features which they must display. The problem now will be to determine the manner in which these features are exemplified in our world. If, for example, the category of intelligent creatures were one entry on the list of features common to all possible worlds, we would want to know the status of minds peculiar to our world; are they material-like computers, or spiritual like God? Deciding the answers to questions like this one will constitute the second stage of metaphysical inquiry.

Wittgenstein does not have much to say about this part of metaphysics, but it is only for this part that we bother with the first, and accordingly, my assessment of his ontology will center upon two issues: first, why does he say so little of our actual world, and, second, does he say enough about possible worlds?

There will be three parts to the discussion. The first will show that various passages in the Tractatus support both of the proposed trans-

475


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476 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH

nations of Sachverhalt and Tatsache. It will also tell how these translations anticipate the two stages of the ontology implicit in Wittgen- stein's remarks. The second part will review Professor Max Black's recent criticisms of the view that 'possible state of affairs' is a frequently acceptable translation of Sachverhalt. The last section will be a critical survey of the metaphysical view outlined above. After considering some of the details of the theory and asking how these details are accomnmo- dated in the Tractatus, I shall say that the theory cannot be made to work. A. A Tatsache is first described as the existence of states of affairs in proposition 2. But if Tatsache is sometimes understood in this way,

so must Sachverhalt be interpreted in the same way, for Tatsachen are only complexes (truth functions) of Sachverhalte (2.034, 4.2211). Sach- verhalte may be conceived as existing atomic states of affairs, and because Tatsachen are described as facts (2), Sachverhalte will also be known as atomic facts.

The second conception of Tatsache and Sachverhalt is stated most clearly in 2.0121: Logic deals with every possibility and all possibilities are its facts. The word translated 'facts' is Tatsachen, and again referring to 2.034 (which is wholly neutral on the issue of whether states of affairs are possible or existent), we infer that Sachverhalte, as the components of Tatsachen, should now be conceived as possible atomic states of affairs and, alternatively, as possible atomic facts. An exemplary passage is 3.0321: Though a state of affairs that would contravene the laws of physics can be represented by us spatially, one that would contravene the laws of geometry cannot. Sachverhalt, here, must mean '(logically) possible state of affairs', because a Sachverhalt which violated physical laws certainly would not be an existing one.

Corresponding to the notions of possible and existing states of affairs are two notions of world. One is stated in 2.04: The totality of existing states of affairs is the world. The second appears in 1.13: The facts in logical space are the world. Logically possible states of affairs surely outnumber the totality of existing states of affairs, but the totality of possibilities in logical space and the sum of existing states of affairs are both said to be identical with a world. Two senses of world must be at issue here.

The world of existing states of affairs is apparently reality, meaning our actual world. The status of logical space is more obscure, and we shall have to collate several of Wittgenstein's remarks in order to make sense of this notion.

The most direct route leading to clarification of the idea begins in his conception of objects. We are told, at 2.021 with 2.027, that objects


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ON TOLOG Y I N THE TRA CTA TUS 477

comprise the unalterable substance of the world, and that, It is essential to things that they should be possible constituents of states of affairs

(2.011). Now it is perfectly clear what Wittgenstein does not mean by essence: essence cannot be made up of external properties, such as color or shape, because these properties depend for their existence upon the fact that objects have essential properties. This is to say that objects are colorless (2.0232) while external qualities are relational (they emerge when objects combine), and that the properties qualifying objects to combine are essential ones. Essential properties are apparently functional ones, and this will have to be provided for in their definition. Two passages are relevant now. First, there is 2.01231, If I am to know

an object, though I need not know its external properties, I must know all its internal properties ; and second, 2.0123, Every one of these possibilities must be part of the nature of the object. Essence is constituted of internal properties, and these are to be understood as possibilities enabling objects to combine.

We are very close now to the conception of logical space, for this notion is implicit in propositions we are well-placed to interpret. There is, for example, 2.014: Objects contain the possibility of all situations.

This follows, because every situation is a complex of objects and every complex is prefigured by the internal properties of objects: If I know an object I also know all its possible occurrences in states of affairs(2.0123). Indeed, it should be possible, given a complete list of objects

and of their internal properties, to describe every possible combination of objects. This is confirmed by 2.0124: If all objects are given, then at the same time all possible states of affairs are given. But, and this is the conclusion we have been seeking, it follows now that when all

objects are given so too are all possible worlds given: a possible world is one in which the members of some subset of all possible combinations are realized; if the totality of objects is implicitly the totality of all possible combinations then the sum of objects is also an implicit deter- mination of what could occur in possible worlds. This, however, is precisely what has to be said about logical space: the facts in logical space like the facts of possible worlds are possible states of affairs (2.0121, 2.013, 2.202); the limits of logical space like the limits of

possible worlds are determined by the possibilities of combination which are essential to objects. Everything said about possible worlds must also be said about logical space. The converse is also true, and 'logical space' must therefore be understood in the plural; logical space is identical with possible worlds. The two conceptions of world signalled by 2.04 and 1.13 are as different from one another as our existing world (a


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possible world made actual) is from worlds existing as mere possibilities.' When these notions of world are correlated to the two proposed

translations of Sachverhalt, we obtain a rudimentary statement of the ontology developed in the Tractatus: there are possible worlds defined by the sum of possible combinations of objects (possible states of affairs), and there is our world composed of a relatively small set of realized possibilities (existing states of affairs). I have deliberately mentioned possible worlds first, because as I understand him, Wittgenstein begins his metaphysical inquiry by analyzing the categorial features common to all possible worlds. He argues that any world must have substance and logical form, and he clarifies these notions without com-

promising their applicability to every possible world. There is no provision in this necessarily very abstract discussion for actually existing states of affairs, and none is required. They are a relevant concern only when the analysis of possible worlds is completed, and when the new problem is to show how categorial features shared by possible worlds are exemplified in our world. What for example will substance be

rational or material? Agreeing that states of affairs in any possible world will have logical form, we nevertheless want to know the manner in which relations of objects occur in our world. Are these relations spatial and temporal, or, as they would be in some conceivable worlds, exclusively harmonic or chromatic? These metaphysical, not (and I shall argue this later) empirical, questions are the ones requiring attention when there is a shift in analysis from talk about possible worlds to the ontological description of our world.

Two things are required if we are to prove that the analysis of possible worlds is central to Wittgenstein's metaphysics, and that this analysis has logical priority over his account of states of affairs existing in our world. First, we must clarify the notion of possible states of affairs. Second, it must be demonstrated that Wittgenstein's attempt to ground metaphysics in the analysis of atomic propositions requires that he consider the categorial features of possible worlds before studying the ontology of our world. Clarification of what is meant by a possible

1 I shall be arguing below that Wittgenstein's metaphysical conclusions derive from and are parallel to his claims about the properties of atomic propositions

(5.4711), and it is relevant to this point that the conception of logical space is one of the ontological notions originating in his analysis of language. The corollary to logical space is grammatical space; the possibilities for the combination of objects as against the sum of possibilities for combining names. Wittgenstein does not speak of grammatical space, but the idea is implicit when he writes at 3.311: An expression presupposes the forms of all the propositions in which it can occur. 3.21 is evidence that Wittgenstein regards the combinatorial possibilities of names as exemplary of the combinatorial possibilities of objects.


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ON TOLOG Y I N THE TRA CTA TUS 479

state of affairs will come in the next section. Discussion of the second point will follow in section C.

B. Professor Max Black is one commentator who takes special pains to acknowledge the significance of possibility in the Tractatus. Still, he is very reluctant to agree that Sachverhalt or Tatsache ought frequently to be translated as 'possible state of affairs', and he categorically denies that possibilities have a place in Wittgenstein's ontology. Professor Black considers these issues while discussing the question of how Sachverhalt should be translated. (A Companion to Wittgenstein's Tractatus: Cam- bridge, 1964; pp. 41-45.) The alternatives, he says, are the F-theory, the view that Sachverhalte are existing and atomic states of affairs (which Black calls 'atomic facts'), and the P-theory which holds that Sachverhalte are possible states of affairs. Eight arguments are proposed in favor of the F-theory, and there are four advanced in support of the P-theory. I shall state and criticize Black's arguments and comments in the order and with the numbers he uses.

1. Wittgenstein himself allowed 'atomic fact' to stand in the revised impression as well as in the original English edition, both of which he had an opportunity to correct. It is implausible to suppose that he did not understand the difference between making Sachverhalt stand for a fact and making it stand for a possibility. This impresses Black a strong argument for the F-theory, but I see nothing decisive in it. Black supposes that there is a fundamental incompatibility between the notions of fact and possible state of affairs, and that Wittgenstein could not have used 'fact' to refer to possibilities; but this is not the case. Propo- sition 2.0121 reads: Logic deals with every possibility and all possibilities are its facts. Tatsache rather than Sachverhalt is the word

translated as 'fact' in this passage, but remembering that Tatsachen are complexes of Sachverhalte (2.034), it seems a fair inference that Witt- genstein would sometimes have us regard complexes of possibilities and atomic ones as facfs. On this interpretation, Sachverhalt will sometimes be interpreted as 'possible atomic fact' or as 'possible atomic state of affairs'.

2. Wittgenstein speaks of a Tatsache as composed of (besteht aus) Sachverhalte. Since a Tatsache is a (complex) fact, this speaks in favor

of regarding a Sachverhalt as a fact. This is surely true, and the only issue is Black's assumption that facts cannot be possibilities. 2.0121 shows conclusively that this is what Wittgenstein sometimes thought them to be.

3. Several times Wittgenstein speaks of a miglicher Sachverhalt (possible Sachverhalt). Now if a Sachverhalt is a possibility, the phrase


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mdglicher Sachverhalt (== 'possible possibility') italicized at 2.0124 be- comes an absurdity. Not at all. Sachverhalt, literally translated, means neither 'existing' nor 'possible state of affairs', but rather 'situation'. Sachverhalt is used in a technical sense whether the reference is to possible or to existing states of affairs, and it is no more absurd that Witt- genstein should use moglicher to emphasize that possible states of affairs are at'issue than that he frequently speaks of bestehenden Sachverhalte, meaning existing states of affairs (2, 2.04, 2.05, 2.06). If we accept Black's view that Sachverhalt means 'atomic fact' or 'existing state of affairs', these passages may be translated as 'existing, (actual, contingent) configurations of objects'. Surely this is no less pleonastic and absurd

than 'possible possibility'. But neither is absurd if we grant that Witt- genstein quite properly uses miglicher and bestehenden to emphasize shifts in his technical usage.

4. A 'configuration' (Konfiguration) of objects constitutes (bildet) the Sachverhalt. Now the configuration is not determined by the substance of the world and is therefore not independent of what is the case: the configuration is mutable. Throughout the text, the 'configuration' of objects is taken to be what is contingent about the world. If a Sachver- halt is a configuration of objects it cannot be a timeless unity of objects, independent of contingent fact. Whenever the objects are in a configuration there will be a fact, not the possibility of a fact. Exception must be taken to two of the points made here.

(1) It is misleading to suggest that 'configuration' has a standard meaning and that this usage recurs frequently throughout the text. 'Con- figuration' appears four times in the Tractatus, and though three of these propositions (2.0231, 2.0271, 2.0272) are clear statements of the

view that configurations are contingent combinations of objects, the fourth proposition (3.21) seems to make an entirely different point. 3.21 reads: The configuration of objects in a situation corresponds to the configuration of simple signs in the propositional sign. 'Configu- ration' in this case refers to the order in which objects are arranged in complexes, and to the arrangement of signs (names) in propositions. The correspondence said to exist between these two sets of relations is reminiscent of 2.2: A picture has logico-pictorial form in common with what it depicts. But as this suggests, 'configuration' in 3.21 means the same as 'form'. Remember now that logical form is one of the unalterable features of the world (2.026). It is for this reason that 3.21 cannot be read as one of those passages where Wittgenstein is speaking of the contingency of states of affairs. This, like every reference to logical form, is to be understood, at least in part, as a reference to possible states of affairs.


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ONTOLOGY IN THE TRACTATUS 481

(2) The phrase timeless unity of objects misconstrues the notion of possible states of affairs. The only configurations of objects for which Wittgenstein provides are those existing contingently, and they are actual states of affairs differing from possible ones precisely in the sense that 'actual' means what is, and 'possible' means what might be. Events which might occur do not exist now; least of all do they exist timelessly. This is not to say that 'possible state of affairs' has no reference, for statements about combinations of objects which might occur are implicit references to those existing factors whose synthesis would result in the occurrence of a state of affairs. The factors of which I am thinking are objects and logical form. Possible states of affairs exist only insofar as

these unalterable sonstituents of any possible world must already exist. We can be even more specific. Logical form in an existing state of affairs is identical with the arrangement of the objects. This might suggest, when objects are not combined, that the relevant logical form is a subsistent structure rather like the walls of an empty house. But this is in no way implied by Wittgenstein or the P-theory, for, as he writes, .. . the possibility of the state of affairs must be written into the thing itself (2.012). This is another way of saying that logical forms, when mere possible modes of combination, exist as internal properties of objects. Wittgenstein often makes clear when speaking of possible states of affairs that he is thinking of the modes in which objects might be combined (2.151), but these allusions to logical form are an elliptical way of talking about objects having internal properties which qualify them to combine with other objects (2.012). In the final analysis, objects having capacities to combine are the referents of statements about possible states of affairs.

5. If Wittgenstein held that objects are combined in complexes, which may or may not exist, he might have been expected to say so, -and to use some word other than Konfiguration or Struktur for the manner in which objects are so combined. This argument is like the last in con- struing the P-theory to hold that possible states of affairs are ready- formed, though presumably ghostly and subsistent, combinations of objects. But this is not the P-theory for it shares Black's, and Wittgen- stein's, aversion to subsistent combinations. It therefore cannot be held responsible for adducing examples of words which Wittgenstein might

have used to indicate these spurious entities. This is not to say that Wittgenstein has no word signifying possible states of affairs. He does have a word, and the idea is clearly expressed in 2.033: Form is the possibility of structure. All assertions about form, and more fundamentally, about objects which could be combined, count as references to possible states of affairs.


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6. If Sachverhalte were mere possibilities, how could Wittgenstein say that what is essential to an object is that it can occur in a Sach- verhalt? On the P-theory, Wittgenstein would surely be committed to saying that an object must occur in all the Sachverhalte of which it is a constituent. Let us consider this objection in two parts corresponding to the two lines composing it.

(1) We should notice, first of all, that the two occurrences of Sach- verhalt in the opening line express two distinct thoughts. Following Black and saying that Sachverhalt in its first appearance refers to possibilities, we must interpret its other appearance as signifying an existing state of affairs. The reason for this is that existing states of affairs are

the only sort of complex which Wittgenstein acknowledges. If objects have capacities for being combined, the combinations will have to be existing ones. Turning now to the point of view expressed in this line, we notice the suggestion that Wittgenstein should not have said that objects are capable of being arranged in configurations if he already believed that Sachverhalte are, in some cases, possible states of affairs. Black implies that there is an incompatibility here, but none exists, for the very notion of possible states of affairs presupposes, first, that there

are logical forms determining the order in which objects shall be arranged if they do combine, and, second, that there are objects to be combined. As before, these two requirements reduce to the single one that there be objects with internal properties qualifying them to combine with other objects.

(2) It does not follow from the P-theory that an object must occur in all the Sachverhalte (translating 'possible states of affairs') of which it is a constituent. This does not follow, because possible states of

affairs are not any sort of combination, and because it makes no sense to say that objects are or must be constituents of these possibilities. Possible states of affairs are not quasi-substantial entities having parts.

7. According to Wittgenstein a name must have an object for which it stands while nothing need answer to a meaningful description; it is therefore important that he speaks of a Sachverhalt as being described by a proposition. For, according to the P-theory, something must answer to a 'that'-clause, namely, the corresponding Sachverhalt. It would there-

fore be correct to treat such a clause as a compound name of the possibility for which it stands. But Witggenstein says that names are simple and argues against the idea that the proposition is a complex name.Black does not tell us why the P-theory must hold that a 'that'-clause

is a compound name, and I see no reason to believe that the theory entails this. The P-theory supposes that the relation between possible


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states of affairs and propositions will be precisely what Wittgenstein claims it to be when he remarks in 2.203 that, A picture contains the possibility of the situation that it represents. Pictures contain this possibility by virtue of sharing logical form with the possible situations they represent (2.2). Black's charge; is so hard to make out, because he interprets the P-theory to claim that propositions name possible states of affairs, though Wittgenstein, as every P-theorist should be expected to argue, de-emphasizes names when telling how propositions represent possibilities, and discusses only the mode in accord with which objects may be combined. Wittgenstein might have discussed two ways in which possibilities may be represented, for he might have said that the terms

of even false propositions are names of objects, and that these objects can be combined. Remarks of this sort could have been interpreted as another way of referring to possible states of affairs, but as it happens, Wittgenstein disregards this way of speaking, and argues instead that, A picture represents a possible situation in logical space (2.202), and that, What a picture represents it represents independently of its truth or falsity, by means of its pictorial form (2.22). All of this is familiar; I only want to stress that none of it is incompatible with the P-theory.

8. The 'picture theory' of the proposition recognizes coordination between names and objects and identity of logical form between the sentence-fact and the fact represented. Wittgenstein does not say that the whole sentence-fact stands for some complex entity - indeed this way of looking at the sentence is alien to his standpoint. Wittgenstein does not say this, and the P-theory never pretends that he does. Again, there are two points to notice. (1) Complex entities are remote from the conception of objects having properties which qualify them to com-

bine with others: it is to these objects that Wittgenstein is ultimately referring when he speaks of possible states of affairs. (2) Sentence-facts stand for possible situations by displaying the form which would be manifest in states of affairs if objects did combine. (This is a point which will be argued in more detail below.) The P-theory abhors any interpretation claiming that sentences represent subsistent complexes or subsistent, bare structures.

These have been the eight arguments supporting the F-theory. Four

arguments for the P-theory and Black's criticisms are as follows. 9. Wittgenstein often speaks of the Bestehen ('holding') or Nicht- bestehen (= 'not holding') of Sachverhalte. Now it is hard to think of a fact as not holding or, in Ogden's translation, not existing. Black's objections to this argument are intended to cover argument 10 as well, and it is best to state that argument before considering them.


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seem, therefore, that a Sachlage, qua sense, should be a possibility, not an actuality; and similarly for a Sachverhalt. Black comments: The plausible error behind point 12 depends upon supposing that if A is a picture of B, B must exist in some sense ... (We) can say on Wittgen- stein's view, that a proposition depicts (or presents) a fact, without in the least committing ourselves to the view that the fact in question must exist. If the proposition does depict a fact, it would be otiose to say that it also depicts something more, namely a possibility ... (There) is no ground here for thinking that Wittgenstein intended a proposition's sense to be a complex entity composed of objects in some non-contingent combination (Companion, p. 45). These objections are unsatis-

factory for the following reasons. (1) The assumption that if A is a picture of B, B must exist in some

sense is wholly innocuous in the present case. Rephrasing Black's statement in order to meet the objection, we may say that the fact of A's being a representation of B necessitates B's existence: A is a proposition, B is logical form, and my premise is that propositions represent specific possibilities in logical space by virtue of displaying the relevant logical form (2.202, 2.172). The conclusion then follows: form which pictures

display must already exist. There is nothing here about non-contingent combinations; logical form is merely the order in which propositions' terms are arranged.

The problem of course, is that this proof fails to explain how logical form can exist in logical space. Nor does it explain how pictures represent logical form in logical space, as opposed to displaying the form themselves. But these issues are crucial, because logical form in logical space is normally the referent for talk about possible states of affairs. We must understand how logical form is represented if we are to vali- date the claim that propositions represent possible states of affairs. Doing this will presuppose that we know the manner in which logical form exists in logical space.

There is a solution to these problems, and we are best prepared to see it, if we begin by understanding what representation in this case cannot be. Let us suppose that a proposition is true; there is an existing state of affairs, and also a proposition whose terms are names ordered in relations corresponding to the relations of the objects in the situation.

The manner in which the proposition represents logical form in this instance is perfectly clear: the relations displayed in the proposition duplicate the ones manifest in the state of affairs. This, however, is not the sort of representation described by the P-theory, for it is concerned

with possible states of affairs. They do not exist (or subsist), and so there is neither a complex of objects nor an empty structure to be


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represented by the proposition. Nevertheless, we can make sense of the representation of possibilities if we surrender one of the fundamental hypotheses operating in some interpretations of the Tractatus. We must not suposse that it is a condition of representation that there be an existent, or at least subsistent, situation or structure sharing logical form with the proposition representing it. We cannot maintain this, and still say that propositions represent possible states of affairs, because the referent of a statement about a possibility is a logical form, and because logical forms in logical space are not structures at all; they are nothing more or less than the internal properties of objects. It is for this reason that the representation of possibilities cannot require that there be any sort of correspondence between existing structures and propositions.

The best we can do in this case is take the idea of representation at its literal worth. 'Represent' means 'stand for;' things represented need not themselves be present or occurrent when they are represented. It is just this sense which has to be ascribed to Wittgenstein's use of 'represent' in the present circumstances. Propositions represent a form in logical space by indicating how objects might combine. Displaying the form themselves, they represent the state of affairs which would exist

if objects did combine. This, I take it, is the message of 2.203: A picture contains the possibility of the situation that it represents.There is a last point, one not elaborated by Wittgenstein, which helps

to clarify the manner in which pictures represent possible combinations. Wittgenstein stresses the importance to representation of the pictorial form displayed by a proposition, and, as previously mentioned, he declines to emphasize the role which names play in this. But names, even in false propositions and those specifically intended to signify possibilities, denote unalterable objects (3.22, 2.021). Denoting these objects, the names tie down the relation between propositions and the possible states of affairs they represent. The roots of possibility are found in the internal properties of these objects; denoting the objects, names make implicit reference to the properties which qualify objects to combine.

(2) Is it otiose to say that a true proposition depicts a possibility? Consider the following passages: What a picture represents it represents independently of its truth or falsity, by means of its pictorial form(2.22); Every picture is at the same time a logical one (2.182);

A picture has logico-pictorial form in common with what it depicts(2.2); A picture represents a possible situation in logical space(2.202). Every picture, true or false, has logical form, and by virtue of

this form, every picture represents a possibility in logical space. The charge of redundancy is misplaced.


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(3) It is against this background that we can show that argument 12 is correct in relating Sachverhalt to sense, and sense to possibility. Thus, 2.221 reads: What a picture represents is its sense, but 2.22 has already claimed that propositions represent by means of their pictorial form, and 2.202 has said that pictures represent possibilities in logical space. The conclusion must be, contrary to Black, that the sense of a logical picture is a possible state of affairs; this, of course, being an elliptical way of saying that propositions display a form which would be manifest in states of affairs if objects did combine. Nothing here supports Black's contention that the P-theory supposes Wittgenstein to hold that a proposition's sense is a complex entity composed of objects in

some non-contingent combination.These have been Black's objections to the claim that Sachverhalt

must sometimes be translated as 'possible state of affairs'. I take the following to be a summary of his comments: The mistake to be avoided is that of peopling Wittgenstein's universe with three types of things (say: 'objects', 'facts', and also 'situations' or 'circumstances'.) There are (timelessly) objects - and (contingently) facts or states of affairs. References to a 'possible state of affairs' should be regarded, according

to context, either as a pleonasm or else as shorthand for reference to logical form (Companion, p. 45). This conclusion is surprisingly similar to that of the P-theory. It

argues that miglicher Sachverhalt is not so much pleonastic as the expression of Wittgenstein's attempt to emphasize the meaning of his technical use of Sachverhalt, but the theory agrees that talk of possible states of affairs is an implicit reference to logical form. Most important, the P-theory is at one with Black in denying that 'circumstances',

'situations', or 'complex entities' should be counted among the elements of Wittgenstein's ontology. The only considerable issue between Black and the P-theory is the failure of his summary to credit the importance of possibility in Wittgenstein's ontology. It is surely correct to say that unalterable objects and contingent configurations of objects are the central themes of the ontology, but this is an unsatisfactory account so long as we fail to make explicit provision for the internal properties which qualify objects to combine, and which serve, thereby, as the

ultimate referents for Wittgenstein's extensive analysis of possible states of affairs. Wittgenstein has written that ... possibilities must be part of the nature of the object and that there must be objects, if the world is to have an unalterable form (2.026). The world's (meaning every possible world's) unalterable form is constituted of the possibilities which comprise the nature of objects. Possibility is at the core of


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Wittgenstein's ontology, and Black has made no specific provision for it here.

C. It is time to justify my earlier claim that the analysis of possible worlds (logical form and objects) must take precedence over the analysis of our actual world (contingent configurations of objects) in Wittgen- stein's metaphysics. I shall suppose in this section that Wittgenstein believed the study of atomic propositions to be the basis for inferences establishing metaphysical conclusions. There is support for this view in 5.4711, To give the essence of a proposition means to give the essence of all description, and thus the essence of the world, and in the Notebooks where Wittgenstein argues that philosophy consists of logic and metaphysics, the fonner its basis (p. 93), and writes, My whole task consists in explaining the nature of the proposition. That is, in giving the nature of all facts, whose picture the proposition is(p. 39). These passages confirm that Wittgenstein's ontological claims

are derived from the results of his analysis of atomic propositions.2 Our problem is to tell why the analysis of language requires that metaphysics should provide for categorial features common to all possible worlds before it considers the specific expression taken by these features in our

world. We have the start of an answer in proposition 2.182, where Witt-

genstein insists that, Every picture is at the same time a logical one.Logical pictures are those whose terms display (2.172) a certain order

of arrangement; they are propositions having pictorial form (2.181, 2.151). Wittgenstein has described pictorial form as the essential 3

2 This is not to say that the presence of categorial features in possible worlds depends upon the existence of language; I am not suggesting that Wittgenstein

claimed for language what Kant claimed for thought. The point is rather that Wittgenstein uses the analysis of language as a means for determining the identity of categories whose existence does not depend upon language though we use it to discover them.

3 There is a relation between the logical form identified here as the essence of a proposition, and the internal properties which constitute the essence of objects: the essence of a proposition is the order in which its terms are arranged; the essence of an object is its possibilities for combining with others in states of affairs. The only disparity here is that between a logical form already manifest (in the proposition) and a logical form which remains a possibility of combination (in the

case of the objects); and this is easily remedied if we expand upon Wittgenstein's conception of essence in two ways. First, it should be reasonable to speak of the essence of a state of affairs, meaning the order in which objects are arranged; second, we should be able to say that it is essential to names that they can be combined with others to form atomic propositions. Structure will be the essence of an atomic state of affairs, and, recalling that only in the nexus of a proposition does a name have meaning (3.3), we will say that the essence of a name is comprised of the rules for its use.


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feature of a propositional sign (3.143 1), and accordingly, his analysis of atomic propositions begins in elaboration of the basic point that each proposition is a configuration of terms.

This is an elementary claim, and one so narrowly linguistic as to have no apparent relevance to metaphysics. Yet this is not the case, for Wittgenstein supposes that propositions could not be used to com- municate information about the world if their essential feature, their logical form, were not also present in the world described (2.16 1, 2.2). The precise nature of the relation between atomic propositions and the world is stated in proposition 2.201, A picture depicts reality by representing a possibility of existence and nonexistence of states of

affairs, and in 2.22, What a picture represents it represents independently of its truth or falsity, by means of its pictorial form. Wittgen- stein is saying that truth and falsity are only two of the relations between propositions and the world, and that they are not the most primitive relations. Representation is also a relation of this kind, and it has logical priority over both of them. Propositions cannot be either true or false unless they display (2.172) a logical form which may be manifest in states of affairs. To know this form as it does or might exist in the world, we must look to the propositions which display it, and it is on this account that a metaphysical inference is said to be consequent upon a claim about language.

It remains to show that this inference is to be construed broadly as a claim about possible worlds rather than narrowly as an assertion about our actual world. But this is beyond dispute, for Wittgenstein's discussion of logical form is the first part of his analysis of possible worlds. He has said that propositions represent the world by virtue of displaying logical form, and he-adds: A picture represents a possible

situation in logical space (2.202). This is our first reason for saying that Wittgenstein's method of analysis requires him to describe possible worlds before considering our actual one: the logical form characteristic of atomic propositions qualifies them to represent states of affairs whose existence is not yet at issue. These are possible situations in possible worlds. The actuality of states of affairs in our world is irrelevant here.

Objects, together with logical form, are at the heart of Wittgenstein's ontology, but here too his analysis is unambiguously a study of how

things must be in any possible world. One argument showing this begins with Wittgenstein's insistence that atomic propositions must be wholly determinate in their meanings if they are to refer unambiguously to specific combinations of objects. The way to eliminate indeter- minacy is to say that all the constituent terms of a proposition are names (3.23). But, and here is the metaphysical side of the argument,


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names are simples (3.202)- having simples for their referents (3.203, 2.02). Moreover, that which is simple cannot be altered; it must remain unchanged in every possible world (2.027). These simples are Wittgenstein's objects (2.02). They are identified as substance (2.021), and ascribed to every possible world. (I have separated possibilities in logical space, meaning logical form, from objects in order to show that these notions have separate derivations. Ultimately, there is just the one, though ontologically complex factor of objects having internal properties.)

Reviewing these conclusions, we see that Wittgenstein's analysis of language has yielded ontological conclusions without his having to refer to existing states of affairs. No mention of them is required, because

Wittgenstein has set out to tell how atomic propositions of any language must be constructed in order to picture affairs in any world, and to describe the categorial features which every world must possess in order that a language of this character will be able to picture situations in it. To put, this more succinctly, analysis of the elementary features of atomic propositions (names and logical form) has logical priority over the analysis of propositional truth and falsity; so then must objects and the modes of their combination be considered prior to the existence of states of affairs.

Wittgenstein does speak repeatedly of true propositions and of existing states of affairs depicted by them, but this in no way compromises the priority of his analysis of possible worlds, for most of these passages are best understood as remarks about possible worlds. I am thinking now of propositions where the existence of states of affairs is mentioned or implied but where emphasis is upon some logical characteristic of affairs, and not upon their occurrence. An example is 2.031: In a state of affairs objects stand in a determinate relation to one another.

This is evidently a remark about an existing state of affairs, because it is only in existing complexes that objects stand in relation to one

another. Nevertheless, existence in this case is hypothetical; the property ascribed to states of affairs is one that would typify combinations existing in any possible world.

Claims about hypothetically existing states of affairs are a consistent development in an ontology that begins with the analysis of possible worlds. Having argued that objects and logical form are the categorial

features common to all possible worlds, Wittgenstein is further required to describe the logical properties of the complexes which would result if objects were combined. The properties of these hypothetical combinations are discovered in the same way as were the two categorial factors themselves: the analysis of propositions leads Wittgenstein to infer that affairs which could be depicted by language would have to


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possess characteristics corresponding to the ones possessed by atomic propositions. An example of this is the justification offered for Witt- genstein's claim that objects in states of affairs stand in determinate relations to one another (2.031). His supporting argument holds that the names comprising a proposition are related determinately to one another (3.21). Proceeding in this way, Wittgenstein is free to ascribe properties to hypothetically existing states of affairs just as often as he can find corresponding properties in atomic propositions.

Talk about possible worlds, even talk about hypothetically existing states of affairs is a metaphysicians halfway house. One large step remains to be taken before Wittgenstein's metaphysics can be regarded

seriously. The description of possible worlds must be completed and applied as part of the analysis of reality itself. Only at this point will existence take on the significance ascribed to it by commentators who insist that Sachverhalt should normally be understood as 'existing state of affairs'. It is only now that states of affairs may be identified as actual, configurations of objects in our world.

Let us suppose that a state of affairs does exist; each of a set of objects stands in relation to the other members of its set. The purpose of our inquiry at this new stage is to describe the manner in which these objects and their logical form are exemplified. Wittgenstein has said that, objects and the modes of their combination are common to all possible worlds, but this general claim fails to tell the precise manner in which these categorial features are expressed in our world (or any other). The problem now is to determine the guise taken by these categories in our world.

Notice that this is not a question about what is empirically contingent; we are not asking about the color of the sky or wrens' eggs. We

want to know if objects, characteristically present in all possible worlds, occur in our world as material particulars, as rational entities akin to angels, or as something different again. These are very different con- siderations. Empirically contingent events are those whose nonoccurrence or replacement by other events would make no difference to the categorial makeup of a world: in a world whose objects are angels, it makes no difference to the defining characteristic of substance if the angels play drums rather than harps. The identity of substance itself, however, is

definitive (together with other categorial factors) of the identity of a world. If there were a change in the expression of substance or any other categorial feature imputed to a world, if angelic objects were to become material particulars, we should have to say, not that a world had changed, but rather that one world had superseded another.

This is what is meant by saying that the exemplification in one world


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of categorial features common to all worlds is logically contingent: is is contingent because these features might have been exemplified in some other way (as objects might be rational or material particulars); it is logically contingent because categorial features, being common to all worlds, must have some kind of expression in this particular world, and because they, in their specific exemplification, will be definitive of the nature of that world. It is for these reasons that logical contingency is a matter for philosophers rather than scientists, and on this account that we should expect an examination of logical contingency in our world from any book purporting to so much as outline a complete metaphysics. The issue is straightforward: does Wittgenstein provide

this analysis? I am assuming that logical contingency is an important idea, and that

it only remains to decide whether Wittgenstein has provided for it. Someone, however, is sure to respond that Wittgenstein has no use for this notion, and that he cannot, therefore, be held responsible for an account of logical contingency in our world. The charge will be that I think otherwise because of neglecting Wittgenstein's explicit statement that objects and logical form are unalterable (2.023, 2.026). His view is that substance remains unchanged in any possible world, and that possible worlds differ among themselves only in the arrangement of these objects (2.0271). The notion of logical contingency is irrelevant here, the point will be, because it presupposes that objects and their relations might assume altered expressions in successive worlds.

These citations are unexceptionable, but one must be careful about the interpretation placed upon them. We can acknowledge that Wittgen- stein speaks of the unalterability of objects and logical form, and still adduce two reasons for saying that this fact has no bearing upon my

contention that Wittgenstein is obliged to provide for logical contingency in our world. Let us suppose, in elaboration of the first reason, that the unalterability of objects entails that all of them must, in every world, be exemplified in the same way. It remains conceivable, even supposing that objects are only material or only monadic, that they might have existed in some other way; being monadic, they might have been material. It is not enough to say that objects have the same mode of expression in all possible worlds, because the question remains: just

what is that mode of expression? References in the Tractatus to Hertz's Mechanics suggest that Wittgenstein, himself, may have thought objects to be material particulars. We, however, must ask whether the Tractatus supports this empirical judgment with a priori arguments.

My second reason for dissenting from the above objection is more basic than the first, because as I now want to claim, the unalterability


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of objects and logical form does not entail that these categorial features have the same mode of expression in all possible worlds. Wittgenstein says nothing which implies the contrary. The propositions (2.023, 2.026, 2.027, and 2.0271) in which he introduces the notion of unalterability fail to tell us the feature of objects which makes them unalterable, and it is precipitous, therefore, to take for granted that the unalterability of objects and logical form requires that their exemplification must remain unchanged from world to world.

A different and plausible interpretation is suggested by 2.01231, ( If I am to know an object, though I need not know its external properties, I must know all its internal properties. ), and by the claim that an

object's internal properties are essential to it (2.011). These propositions make it reasonable to say that the unalterability of an object is grounded in the possibilities for combination (internal properties) which constitute its essence (2.0123). Indeed, there appears to be no evidence in the text for any statement denying that this is the only factor which has to be considered in providing for unalterability. Objects, we may say, remain unchanged just to the extent that the sets of combinations into which they can enter remain the same in all possible worlds.

This account also applies to logical form. Wittgenstein has said that, Objects are just what constitute this unalterable form (2.023), and the unalterability of forms existing as possible modes of combination must therefore be identical with the persistence of internal properties of objects.

This is the basis for my saying that the unalterability of objects does not preclude our holding that Wittgenstein's discussion of possible worlds requires fulfillment in a discussion of logical contingency in our world. Wittgenstein's objects, when conceived as unalterable constituents of

possible worlds, are the barest of intelligible entities. They exist only to the point of being foci for sets of possibilities of combination. This, however, is a conception emerging from the most formal and abstract analysis of objects. It cannot be the final statement about them, because possibilities are not free-floating, and because objects must have concrete exemplification in order to fix the locus of these possibilities. Notice, however, that the mode in which objects are concretized in specific worlds is left entirely undetermined by the formal analysis of

objects, and that there is nothing in the idea of unalterability to entail that their mode of exemplification cannot differ from world to world. The same thing may be said of the logical form manifest in states of affairs occurring (hypothetically) in possible worlds. Its expression may also vary, though a world in which objects are material particulars will necessarily be one where relations are spatial and temporal. Mathe-


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matical, mentalistic, and musical particulars would similarly combine in fashions relevant to the mode of their particular exemplification.

There is only one proviso for which accommodation must be made. Where internal properties comprise the unalterable essence of objects, it is a limitation placed upon logical contingency that any mode in which objects are expressed must be one permitting the realization of their possibilities for combination. If, for example, monads must be 'windowless', meaning that they cannot be related to one another, this would be a sufficient reason for denying that monads can be objects.

This proviso has a noteworthy consequence. Supposing that there is more than one mode of exemplification satisfying the proviso, it will

follow that there are at least two modes in which all the possibilities of objects can be realized. This makes it conceivable that there might be two worlds such that the set of configurations in one would be isomorphic with the set of configurations in the other. These worlds would appear to be different, because the objects and logical form of one would be exemplified in a different mode from those of the other, but in essence (meaning the pattern of their relations) they would be identical. This would be an instance of the general rule that possibilities of combination can be expressed in various ways. Music is a familiar example, for it may be played, printed on scores, stamped upon phono- graph records, and described mathematically. In each case the same possibilities of combination are realized in a different mode.

My conclusion is that the unalterability of objects and logical form does not in any way entail that logical contingency is not an issue deserving Wittgenstein's attention. If I am right, the contrary is true: the grounding of unalterability in the essence of object requires us to supplement our account of objects with a description of the concrete

and logically contingent exemplifications whereby objects in specific worlds collect and hold the possibilities which enable them to combine. It follows that Wittgenstein is responsible for a description of logical contingency in our world, and that the question is just as it was: does he provide this analysis

Looking to the Tractatus for signs that Wittgenstein has shifted from the analysis of possible worlds to a metaphysical account of our world, we find, contrary to the expectations encouraged by interpreters who

emphasize the existence of states of affairs, that he has almost nothing to say. There are a few places where he alludes to the occurrence of a state of affairs, and worries, or seems to, about what is the case rather than about logical features of hypothetically existing states of affairs, but in each of these cases (2, 2.04 and 2.06 are examples) little of metaphysical interest emerges. Each of these propositions makes a


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reference to existence, but none of them says anything about the logically contingent features of actual configurations. There is no explicit account of the manner in which objects are exemplified in our world, and apart from possibly metaphorical references to spatial relations, nothing is said about the manner in which these objects are combined in our world. Let me be clear that I am not concerned to debate whether Wittgenstein has said anything to help us determine whether his Gegen- stande are particular only, or particulars, qualities and relations. How- ever this issue is resolved, it remains to determine whether particulars, for example, 'are material, monadic, mentalistic, or something different again. Wittgenstein has said nothing on these topics. His serious thought

seems never to have penetrated beyond the metaphysics of possible worlds.4

It is in this context that the conversation reported by Malcolm is specially significant: I asked Wittgenstein whether when he wrote the Tractatus, he had ever decided upon anything as an example of a 'simple object'. His reply was that at the time his thought had been that he was a logician; and that it was not his business, as a logician, to try to decide whether this thing or that was a simple thing or a complex thing, that being a purely empirical matter (Memoir, p. 86). We should notice that Wittgenstein fails to acknowledge a difference between the logically contingent (that substance might be rational rather than material) and the empirically contingent (that an apple is red, yellow, or green, but never blue), and that his use of 'empirical' has the effect of disparaging references to both of these. Given his failure to see that logical contingency has metaphysical interest, we should not expect Wittgenstein to concern himself with the analysis of the manner in which our world exemplifies the categorial features common to possible worlds. This explains why there are no examples, and why Wittgenstein's notions of object and logical form remain the obscure product of a logical analysis of the features, necessarily most abstractly conceived, which must obtain in all possible worlds.

One explanation for Wittgenstein's oversight may suggest itself. It could be said that the generality of his metahpysical claims is a neces- sary consequence of his having chosen to derive metaphysical arguments from the results of his linguistic analysis. The point would be that

4 When Wittgenstein says in the l's that 'the world is all that is the case' or that 'the world divides into facts', this is not intended as a truth about the world as in fact it is. He does sometimes speak of 'the world' meaning 'the world as in fact it is' but only to say, in effect, that describing 'the world' in this sense is not his business. Griffin, James, Wittgenstein's Logical Atomism, (Oxford, 1964), p. 29.


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Wittgenstein has no way to determine the logically contingent expression of objects in our world, because the analysis of atomic propositions does not enable him to say more of propositional terms than that the requirements of absolutely determinate sense entail that the constituent terms of a proposition must be names. We may go on to infer, as Witt- genstein does, that the referents of these terms are simple, unalterable objects, but just as analysis of the formal relation of naming as it occurs in all possible languages does not give us anything so specific as examples of names, so it cannot indicate the peculiar manner in which substance will be exemplified in a particular world. Similarly, though we say that atomic propositions have pictorial form, and infer that this

form would be shared by combinations of objects in any possible world, no formal analysis of the properties possessed by atomic propositions in every possible language can tell how this combinatorial form will express itself in a specific world. It is irrelevant to the linguistic analysis and beyond the capacities of the metaphysical inquiry based upon this analysis to tell whether these relations will be spatial, temporal, mathe- matical, or musical. As this argument would convince us, Wittgenstein should not be expected to say more than he has: his linguistic starting point limits him to inferences specifying the categorial features of possible worlds. There is nothing he can say of their logically contingent exemplification in our world.

This explanation is hard to fault, but there is a residual problem. Wittgenstein has spoken of actually existing states of affairs in a manner suggesting that he would like to bring them within the scope of his metaphysics. Perhaps the final answer, and this is very speculative, is that Wittgenstein's several but inconclusive references to actual configurations of objects are symptomatic of his original interest in the fact that human beings do use living languages to describe events in our world. This, of course, is far from saying that Wittgenstein was deeply concerned with the metaphysical analysis of our world. The omissions of the Tractatus indicate that he was not.

Nevertheless, the metaphysics of possible worlds requires fulfillment in an analysis of logical contingency in our world, and Wittgenstein's philosophy must be assessed in terms of his failure to provide that analysis. It is true, we grant, that analysis of the properties of atomic

propositions in any language affords no basis for determining how categorial factors are exemplified in our world. But it is not the case that Wittgenstein was obliged to restrict his analysis of language to the study of logical syntax, or that he was compelled to neglect the properties of atomic propositions in living languages. Semantical and pragmatic analyses of language are also appropriate, and Wittgenstein, if he had


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been seriously concerned to describe the ontology of our world, might have tried to approach the issue by carrying linguistic analysis to an examination of the semantical and pragmatic rules governing the for- mation of atomic propositions native to languages used in our world. In keeping with his interests at the time of writing the Tractatus, these might have been improved scientific languages. Languages of this sort were available to him, at least in primitive form as scientific theories, and Wittgenstein might have been able to determine something about logical contingency in our world by examining the ontological commit- ment of these languages: what sense is bound up in the notion of thinghood in these language? are objects regarded as material particu-

lars, or as minds? It is a considerable jump from the claim that a language makes certain ontological assumptions to the view that the world in which the language is used has the categorial features ascribed to it by the language. But this procedure, questionable though it is, is the one which Wittgenstein has already applied in his analysis of possible worlds. Extending the analysis as I am suggesting would, at least, have been a step in the direction of completing an otherwise fragmentary metaphysics.

Someone may respond that my suggestion is pointless, because no one, including Wittgenstein, could identify an atomic proposition in a living language. Atomic propositions, he will say, are a fiction; they are merely part of a story about languages which are conceivable, but non- existent. This, however, entails that Wittgenstein's ontology of possible worlds, based as it is upon the analysis of language, should be as mythic as are atomic propositions. Objects and logical form will, also be fictions then, and the search for their logically contingent expressions in this world will necessarily be abortive.

Of course, one might argue for this view, but the result is to trivialize the entire Tractatus. Is it not better to take Wittgenstein seriously, to suppose that his analysis of atomic propositions in any language is perhaps valid, and to hold him responsible for indicating the characteristics of these propositions as they occur in living languages? Using these propositions as the basis for describing logically contingent features of our world, Wittgenstein might have filled the considerable gap in his ontology.

I have so far refrained from asking certain more basic questions, but these should be stated now. First, is it important that metaphysics should provide an analysis of possible worlds before going on to describe the exemplification of categorial features in our world? Second, does Wittgenstein succeed in providing an ontological analysis of all possible worlds by way of his theory of atomic propositions? If he has


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failed, is his approach so comprehensive that another philosopher might have used it and succeeded?

I believe that the answer to the first question is yes. It is a considerable advantage to enter a foreign city with a map showing the major streets and monuments, and similarly the metaphysical analysis of events in our world is immeasurably advanced when we can begin the analysis with a list of the categorial features which we are certain to find exemplified in this world. The alternative method for discovering these categories is arduous, more indirect even than Wittgenstein's method, and largely hit or miss. It is some version of the Aristotelian method with its beginning in observation, its advance through the study of cate-

gories assumed by the sciences, and its termination in the piecemeal elucidation of the categories prevailing in nature. When we finally come around to imagining how categories might be expressed differently in other worlds, and to understanding that even the exemplification of substance is in one sense contingent, Wittgenstein's method, starting where we have ended, must seem the preferable one.

This is why it is so distressing that the answer to the second question and to its corollary is no. Wittgenstein's analysis fails to describe the categorial features which must occur in every possible world. We can establish this by considering two examples. First, there is a world having no logical form: there are no ways for objects to combine, and, therefore, relations have no place in this world; the objects are all that exist. Second, we can imagine a world like the one conceived by Meinong, a world whose constituent entities divide into positive and negative facts; it is a positive fact that something is the case, and a negative fact thet something is not the case. These are possible worlds, meaning that their conception does not embody a contradiction, but evidently

Wittgenstein's metaphysics does, not provide for them. This is what makes the corollary to question two so important, for Wittgensitein's failure is not so much a flaw in execution as the symptom that his method for analyzing possible worlds is defective.

This defect has its origins in the fact that Wittgenstein's metaphysics is grounded in the analysis of atomic propositions: what he says of them is his basis for claims about possible worlds, and whatever he finds there must correspond to a feature of the propositions. It is in support

of this criticism that I want to consider the possible worlds described above. Evaluation of the first prompts reference to proposition 2.161: There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all. What we have to do is find the element which propositions and possible worlds must share in order that the one can represent possible situations in the other.


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But this is easy, for the essential feature of atomic propositions is form (3.1431). It is form, moreover, which is common to atomic propositions and to logical space (2.17, 2.18), and form, therefore, which both must have if the one is to represent the other. Recall now that, The limits of my language mean the limits of my world (5.6). Worlds in which there is no form to be represented by atomic propositions are not worlds at all. The principle is clear: possession of logical form is the defining property of a possible world. The world of our example, however, is ex hypothesi a world without form, and it is, consequently, a world which is not possible on Wittgenstein's terms. Because he has based his metaphysics on the analysis of atomic propositions, Wittgenstein over-

describes possible worlds; some possible worlds will have the categorial features which he ascribes to all of them, but at least one will not.

We can also say the contrary: there are some possible worlds about which Wittgenstein cannot say enough because of deriving ontology from the analysis of atomic propositions; he under-describes them. The second possible world suggested above is an example. That was a world having negative facts, a world in which negation has ontological status. Wittgenstein, however, defines an atomic proposition as a set of names (4.22). He adds that names denote objects and that logical constants such as negation are not names (4.0312). Now the second world which I described is a possible world because of having logical form, but at the same time, it has a constituent, namely negative facts, which Witt- genstein is unable to accommodate because his atomic propositions are only qualified to depict positive facts.

Our overall conclusion must be that Wittgenstein's metaphysics does not provide for all possible worlds (we have already said that is fails entirely to make specific claims about the logically contingent features

of our world), and that it cannot provide for them because of Wittgen- stein's reliance upon the analysis of atomic propositions. This was a courageous method of procedure but it was doomed to failure from the start. Let us suppose, by way of proving this, that the analysis of atomic propositions yields a certain list of properties which can be ascribed to the atomic propositions of any language: it is very doubtful whether each atomic proposition of every possible language must have a certain fixed number of properties, but let us assume that all of them do. Even

on this assumption, could it ever be said that one can give a complete characterization of the categorial features of all possible worlds by supposing them to have ontological correlates for every one of the features claimed for atomic propositions (e.g., objects for names, and logical form for pictorial form)? We may be able to ascribe a single list of properties to any possible atomic proposition, but will it count as a


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thorough analysis of all possible worlds if we transform each of the entries on this list into an ontological category, and then ascribe all of the entries, no more and no less, to every possible world? Our two examples show that this cannot suffice, and that the result must be over- and under-description of some possible worlds.

This is an embarrassing result for Wittgenstein, because discussion of possible worlds is merely preliminary to analysis of the logically contingent expression of catelgorial factors in our world. If the analysis of possible worlds fails to turn up all of the categorial features which are present in some possible worlds and ascribes to all possible worlds characteristics possessed by only some of them, we will have no assur-

ance that the metaphysics of possible worlds has specific relevance to that actualized possibility which is our world. Our world might be one of those that is over- or under-described. But this is the demise of a metaphysics originally considered important for the sole reason that it promised to be an illuminating antecedent to the analysis of logical contingency in our world. The purport of Wittgenstein's metaphysics is that it affords a map of the ontology of our world and any other, but the effect of using his analysis as a guide to the investigation of logical contingency in a world (ours or some hypothetical one) is like that resulting if someone were to draw a grid of horizontal and vertical lines, and then set out to find his way through whatever city, town or village he might happen to pass by consulting this sketch. It is accidental to the manner of its invention that the map would be useful in Chicago, and more important that it would be too complicated or too simple for most other places.

The difficulties of applying a method like Wittgenstein's begin to appear overwhelming. We may try to redeem his procedure by dis-

covering a basis, in language, thought, or being itself, which will provide for the variation of categorial factors in all possible worlds while indicating whether there are also certain categorial features common to all of them. In the best of circumstances then, we might have a set of unlabeled maps, one of them suitable, when beginning the analysis of logical contingency in our world. But even now the outlook would be bad, for there is no advantage to this approach if the number of possible worlds having different categorial features is large; sorting through

a possibly infinite number of ontological maps in order to find the one fitting our world would not be worth much effort. When we add that no viable basis for analyzing uniformity and variation in the categorial features of all possible worlds is known or likely to be discovered, it will follow that Wittgenstein's ontology is a failure, and that no one following his example should hope to do better.


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ONTOL OGY I N THE TRA CTATU S 5 1

It will also follow that an Aristotelian-type approach to metaphysics is the only one remaining to us. Cartographers who draw separate maps of Chicago and London before looking for similarities and differences between the two are like ontologists who imagine possible worlds alternative to our own in order to sharpen a distinction previously exposed in the analysis of this world.

DAVID WEISSMAN.

CITY COLLEGE OF NEW YORK.

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