Why the Tractarian Objects Cannot Be Properties and Relations
In this paper I reinterpret and offer a solution to one of the most famous debates in Wittgenstein's early philosophy: the debate whether the Tractarian objects include properties and relations (hereinafter 'PRO' for the thesis that properties and relations are Tractarian objects, 'PRO debate' for the debate whether properties and relations are Tractarian objects, and 'PRO issue' for the issue whether properties and relations are Tractarian objects).
Since the very beginning, PRO debate has been equated with the debate whether objects include universals in many secondary literatures. However, it seems to me that these two debates are not exactly the same thing, for the following reasons: PRO debate is in fact a debate concerning whether properties and relations are objects or "modes of configurations of objects" (hereinafter 'MCOs'), insofar as object and MCO are two distinct and exhaustive types of components of states of affairs. Since the essential difference between objects and MCOs is that objects can be the subject matter of states of affairs while MCOs cannot, PRO debate is essentially a debate concerning the logical status of properties and relations, i.e., whether properties and relations can be the subject matter of states of affairs. However, the debate whether objects include universals is a debate concerning the metaphysical nature of objects, i.e., whether some objects can have multiple instances at the same time. The two debates are clearly not logically equivalent, for on the one hand, we can hold that properties and relations cannot be the subject matter of states of affairs, and yet insist that the Tractarian objects be abstract entities, e.g., Platonic forms; on the other, we can hold that properties and relations are also what states of affairs are about, and yet claim that they are nominalized properties and relations, and moreover, all of the Tractarian objects are particulars, e.g., the Hintikkas' version of PRO (, 38-39). So, it is important that we distinguish a logical debate PRO debate from a metaphysical debate whether objects include universals. And our concern in this section is the former.
PRO has two main versions: Gustav Bergmann's version, which claims that properties and relations are universals, and there is only one MCO the "exemplification" that relates objects to form states of affairs (, 346-349); and the Hintikkas' version, which holds that property-objects and relation-objects are nominalized properties and relations (e.g., what the linguistic relation of two particular symbols 'a' and 'b' flanking 'R' expresses: a's standing in R to b), and objects attract each other to form states of affairs there is no analogous notion of MCO in the Hintikkas' theory (, 38-44).
PRO is not wrong in itself. Nevertheless, a close study of the text will show that Wittgenstein did not hold PRO in Tractatus. It is this aspect that I will focus on in the remaining part of this paper.
The passages in Wittgenstein's early works that have been or can be cited to support PRO are these:
1. "Symbols are not what they seem to be. In 'aRb' 'R' looks like a substantive but is not one.
What symbolizes in 'aRb' is that 'R' occurs between 'a' and 'b'. Hence 'R' is not the indefinable in 'aRb'.... The indefinables in 'aRb' are introduced as follows: 'a' is indefinable; 'b' is indefinable; Whatever 'x' and 'y' may mean, 'xRy' says something indefinable about their meaning" ([NL], 98-99).
2. "When we say of a proposition of [the] form 'aRb' that what symbolizes is that 'R' is between
'a' and 'b', it must be remembered that in fact the proposition is capable of further analysis because a, R, and b are not simples. But what seems certain is that when we have analyzed it we shall in the end come to propositions of the same form in respect of the fact that they do consist in one thing being between two others" ([NM], 111).
3. "Relations and properties, etc. are objects too" ([NB], 61).
4. "But logic as it stands, e.g., in Principia Mathematica can quite well be applied to our ordinary propositions, e.g., from 'All men are mortal' and 'Socrates is a man' there follows according to this logic 'Socrates is mortal' which is obviously correct although I equally obviously do not know what structure is possessed by the thing Socrates or the property of mortality. Here they just function as simple objects" ([NB], 69).
5. "A name designating an object thereby stands in a relation to it which is wholly determined by the logical kind of the object and which signalizes that logical kind" ([NB], 70).
6. "The arguments of functions are readily confused with the affixes of names. For both arguments and affixes enable me to recognize the meaning of the signs containing them.
For example, when Russell writes '+c', the 'c' is an affix which indicates that the sign as a whole is the addition-sign for cardinal numbers. But the use of this sign is the result of arbitrary convention and it would be quite possible to choose a simple sign instead of '+c'; in '~p', however, 'p' is not an affix but an argument: the sense of '~p' cannot be understood unless the sense of 'p' has been understood already. (In the name Julius Caesar 'Julius' is an affix. An affix is always part of a description of the object to whose name we attach it: e.g. the Caesar of the Julian gens.)" ([T], 5.02.)
Now, let me argue one by one that each of the above passages does not really provide support for PRO.
"1" was cited by the Hintikkas to support the claim that the relation of flanking 'R' stands for an object (, 38). Their reason is this: since "1" says that the relation of flanking 'R' is an indefinable, and since indefinables are names, the relation of flanking 'R' stands for an object (, 38). However, it seems to me that Wittgenstein never held the view that all indefinables are names. In First MS of the same text, Wittgenstein said: "Indefinables are of two sorts: names and forms. Propositions cannot consist of names alone; they cannot be classes of names" ([NL], 96). This clearly means that Wittgenstein took not only names, but also logical forms, as indefinables. So, what "1" really means is that the logical form of 'aRb' the mode of configuration that relates two symbols in the way of flanking 'R' expresses something indefinable about two objects ([NL], 99). Since we have distinguished logical forms/MCOs from names/objects in section I, and the phrase 'the relation of flanking 'R'' is just an abbreviated description of the logical form of 'aRb', the relation of flanking 'R' in no way stands for an object.
"2" seems to suggest that a relational term is a "thing," by claiming that the analysis of 'aRb' will end up with a proposition of the same form which consists in one thing being between two others. But first, here by "things" Wittgenstein meant symbols which are not objects and are not necessarily names; second, the phenomenal appearance of a proposition's consisting of three symbols does not imply that the propositional fact of the proposition is about these three symbols; and hence, "2" does not imply that a relational term is a name. (Also, the paragraph of "2" is lightly deleted.)
"3" is most extensively cited to support PRO. However, a close look at the context of "3," it seems to me, will show that "3" is probably a momentary aberration. "3" appears in the context where Wittgenstein strived to prove that an ordinary proposition must have a complete analysis (and hence there are simple things). There the difficulty with which Wittgenstein was struggling is this: When we understand or utter an ordinary proposition, we do not seem to have a complete analysis of the proposition in our mind. And when we proceed to analyze the proposition, it is likely that the process of analysis will go on forever, where we will not reach a complete analysis of the proposition ([NB], 60-61). To solve this difficulty, one strategy Wittgenstein tried is to ask what is given to us a priori in understanding, using, and analyzing a proposition. He then got the idea that the concept "This" is given to us a priori in understanding, using, and analyzing a proposition, there is always something that we directly point to. Then, he equated the concept "This" with the concept "object", and remarked further that "Relations and properties, etc. are objects too," insofar as ordinary relations and properties can be directly pointed to. Immediately after that, Wittgenstein recognized that the idea of equating "This" with "object" did not help him solve the difficulty, because that idea did not settle the issue whether the analysis of a proposition will terminate or not ([NB], 61). And then, he jumped to another idea, that the sense of a proposition must be determinate, which ultimately helped him to reach the conclusion that a proposition must have a complete analysis ([NB], 61-63) (whether this argument works or not is not my concern here I just want to sort out the context of "3"). In this context, it is clear that "3" is just a corollary of the idea of equating "This" with "object" only because we equate "This" with "object" and we can directly point to relations and properties in ordinary language, do we say that relations and properties are objects. However, since the idea of equating "this" with "object" did not help Wittgenstein solve the difficulty with which he was struggling, and the idea never showed up again in Notebooks, it is quite likely that that idea is just a passing thought which Wittgenstein immediately abandoned or neglected once he explored it and found it useless. And if so, "3" is nothing other than a bubble of a passing whim.
"4" says that the logical rules that govern the fully analyzed propositions can be applied to ordinary propositions as well. And because of that, some terms in ordinary propositions, e.g., 'Socrates' and 'mortality', are analogous to simple names. Clearly, here the analogy between 'mortality' and a simple name is drawn on the basis that in applying logical rules to ordinary propositions, some terms, e.g., 'mortality', can be systematically replaced by simple names without affecting the validity of inference rules, not on the basis that 'mortality' and a simple name share the categorical type of predicate.
"5" says that objects are not all of one and the same "logical kind." The key issue here is what Wittgenstein meant by 'logical kind'. Commentators such as the Hintikkas seemed to take it as a sort of categorical type (in a broad sense) type of things, type of properties, etc., and thereupon they concluded that "5" indirectly supports PRO (, 31). However, in the preceding paragraph of "5" Wittgenstein said: "If, e.g., I call some rod 'A', and a ball 'B', I can say that A is leaning against the wall, but not B. Here the internal nature of A and B comes into view" ([NB], 70). Given this context, it is clear that there by "logical kind" in "5" (and "logical nature" in the preceding paragraph of "5") Wittgenstein meant combinatory possibilities (internal properties) of objects which, at least in that context, do not capture the Hintikkas' categorical type. Hence, "5," understood in its context, does not support PRO.
With respect to "6," the Hintikkas said: "Here Wittgenstein implies in two different ways the symbols for addition is a name and hence stands for an object. First, it can have an [affix], which is a characteristic of names. Second, it is equivalent with a simple sign, i.e., a name" (, 33). However, a careful consideration of Tractatus 5.02 will show that here the Hintikkas did not make a good case either. First, the Hintikkas' two arguments are not conclusive, since (1) with respect to the first argument, Wittgenstein did not say in 5.02 that affixes can only be attached to names (he did say that "An affix is always part of a description of the object to whose name we attach it," but he said it right after he gave the Julius Caesar example, and the claim can thus be viewed as an explanation of the character of the affix in that or similar examples); and (2) with respect to the second argument, we can say that since in 5.02 Wittgenstein used the term 'simple sign' in contrast to a sign which is physically complex (e.g., '+c'), what he meant there by 'simple sign' is probably just a sign which does not contain another sign as its part, not necessarily a simple name as the Hintikkas claimed. Second, there is some evidence in 5.02 suggesting that '+c' is not a name. Let us consider the Julius Caesar example and ask why Wittgenstein introduced it in 5.02. If '+c' is a name, then through the contrast between the +c example and the ~p example, the difference between affixes of names and arguments of functions will be well illustrated, and then, adding the Julius Caesar example will seem to be redundant. A more plausible explanation is this: Since '+c' is not a name, through the contrast between the +c example and the ~p example, only the difference between affixes in general and arguments is illustrated. And then, in order to further illustrate the difference between affixes of names and arguments of functions, Wittgenstein introduced the Julius Caesar example, where he explained the specific character that belongs to affixes of names but not to affixes in general. So, we had better not take '+c' as a name in order to make sense of the structure of the argument in
5.02. In sum, according to my foregoing analysis, "6" (Tractatus 5.02) does not seem to support PRO.
Having argued that none of the above six passages really supports PRO, let me argue for the claim that properties and relations are MCOs in Tractatus, using the following three arguments.
The first argument appeals to the continuity of Wittgenstein's thought. First of all, we observe that during the pre-Tractatus period, from 1913 onwards, Wittgenstein seemed to treat properties and relations as MCOs all along. In a letter to Russell on 16 January 1913, Wittgenstein said: "I have changed my view on 'atomic' complexes [states of affairs]: I now think that qualities, relations (like love) etc. are all copulae! That means I for instance analyze a subject-predicate proposition, say, 'Socrates is human' into 'Socrates' and 'something is human', (which I think is not complex). The reason for this is a very fundamental one: I think that there cannot be different Types of things!" ([LR], 121-122.) From then on, at numerous places, e.g., [NL], 96, lines 39-42; [NL], 104, lines 12-15 & 20-36; [NL], 107, lines 33-40; [LR], 128, lines 25-29; [NM], 111, lines
10-13; [NB], 14, lines 25-27; etc., Wittgenstein took properties and relations what logical forms express as MCOs. These extensive textual evidence seems to suggest that from 1913 to 1916 Wittgenstein held all along that properties and relations are MCOs rather than objects. Now, if Wittgenstein had changed his view on PRO issue when he wrote Tractatus, he would have emphatically marked the change, since (1) PRO issue is a significant one, and (2) when Wittgenstein first changed his view on PRO issue in January 1913, he marked the change. But since we did not find any passage in Tractatus which says or implies that Wittgenstein changed his view on PRO issue again, it is reasonable to extrapolate that in Tractatus Wittgenstein still held his old view, although there he formulated the old view from a slightly different perspective, using different terminologies (e.g., 'configurations of objects' instead of 'logical forms').
The second argument is an old one, based upon Tractatus 3.1432: "Instead of, 'The complex sign "aRb" says that a stands to b in the relation R', we ought to put, 'That "a" stands to "b" in a certain relation says that aRb.'" As Copi pointed out (, 176-177), the relation between 'a' and 'b' is what relates 'a' and 'b' to form a propositional fact. For using the analogy between spatial arrangement of things ([T], 3.1431) and relation of symbols, by claiming that "that 'a' stands to 'b' in a certain relation says ...," Wittgenstein clearly meant that the propositional fact of 'aRb' is about only two symbols 'a' and 'b'. Now the Hintikkas objected that since the relation between 'a' and 'b' as stated in 3.1432 should be understood as the linguistic relation of two symbols flanking 'R', the propositional fact that 'a' stands to 'b' in a certain relation must contain a third name (, 37-39). I agree with the Hintikkas that the relation between 'a' and 'b' in 3.1432 is a linguistic relation (although I do not agree with them that the relation is a nominalized relation), but I do not see why it follows from this that there is a third name in the propositional fact. The third name in the Hintikkas' account is certainly not 'R', since the
Hintikkas agreed with Wittgenstein that 'R' is not a substantive (, 38). It is not 'aRb', since 'aRb' is a proposition, not a name. It is not 'xRy' either, since the propositional fact is clearly not about the symbol 'xRy'. What then can the third name be? What the Hintikkas seemed to have overlooked is that it is one thing to say that the phenomenal appearance of the propositional fact of 'aRb' consists of three symbols (i.e., 'a', 'R' and 'b'), and it is another thing to say that the propositional fact is about these three symbols (i.e., it has three names).
The third and last argument resorts to Tractatus 4.24, where Wittgenstein said:
This passage suggests two things: (1) there are more than one MCOs (since the logical forms of 'fx' and 'í(x, y)' are different); and (2) a state of affairs can have only one object (e.g., the state of affairs corresponding to 'fx' has only one object the object 'x' denotes). Now, (1) and (2) are at odds with both Bergmann's and the Hintikkas' versions of PRO. With respect to (1), it is against Bergmann's version of PRO, because in Bergmann's theory we have only one MCO, viz., the exemplification; and it is against the Hintikkas' version of PRO, because the Hintikkas' theory has no analogous notion of MCO, let alone different MCOs. With respect to (2), it is at odds with Bergmann's theory, because in Bergmann's theory a state of affairs must have at least two objects (e.g., a thing-object and a property-object); and it is at odds with the Hintikkas' theory, for the following reason: If the Hintikkas were to allow a state of affairs to have only one object, the one object in the state of affairs had to be either a particularized-property-object or a particularized-relation-object. But then there is no difference between a particularized-property-object (or a particularized-relation-object) and the one-object-state-of-affairs consisting of that object (insofar as in the Hintikkas' account there is no analogous notion of MCO), and hence, the important distinction between objects (names) and states of affairs (propositions) is blurred. To get around with this problem, the Hintikkas have to introduce some analogous notion of MCO into their theory so that a state of affairs can be distinguished from a mere collection of objects.
But even in that case another serious problem remains: what would be the difference between a state of affairs consisting of only one particularized-property-object (particularized-relation-object) and a state of affairs consisting of the same particularized-property-object (particularized-relation-object) and the thing-object(s) which that particularized-property-object (particularized-relation-object) attracts? Nothing in the Hintikkas' account, it seems, would suggest that there is a difference. And if so, it follows that a state of affairs would not have a fixed number of constituents, which is absurd. In sum, my point here is that once properly understood, (2) implies that properties are MCOs, for otherwise we cannot make sense of a one-object-state-of-affairs. And if properties are taken as MCOs, it will be remarkably awkward if we do not take relations in the same way. This then concludes my last argument.
To sum up, in the foregoing I have reinterpreted PRO debate, and on the basis of my interpretation and three arguments, I have argued that the Tractarian objects cannot be properties and relations.
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[NL] Ludwig Wittgenstein, Notes on Logic, in [NB], 93-107.
[LR] Ludwig Wittgenstein, Extracts from Wittgenstein's Letters to Russell, 1912-20, in [NB], 120-132.
[NM] Ludwig Wittgenstein, Notes Dictated to G. E. Moore in Norway, in [NB], 108-119.
[NB] Ludwig Wittgenstein, Notebooks 1914-1916, ed. by G. H. von Wright and G. E. M.
Anscombe (Chicago: The University of Chicago Press, 1979).
[T] Ludwig Wittgenstein, Tractatus Logico-Philosophicus, trans. by D. F. Pears and B. F.
McGuinness (Routledge & Kegan Paul Ltd, 1974).
[LC] Ludwig Wittgenstein, Wittgenstein's Lectures, Cambridge, 1930-1932, ed. By Desmond Lee (Oxford: Basil Blackwell, 1980).
[PG] Ludwig Wittgenstein, Philosophical Grammars, ed. by Rush Rhees, trans. By Anthony Kenny (Oxford: Basil Blackwell, 1974).
[PI] Ludwig Wittgenstein, Philosophical Investigations, trans. by G. E. M. Anscombe (Oxford: Basil Blackwell, 1953).