Filosofía de las ciencias de la complejidad

In this section, I will discuss three kinds of problems with the view that truth and falsehood are primitive properties of propositions. It has often been argued in the literature that some of these problems were crucial in persuading Russell to reject the ontology of propositions in favour of the multiple-relation theory of judgment. However, it will be seen that he did not regard them as genuine problems.

6.2.1 Indefinability of truth and falsehood

In this subsection I will first introduce how Russell argues for the indefinability of truth and falsehood in endorsing the ontology of propositions. I will then try to indicate that although his argument poses a certain problem to his own standpoint, he does not view it as a genuine problem.

Let us begin by briefly introducing Russell’s view of truth and falsehood as indefinable properties. In PoM, he gives the notion of truth only a marginal treatment except for an obscure discussion on the notion ofassertion (cf.PoM,§1, §84). It is in some subsequently written papers that his view of truth and falsehood enjoys an extensive discussion. He wrote ‘Meinong’s Theory of Complexes and Assumptions’ (henceforth, MT) in 1903 and

published it in three parts in 1904. It is in this paper that he states his position on truth and falsehood expressly for the first time since his endorsement of the ontology of propositions. He concludes, through a detailed discussion of Meinong’s theory of Objectives, ‘that there are, apart from and independently of judgment, true and false propositions, and that either kind may be assumed, believed, or disbelieved’ (CP4, p.472). As we will see in Section 6.3.1, Russell is somewhat sceptical about false propositions but in the end he holds that ‘some propositions are true and some false, just as some roses are red and some white’ (ibid., p.473). His comparison of truth and falsehood with redness and whiteness suggests that truth and falsehood are considered simple, indefinable properties of propositions, since he arguably counts redness and whiteness as such properties (cf. Moore, 1900-1). In fact he explicitly argues for this view of truth and falsehood in ‘The Nature of Truth’ (henceforth, NT), which he read to the Jewett Society, Oxford in June 1905. The impossibility of defining truth and falsehood is among the main themes of the paper: ‘I have no positive doctrine to advocate, but am content to try and refute whatever positive doctrine comes into our discussion’ (CP4, p.492). He thus maintains that it is impossible to define truth and falsehood. He also makes it plain that they are considered to be certain properties of propositions: ‘Truth and falsehood, in fact, are properties attaching to propositions as wholes, and are not themselves, in general, parts of propositions’ (ibid., p.504). In endorsing the ontology of propositions, he thus holds that truth and falsehood are simple, indefinable properties of propositions.

Let us turn to Russell’s argument for the indefinability of truth and falsehood. In NT, he presents the following argument against the correspondence theory of truth and effectively

against any attempts to define truth and falsehood1_:

If we don’t know the difference between a proposition’s being true and not being true,

we don’t know the difference between a thing’s having a property and not having it,

and therefore we can’t define a thing as true when it has a certain property such as correspondence with reality.

(CP4, p.494) The idea is that every proposed definition of truth will presuppose the very notion of truth and hence fail to be a proper definition of it. The argument is arguably based on the assumption that an entity’s possession of a property consists in the corresponding proposition’s being true. Given this assumption, it indeed follows that any account of truth and falsehood ultimately relies upon the very notion of truth. For in order to say that an entityaactually possesses a propertyF, we need to check whether the proposition ‘Fa’ is true or not.

It should be observed that this assumption in turn implies that even if an entityaisconnected

witha propertyFto form a propositionFa, the proposition itself remains neutral as to whether the entityactually possessesthe propertyF. It will possess the property, if the proposition is true; and it will not, if the proposition is false. Russell thus effectively distinguishes between

an entity’sbeing connected witha property and itsactually possessingit. Hence, the unity of a proposition requires, in his view, just one mode of combination: entities only need to be

connected witha relation.

As Hylton, Ricketts and Korhonen point out, this argument against any definitions of truth and falsehood backfires (Hylton, 1990, p.140; Ricketts, 2001, p.105; Korhonen, 2009, p.173). If truth and falsehood are included among ordinary properties, we can generate a certain regress within the view of truth in question precisely in the same way in which Russell does against any definitions of truth and falsehood. ‘The ontological primacy of propositions and of truth,’ Hylton explains, ‘arises from the fact that for an object to have a property (or for two objects to be related by a given relation) is taken to consist in the truth of the corresponding proposition’ (Hylton, 1990, p.178). He then points out that an infinite regress arises from this account: ‘For a given proposition, call it a, to have the property truth is for another proposition, thata is true, to have the property truth; for this to be so, the proposition that the proposition thatais true is true must in turn have the property truth, and so on’ (ibid.). I shall call this regress ‘the regress of predication.’

This regress indeed undermines the ontology of propositions, because it establishes that nothing in the ontology could constitute an entity’sactual possession of a property. For the regress generates a chain of propositions in each of which a certain proposition is merely connected with—and does not actually possess—the property of being true. However long the chain may be, it never reaches a proposition which actually possesses the property of being true. The neutral mode of combination that propositions are all considered to have cannot yield any complexes where an entity actually possesses a property. The problem is, in other words, not an infinity of propositions involved in the truth of a proposition but rather the absence of what can let a proposition actually possess the property of being true.

Russell was arguably aware of the regress of predication while endorsing the ontology of propositions. Hylton, Ricketts and Korhonen point out that that the regress underlies the notoriously obscure discussion ofassertionin thelogicalsense inPoM.2_{Although, contra their}

claim, Russell does not seem to speak of the regress of predication in the body of the book, he indeed tries to resolve it by appealing to the notion ofassertionin Appendix A:

If p is a proposition, “p’s truth” is a concept which has being even if p is false, and thus “p’s truth” is not the same aspasserted. Thus no concept can be found which is

equivalent topasserted, and therefore assertion is not a constituent inpasserted. Yet, assertion is not a term to whichp, when asserted, has an external relation; for any such relation would need to be itself asserted in order to yield what we want.

(PoM,§478) Russell thus attempts to resolve the regress by distinguishingp’s being asserted from a concept

p’s truth, holding that the former cannot be turned into aterm.

It is, however, implausible that Russell came to abandon the ontology because of the regress of predication. On the contrary, it seems as though he remained optimistic that the regress would not do his ontology of propositions any harm. In MT, he remarks, after a discussion of false propositions, that ‘there is no problem at all in truth and falsehood’ (CP5, p.473). In NT, he introduces an epistemological problem caused by a regress analogous to the regress of predication and, importantly, he presents it to support his primitivist view of truth:

How then do we know whether a proposition is true or false? The first answer is, that the difficulty would be just as great if there were such a difference between true and

false propositions as is desired. If all propositions having a certain property are true, and all others false, the question arises: How do we know which propositions have this property? Presumably by observing whether the proposition that they have the property has the property; but this plainly won’t do.

(CP4, p.505) Any appeal to a ‘further quality’ is thus subject to the same objection which he makes against the correspondence theory, and this constitutes his ‘first answer.’ His second answer is that the difficulty with our knowledge of truths only reinforces his claim that truth and falsehood

are inexplicable. Of course, he might have changed this optimistic attitude towards the regress of predication after NT. But if he had abandoned the ontology because of it, he would certainly have mentioned it in ONTF.

It is not perfectly clear why Russell thus thought the regress of predication harmless. There are at least two possible ways to resolve it, though neither of them is entirely satisfactory. One is to hold that truth and falsehood are different from other properties and that if a proposition

is connected with one of these two properties, the proposition is indeed true or false as the case may be. This idea amounts to the claim that truth and falsehood aresui generisobjects. Korhonen indeed attributes this view to Russell (Korhonen, 2013, pp.124-6). But this idea, as Korhonen himself observes, leaves it inexplicable why Russell would then employ such a misleading expression as ‘properties attaching to propositions’ without any qualification.

Another solution is to accept more than one mode of combination. One might attempt, as Moore in NJ seemingly does, to distinguish between the true-proposition-constituting mode

of combination and the false-proposition-constituting one. ‘A proposition is,’ he remarks, ‘constituted by any number of concepts, together with a specific relation between them; and according to the nature of this relation the proposition may be either true or false’ (NJ, p.180).3

This distinction certainly resolves the regress of predication, as it prevents the very first step of the regress. However, this approach is flawed or at least Russell thinks so. ‘If truth and falsehood were,’ he argues in NT, ‘respectively constituents of true and false propositions, we could tell by inspection (at least as a rule) whether a proposition is true or false’ (CP4, p.504). It is reasonable for him to think that to understand a proposition is to have acquaintance with all the constituents and with the way in which they are combined with each other. But if so, and if a proposition is true or false depending on the way in which terms are combined to form it, we would be able to tell whether a proposition is true or false, simply by understanding the proposition, that is, the meaning of a sentence. Russell was presumably aware of this problem as early as in 1899 or 1900. For Moore seemingly rejected the distinction between these two modes of combination by the time he wrote his entry on truth in Baldwin’s Dictionary of Philosophy and Psychology(Moore, 1902, pp.716-7).4

A plausible way of accepting more than one mode of combination is to distinguish be- tween the proposition-constituting manner and the fact-constituting manner. The distinction resolves the regress because it enables us to think that the truth of a proposition consists in the substance of a corresponding fact, a complex in which entities are connected in the fact- constituting manner. I will call this account of predication thedualistaccount of predication. As we will see in Section 6.3, Russell in NT and some other papers makes various attempts to accommodate complexes in which entities are connected in such a manner. One might think that he does so because he tries to resolve the paradox by means of the dualist account. However, it should be remembered that it is in NT that he argues for the impossibility of defining truth and falsehood, invoking two kinds of regress, both of which are akin to the regress of predication. He would not do so if he found the regress problematic there. It seems to me that his reason for accepting complexes other than propositions stemmed from something else.

Attributing the dualist account to Russell inPoM, Ricketts offers an elaborate account of

the abandonment of propositions. According to Ricketts, Russell inPoMtries to resolve the regress of predication by holding that there are two ways in which a proposition can be formed out of individual entities—‘the true way or the other way.’ Ricketts’ interpretation

3_{To be precise, Moore in NJ also understands ‘truth and falsehood as properties of certain concepts, together}

with their relations-a whole to which we give the name of proposition’ (ibid., p.181).

4_{Hylton points this out (Hylton, 1990, p.138fn). Later inSome Main Problems of Philosophy, Moore remarks that}

given the dyadic-relation theory of judgment, truth is ‘a property which can only be possessed by propositions, andisonly possessed bysomeamong them’ (Moore, 1953, p.262).

will be discussed in the following subsection. 6.2.2 Proposition and falsehood

In search for Russell’s substantial reason for giving up the ontology of propositions, some philosophers have appealed to an argument that if the object of a judgment is a proposition it is impossible to make a false judgment. I will call the argument ‘the impossibility argument.’ In this subsection I will argue against a simple interpretation that presents the argument as the reason for his abandonment of propositions, before I turn to Ricketts’ one, which combines the argument with the dualist account of predication.

Olson, Cartwright and B. Linsky have argued that Russell abandoned propositions directly because of the impossibility argument.5 _{Cartright summarises the argument as follows:}

We thus appear to have at hand a demonstration that there is no such thing as the proposition that there are no subways in Boston: if there is, then there is such a thing as the nonexistence of subways in Boston; and there is such a thing as the nonexistence of subways in Boston only if there are no subways in Boston; but therearesubways in Boston.

(Cartwright, 1987, p.82) The idea is that if each judgment has a proposition as its object and if the proposition is a complex constituted by the entities about which the judgment is made, then the subsistence of the proposition implies that the entities in question arein factcombined with each other in the way in which the judgment describes them, which in turn makes the judgment true. This is what I call the impossibility argument. It is meant to show that if the dyadic-relation theory of judgment holds, that is, if our judgment is always a binary relation between the judging mind and a proposition, then every judgment would be true, which is preposterous. One cannot avoid the argument by appealing to the distinction betweensubsistandexist, which Moore and Russell indeed had when they advocated the theory of truth as primitive. For the argument is concerned only with the former notion. This is perhaps why Cartwright does not pay much attention to the distinction in stating the impossibility argument as above.

The impossibility argument involves a notion that is arguably foreign to Russell, however. The crucial step in the argument is from the subsistence of the propositionBrown is taller than Smithto the claim that Brown isin facttaller than Smith. According to Cartwright, Russell had to take this step because of his account of the unity of the proposition. Russell inPoMholds that ‘[t]he verb, when used as a verb, embodies the unity of the proposition,’ where ‘verb’ here means the relation which a verb designates (PoM,§54). In the case of the propositionA

differs from B, he explains that ‘[t]he difference which occurs in the proposition actually relates

AandB’ (ibid.). Thus, on his account, each proposition has among its constituents a relation which relates the other constituents to form a single entity. This accountappearsto entail that when the proposition ‘Brown is taller than Smith’ subsists, Brown has the relation ofbeing taller thanto Smith, that is, Brown isin facttaller than Smith. However, it should be observed that Russell does not accept the equivalence expressed by ‘that is’ here: the subsistence of a proposition is in his view not the same thing as Brown’sactually being taller than Smith. As we saw in the preceding subsection, the subsistence of the complex ‘Brown is taller than Smith’ is supposed to be neutral as to whether Brown isactuallytaller than Smith. For, on his account, if the complex possesses the property of being false, Brown is not taller than Smith. The proposition itself is understood as the result of Brown and Jonesbeing connected with—as opposed toactually possessing—the relation ofbeing taller than(in the relevant order). Hence, in his view, the proposition ‘Brown is taller than Smith’ is neutral as to whether it is true or false, waiting for truth or falsehood to attach to it. This account of truth and falsehood is precisely why the regress of predication arises within the ontology of propositions. ‘There is,’ in Russell’s view, ‘no hint at all that insofar as it [a proposition] contains a relating relation, the proposition must be true’ (Landini, 1996, p.323).

An argument presented in ‘Meinong’s Theory of Complexes and Assumptions’ (1904; henceforth, MT) illustrates that Russell indeed thinks that entities in a proposition are only connected with each other in a way that does not automatically render a judgment about the proposition true. In this paper, he uses the notion of ‘particularized relation’ to discuss Meinong’s idea that ‘when a relationRis affirmed to hold betweenaandb, as in (say) “ais the