Fact-based and Object-based Correspondence Theo- Theo-riesTheo-ries

Wolfgang K¨unne distinguishes in [K¨03,§1, page 5] between fact-based and object-based correspondence theories of truth, and Marian David follows him in [Dav09]. K¨unne argued in [K¨03,§3,1, pages 93-112] that the earliest correspondence theories such as Aristotelian theories of truth and Kant’s theory of truth were object-based correspondence theories⁹. Such earliest correspondence theories did not suppose that the entities truth-bearers cor-responded with were facts. As to their positive nature, this was more ob-scure, but K¨unne concluded in [K¨03, page 108] that according to such the-ories a mental or verbal predication was true if the predicate fit the object it was predicated of.¹⁰ In the case of a verbal predication the object of the

9I will later in Section 4.2.3 examine in more detail whether this interpretation of Aristotle’s theory of truth is correct.

10How is the word ”object” to be understood in the characterization of object-based correspondence theories? It must not be understood as referring to any specific ontological or semantical category, as in Frege’s distinction between objects and functions or in the distinction between objects and events. Even if Frege’s controversial distinction were correct, functions could still be objects in the sense in which object-based correspondence theories make use of the word. K¨unne may seem to contradict this, when he says that paradigmatic elements of the right field of the correspondence relation thus understood are material objects such as mountains and people and when he distinguishes event-based correspondence theories from object-based correspondence theories. However, telling what

predication was typically the grammatical subject of the sentence. Accord-ing to David this actually involves two relations to an object: (i) a reference relation, holding between the subject term of the predicative judgment and the object the judgment is about (its object); and (ii) a correspondence relation, holding between that object and the predicate of the judgment¹¹. However, there are really two more relations at work, (iii) a reference (or denotation) relation between the linguistic predicate and the property or set it refers to and (iv) a correspondence relation between the linguistic sub-ject of the judgement and the property that its referent is predicated of.

Of course, we could equivalently say that a predication is true if an object fit the predicate it was predicated of. We could then equally well take the correspondence to consist of a relation between the subject term and the de-notation of the object term.¹² The great limitation of this theory, of course,

are the paradigmatic examples of some class does not tell what the limits of this class are, so he need not mean that all objects would have to be material enduring objects like his examples. In fact K¨unne admits in [K¨03, page 100] that such things as Helen’s beauty (a property) and the fading of her beauty (an event or process) count as objects in Aristotle’s theory, and therefore presumably in object-based correspondence theories generally. However, he still says that anything denoted by a singular term is an object;

this seems too restrictive since I see no reason why entities denoted by predicate terms or expressions of other syntactic categories could not be objects as well (especially given that the same entity can be denoted by expressions from different syntactic categories, as I will argue later to be the case). Whatever he thought, it is in any case clear that the objects in question are in the original version of the theory just the objects of the ideas or presentations which a belief or judgement or assumption which is taken to be a truthbearer contains, whether as subjects or predicates. Therefore in the case of a revised sentential version of the object-based correspondence theory such as I argue Tarski’s theory to be they have to be the objects of the terms (whether singular or predicate terms) a sentence or statement contains, i. e. the entities they designate or have as extensions etc. It seems that entities of any ontological category could be objects in this sense, be the subjects of predications or predicated of such subjects or designated. Events and even facts can be taken to be objects in this wide sense if they happen to exist, at least in the case when a sentence speaks explicitly of events and facts (as for example this very sentence does);

what differentiates object-based from fact-based and event-based correspondence theories is that according to the former we do not need facts or events to explain the truth of everytruth-bearer (or even every contingent or atomic truth-bearer). However, not all objects in every sense of the word should be allowed among the objects in question, for instance objects in the Meinongian sense, such as the round square, should not be allowed among the objects in question; therefore it might have been better to speak of entity-based correspondence theories than of object-based correspondence theories.

11Using such modern notation of as I use elsewhere in this work we can say that if

∥α∥g signifies the denotation of an entityα, specifically a linguistic predicate) relative to assignmentgwhereαis an individual variable (of the metalanguage) denoting in this case a predicate variable of the object language, then the correspondence relation would be the dyadic relation (λα)(λβ)(α∈ ∥β|g.

12We could also (to anticipate suggestions I will develop at length later) take the corre-spondence relation itself to be the four-place relation (λα)(λβ)(λγ)(λδ)(α=∥β∥ ∧ ∥γ∥=

is that it presupposed that all sentences were of the subject-predicate form.

It seems to me that Tarski’s theory can be viewed as a modernized version of object-based correspondence theories, even though it cannot be viewed as a fact-based correspondence theory or a modernization of such. Davidson saw this in [Dav69], even though he did not use the phrase ”object-based cor-respondence theory”, yet his basic notion of a corcor-respondence theory without facts was essentially similar. However, later he seems to have thought for some reason that the very notion of a correspondence theory without facts did not make sense. Tarski himself may have been aware (even if dimly) of this and this may have been why he said that the Aristotelian formulation is more precise and clearer than the modern ones. Of course, Tarski is not very precise himself in saying that the difference is that the modern formulations would be less clear; that is clearly not the only difference, since at least the second modern formulation has on any natural interpretation stronger implications than the Aristotelian formulation Tarski quotes (though as I show elsewhere there are other statements made by Aristotle that may have equally strong implications).

Of course, there are significant differences between Tarski’s theory and traditional versions of object-based correspondence theories; Tarski does not think that truth-bearing items (which with him are sentences) would always have subject-predicate structure. Only atomic sentences have a structure like that, and even in their case it is a predicate-arguments structure rather than a subject-predicate structure. However, even in the case of complex sentences it is a relation to objects denoted (whether absolutely or with respect to a sequence or assignment) by the terms of those sentences that determines the truth of the sentence.

K¨unne says in [K¨03, page 5] that what is essential to all correspondence theories of truth, both object-based and fact-based, is that truth is a rela-tional property¹³ and the implied relation is not one in which truth-bearers

δ∧α∈γ).

13In fact this assumption, that truth is a relational property is problematic for me since I want to find a metaontological criterion for ontological claims that would help me to decide the problem of universals, and such a criterion should have to be independent of any substantive solution to the problem of universals. Therefore I cannot assume that truth is a relational property as I cannot assume that it is a property at all since I cannot assume that properties exist, for this might be begging the question against nominalism. Besides, as I will show later, even if we find out in the end that there are some properties, there may be special reasons to think that truth cannot be a property (for instance, because there may be reasons to think that there are no relational properties or because this might lead

stand to other truth-bearers.

This definition of a correspondence theory was anticipated by Bertrand Russell in the third of the requisites he gave in 1912 to a satisfactory theory of truth; this requisite was very similar to K¨unne’s definition of a correspon-dence theory, though it was not exactly the same and is not quite equivalent.

Russell said in [Rus12b, page 189]:

But, as against what we have just said, it is to be observed that the truth or falsehood of a belief always depends upon something which lies outside the belief itself . . . Hence, although truth and falsehood are properties of beliefs, they are properties dependent upon the relations of the beliefs to other things, not upon any internal quality of the beliefs.

Of course, Russell’s definition can be modified as K¨unne does so that the idea that the truthbearers are beliefs (which is an earlier one of Russell’s requisites and is presupposed by Russell here) is removed from it and it becomes neutral with respect to the question of what truth-bearers are, though even so it is not quite equivalent with K¨unne’s definition¹⁴. Also it

to the Liar Paradox). However, K¨unne’s point can be reformulated so that we do not have to assume the existence of properties; e. g. we can say following Devitt in [Dev01b, page 580] that for correspondence theorists the truth term is a one-place relational predicate and add for the sake of clarity that it must be this not only in surface syntax but also in logical form. Devitt himself did not think that this was enough for a correspondence theory of truth, since he thought that a correspondence theory of truth would have to hold truth to have an explanatory role; however, I will argue later that for historical reasons this cannot be part of the definition of a correspondence theory. Devitt also added that correspondence theorists think that the truth-predicate has the standard sort of semantics of such predicates; however, this assumption is problematic, since it is not clear that there is any standard semantics for one-place relational predicates, but it may be that different one-place relational predicates generally have very different semantics.

14Clearly it makes as much sense to speak of entities being external to sentences - at least in the case of token sentences or utterances - as to speak of them being external to beliefs (where again externality must mean externality to token beliefs, belief acts or states of believers, not externality to belief types, whose meaning is less clear). However, in the case of substantially conceived propositions, which are generally supposed to be outside time and space, it is not so clear what externality might mean. We can still make sense of it most plausibly in mereological terms by taking externality to mean the lack of common constituents or more weakly the existence of a non-common proper constituent. However, at least a Russellian proposition cannot in this sense be external to the entities on which its truth depends, since if that entity is a fact then it shares its proper constituents with the proposition and if those entities are the entities which the proposition is about then those entities are the (immediate and therefore proper) constituents of the proposition. This, of course, is as it should be; while Russell did not make clear what he meant by externality, he gave this definition after he had abandoned the idea that Russellian propositions were

is surely an exaggeration to say that the truth of the belief always depends on something external; you can have beliefs about beliefs, and if Othello believed that he is believing something the truth of this (very rare) kind of belief would not depend on anything external. In the sentential case it is surely possible to have sentences like ”This sentence is longer than two words.”; in this case the truth of the sentence depends on the sentence itself. It is better to say more weakly that the implied relation is sometimes or often a relation to something other than a truthbearer, whether a belief or a sentence.

This definition (so modified) appears to go beyond the famous Aris-totelian formulation I quoted before, though it is consistent with it, and leads us towards a slightly (very slightly) more substantive theory of truth.

If the Aristotelian formulation is considered to be consistent with some

de-the bearers of truth and had even begun to doubt de-their existence. In fact even if we do not demand that the entities on which the truth of a truth-bearer depends have to be external to it we still cannot reconcile a theory of propositions which takes them to be Russellian with the view that propositions are truth-bearers and with a fact-based correspondence theory, if we assume mereological extensionality (as is standardly done in mereology), since in this case as the Russellian proposition and the fact share their proper constituents, they must according to mereological extensionality be identical. Now it is not clear whether Russell himself was motivated by this kind of considerations, since he rather appeals to the unintuitiveness of objective falsehoods (which is a far weaker argument since other philosophers have not found objective falsehoods unintuitive at all) and Russell of course did not have any explicit theory of parts and wholes i. e. mereology and since Russellian logic was to a large extent intensional he might not have accepted mereological extensionality even if the option had been presented to him. However, many later philosophers have surely noticed at least dimly this inconsistency and been motivated by it in their theories of truth to reject either facts or Russellian propositions. The common argument that true Russellian propositions cannot be distinguished from facts that would make them true appeals tacitly to mereological extensionalism; the only reason to think that facts and true Russellian propositions would be identical is that they have the same constituents and according to mereological extensionalism entities with the same constituents (or rather an identical partition) will have to be the same. However, many important ontologists have rejected mereological extensionality, for instance because such rejection solves problems associated with material constitution even though it is at the price of a bigger ontology. If we reject mereological extensionality and adopt an intensional mereology, where two different entities can share a partition, then we can even reconcile a Russellian theory of propositions and the view of propositions as truth-bearers with a fact-based correspondence theory; we can then take a true Russellian proposition and the fact that makes it true to have the same constituents (i. e. share a partition) but be different since they are put differently together to form diffferent wholes. Whether such a combination is plausible is a different question (though there are many plausible arguments against mereological extensionality), but at least it is possible, and of course if your conception of propositions is not Russellian (but e. g. Fregean) then you can have a correspondence theory for propositional truth with even less cost. So the options in the theory of truth are very wide indeed (and since truth is not the main topic of this work I must leave them so wide open).

flationist theories which are held to be inconsistent with a correspondence theory (both by themselves and their opponents), then this Russellian def-inition might formulate the minimal genuine correspondence theory. It is indeed rather weak, so some might call it also deflationary; however, it is by no means completely trivial since it has been denied by most deflation-ists. Many of the more extreme deflationists, such as most prosententialists (like Dorothy Grover and Nuel Belnap) have denied not only that truth is a property-ascribing predicate, but even that it would be really a predicate at all. Even more moderate deflationists such as Paul Horwich, though they accept that the truth term is a predicate and even that truth is a property, deny that truth is a complex relational property or even that the truth term would be a relational predicate¹⁵. Therefore this is already a somewhat controversial principle and substantial at least to a minimal degree.

It is important to notice that this definition leaves a lot of leeway for what kind of relation the implied relation may be¹⁶ - and what kind of entities have to be in its range - so it leaves room for a very great variety of different correspondence theories of truth. Russell inexplicably went on to say that this requisite, the third in his theory of truth, leads us to adopt the view - which he says has on the whole been the commonest among philosophers - that truth consists in some form of correspondence between belief and fact. However, if Russell means by ”leads” anything like ”implies logically” or ”entails” and uses the word ”fact” in any technical sense he commits a clear non sequitur here. This requisite as he initially formulated it by no means implies that truth consists in correspondence between belief and fact, only that it consists in some relation between belief andsomething external to it. Russell’s claim is at most true if ”leads” means something like ”suggests” but in this case the suggestion can be resisted and probably should be resisted given Russell’s own commitment to Occam’s razor¹⁷. It

15On the other hand, Russell’s formulation is (like K¨unne’s) clearly inconsistent with the inflationist view of truth that would take it to be sparse property, since it implies that truth is a relational property, and sparse properties are by definition intrinsic, i. e.

such that they (or more rigorously expressed their instantiation) cannot depend on any relations of their possessor to other things.

16It is not or at least need not be dependence - Russell spoke of dependence, but so that according to him the relation is something on which truth depends, the relation itself is not dependence.

17Of course, you could say that Russell does not in this passage use the word ”fact” in any technical sense here. However, Russell later in any case makes use of a very technical notion of fact which is associated with a substantive theory, which says (see [Rus12b, page

is very significant that though Russell’s theory of truth is a paradigmatic fact-based correspondence theory, yet Russell’s initial characterization of the motivation for the correspondence theory of truth does not mention facts or logically imply that correspondence would have to be correspondence to facts. This shows that object-based correspondence theories are a viable option and do not just constitute changing the subject.

In fact, this definition does not even imply that the implied relation could be naturally described as a correspondence relation, even though K¨unne is not willing to go this far; he says that you cannot have a correspondence theory without correspondence, but his own definition of the theory implies

In fact, this definition does not even imply that the implied relation could be naturally described as a correspondence relation, even though K¨unne is not willing to go this far; he says that you cannot have a correspondence theory without correspondence, but his own definition of the theory implies