Two Concepts of Correspondence Defined Notions

Without doubt, 'correspondence' is a key term of the most popular theory of truth, namely the correspondence theory of truth. My aim in this paper is to show that in fact at least the concepts of correspondence are involved in so-called correspondence or classical tradition in truth-theory. I will call those concepts 'strong correspondence' and 'weak correspondence' respectively, following the terminology introduced in Wolenski-Simons 1989. The idea that two concepts of correspondence are in use is by no means new. One can find it in Moritz Schlick's distinction of correspondence as an agreement consisting in picturing and as an agreement consisting in coordination (see Schlick 1918). For Schlick, the concept of truth was almost always defined as an agreement between thought and its object -- or, better, between judgement and what is judged … here is no doubt that this definition expresses a correct conception. But which conception? … the notion of agreement, in so far as it is to mean sameness or similarity, melts away under the rays of analysis, and what is left is unique coordination. It is latter that the relationship of true judgments consists, and all those naive theories according to which our judgements and concepts are able in some fashion to 'picture' reality are completely demolished. No other sense remains for the word 'agreement' than that of unique coordination or correspondence. (Schlick 1918, p. 61)

George Pitcher (see Pitcher 1964) speaks about correspondence-as-correlation and correspondence-as-congruity. A particularly clear description of Pitcher's idea is this:

We come now to … correspondence theories [of truth] of which there are two types: correspondence as correlation and correspondence as congruence. The first of these… says that every truth bearer is correlated to a state of affairs. If the state of affairs to which a given truth bearer is correlated actually obtains, then the truth bearer is true; otherwise is false. What the correspondence-as-correlation theory does not claim is that the truth bearer mirrors, pictures, or is in any sense structurally isomorphic with the state of affairs to which it is correlated. A truth bearer as a whole is correlated to a state of affairs as a whole. On the other hand, correspondence as congruence does claim that there is a structural isomorphism between truth bearers and the facts to which they correspond when the truth bearer is true…. The structure of beliefs (propositions, sentences, or whatever is taken to be the truth bearer) mirrors or pictures the structure of facts much in the way in which a map mirrors or pictures the structure of that part portion of the world of which it is a map. (Kirkham 1992, p. 119).

As the third example of anticipation, let me quote the following fragment:

Consider what one might call 'the correspondence formula': A sentence (proposition, statement, belief) is true just in the case it corresponds to (agrees with, copies, mirrors) the facts (reality). This formula can be interpreted either with or without teeth. Without teeth, it is

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taken idiomatically, as no more than a variation on 'S is true just in case really, in fact, p'. With teeth, the formula is taken to involve a commitment to an ontology of facts, and to an explanation of truth as a structural-isomorphism of truth-bearer to fact. (Haack 1987, 288/289)

Although these quoted fragments are not fully equivalent, we can form the two following sequences capturing various proposals concerning the concept of correspondence (a) correspondence as picturing; correspondence as a congruence; correspondence with teeth, and (b) correspondence as a coordination; correspondence as a correlation; correspondence without teeth. One can think on (a) as a bundle of intuitions approaching the concept of strong correspondence (s-correspondence, for brevity), and (b) as the concept of weak correspondence (w-correspondence). Now, if we agree that both concepts are different to some extent, then the general correspondence formula: a truth-bearer A is true if and only if it corresponds to reality, is simply ambiguous. However, the point goes beyond matters of lexicography. It seems that actual merits of the distinction represented by (a) and (b) are closely related with historico-systematic problems of truth as a philosophical problem. I guess that (a) and (b) represent quite different concepts of correspondence to the effect that truth-theories based on them must be sharply distinguished, even so radically that there is no common concept of correspondence with w-correspondence and s-correspondence as its species. Thus, if we look at the distinction in question seriously, the whole history of the problem of truth is to be reinterpreted in many points, because, for example, problems which must meet strong theories essentially differ form those challenging weak theories.

In particular, it may be shown that although the usual objections to strong truth-theories do not plague weak ones, the latter seem to lose some intuitions traditionally linked with the concept of correspondence. In order to illustrate some questions, let us quote and then consider a sample of statements about the concept of truth from Aristotle to the present day. (This sample contains only statements of those philosophers who are correspondence theorists. I omit various 'correspondence formulas' to be found in works of such authors as Descartes, Spinoza, Leibniz or Kant who do not belong to the correspondence tradition; see Wolenski 1994 for an account of 'correspondence formulas' used by philosophers outside the correspondence camp).

(1) to say of what it is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true. (Aristotle, Metaphysics 1011b; all quotations from Aristotle in this paper are from Ross 1928.)

(2) But since that which is in the sense of being true or is not in the sense of being false, depends on combination and separation, and truth and falsity together depends on the

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allocation of a pair of contradictory judgements; for the true judgment affirms where the subject and predicate really are combined, and denies where they are separated, while the false judgement has the opposite of this allocation. (Aristotle, Metaphysics 1027b)

(3) he who thinks the separated to be separated and the combined to be combined has the truth, while he whose thought is in a state contrary to that of the objects is in error. (Aristotle, Metaphysics 1051b)

(4) Propositions correspond with facts. (Aristotle, Hermeneutics 19a 32-33).

(5) The sentence p is equivalent with 'p is true' if and only if p is the case. (Abelard, Logica Ingrendiendibus, in De Rijk 1956, p. LIV)

(6) Veritas est adequatio intellectus et rei, secundum quod intellectus dicit esse quod est vel non esse quod non est. (Thomas Aquinas, De Veritate I, 2).

(7) Veritas autem enuciationis seu iudicii nihil aliud est quam conformitas ore factae aut iudicii mente peracto cum ipsa enuntiata seu iudicata. (Gassendi, Syntagma philosophiae Epicuri I, 1)

(8) Veritas transcendentalis significat entitatem rei, conno- tondo cognitionem seu conceptum intellectus, cui talis entitas conformatur vel in quo talis res representatur. (Suarez, Disputationes metaphysicae 6, 2, 25)

(9) Truth is the marking down in words the agreement or disagreement of ideas as it is… [Signs]… contain real truth when… are joined, as our ideas agree, and when our ideas are such as we know are capable of having an existence in nature but by knowing that such. (Locke, An Essay Concerning Human Understanding, IV, V, S2).

(10) Those propositions are true which express things as they are; or truth is conformity of those words or signs, by which things are expressed, to the things themselves. (Wollaston, The Religion of Nature Delineated, I).

(11) Veritas est consensus iudicii nostri cum objecto seu re representata. (Wolff, Philosophiae rationalis sive logica, S505)

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(12) I shall mean by a truth in itself any proposition which states something as it is (Bolzano, Wissensschaftslehre S25; Eng. tr. after Bolzano 1972, p. 32)

(13) The truth of a judgement consists in that it ascribes something concrete to an object while this is given as one with this object; or it denies of an object something concrete that is not given as one with this object. In the case of the simplest judgement however, it consists in that affirms that there is something concrete, when there is, or that it is not, when it is not. In this consists the correspondence of a true judgement and concrete things. (Brentano 1930, p. 21; Engl. tr. after Srzednicki 1965, p. 23)

(14) Die Wahrheit unserer Erkenntnis ist die, Uebereinstimmung unserer Urteile mit der Wirklichkeitswelt; da unsere Urteile rückschreitend bis auf Sinneseindrücke zurückführen so ist die Wahrheit unserer Erkenntnis schliesslich auch die Uebereinstimmung unserer Vorstellungen und Sinneindrücke mit der 'Wirklichkeit'. (Mauthner 1902, p. 360).

(15) Ungesucht bietet sich die alte aristotelische Antwort dar, die bis in die gegenwart herein ihr ansehen behauptet hat: das Urteil mit sich, indem es wahr sein will, an der Wirklichkeit übereinstimmen. Die Unhaltbarkeit dieser Definition fällt indessem in die Augen, sobald man ihr nun ihre genaue Fassung, gibt. Nicht von einer Übereinstimmung des Urteils, sondern nur von einer Übereinstimmung des Urteilsgegenstandes mit der Wirklichkeit kann die Rede sein. In der Tat is dies der genuine Sinn der aristotelischen Wahrheitstheorie. (Maier 1926, p. 223).

(16) Materiale [Wahrheit] ist, ganz allgemein, 'Übereinstimmung' (Konformität) des Denkens mit den Sein. Es gibt aber zwei Arten der Materialen [Wahrheiten]: a) Empirischimmanente…. Hier bedeutet die 'Übereinstimmung' von Denken und Sein… nicht die Abbildung u. dgl. des Sienden im und durch das Denken, sondern Übereinstimmung des Einzelurteils mit der methodisch gesetzen Reälität, die in einem System von Wahrnemungs- und Urteilsnotwendigkeiten sich darstellt… b) Metaphysische [Wahrheit] ist die Übereinstimmung des Denkens mit der absoluten Wirklichkeit… Auch hier kann von einen 'Abbilden' keine Rede sein, sondern die 'Übereinstimung' bedeutet hier ein mehr oder weniger treffendes 'Nachkonstruieren' der transzendenten Wirklichkeits-Verhaltnisse inimmanenten, beggrifflichen Symbolen. (Eisler 1930, pp. 450/451).

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(17) Every judgement is a relation of mind to several objects, one of which is a relation; the judgement is true if the relation which is one of the objects relates the other objects, otherwise it is false. (Russell 1910, p. 156).

(18) The belief is true when the objects are related as the belief asserts that they are. Thus the belief is true when there is a certain complex which must be definable function of the belief, and which we shall call the corresponding complex, or the corresponding fact. (Russell 1984, p. 144).

(19) A judgment that uniquely designates a set of facts is called true. (Schlick 1918, p. 61)

(20) A proposition is a picture of reality…. A proposition is a model of reality…. A proposition shows how things stand if it is true…. Reality is compared with proposition. Propositions can be true or false only by being pictures of reality. (Wittgenstein 1922, 4.011, 4.022, 4.05, 4.06)

(21) An affirmative judgement is true if its object exists, and a negative judgement is true if its object does not exist. An affirmative judgement is true if its object does not exist, and a negative judgement is false, if its object exists. (Twardowski 1974, p. 203)

(22) [The] propositional function p is true is simply the same as p. (Ramsey 1931, p. 143)

(23) We should like our definition to do justice to the intuitions which adhere to the classical Aristotelian conception of truth [see (1) above: J.W.] If we wish to adapt ourselves to modern philosophical terminology, we could perhaps express this conception by means of the familiar formula:

The truth of a sentence consists in its agreement with (or correspondence to) reality.

(For a theory of truth which is to be based upon the latter formulation the term 'correspondence theory' has been suggested.) … we could possibly use for the same purpose the following phrase:

A sentence is true if it designates an existing state of affairs.

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However, all these formulations can lead to various misunderstandings, for none of them is sufficiently precise and clear (though this applies much less to the original Aristotelian formulation than to either of the others; at any rate, none of them can be considered a satisfactory definition of truth. It is up to us to look for a more precise expression of our intuitions….

Thus, if the definition of truth is to conform to our conception, it must imply the following equivalence: The sentence 'snow is white' is true, if and only if snow is white (Tarski 1944, pp. 342/343)….

we arrive at a definition of truth and falsehood simply by saying a sentence is true if it is satisfied by all objects, and false otherwise. (Tarski 1944, p. 353)

(24) Reverting to the analysis of truth, we find that in all sentences of the form ' is true', the phrase 'is true' is logically superfluous. When, for example, one says that the proposition 'Queen Anne is dead' is true, all that one is saying is that Queen Anne is dead. Thus, to say that a proposition is true is just to assert it, and to say that it is false is just to assert its contradictory. And this indicates that the terms 'true' and 'false' connote nothing, but function in the sentence simply as marks of assertion and denial. (Ayer 1946, pp. 117/118)

(25) An atomic sentence… consisting of a predicate followed by an individual constant is true if and only if the individual to which the individual constant refers possesses the property to which the predicate refers. (Carnap 1947, p. 5)

(26) A proposition A is true if and only if a state of affairs determined by its content holds in the domain of being in which is located by A, provided that this state of affairs holds independently of the existence of A (Ingarden 1966, p. 396).

(27) I accept the common sense theory (defended and refined by Alfred Tarski ) that truth is correspondence with facts (or with reality); or, more precisely, that a theory is true if and only if it corresponds to the facts (Popper 1972, p. 44).

(28) A sentence is true provided only (i) it expresses a certain state of affairs and (ii) that state of affairs obtains. (Chisholm 1977, p. 89)

(29) A … proposition is true if and only if the state of affairs (Sachverhalt) described by it exists (Borkowski 1985, p. 33)

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(30) The combination 'it is a fact that' is vacuous…. 'It is a fact that snow is white' reduces to 'Snow is white'. Our account of the truth of 'Snow is white' in terms of facts has now come down to this: 'Snow is white' if and only if snow is white…. Here, as Tarski has urged, is the significant residue of the correspondence theory of truth. To attribute truth to the sentence is to attribute whiteness to the snow. Attribution of truth to 'Snow is white' just cancels the quotation marks and says that snow is white. Truth is disquotation. (Quine 1987, p. 213).

Let me add at this point that the terminology employed by correspondence theoreticians developed gradually. Aristotle had no special words suggesting that a correspondence relation is the base for the concept of truth. The fragment (6) runs in Greek as follows: hoi logoi aletheis hosper [kai] ta pragmata, and it literally means: sentences are true if they are such as things. Thus, the translation is obviously influenced by the later development of the correspondence theory. The first technical terms referring to the concept of correspondence appeared in philosophical Latin of the Middle Age, partly as translations of Arabic terms. Except adequatio, Schoolmen used convenientia, aequalitas, and conformitas. The French conformité and correspondence were invented not later than in Descartes's era; he used conformité, but Leibniz used correspondence. German Übereinstimmung occurs in works of Reimarus, Tetens and Kant. It was Samuel Coleridge who introduced (in 1809) the term 'correspondence' into philosophical English as referring to what he called 'verbal truth' (see O'Connor 1975, p. 7). The label 'the correspondence theory of truth' appeared nearly hundred years later in Baldwin 1902 (see the entry on truth). Harold Joachim speaks about 'the correspondence-notion of truth':

In most of the everyday judgements of common sense, and in many philosophical theories, a certain conception of truth is implied or expressed, which I shall call the 'correspondence-notion' of truth. Thus e.g. to 'speak the truth' is to speak 'with accordance with' or 'in conformity to the facts'. (Joachim 1906, p. 7)

Russell popularized the idea of correspondence theory of truth in his writings published around 1910. He was particularly important in this respect because of his famous conditions for any correct theory of truth (see Russell 1910):

(a) the theory of truth must also explain the nature of falsehood;

(b) truth is a property of beliefs;

(c) truth consists in a relation of beliefs to something existing outside them.

(c) states the leading idea of the correspondence theory. The label 'the correspondence theory of truth' is often replaced by 'the classical theory of truth'. This latter name is particularly popular in Poland and perhaps even it was invented there.

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If we want to interpret (1)-(30) in terms of the strong/weak correspondence distinction, the meaning of some items included in this list is clear. The items (5), (12), (22)-(24), and (30) are certainly based on the concept of weak correspondence. On the other hand, (14)-(18) and (22) assume the strong concept. Other cases can be (and actually, some of them are) controversial. Take (1) for example. Tarski regards his semantic truth-definition as a modern version of (1) taken as Aristotle's principal definition of truth. Tarski understands (1) as built upon the weak concept, of course, under the plausible proviso that he himself employed this concept of correspondence in (23). On the other hand, radically different interpretations of what Aristotle says on truth have also appeared. Although (15) is an example here, a more recent case would be more interesting. Garth Hallett locates Aristotle inside the isomorphism tradition. Halett says that for Aristotle

A judgement is true … if the one who makes the judgement is related to things in a way which corresponds to them. (Hallett 1988, p. 8).

Hallett quotes then (2) as the textual basis for this reading of Aristotle. Now, we encounter a question: are (1) and (2) (or (3)) equivalent or do they say different things? I think that we are not able to answer the question without further analysis. It seems that Aristotle is simply ambiguous in many of his fragments on truth, at least at those places which involve the concept of correspondence. The interpretation of Aristotle in this respect depends of how one understands such words as 'is', 'separated' or 'combined' in (1)-(3) and of how the words are mutually related. If 'combined' means that a predicate P and an individual constant a are combined in the sentence P(a) if and only if a is P (i.e. the object designated by 'a' possesses the property to which 'P' refers) this truth-definition for P(a) by combination in this meaning is very closely related to what Tarski's definition states for elementary truth-bearers. However, if the combination of P and a in P(a) is conceived as a structural (or other) picture of an ontological bond holding between objects and their properties, the concept of strong correspondence comes to mind. Thus, each of (1)-(3) can be interpreted in a double way, depending on understanding of those words which express the concept of correspondence. In order to simplify the situation, let me assume that (1) employs the weak concept of correspondence, but (2) and (3) the strong one. Now, (4) isolated from other Aristotelian passages on truth does not say very much, because 'propositions correspond with facts' refers to the weak correspondence if it is joined with (1), but to the strong correspondence if occurs together with (2) or (3).

This ambiguity can be found in many post-Aristotelian definitions of truth, particularly: (6) (adequatio), (7) (conformitas), (8) (conformatur, representatur), (9) (agreement), (10) (conformity), (11) (consensus, representatur), (19) (uniquely designated), (26) (determined by

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the content), (27) (correspondence), (28) expresses), and (29) (describes). Perhaps (5) is the most interesting example. The part which begins with the word secundum, is simply a repetition of (1), but the preceding sentence, namely veritas est adequatio intellectus et rei is an addition to Aristotle, perhaps even related to (2) or (3). Traditionally, (5) is quoted in its simplified version limited just to veritas est adequatio intellectus et rei and this formula is the most popular statement of the correspondence (classical) truth-definition. However, we do not know whether adequatio in (5) refers to strong or weak correspondence.

There is still another problem in the interpretation of Aristotle. It was Brentano who proposed the existential understanding of (1) as faithful to Aristotle's intentions. Except (13), the items (21), (28) and (29) represent this line of thinking. In fact, we have two existential interpretations, because some authors (Brentano, Twardowski) see entities denoted by nouns as genuine objects of truth-bearers, while other proponents of such a reading (Chisholm, Borkowski) say that states of affairs are objects in question. Disregarding this difference here, we encounter a very important question whether the existential interpretation does involve the strong or weak concept of correspondence, provided that we limit ourselves to the statement 'A is true if and only if the object of A exists' without assuming that there is any mapping relation between A and its object. Since Aristotle's definition of truth under its existential reading and the semantic truth-definition are equivalent (see Borkowski 1991, Borkowski 1993, Bilat 1994), we can consider the former as a variant of the latter; note, however, that Bilat (see Bilat 1994) considers the existential interpretation as a variety of the strong concept of correspondence.

I hope that my foregoing remarks sufficiently illustrate that, historically speaking, the correspondence theory of truth is not so simple as it is usually assumed. Let me now consider more closely the two concepts of correspondence taking into account paradigmatic cases. Russell's approach (see (17), (18)) is commonly considered as a typical example of the strong correspondence theory. For Russell, a belief is a relation between subject and object terms. Imagine that a subject X believes that Martin Heidegger was a member of an anti-Nazi resistance movement. Denote this belief by B. How should we describe the situation in which B would be true? (I follow here Kirkham 1992, pp. 120-122; the example is mine). B is simply a relation which holds between four-terms, namely X, Heidegger, an anti-Nazi resistance movement, and being a member. Now, the fact related to B in the case is a three-term relation with Heidegger, anti-Nazi resistance movement and being a member as its terms. X's belief B would be true if and only if the things in question do stand in the relation expressed by the belief.

However, Russell's theory raises serious doubts, because it is based on a non-standard idea of truth-bearers. In order to apply it to accounts in which truth-bearers are semantic entities, for example sentences or propositions, the correspondence relation must be defined on facts and their

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representations (pictures, maps, etc.). Thus, in the case in which the truth-bearer 'Heidegger is a member of an anti-Nazi resistance movement' is true, the truth-bearer is related by a relation (call it 'RP') to a fact. Now, any further analysis of strong correspondence defined for semantic items essentially depends on properties of RP. For example, one must decide whether RP fulfills the principle of compositionality: whether the representation carried by a truth-bearer as the whole is a function of representations of its particular constituents. Another question consists in describing the nature of representation: is it a structural similarity or is it picturing?

As I have indicated earlier, Tarski's semantic theory of truth is based on the concept of weak correspondence. However, it is not quite clear which element of this theory was for Tarski himself a mark of its link with the correspondence tradition. It seems that Tarski looked at the (T)-scheme:

(T) X is true if and only if A

as an 'Aristotelian' component of his theory, but, at the same time, regarded the definition itself

(D) A sentence is true if and only if it is satisfied by all sequences of objects

as a purely formal and perhaps even artificial construction which enabled him to define truth via satisfaction. Since there is not sufficient evidence to reconstruct Tarski's own attitude toward the correspondence relation, I would like to propose an account which assumes that the concept of satisfaction is fundamental not only for defining truth, but also correspondence.

Take an open formula 'x is a prime number'. We can say that 2 is a prime number is what this formula corresponds to, but it does not correspond to that 4 is a prime number. Generally speaking,

(C) An open atomic formula Px corresponds with that, that a is P if and only if an object a satisfies the formula Px.

Using (D), we easily formulate the definition for sentences:

(CS) A sentence corresponds with what it speaks about if and only if the sentence is satisfied by all sequences of objects.

The above explanations quite intentionally avoid such phrases as 'corresponds with (to) facts, states of affairs, situations, reality, etc.', but if one wants to insert them, one can do it without any difficulty. However, such changes do not add any new content to (C) or (CS).

Let us now check how (C) and (CS) are related to definitions of weak correspondence as coordination, correlation and the correspondence without teeth. For Schlick, the correspondence

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should be defined as unique coordination. Although the sense of "unique" is unfortunately not quite definite in Schlick's explanations, the idea of coordination of truth-bearers and something else (for example, objects) finds its good dressing in the concept of satisfaction. Pitcher defines correspondence as correlation via saying that states of affairs correlated with truth-bearers obtain. Now, using the equivalence of semantic and existential reading of the definition of truth, we can say that satisfaction of a formula means that something what is correlated with this formula obtains. Haack's definition of the correspondence without teeth can also be explained via satisfaction. Thus, (C) and (CS) preserve basic old intuitions connected with the concept of weak correspondence. Since (C) and (CS) define weak correspondence in a semantic manner, we can speak about semantic correspondence as a new explicans for w-correspondence.

Interpreting the concept of truth through s-correspondence is certainly rooted in an important intuition: if truth-bearers are true, they are in virtue of definite portions of reality, but not reality as the whole. For example, a truth-bearer 'a meeting on facts and properties occurred in Prague in September 1993' is true in virtue of the fact involving Prague, the conference on facts and properties, the relation 'in', and September of 1993. On the other hand, the fact that the Frege conference held in Jena in October 1993 is not relevant to the truth of 'a meeting on facts and properties occurred in Prague in September 1993'. Thus, the definition of truth requires a special relation between truth-bearers and the corresponding portions of reality.

Unfortunately, this approach must address several difficulties. Some of them were traditionally noted. I mean here the nature of RP, the problem of universal and negative facts, ad the problem of the Great Fact. Since I have nothing new to say in this context about the nature of representation, negative and universal facts, I will do not enter these difficult questions. On the other hand, the problem of the Great Fact still deserves some attention. This problem was stated by Bradley and Frege. The objection is that if a truth-bearer A corresponds to a fact F, it also remains in correspondence to the whole reality which is the Great Fact. I think that this objection is correct. Assume that I consider a truth-bearer 'I am now in Villa Lana'. It corresponds to the fact that I am presently in Villa Lana. But this truth-bearer also corresponds to several other facts, among others that I am now in Prague, in Czech Republic, in Europe, etc. Thus, if A corresponds to the fact F, it also corresponds to any 'bigger' fact assuming that we consider 'bigger' facts having other facts as their constituents. This last proviso is necessary for the following reason. Consider the fact: I am now in Prague or in Warsaw, provided that I am now in Warsaw. Of course, it is a 'bigger' fact than the fact that I am now in Warsaw. However, this disjunctive fact does not make true the truth-bearer 'I am now in Villa Lana in Prague'. Thus, 'bigger' facts are not always truth-makers for constituents of truth-bearers. Clearly, the objection of the Great Fact assumes that 'bigger' facts are truth-makers for their constituents.

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Some authors (see Pendlebury 1986) propose elementary truth-makers as proper truth-makers. However, it not quite clear how to define minimal truth-makers. In order to give such a definition, a satisfactory algebra of facts must be constructed. But which one: set-theoretical or mereological? What is a minimal truth- maker: a mereological part of 'bigger' fact or a member of such fact considered as a set? How to check which fact is the minimal? Consider once more my location in Villa Lana. However, I am in a definite room in Villa Lana. What is the minimal fact which is involved here: my being in Villa Lana or my being in a definite room in Villa Lana? Of course, we can continue this game, because it is not easy to draw boundaries between 'smaller' and 'bigger' facts. I guess that the concept of s-correspondence without a clear algebra of facts as its foundation is very vague. There are also other troubles. At first sight, we perhaps could assume: well, let us take us only elementary facts as truth--makers. This does not work. One elementary fact is: I am now in Villa Lana, but another is: I am now in room 10 of Villa Lana. Still we need the minimal elementary fact. To avoid the Great Fact objection one must assume that elementary facts are independent, because on the contrary one could argue: perhaps obtaining of a particular truth-maker is dependent on its connections with other parts of reality, and in consequence on the whole reality as the ultimate truth-maker. Thus the strong correspondence theory must solve the challenge of monism.

The concept of semantic correspondence avoids these problems. In particular, sequences of objects are by no means counterparts of facts or truth-makers. In order to see the point let me note that if A is satisfied by some sequence it is also satisfied by any other sequence. This does not hold for facts as truth-makers, since if A is made true by F, it is not true that A is made true by any other G which is different from F. Consider truth-bearers A and not-A. It follows from the definition of satisfaction that a sequence s satisfies 'A or not-A' if and only if s satisfies A or s satisfies not-A. Moreover, we can prove that for any s, s satisfies 'A or not-A'. But the same does not hold for facts as truth-makers. Assume, by analogy, that F is a truth-maker of 'A or B' if and only if F is a truth-maker of A or F is a truth- maker of B. The fact that Warsaw is the capital of Poland is no truth-maker either of 'I am in Villa Lana' nor of 'I am not in Villa Lana'. However, one probably want to have tautologies made true by arbitrary facts. This observation does not put the blame on the logic of truth-makers, but it only shows that it is different from the logic of sequences used in the semantic definition of truth. This difference is fairly important, because although we have (in the logic of the semantic theory) that if a sequence s satisfies a sentence A, then it also satisfies any other true sentence. Thus, if a sequence s satisfies the sentence 'I am now in Villa Lana', it also satisfies the sentence 'Warsaw is the capital of Poland'. However, this does not give reason for the objection of the Great Fact, just because sequences are not facts. However, we must made a decision about what is the logic of truth: logic of sequences or logic of facts (truth-makers). I vote for the former.

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The logic of truth-makers is rather a logic of truth-criteria, because in order to check that a truth-bearer is true or false, one must find 'a portion of the world' which enables us to solve this problem. Thus, I am inclined to regard facts rather as verifiers or falsifiers of truth-bearers, and not as their truth-makers. This means that the definition of truth should be based on weak (semantic) correspondence, but the theory of truth- criteria is based on the strong concept. If we accept this standpoint, the idea that truth of a truth-bearer consists in its correspondence with the definite fragment of reality must be abandoned.

REFERENCES

Ayer, A. J. 1946 Language, Truth and Logic, Gollancz, London

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