From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

1. Introduction

The semantics of falsehood and negation represents a problem for realist and descritivist accounts of truth. We can hold here the realism in semantics as a conjugation of two main theses, both largely intuitive and reasonable which are part of our natural vision of descriptive sentence sense and truth. Namely:

• i) we must find in the reality what would make a descriptive proposition true.
• ii) we must be able to identify in the reality the part or portion of it – it does not matter if either a state of affairs, or a fact, or a complex of entitities, etc. – which would make it true.

These two theses, when conjugated, reflect the assumption of a correspondentist paradigm as the basis to the condition and truth value determination of a proposition. To understand a proposition is thus to be able to identify the part of reality that should be actualized in order to make it true. This account represents, in principle, the possibility to identify the truth value of a proposition by comparing it to reality. Their sense should logically come prior in comparison to the truth values. The elegant naturality of realist account of truth is remarkable: in oder to know whether a sentence is true or false, we have “to take a look” at reality. This sort of natural procedure makes such an account more congent as other truth theories which lie on strictly pragmatical or contextual elements.

As the correspondentist account of truth holds, true propositions stand for, substitut, describe, represent or identify actual facts of reality, that is, what is the case. This demand seems not to be problematic in the true–propositions field. Nevertheless, when this descriptive feature is given, which would false propositions identify in the reality? Do they not identify anything? Do they fail in descriptveness? Are they, thus, a sort of bad symbols? Are they no propositions at all? Aber mann kann aus einem falschen Satz Schlüsse ziehen. Their sense is legitimate. They do make sense, although they are not true. Their falsehood does not damage their sense (TLP 4.023). Hence, must also the false propositions describe something when we follow the correspondentist principles? However, if we follow this reasoning, what they should identify? Do they describe negative facts, merely possible and not actual facts? Do they identify the not–being, what is not the case? Comparatively, does the truely negated proposition after the negation begin to identify estipulative negative aspects of reality? When we keep on demanding a uniform treatment of propositions in the descriptiveness mainframe, what would the ontological correlate to linguistic contradictions be like? Would they be contradictionary facts, impossible facts, real or actual absurds? Should we thus demand that reality should also be compound by contradictory facts?

“Only the conjunction of some objective elements can make a sentence true”. This kind of classical realism which demands a metaphysics with independent object is a main feature of the suis generis ontology of Wittgenstein’s Tractatus. The tractarian system pressuposes a net of discrete and eternal objects coumponding reality which defines an exhaustive net of possible combination of complexes (der logische Raum). Question: How does this peculiar realist, but paradigmatic, system heritage and treat this problem with false and truely negated propositions?

2. Development

The philosophy exposed systematically in Wittgenstein’s Tractatus Logico–philosophicus is an attempt to determine the semantic limits of every possible language. This is done by a logical investigation of the propositional symbolism i.e. by an analysis of our capacity for representation using statements or sentences (Sätze) which describes states of affaires (Sachverhalte). As Wittgenstein states just in the beginning of his preface, “this book intends to determine the limits of what can be expressed by our thoughts”. Wittgenstein argues that the essence of language is descriptive. As a result, all other possible use of language should be analyzed in terms of descriptive use done by descriptive sentences. Every proposition is a logical representation from a fact, because the names in an all–analyzed proposition are symbols to the objects which compound the represented fact. The name and the named object must have the same logical form. The possible articulation of names in proposition has to be necessarily suitable to the possible articulation of objects in facts. The syntax of language, i.e. all meaningful linguistic structures, has to match the “syntax” of world. In clear opposition to Frege, the complex logical forms are guaranteed by the names in proposition which have the same possible articulations of objects that constitute the facts in the world. Futhermore there is no possibility of lack of truth value or non–denotative names. All legitimate propositions have a truth value because all names have its own referenced object (TLP 5.4733). Logical forms, to Wittgenstein, are not given by complex propositions as Frege thought but by the existence of objects denoted by the names in a proposition. What sustains this account is the assumption that propositions are Bilder of reality (TLP 4.01–4.016).

To express representation Wittgenstein uses Bild in Tractatus, word that has little technical sense, but a broad semantic scope and application, from simple drawings, portraits and pictures to complex maps or scientific models. It seems clear that the tractarian Bild must be understood preferably as maps or models, given that some exegetic problems should be avoided.

One can hold that an exegetic problem to be avoided by this understanding is the requirement of negative facts in order to allow the sense of false or truely negated propositions. When we understand propositions as maps of reality, we do not need to assume the existence of negative facts coumponding the reality. Here, we have to draw an aparently trivial but important distinction. The propositions in Tractatus should not be held as portraits or pictures, but as maps or models. All portraits are Bilder, but there are Bilder which are not portraits. Following the tractarian account, the propositions are not portraits, they are maps, models. A portrait demands certain iconicity, certain material similiarity or likeness between representation and representated complex. For all intents and purposes, the important step by the tractarian theory of sense is to state that the propositions must have certain logical or structural similiarity to the represented complex, and not material. The propositions have to be able to expose or to show, by means of their structural articulation, the representated complex form, that is, the possibility of articulation shown by the representated complex constituents. The representation constituents and the represented complex constituents can, but do not have to be, materially similar. Moreover, it makes no sense to have portraits from non–existent facts. On contrary, we can have models or maps of complexes which neither exist nor have ever existed. We can not have portraits from future facts, but we can have models or maps of complexes which do not exist, but can exist.

As a result, it would be misleading to understand Bild as portrait in Tractatus, the more direct and secure analogy would be with models, or even maps, that simulate by means of their constituents a reality (possible) part. In fact, when we talk about maps, we only need to understand the “cardinality” of the map, how many and which are its relevant constituent points. We have to be able to understand the reference of these constituents and understand how they are articulated, that is, its configuration (cf TLP 2.1–2.182). Once we have understood the map, we can search a correspondent fact in the world. In this case, we do not search a negative fact, but an obviously positive one, namely: the fact understood through the map, the fact shown by the map. If the fact is not actualized in the world, the map is so to speak “false”. If it is actualized, the map is “true”. Hence, just as understanding a map does not imply that the represented complex indeed exists, to understand a proposition does not imply that the represented complex must exist in the world either.

The map and its constituent points represent differently, just as the proposition and its names. “Namen gleichen Punkten, Sätze Pfeilen, sie haben Sinn” (cf. TLP 3.144). We understand maps and propositions through the determined articulation of their points or names which refer to points and objects of a reality part. We build the map sense through the reference and articulation of its points. We build the proposition sense through the reference and articulation of its names. This feature is especially clear in fictional books which contain sophisticated but “false” maps. Despite this “falsehood” they can be understood and systematically studied. For instance, we can mention the sophisticated maps in Tolkien’s classic Lord of the Rings. We do not have to assume that there is a fantastic place somewhere in reality, neither positive nor negative, in order to understand Tolkien’s maps. We only need to understand their constituents, what they stand for, and how they are articulated. The irrelevance of negative facts is also clear in another analogy to maps. In spite of being a unsound map, we can understand a map which depicts Berlin as the capital city of Brazil. That is because we know what its points (names) stand for and we know furthermore their so to say grammar (ihr “logischer Raum”). For example: Brazil is a country, and countries are compound by cities, and not vice versa. Comparatively, a map that would draw Brazil as the capital of Berlin would be rather hard to understand in this context. In both cases, in order to understand the sense of the map, we do not need to assume that the referent complex exists, whether in a positive or negative sense (for example, neither an actual or unactual fantastic fictional place, nor a positive or negative fact “Berlin Capital Brazil”).

In 4.025 Wittgenstein makes these exigencies to the understanding of a Bild even clearer: “Die Übersetzung einer Sprache in eine andere geht nicht so vor sich, dass man jeden Satz der einen in einen Satz der anderen übersetzt, sondern nur die Satzbestandteile werden übersetzt (…)” dictionaries deal with names, and not with propositions. In order to understand a proposition in an idiom we need to know mainly the constituent names, their reference or sense and how they articulate with other names. In principle, we can even have an inventory of all possible propositions in a language.

The tractarian elementary propositions are the proper ground to the demand of isomorphism which articulates in a 1-1 manner the logical form of objects and their names. In this way, Wittgenstein could avoid ambiguities, synonymies, and ensure the represented complex exhaustion by the representing complex. In order to understand the sense of fully analyzed propositions we would need objects, their names, and their shared possible articulations. Even if all propositions were false, the world should contain objects in state of affaires. The relation possibilities of which should be respected by the names in the false propositions. In a nutshell, in this case we would need a world with objects, not empty, in oder to understand their falsehood. We need objects which are articulated in some fact to be able to project the sense of propositions, even if they were false.

3. Conclusion

Atomic facts are irrelevant for the tractarian theory of sense, if we understand that it compounds two distinct and assimetrical levels: the sense composition by means of a logical projection and the truth value determination by means of a comparison to reality. We need the sense to determinate the truth value, but we do not need the truth value to understand a proposition. In this way, a true proposition p shows a fact x that is actualized in the world. If the proposition p were false, it would show the same fact x, which, in turn, would not be actualized in the world. If the true proposition p were negated, its sense would be inverted, but without showing a new fact, but, in a manner of speaking, it has bet wrongly, that is, that not–p is true, when p is actualized. The fact that we understand from not–p is exactly the same fact that makes p true (cf. TLP 4.0621). That is, to understand a proposition, irrespective of being true or false, it is to understand the same fact, independent of being positive or negative. In order to understand a proposition, just as the understanding of a map, it is mandatory to understand through its articulated constituent points the complex which, when actualized, makes it true. The actualization of this complex in the world (positive fact) or its non–actualization (negative facts) is neither a necessary nor a sufficient condition in order to understand a proposition. Are the negative atomic facts really important to the understanding of the tractarian sense theory? No, if we understand, as Wittgenstein affirms, that propositions are models, or maps of reality. In this way, we have the protection of our best intuitions. “The world is something entirely positive, it is an effectiveness, it is Wirklichkeit”.