Tractatus Logico-Philosophicus by Ludwig Wittgenstein + comments by Maarten Maartensz |

Notation In the following text I use some conventions to refer to Wittgenstein's text or my remarks. These conventions have most to do with Wittgenstein's peculiar format: The Tractatus consists of theses numbered in such a way as to show their logical dependencies. To refer to a thesis in the Tracatus I enclose its number in square brackets, as in "[2.01]". To refer to a thesis in the Tractatus together with the theses Wittgenstein numbered in such as a way to indicate that they are dependent on it, I enclose its number in square brackets followed by two dots, as in "[2.01..]". And to refer to my comments on a thesis or group of dependent theses I enclose the number (possibly followed by two dots) in normal brackets, as in "(2.01)" or "(2.01..)". To set off the theses of Wittgenstein from my comments they are indented. Also, to most of the times I will write "W." instead of Wittgenstein. Introduction The propositions [1..] provide an ontology of facts in analogy with propositional logic. The basic ideas involved seem to be that
The analogy with propositional logic may be made clear by presenting some of the foundations of propositional logic in a The standard way is to leave out ideas and be vague about possible facts, but neither can be easily combined with W.'s remarks in the Tractatus, while in fact the following non-standard way, whatever its ultimate merits, makes perfectly good intuitive sense. It is convenient to have a handy and short notation, and there is an obvious one available: we shall write statements between double quotes; the ideas they express between single quotes; and the possible facts they refer to without quotes. Since all of this in fact is done within language, sometimes clarifying phrases are added. Accordingly, for example, the English statement "it rains" expresses the idea that 'it rains', which happens also to be expressed by the German statement "es regnet", and both refer to the possible fact that it rains. That is, we shall assume semantical assumptions that may be formulated as S1. "p" represents 'p' or nothing (and if nothing "p" is meaningless) which may be read as S1. a statement "p" represents an idea 'p' in which "(real)" merely serves to emphasize that this fact is not just possible but exists (in some sense, depending on some criterion). One may well ask what the use of this non-standard and simple-minded propositional semantics is, especially since it doesn't change anything fundamental about propositional logic. There are three pertinent differences with the standard way. 1. In the standard way each proposition has, it is assumed, a truth-value T or F, somehow mysteriously depending on what the facts are. The assignment of truth-values to propositions without propositional operators in them is not a matter of logic, and anyhow logic needs to consider both possible outcomes. In the non-standard way the reason why a proposition gets a T rather than an F is explicated as: Because the So the first difference is that the non-standard way reduces truth-values to a notation for succeeding or failing to represent a fact rather than construing In the non-standard way the basis of propositional logic is the assumption that propositions represent ideas and ideas represent or fail to represent facts, and truth-values are mere notational devices to indicate whether or not a proposition represents the fact it expresses; in the standard way the basis of propositional logic is the assumption that propositions somehow have truth-values, that are assigned by some extra-logical process. 2. The standard way does The non-standard way explicitly assumes that propositions do The non-standard way, accordingly, presumes an This may seem a trivial difference, but it is a fact that the absence of an assumption that coordinates ideas and statements has caused a lot of muddle in the presentations of propositional logic. Indeed, the term "proposition" is often ambiguously used with the senses of "idea expressed by a statement" and "statement expressing an idea" and even "fact represented by the idea expressed by a statement". Furthermore, on an intuitive level it seems absolutely self-evident that propositions express And finally, the fact that - seen from the point of view of the nonstandard way - meanings and facts are confused has led to other confusions, such as the verificationist theory of meaning, and the confusion of meaning and truth. 3. The standard way cannot give an obvious, clear and direct account of when a proposition is meaningful rather than true. The non-standard way does suggest an obvious, clear and direct account of when a proposition is meaningful, namely that the terms of which a proposition is composed represent ideas which in turn represent or fail to represent possible things, and that a proposition a proposition is meaningful if its terms are understood. |