What is this pre-understanding? One would not readily associate Ludwig Wittgenstein's Tractatus with the epistemological position of hermeneutics. But if one starts from the assumption that the Tractatus holds a linguistic-pragmatic and constructivist view of knowledge and reality (Niedermair 1987), then one can find in its subtle reflections on the logic of the proposition explanations of what understanding and pre-understanding could be, why an AI system cannot understand, and why human intelligence and so-called artificial intelligence are to be distinguished in principle. In this connection I draw in what follows on the essay Sprachspiel, Sprachsystem, Sprachideal (Niedermair 1990). On the occasion of the present Festschrift it may be noted that this article from 1990 is connected with Theo Hug in several respects. It appeared in the volume "Die soziale Wirklichkeit der Theorie" (Hug 1990) edited by Theo, to my knowledge his first book. And, what is more important, it arose in conversations and discussion with Theo during our first time together in the academic world. In 1986 Theo and I worked for a few months at the Department of Philosophy of the University of Innsbruck within the framework of the so-called Akademikertraining, a measure of the Austrian Public Employment Service for university graduates who, as far as their work was concerned, had not yet arrived where they wanted to be – for both of us that was the university. Our workload at the department was divided in two: half the day library, half the day research. We carried out a stock revision of the departmental library, stuck labels with call numbers on the books and, under the supervision of a librarian on site, corrected the cards in the catalogue. In the second half of the day we devoted ourselves to scholarship, sat opposite each other in the library and worked with current literature and with our own texts and projects. This went on for half a year; then the course was set anew: half-day library and half-day scholarship became full-time scholarship for Theo, full-time library for me. Theo has remained faithful to the library mutatis mutandis; I refer, for example, to the Ernst von Glasersfeld Archive (Hug et al. 2013) and to his reflections on the visualization of knowledge structures (Hug 2018). My interest in scholarship was lasting too, and I am – this is to be the motto of my contribution to this Festschrift – indebted to Theo: he contributed to my being able, since then, to make my way in scholarship, not at a gallop like him, but at least at a walk. Theo offered me opportunities to be active in research and teaching alongside my library job, he invited me to collaborate on publication projects, and over the years we have been able to cultivate our scholarly conversation.

With regard to understanding and pre-understanding, the position of Wittgenstein's Tractatus can be reduced to a simple formula (Niedermair 1990): one understands the sense of a proposition if one has a pre-understanding of the meanings of its constituents (its names). In detail:

"Only the proposition has sense; only in the context of a proposition has a name meaning." (Tractatus, TLP 3.3)

A proposition can be true or false, but the possibility of its truth (its sense) is grounded a priori by the meaning of its names. The meaning of a name cannot be true or false but must be presupposed so that a proposition can be true or false, i.e. significant. The proposition has sense; names have meaning – they mean possibilities of sense, and these are the condition for the proposition's having sense and for its being understood. These possibilities of sense are the pre-understanding.

The possibilities of sense, for their part, are available only in their application in propositions, for "only in the context of a proposition has a name meaning" (TLP 3.3).

"The meanings of primitive signs can be explained by elucidations. Elucidations are propositions which contain the primitive signs. They can, therefore, only be understood when the meanings of these signs are already known." (TLP 3.263)

Here too, then, the hermeneutic circle comes into play, and with it the self-reference of language: recognizing, meaning, understanding, communicating – linguistic competence, communicative competence – are possible only on the basis of this circle between sense and possibility of sense (meaning). Depending on the direction, this circle can be called formalization or de-formalization (Niedermair 1987, 1990).

Formalization: in order to be able to understand a proposition, it is analysed with regard to possibilities of sense – formulated in terms of logic: its constituents are replaced by variables.

"If we change a constituent part of a proposition into a variable, there is a class of propositions which are all the values of the resulting variable proposition. This class in general still depends on what, by arbitrary agreement, we mean by parts of that proposition…" (TLP 3.315)

One thus arrives at names, whose meaning is a "common characteristic mark of a class of propositions" (TLP 3.311); these are propositional variables, possibilities of sense. The next step of formalization:

"…But if we change all those signs, whose meaning was arbitrarily determined, into variables, there is always still such a class. But this is now no longer dependent on any agreement; it depends only on the nature of the proposition. It corresponds to a logical form, to a logical prototype." (TLP 3.315)

The meaning of a logical form or of a name is the presupposition for its proposition's having sense, being able to be true or false; the meaning itself is valid a priori – that of a name provided there is an agreement.

De-formalization is the opposite movement from the possibilities of sense of the propositional constituents (the variables, the logical forms) to sense, to the application of these possibilities of sense. The proposition "The house is red", for example, is the de-formalization of the possibilities of sense "The house is colour-determinable", "The house is determinable", "x is colour-determinable", "x is determinable", "x is red" and so on. This is a very simple example; the actual set of rules of language is more complex, but the aim was to illustrate the principle of how significant propositions are possible and are understood. In short: the proposition has sense; it is the de-formalization of possibilities of sense. A propositional constituent has a meaning, which is a possibility of sense, a formalization of the sense of a proposition.