Wittgenstein

The Architecture of Meaning:
Wittgenstein’s Tractatus and formal semantics
Martin Stokhof
To appear in:
David Levy and Eduardo Zamuner (eds), Wittgenstein’s Enduring Arguments,
Routledge, London
1 Introduction
With a few notable exceptions formal semantics, as it originated from the seminal work
of Richard Montague, Donald Davidson, Max Cresswell, David Lewis and others, in the
late sixties and early seventies of the previous century, does not consider Wittgenstein
as one of its ancestors. That honour is bestowed on Frege, Tarski, Carnap. And so it has
been in later developments. Most introductions to the subject will refer to Frege and
Tarski (Carnap less frequently) —in addition to the pioneers just mentioned, of course—
, and discuss the main elements of their work that helped shape formal semantics in some
detail. But Wittgenstein is conspicuously absent whenever the history of the subject is
mentioned (usually briefly, if at all).
Of course, if one thinks of Wittgenstein’s later work, this is obvious: nothing, it
seems, could be more antithetic to what formal semantics aims for and to how it pursues
those aims than the views on meaning and language that Wittgenstein expounds in,
e.g., Philosophical Investigations, with its insistence on particularity and diversity, and its
rejection of explanation and formal modelling. But what about his earlier work, the
Tractatus (henceforth TLP)? At first sight, that seems much more congenial, as it develops
a conception of language and meaning that is both general and uniform, explanatory
and formal. In view of that, the general lack of reference to TLP is curious.
The central claim of the present paper is that, actually, this is an oversight. Perhaps
Wittgenstein was no conscious influence on the minds of Montague c.s. at the time,
but he did play a major role in establishing the fundamental principles and philosophical
assumptions that helped shape formal semantics and make it such a successful enterprise,
in linguistics and in philosophy. The actual channels through which this transmission
of concepts and ideas has taken place is not what we will be focusing on here. That is
another story, and a complicated one, which requires more historical knowledge and
skills than we can muster. Rather, we will be content with discussing some systematic
 ILLC / Department of Philosophy, Universiteit van Amsterdam. I would like to thank Michiel van
Lambalgen and the editors of this volume for their helpful comments.
1
analogies (and differences, for there are those as well, of course) between Wittgenstein’s
conception of language and meaning in TLP, and the one that was prevalent in formal
semantics at its inception and that continues to exert a major influence in the field until
the present day.
The reasons for being interested in these connections are twofold. First of all, it
appears that formal semanticists do not always appreciate what philosophical assumptions
are behind their enterprise. This is deplorable since an awareness of that part of its
legacy could help formal semantics answer questions regarding its proper status as a
scientific discipline. The diversity that is characteristic of the state in which formal
semantics finds itself today, raises the question how this came about, and how it can be
justified. And part of the answer may well have to do with diverging ways of dealing
with the problems caused by these philosophical assumptions. The second reason why
tracing some systematic connections between Wittgenstein’s early work and the origins
of formal semantics is of interest stays ‘closer to home’, i.e., closer to Wittgenstein. At
many points in his later works Wittgenstein formulated penetrating criticisms of his
earlier ideas. In as much as formal semantics incorporates some of the latter the former
might apply to it as well. These are related but distinct considerations, that each in their
own way put formal semantics to the test: Is it really an empirical discipline? Or does it
remain rooted in its philosophical ancestry?
The approach taken in what follows is by and large systematic. In section 2 we
will review the main characteristics of TLP’s ‘architecture of meaning’ —what meaning
is, how it is structured, how its relates to language and to the world—, isolating three
aspects that are particularly relevant for a comparison with formal semantics. Section 3
contains brief sketch of the way in which some ideas from TLP were transmitted through
the work of Rudolf Carnap. Then, in section 4 we turn to a detailed analysis of the conceptions
that are prominent in the work of the pioneers of formal semantics. The focus
will be on the work of Richard Montague and Donald Davidson, but where relevant
we also refer to the writings of other authors such as David Lewis and Max Cresswell.
After this exposition we turn to an exploration of resemblances and differences between
TLP and formal semantics in section 5. Finally, in section 6, we will address the two
issues identified above: the consequences for the nature of formal semantics as a scientific
discipline, and the potential relevance of Wittgenstein’s own criticisms on the
TLP-framework for formal semantics.