Language and thought: some metaphysically skeptical reflections

Conceptual frameworks are always provisional

The logical positivists took a very hard anti-metaphysical line. They were right, in my view, to see traditional metaphysics as being futile and pointless. The essential problem with metaphysics is epistemic. How (given a basically scientific view of the world) can purely metaphysical statements be justified? Rudolf Carnap and most of his Vienna Circle colleagues didn’t think they could and consequently saw no place for metaphysics as a serious discipline.

There is no denying that fundamental, foundational and relational questions arise naturally in the course of scientific and other forms of rigorous inquiry. These kinds of questions are not only worthwhile, they are necessary and inescapable, and to call them philosophical or (in certain cases) metaphysical is not out of line with common usage. Problems arise, however, when philosophical or metaphysical thinking becomes detached from empirical reality and begins to feed on itself.

In the 1940s and ’50s, Carnap articulated a nuanced account of ontological claims in the context of mathematical and scientific inquiry. He saw such claims as being either trivially true or false (if considered within the theoretical framework in question) or nonsensical (if not). The former were associated with “internal” questions, the latter with “external” questions. Internal questions are asked with a particular framework in mind. Do numbers exist? Within the framework of arithmetic, (trivially) yes. But do numbers really exist in some absolute sense? The question, arguably, is meaningless.

This approach works for formal disciplines and strictly scientific theoretical concepts but the sciences are not entirely formal. They have their origin in our interactions with, and natural curiosity about, the world. It is a mistake to imagine that we are ever entirely locked into specific and rigid linguistic or theoretical frameworks. Frameworks are fluid and necessarily provisional.

Ordinary thinking is an element of our engagement with the world and is never entirely mechanical or formal. It is not formal because interpretation of one kind or another is always involved, in the sciences and elsewhere. And it is holistic in the sense of not being comprised of discrete levels or completely self-contained modules.

Not only are various parts of the brain interconnected in complex ways, the broader physical (somatic and extra-somatic), social and cultural matrix within which neural processing occurs and upon which it depends is also holistic and massively interconnected. Our thinking cannot be separated from this broader physical and cultural context. This fact has important implications for how we think about thinking.

An ability to conceptualize and deal in a practical way with a wide range of contingencies involves various forms of thinking and meta-thinking. My focus here is on aspects of thinking and meta-thinking which relate respectively to language and number.


Metalinguistic awareness

Alfred Tarski developed the notion of metalanguage, though he was concerned mainly with formal rather than natural languages. Karl Popper explicitly drew on Tarski’s concept of metalanguage to defend a form of the correspondence theory of truth. The linguist Roman Jakobson appealed to the same basic idea when, late in his career, he outlined what he saw as the functions of language. One of these was the metalingual (or metalinguistic) function. It applies when a language is used to talk about itself.

The notion of metalinguistic awareness is often employed in discussing such phenomena as code-switching and language alternation. But metalinguistic awareness also applies to phenomena which occur in strictly monolingual environments. As noted above, languages are routinely used in a reflexive way (i.e. to refer to themselves). What's more, a speaker’s awareness of implied as distinct from literal meaning and the use and understanding of various figures of speech also require a certain level of metalinguistic awareness.

Using and understanding irony requires a relatively high level of metalinguistic awareness. Sarcasm is less subtle than irony but provides a clearer illustration that what is literally being said is not always what is actually being said, the intended sense being (in the case of sarcasm) the converse of the literal sense.


Gödel's incompleteness theorems

The general idea that a broader context always obtrudes applies not just to ordinary life and language use but also to specialized scientific and scholarly work. No significant area of study is self-contained. Not even formal disciplines, such as arithmetic.

Gödel’s work demonstrated the limitations of formal axiomatic systems. He showed that no such system is capable of proving all truths about the arithmetic of natural numbers. He also demonstrated that no formal system which is complex enough to model basic arithmetic can prove its own consistency.

Formal systems then (at least those beyond a certain level of complexity) are not self-contained, not sufficient unto themselves. They are necessarily situated in – and in a real sense are dependent on – a broader context. And any expanded system is dependent on a yet broader context in the same way.

Gödel was a Platonist and saw his incompleteness theorems as vindicating his position on the power of the human mind. The main lesson I take from his work, however, is that productive thinking is necessarily contingent rather than self-contained; that it necessarily engages with a wider world.

What this wider world consists in or of is open to debate. It comprises seemingly very different kinds of things and/or processes: the processes studied by mathematicians; the physical processes studied by physicists and biologists; social and cultural processes; etc..

But on what basis – other than practicality or convenience – do we draw dividing lines between these different kinds of process (and, by extension, between disciplines)?


Mundane concepts

Because of the problems of justifying metaphysical statements I prefer to remain metaphysically agnostic and to avoid making claims about the world which go beyond common sense, common usage and the findings of science and scholarship. Neither ordinary thinking nor rigorous intellectual inquiry requires an explicit metaphysical foundation. Effective thinking, speaking and research do have prerequisites, but such a foundation is not one of them.

Sure, our natural habits of thought involve implicit assumptions and commitments which are often reflected in the grammar of language. This is something to be aware and wary of, however, not something which should form a basis or foundation for serious metaphysical claims or systematizing.

In respect of the existence or non-existence of entities postulated by scientific theories, Carnap’s approach works well because the theories in question are identifiable and distinguishable one from another. If you move beyond particular theories, however, and focus on mundane concepts which we can approach from many directions and in many ways, there is no single language or system or theory to which we can appeal (and so no clear way of distinguishing internal from external questions). Such mundane concepts include concrete things that we might touch or eat or bump into, as well as more abstract notions and social phenomena.

Even something like the concept of number can be approached and conceptualized in very different ways: via formal arithmetic or via psychology and the social sciences, for example.

And what are we to make of birds that keep track of the comings and goings of their potential prey by counting and remembering how many entered or exited the burrow they are spying on? These predators would not be much interested in questions about the concept of number, but their counting abilities derive from a pattern of neural processing which necessarily represents or instantiates the concept in some form. Arguably, some such primitive, pre-linguistic and pre-theoretical notion of number underlies even our most sophisticated mathematical ideas and capacities.



[This is a revised and abridged version of a piece which was published a few weeks ago at The Electric Agora.]

Language and metaphysics

Bertrand Russell and Ludwig Wittgenstein had many profound disagreements. They were, for example, diametrically opposed in their respective attitudes to science and religion. But they were united in one respect at least. They both rejected the metaphysics of idealism. Metaphysically speaking, Russell was concerned mainly to counter idealist notions and to defend a science-friendly and empirical view of the world. And Wittgenstein, like many of his contemporaries, saw no role for metaphysics as a discipline in its own right.

Early in his life Russell had accepted the general framework of Hegelian metaphysics that dominated English philosophy at the time. But he soon came to see problems with this point of view and felt a sense of excitement and liberation when he finally extricated himself from this way of seeing the world. He talks in his intellectual autobiography about his early rejection of the doctrine of internal relations which was a key feature of Anglo-Hegelian idealism.

Very roughly, this doctrine constituted a form of coherentism or holism according to which everything is related to everything else and nothing can be satisfactorily understood except in terms of the totality of these relations (i.e. ultimately in terms of the Absolute). This kind of idealism fell out of favour, but gained renewed intellectual respectability when Willard Van Orman Quine proposed a form of holism which was (ironically) partly inspired by the writings of Pierre Duhem, an historian of science who was not only a deeply religious man but also an orthodox and militant Catholic.

Wittgenstein, by contrast to Russell (and Quine), was not well-read in Western philosophy. He was blissfully ignorant both of classical and medieval thought as well as of German (and English) idealism, and the “metaphysical stance” which he himself came to identify in his Tractatus Logico-Philosophicus derived from its logical absolutism: the attempt to reduce the intelligibility of the world to pure logical objects in logical space. The Tractatus was an attempt to give definitive expression to the scientific project and by so doing to reveal its limits. The particular understanding of language, logic and mathematics which was at the heart of the Tractatus Wittgenstein gradually came to see not so much as false but rather as unnecessarily narrow.

One of the factors which led him to see this was hearing, in 1928, three lectures by L.E.J. Brouwer. Brouwer’s mathematical intuitionism was focused on numbers rather than geometry and on finite constructions rather than on infinite logical space. Wittgenstein had to face the fact that there were various ways of conceptualizing the basis of logic and mathematics, and he started to develop a philosophy of logic and mathematics which tried to explain these practices in terms of the sorts of common agreements which make social life possible. But most of his later work was focused not on mathematics or logic but on ordinary language and the ordinary social conventions which sustain it.

Friedrich Nietzsche had noted that each natural language is, as it were, pregnant with a metaphysics, the metaphysics of one language being different from the metaphysics of another. Metaphysics (as he saw it) was largely a projection of the structure of a particular language on to the world.

This general way of seeing metaphysics as a function of language can be applied not just to natural languages but also to more formal, constructed languages or logical systems such as those which were developed from the late 19th century onward. The crucial point is that metaphysics is seen as a kind of gratuitous by-product of a language and its use – or misuse. As such it is not something that can be studied in itself as the natural or social worlds may be studied.

The Vienna Circle is well-known for taking such a line and Wittgenstein, as a close friend of Moritz Schlick and an early participant in the deliberations of Schlick’s invitation-only group, played a crucial role in the development of the ideas which would come to be known as logical positivism.

Wittgenstein’s view of language developed beyond the position outlined in the Tractatus but there is a lot of continuity in his thinking and the Tractatus itself can be read as a critique of traditional metaphysics. It is this aspect of it which appealed to Schlick and the Vienna Circle. At no time did Wittgenstein write anything resembling traditional metaphysics (or ethics, for that matter).

But Wittgenstein also came to see the standard scientific view of the world as logically flawed and as incorporating metaphysical assumptions. The law of identity (‘A is A’) has a long history as a basic axiom of Western logic and plays an important foundational role in most modern formal systems. But in the Tractatus Wittgenstein was already moving away from this kind of approach, explicitly calling the law of identity into question. “To say of one thing that it is identical with itself is to say nothing at all,” he wrote. (5.5303)

What’s more, as a Christian primitivist in the tradition of Leo Tolstoy, Wittgenstein was not sympathetic to the anti-religious stance of most logical positivists. Probably on account of his religious commitments (which are often downplayed by philosophers), he was also rather less interested in scientific questions or in articulating a scientific view of the world than his erstwhile empiricist colleagues.

Wittgenstein certainly disappointed his old mentor, Bertrand Russell, by moving away from dealing with the sorts of science-and-logic-related questions which Russell himself was concerned with as a philosopher and focusing instead on an informal approach to language and other matters.

Wittgenstein saw language as something that has the potential to lead us astray, and much of his later work is designed to highlight the pitfalls of language (especially as deployed by philosophers). Metaphysical questions can usefully be approached in this way: in terms, that is, of language (whether natural or constructed). And often apparent problems can be dissolved.

Rudolf Carnap was a major 20th-thinker thinker who followed this general approach and sought to downplay the significance of ontological claims, characterizing philosophically-based metaphysical – and, specifically ontological – claims as being either trivial or problematic.

Carnap saw ontology, understood as “the study of what there is”, as being misguided. Questions about the existence of things which are assumed to be in a given linguistic or conceptual framework are trivially true. In his paper, “Empiricism, Semantics and Ontology” (first published in 1950), Carnap writes: “A question like: ‘Are there (really) space-time points?’ is ambiguous. It may be meant as an internal question; then the affirmative answer is, of course, analytic and trivial…” But if the question about existence is seen as general and unrestricted it becomes very problematic.

Thomas Hofweber (writing on Language and ontology in The Stanford Encyclopedia of Philosophy) summarizes Carnap’s view:

"Ontology, the philosophical discipline that tries to answer hard questions about what there really is is based on a mistake. The questions it tries to answer are meaningless questions, and this enterprise should be abandoned. The words ‘Are there numbers?’ thus can be used in two ways: as an internal question, in which case the answer is trivially ‘yes’, but this has nothing to do with metaphysics or ontology, or as an external question, which is the one the philosophers are trying to ask, but which is meaningless."

I am inclined to agree with this general position though I shy away from the word ‘meaningless’. Carnap termed such (external) questions “pseudo-questions”, and characterized the ontological pursuits to which they lead as “useless” and “futile”.

There is no question that metaphysical and logical ideas are related. The logical framework which one chooses has metaphysical implications. For example, if you reject the law of non-contradiction (as Hegel did, for example) this will have implications not just for what you see as valid forms of argument but also for how you see the world more generally.

I want to say something here – by way of clarification – about the various meanings and connotations of the word ‘metaphysics’. Sometimes it is used to refer to an intellectual discipline, sometimes more broadly to refer to a general view of the world. In the latter case, sometimes (but not always) there is a connotation to the effect that the view in question is akin to a religious view.

This can be confusing. For example, in his later writings, Martin Heidegger is often (and quite rightly, I think) seen as moving away from specifically philosophical and metaphysical discourse, at least as traditionally understood in the context of the Western academic tradition. But in another (quite valid) sense what he is doing is very metaphysical. When Graham Priest applies the term ‘metaphysical’ specifically to Heidegger’s later work (as he does around the 13-minute mark in this interview) he is using the term in my latter sense (and with the religious connotations, I think). I want to make it clear that this is not the kind of metaphysics which I am implicitly criticizing here. Nor (as I see it) is it the kind of metaphysics which (in their different ways) Nietzsche, Wittgenstein and Carnap were attacking. (In fact, a good case can be made that that Nietzsche, (the later) Heidegger and (the later) Wittgenstein have a lot in common.)

The sort of metaphysics that Wittgenstein, Carnap et al. were concerned to counter was the traditional scholarly kind which (on their view) is based on pseudo-questions arising from a misreading or misuse of language. They both rejected the view that there is a deep “ontological” sense in which the implicitly projected objects can be said to exist. Various kinds of objects exist, but only in an ordinary sense. And a keen sense of what language is and how it works – such as Nietzsche (as a philologist) certainly had, and as Wittgenstein and many of his philosophical contemporaries also had – helps to make this clearer.

Nouns are useful abstractions. The objects that concrete nouns describe exist individually in a practical or pragmatic sense (this dog, that fork…); or not, in the case of unicorns, etc.. Useful abstractions like nation states or agreements can also be said to exist in a practical and pragmatic sense. They are social realities. But all too often, and especially in the context of philosophical discourse, useful – or not so useful – abstractions are taken to be real in a metaphysical sense, or something real or substantive is seen to lie behind an abstract noun which is merely a convenient tool facilitating concise expression.

One thing which is particularly interesting, as I see it, is the relationship between metaphysics (as a discipline) and religion. Western metaphysics – from Plato to medieval and through to modern times – grew out of what came to be called natural theology and was usually associated with a particular kind of (intellectualized) religion.

But other religious tendencies existed within the Judeo-Christian West which were hostile to metaphysics and which saw metaphysicalized religion as a betrayal of the more direct and intuitive form of religion to which they were committed. Blaise Pascal typified this approach. He rejected the “God of the philosophers” entirely, and embraced the God of Abraham, Isaac and Jacob. Tolstoy and Wittgenstein were decidedly within this fideist tradition.

A commitment to metaphysics is often associated with a commitment to religion. But a hostility to metaphysics can also be driven by religious commitments.


[This is a slightly edited version of an essay first published at The Electric Agora.]