Wittgenstein and Russell on metaphysics, language and science

In his youth, Wittgenstein worked with Bertrand Russell and then subsequently had dealings with the Vienna Circle before taking a rather different direction from the late 1920s on. But the main elements of his thinking remained the same: his distrust of metaphysics, for example. He even came to fault his earlier work (which was heavily influenced by Russell) as being too metaphysical.

A piece I wrote on these themes for The Electric Agora (and subsequently republished here in a slightly revised form) triggered some discussion about the extent to which Russell’s outlook was truly scientific. It was suggested that Russell, driven by unwarranted metaphysical assumptions, got things fundamentally wrong about language and logic. By contrast, the later Wittgenstein and the Oxford school of “ordinary language” philosophy which developed in the 1950’s got things fundamentally right.

In the course of the discussion, I made the point that Russell was committed to a view of the world based on evidence and reason and was an energetic advocate for science and for a scientifically-oriented philosophy. This claim prompted the suggestion that, while Russell’s attitude to science was indeed positive, he made a fetish of science.

There is something in the fetishization idea. As an adolescent Russell had found comfort in the certainties of mathematics. And it takes a particular kind of mentality to be so concerned about the foundations of mathematics as to devote many years to attempting to elaborate a sound logical basis for the discipline.

This story, however, can be told many ways. And it is not just a story about one man’s obsessions. It was a remarkable time in European intellectual circles, and arguably what made it so remarkable was the way that scientific advances in a range of areas – especially historical linguistics, textual criticism, natural history, mathematics and physics – mattered for the general culture. There was a sense that the world had changed irrevocably since the Enlightenment; that it was no longer business as usual. Too many established truths had been shown not to be truths at all. Given this intellectual upheaval, it is no wonder that the new world sensed or foreseen by many 19th-century thinkers and artists was a disturbing and disorientating one.

Despite their various metaphysical commitments or assumptions, I don’t think it plausible to see the likes of Frege and Russell in the same terms as the Hegelian metaphysicians who preceded them, if only because they were committed to scientific methods and open to the possibility that their various projects would fail. They were intellectual pioneers; explorers, not dreamers. And they were bound in a very productive way to the spirit of their time.

The grand plan to create an explicit and complete logical system which could encompass arithmetic was demonstrated – by Kurt Gödel in the early 1930s – to be impossible. But, as Karl Popper pointed out, this is precisely how science works and progresses: by bold conjectures and refutations. Without the prior work by Frege, Russell and others, Gödel would never have come to devise his remarkable proof. And it’s not as if Frege’s and Russell’s work was successful only in this negative sense. After all, their technical achievements helped to lay the groundwork for – and even shaped in certain ways – the revolution in digital computing as well as providing fruitful ideas in specific areas (such as formal linguistics).

I certainly don’t want to mount a defense of Russell’s logical atomism. I see the whole project of trying to construct a perfectly clear and perspicuous language (even if it is meant only for scientific purposes) as being doomed to failure. Russell’s own views changed over time. In his later works, he defends an approach to human knowledge which is (in my opinion) eminently defensible.

Russell was drawn to a correspondence view of truth. And, though his original insistence on a structural isomorphism between language and the world may not be sustainable, it seems to me (as it did to figures as different as Karl Popper and J.L. Austin) that there are objectively existing states of affairs – in both ordinary and scientific contexts – to which most statements refer and against which their truth or correctness (or whatever term might be appropriate) depends.

I see this view (or something very like it) as a prerequisite for science and scholarship as those pursuits have been traditionally understood. Sure, such a view has been challenged by various forms of idealism and radical epistemologies over the years. It is currently under sustained attack. Is it worth defending? Absolutely. How one sees these matters has serious intellectual, cultural and even political consequences.

Much of Austin’s work is descriptive and classificatory and, as I understand it, Austin saw himself as doing something like proto-science. He believed that his work on language would eventually form the basis for a mature science, and indeed his work has been picked up by linguists as well as by philosophers. Austin’s intellectual orientation was clearly quite different from Wittgenstein’s. Both thinkers had an appreciation of the power, complexity and expressiveness of natural language. But Wittgenstein was not interested in the sort of painstaking explicitness and classificatory thoroughness to which Austin aspired.

Previously I contrasted Russell’s scientific view of the world with Wittgenstein’s view. I am now suggesting a similar (but more limited) contrast between Austin and Wittgenstein. I want to make it clear, however, that I am not taking sides with respect to the thinkers involved. There is value both in Wittgenstein’s and in Austin’s writings on language. It’s just that their respective approaches and orientations are different.

On Russell and Wittgenstein, there are some issues on which I side with one, and some issues on which I side with the other. With respect to the status of science and scientific knowledge I am very much in Russell’s camp, not Wittgenstein’s.

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.]

Language and thought

Some people believe that all thoughts and concepts are language-based; others see language as playing a less crucial (or central or primary) role. This issue came up during a discussion of my recent essay at The Electric Agora on Wittgenstein's (mainly non-verbal) antics, though the essay itself was not concerned with this particular question. There are a lot of potential confusions here, a few of which I will try to disentangle as I put my point of view.

How one answers this question depends on how one frames it and what exactly one means by 'thoughts' and 'concepts' (specifically, how broadly or narrowly one defines them). But it also depends on what we mean by language. Are we talking about natural language, that is, human languages as they are in all their complexity? Or are we talking about language in a looser, more general sense?

Wittgenstein, for example, talked about an imagined primitive language that a tribe of builders might use. Clearly he is not concerned directly with actual human languages here (i.e. natural language, as the term is usually understood) but rather with the basis of the meaningfulness of language in general, of any possible language. Whatever he talking about, it is certainly not the complex thing (or set of systems or suite of behaviours) which is normally called natural language and which our brains are specifically primed to acquire. Or, if he is talking about it, it is in very oblique terms: telling a story about an imagined simplified language to demonstrate something about how these actual complex languages came to – or can – have semantic content.

If you wanted to understand how language gets meaning surely you would want to look closely at how children acquire language. Speculations about how language itself developed are something else again. But whatever Wittgenstein is doing, he is not doing science and he is not suggesting an hypothesis about anything.

His general point seems to be that language is a social thing and that meaning arises through social interaction. But who is disputing this? (The main target of Wittgenstein's criticism seems to be certain philosophical ways of thinking, and to some extent his earlier self.)

He is not using the term 'language' in its usual sense to refer to natural language (i.e. to existing human languages). But if – unlike Wittgenstein – you are using the word 'language' in this way, then the idea that all thought and concepts are language-based is very implausible.

As I wrote in a comment...

"The brain’s language modules (contentious term but I am just using it to mean “brain systems involved directly in linguistic processing”) interact with other modules, and constitute only a part of the total cerebral activity which is associated with conscious experience. It seems a bit forced to characterize the multiple and various conscious experiences not associated with linguistic processing as ‘not-thought’.

"[One commenter] talks about “thoughts of a significant kind” [as being language-based]. This needs further unpacking, but at least the qualification is there."

Having language makes us special, that's for sure.

My comment continued:

"... [T]he capacity for complex language changes the nature of ‘thinking’ in radical ways. This relates to the capacity for abstraction. I see a link between natural language and artificial languages (like mathematics). Certain non-linguistic animals can count and maybe subtract in an intuitive kind of way, and may enact certain processes which could be represented in terms of formal logic. But building and using explicit abstract systems can only be done by humans, and I think these formal systems are modelled to a large extent on natural language. Even ordinary natural language involves a high degree of abstraction. It is a big deal and a game-changer.

"I think some philosophers have erred, however, in pushing what I see as an extreme line on the question of language and thought. I am thinking in particular of the views of a couple of my teachers. As an eighteen-year-old undergraduate I was given what I now believe was a false perspective on language and thought in philosophy lectures and tutorials. It took me years to work my way out of it.

"I don’t think I entirely agree with Brendan Larvor’s criticisms of philosophical practice. [Larvor is an academic philosopher working in the U.K. who was cited in my essay and who finds fault with the argumentive practices of philosophers, seeing them as designed primarily to silence opposing voices.] I was not so much bullied as persuaded. But there was a definite sense of cultishness; an unspoken understanding that “We have this special [curiously ineffable] insight which is denied to others.”"

And you'd have to say, I think, that much of this cultishness drew – and continues to draw – on Wittgenstein's later work, including his discussion of imaginary 'languages' and use of the (arguably ill-defined) concepts 'language games' and 'forms of life'.

Philosophical performance

Whether we like it or not – and whether we like to admit it or not – we all too often find ourselves on a communicational battlefield where the performance of bewilderment, contempt and nausea combine with other forms of shaming and ostracism to play a major role in determining who prevails.

My latest piece at The Electric Agora, Wittgenstein's Antics, is about some of the non-verbal methods which people use to promote themselves and their ideas and get their way. The focus is on philosophical head-clutching and similar antics which not just Ludwig Wittgenstein but many other philosophers have been prone to. [That's Karl Popper in the photograph.] The topic is amusing, sure, but serious questions can be asked about the causes, the functions and the consequences of these general patterns of behaviour.

And, by the way, an interesting discussion developed in the latter part of the comment thread on the extent to which thought is necessarily language-based.

Quietism; Wittgenstein

This site was originally conceived as an ideology-free zone. Impossible, of course, for a blog which consists largely of opinion pieces (even if they are mostly on science- and philosophy-related topics).

Partisan politics free? Yes, that's quite easy to do, especially since political views are not directly relevant to most of the topics discussed here anyway.

But ideology is inescapable. Understood as a culturally-generated framework of purposes, facts and values which is adopted – and adapted – by individuals more or less voluntarily and more or less consciously, it pervades and motivates virtually all culturally-significant human activity.

For a while there I had been thinking about collapsing my two blogs into a single new site with a new title, shorter and sharper than 'Language, Life and Logic' but not suggestive (like 'Conservative tendency') of a particular political orientation. The latter is a strong title but could (my thinking went) be a liability, especially if it were my sole site and I wanted to focus on more science-oriented topics.

I have been posting at this site mainly pieces on language or the philosophy of mathematics or other more or less philosophical topics: relatively dry stuff, but ideological nonetheless a lot of the time. In fact, the generally deflationist, anti-metaphysical and quietistic orientation on display here might even be characterized – though not in a specifically political sense – as conservative.

Quietism has, after all, a distinct conservative (albeit anti-libertarian) flavour. It is all about respecting the power and efficacy of what is beyond the individual.

In religion (where the term had its origin) it was a borderline-heretical mystical movement within French and Spanish Catholicism which advocated a kind of willing surrender of one's will to an all-powerful deity.

These days, however, quietism usually refers to a political orientation characterized by skepticism about social activism, etc.; or to a position in the philosophy of language characterized by the rejection of a reformist approach to natural language.

The later Wittgenstein is often referred to as a quietist as he saw philosophical problems as arising not from the deficiencies but rather from the misuse of natural language. If language is seen as deficient, then some kind of revisionism seems called for – let's fix it (or replace it with something better). But Wittgenstein sought, as he put it, to leave everything as it was.

Arguably, this quietistic streak carried over into other areas of his life. Though he was deeply influenced by Tolstoy's radical views and had left-wing connections and friends (e.g. his colleague, the economist Piero Sraffa), Wittgenstein's radicalism was more moral than political. He was not (so far as I know) politically active, and he remained conservative in many ways. He was certainly a cultural conservative.

Let me make it clear that I am not endorsing Wittgenstein's view of the world – and certainly not his religious leanings or his curiously negative attitude to science.

All I am suggesting here is that there is a degree of overlap between (different forms of) quietism and (different forms of) conservatism, and that the case of Wittgenstein may be seen to illustrate this to some extent.

Anti-metaphysical musings

I have been looking recently at some material relating to "the metaphysics wars", and thought it worthwhile to jot down a few notes.

No doubt, my general position would be characterized by those with other views as scientistic. It is also anti-metaphysical in that I don't see the traditional philosophical discipline of metaphysics as having much point these days.

I don't deny that there are very interesting questions in the philosophy of physics, the philosophy of mathematics and the philosophy of logic which may be characterized as metaphysical. The meta-thinking that goes on at the margins of physics, other sciences and mathematics, etc. is necessary and valuable.

But somehow, when such thinking moves away from the discipline in question and becomes more generally philosophical, problems arise.

Timothy Williamson is perhaps the most powerful and impressive advocate for this broader kind of metaphysics (and analytic philosophy generally). As an avowedly non-religious person, he can't be dismissed as having ulterior motives of a religious nature; and, being at home with formal – and specifically modal – logic, he can't be dismissed as natural language-bound or as being daunted in any way by technical rigor.

Some of the points he makes in this interview are good ones – such as noting the light that modal logic can undoubtedly throw on the workings and nature of natural language (via Montague grammar, for example), and perhaps also on the foundations of set theory – but I have to say that I am strongly inclined to reject the basic thrust of his argument in defense of metaphysics, and, by extension, philosophy (as he understands it).

Essentially the questions he seems most interested in are reminiscent of medieval scholasticism. I too have great respect for thinkers such as Avicenna (to whom he refers approvingly) and respect also for more recent – and more mathematically sophisticated – exponents of that general tradition of thought (such as Bolzano, to whom he also refers), but it seems to me that it is now incumbent upon any thinkers who aspire to deal with questions of what there is in a fundamental sense to base their accounts – at least in large part – on contemporary physics; or on mathematics if they are restricting their focus to mathematical realities.

Williamson seeks to defend the relative independence of his core preoccupations from science by invoking the old shibboleths, scientism and reductionism, and rejecting naturalism as a confused and inadequate concept.

I grant that mathematics does pose problems for advocates of strong forms of naturalism and empiricism, and there are real unresolved issues in the philosophy of mathematics. But my preference is to address these issues in a broadly scientific and mathematical context rather than in a purely logical or philosophical one, or – worse – not to address them at all and instead merely to use them as a kind of justification or license for logical excess and metaphysical self-indulgence.

Williamson cites Quine as an example of scientistic naturalism.

"Quine privileged natural science, and in particular physics, over all other forms of inquiry, to the point of not taking very seriously any theory that couldn't be reduced to part of natural science."

Williamson's view, by contrast, more or less allows the analytic metaphysician carte blanche, and Williamson's own approach to analytic metaphysics is clearly – in my view at any rate – insufficiently constrained and guided by science.

Here, for example, is an extract from an old interview in which he explains his developing views:

"My work on vagueness and ontology doesn’t really concern ontology. Probably my most distinctive ontological commitment comes from my defence of a controversial principle in logic known as the Barcan formula, named after the American logician Ruth Barcan Marcus, who first stated it. An application of this principle is that since Marilyn Monroe and John F. Kennedy could have had a child (although they actually didn’t), there is something that could have been a child of Marilyn Monroe and John F. Kennedy. On my view, it is neither a child nor a collection of atoms, but rather something that merely could have been a child, made out of atoms, but actually has no location in space and time. The argument can be multiplied, so there actually are infinitely many things that could have been located in space and time but aren’t. It takes quite a bit of work to show that the Barcan formula is better than the alternatives! That’s what my next book will be on. The working title is Ontological Rigidity."

The book was actually called Modal Logic as Metaphysics, and this is how he recently stated its main point:

"I am ... saying that it is necessary what there is. Necessarily everything is necessarily something. There could not have been more or fewer things than there actually are, and which particular things there are could not have been different. What is contingent is only what properties those things have, and what relations they have to each other. I call that view necessitism. Its denial is contingentism. Who knows how far back necessitism goes? Maybe Parmenides was some sort of necessitist..."

On the face of it, talking about (apparently countable) things (minus their properties and relations!) as given strikes me as breathtakingly naïve in the context of a physics-based understanding of reality. I can only imagine that Williamson is – like the medieval scholastics – implicitly asserting a privileged role for logic.

Quine's assertion of a privileged role for physics makes a lot more sense to me.

Admittedly I haven't looked at Williamson's ideas in any depth, but what I have seen so far – and what he says in this latest interview – really makes me question whether it would be worth the effort. I am intrigued, however, by what is driving such thinkers.

Strangely, Williamson appears not to be quite sure whether his latest work is meaningful or not – or at least seems unwilling to commit himself on the matter. There is (don't you think?) just a touch of arrogance in this passage (from Chapter One of Modal Logic as Metaphysics)?

"This book compares necessitism and contingentism. Which is true? Of course the question has a false presupposition if the definitions of 'necessitism' and 'contingentism' lack meaning or content. But if every enquiry must first establish its own meaningfulness we are on an infinite regress, since the enquiry into the meaningfulness of the previous enquiry must first enquire into its own meaningfulness, and so on. Better to act on the assumption of intelligibility: readers can decide for themselves whether they understand the book as they go along, and recycle it if they don't."

This passage is a combination of facile reasoning and rhetorical sleight of hand. By using the word 'understand' in the final sentence, he subtly shifts the focus to the reader's possible inadequacy and away from the original question concerning the work's meaningfulness.

In fact, I am tempted to see Williamson's work as emblematic of a broader trend. On the basis of my (admittedly limited) knowledge of the history of the relevant intellectual cultures, I discern, since the middle years of the 20th century, a disturbing falling off in intellectual seriousness in secular circles accompanied by an equally disturbing rise in anti-scientific name-calling and credulity amongst those thinkers who remain favorably disposed towards religion.

I'll finish here with a few comments about Paul Horwich, Williamson's great philosophical antagonist, whose deflationary views on truth I have referred to favorably in the past.

Horwich is opposed to the sort of traditional theoretical philosophy ('T-philosophy') which Williamson defends. I have made the point that, though I broadly accepted Horwich's account of truth, I doubted that his Wittgensteinian view of philosophy was compatible with a continuation of philosophy as an academic discipline. And, interestingly, Williamson makes a similar point in the recent interview.

"...Horwich didn’t explicitly call for T-philosophy not to be funded. I pointed out that if the picture of philosophy in his book were accurate, philosophy should be abolished. The reader encounters just two sorts of philosophy: irrational T-philosophy, and level-headed Wittgensteinian debunkers of T-philosophers. Philosophy is presented as an activity in which some people make a mess and others clear it up. Why on earth should taxpayers fund that? It looks as though we’d be better off simply abolishing the activity altogether."

Finally, I was surprised (and a bit disappointed) to learn recently that Horwich rejects naturalism, and even more unequivocally than Williamson does. He cites not only mathematical but also moral claims as a basis for his view.

Horwich is more thoroughly Wittgensteinian than I had previously thought.

Timothy Gowers and the philosophy of mathematics

Following on from my previous post, here are a few more thoughts on the philosophy of mathematics and on Timothy Gowers's views.

On rereading his talk, I thought the section on what it could mean for 2+2 to equal 5 in an alien world to be too clever by half and ultimately unconvincing. (Gowers virtually concedes this himself, so why include the material in a short talk?) It reminded me of Wittgenstein's equally unconvincing (to me) arguments about deviant forms of counting.

And then there is Gowers's politics, including his role in the campaign against the scientific publisher, Elsevier. (Wittgenstein too had strong moral and social convictions - including a conviction that ideas should not be 'owned' - but, unlike Gowers, he was, so far as I know, never an activist.) I am not aware of Gowers speaking anywhere of his general ideological or political position. I would guess that his views are left-leaning, but I don't know for sure, and I don't know what effect (if any) his general political and moral views might have had on his views on the philosophy of mathematics.

Which brings me back to the main point of the previous post: there seems to be no objective way of deciding on the truth or otherwise of the many and various options within the philosophy of mathematics. So when someone shows a strong commitment to a particular view, I wonder whether extraneous factors - such as ideology - might be playing a role.

I should also say something about neo-Meinongianism, having raised the topic in my previous post. Needless to say, it's complicated, but the general gist of it is something like this. Neo-Meinongians think that you can make statements about mathematical objects (like numbers) without being committed to believing they exist. They would claim that the statement that there are infinitely many prime numbers is literally true even though numbers may not exist as such. This view is based on the (I think) plausible idea that expressions like 'there is' or 'there are' are used in various ways and do not necessarily entail any ontological commitment.

As I understand it, (non-neo) Meinongianism is supposed to countenance gradations or different kinds of existence or being, whereas neo-Meinongians claim that certain uses of expressions such as 'there is' involve no ontological commitment.

In fact, Gowers makes a somewhat neo-Meinongian point in his talk, endorsing Rudolf Carnap's distinction between internal and external questions, only the latter (possibly) involving ontological commitments. So, on this view 'there are two senses of the phrase "there exists". One is the sense in which it is used in ordinary mathematical discourse - if I say that there are infinitely many primes I merely mean that the normal rules for proving mathematical statements license me to use appropriate quantifiers. The other is the more philosophical sense, the idea that those infinitely many primes "actually exist out there". These are the internal and external uses respectively.'

Or again, Gowers writes: 'One view, which I do not share, is that at least some ontological commitment is implicit in mathematical language.'


I'm not sure where I stand on all this. I have doubts about the worthwhileness of much of what goes on under the designation of 'philosophy of mathematics', but see some issues which seem real and important. Though I am certainly drawn to the position outlined by Gowers, I am acutely aware that this general orientation may be, like general religious or political predispositions, largely a function of inherited or early-environmental factors.

It seems to me that platonistic or anti-platonistic intuitions lie behind most philosophical work in the area. But what are these intuitions worth if they are in large part the result of arbitrary genetic and developmental factors?

The fact that little progress has been made in answering apparently real and interesting questions in the philosophy of mathematics and related areas suggests to me that the standard, traditional philosophical approaches are somehow flawed. Or perhaps the questions are ill-conceived, based on an inadequate understanding of the intellectual disciplines in question.

In fact, the advent of digital computers and new ways of conceptualizing information and information processing is changing the way we see mathematics (and much else besides). As new ways of doing and looking at mathematics and science emerge, questions that once seemed meaningful and important may no longer seem so.

Wittgenstein's anti-metaphysical stance

One thing I share with Ludwig Wittgenstein is a hostility towards metaphysics.

Henry Le Roy Finch argues* that the origin of metaphysics lies in the idea of identity, which he traces to Plato's conception of original or self-existing things, and to Aristotle's (and the Aristotelian tradition's) more systematically logical approach to the notion of self-identity.

That a thing is identical with itself (traditionally referred to as Aristotle's first law of thought) is often seen as the foundation for all logic.

Wittgenstein, on the other hand, thought that there was no more meaningless statement than a statement of self-identity. "To say of one thing that it is identical with itself is to say nothing at all." (Tractatus 5.5303)

Quite.

But Finch goes further and suggests that this skepticism about self-identity is linked to Wittgenstein's rejection of the popular notion of personal identity, the Cartesian thinking self. This is a central theme of Wittgenstein's (subsequently taken up by Gilbert Ryle). As Wittgenstein put it: "There is no such thing as the subject that thinks or entertains ideas." (Tractatus 5.631)

Certainly, both this claim and the previously-cited one are anti-metaphysical. And, significantly, Wittgenstein saw metaphysics and religion (or at least the sort of religion he embraced) as being in opposition to one another rather than as allies.

Finch rightly points out that "identitylessness" is at the heart of some important religious traditions, notably Buddhism, certain forms of Christianity** and Islam in its Sufi aspect.

Wittgenstein said that his goal was to "show the fly the way out of the fly-bottle", which can be interpreted as referring to the freeing of the human being from his or her false self-perception as a thinking self in its own private world. And this view of freedom is quite consistent with the religious traditions listed above.

On the other hand, as Finch points out, it is not consistent with other religious and philosophical approaches:

"The Stoic (and some would say also Judaic) idea of freedom is essentially that of Kant, which is that of the ethical self or free will, in which the self still retains its identity through its capacity to decide."

I remain uncomfortable with religious language and concepts, but I don't think someone like Wittgenstein can be understood (and I think he is worth trying to understand) if one ignores the implicit religious dimensions of his thought.

Also, having grown up (and so having invested a lot) in a religious tradition which I subsequently rejected, it's satisfying to see elements of that tradition coming into play here in a positive way.



* See his Wittgenstein, published by Element Books as part of the series Masters of Philosophy.

** I would single out the tradition known as fideism, and also the various mystical traditions. Pauline themes are important here; and it is worth noting in this connection that Wittgenstein liked the writings of the twentieth-century theologian Karl Barth.

Thinking about Vienna

In his later years, Ludwig Wittgenstein had many insightful and salutary things to say - about language especially. He had freed himself from a rigorous but narrow view of logic and language, and thought his way back to what looks like a very sane and sensible and quite ordinary point of view which respects the fact that human language is embedded in human life in all its forms and activities, and reflects this variety. There is nothing metaphysical about language and meaning, no mystery (though many philosophers continue to operate as if there were*).

But there is another side of Wittgenstein which I find less appealing: his negative attitude towards science, his tendency to play the sage, and his religion.

He was, I think, very close to Tolstoy in his religious views, and very much a Christian. He gave away his share of the family fortune (and in so doing incurred the lifelong enmity of his brother Paul). He prayed. He read the New Testament.

I say that Wittgenstein played the sage. He did so in his writings, which often have an oracular tone, but also in life (as a teacher, etc.). He was a notorious philosophical head-clutcher.

And, as befits a sage, Wittgenstein had and has disciples. Philosophical Wittgensteinians often play down the religious dimension of his thought, but this is not the case with Henry Le Roy Finch, who, having completed a PhD at Columbia, taught philosophy for more than forty years, mainly at Sarah Lawrence College and CCNY (later CUNY).

I am currently reading a short work of Finch's in which he presents Wittgenstein and Heidegger as harbingers of an epochal change in Western civilization.

"We may not expect the change, which seems to be seeping in from many directions, to be forecast or presaged by any one particular philosopher or prophet. However, the thinker who is attuned to his or her own time as well as to deeper currents may pick up the seismic tremors well before others do and express some critical formative ideas in advance of the more general historical changes. Such a thinker, in the opinion of many, is Ludwig Wittgenstein (1889-1951)... [He] was a thinker of such originality that no one claimed to understand him fully in his lifetime and the attempt to comprehend his 'new way of looking at things' and make it available to the mainstream continues."

For many of Wittgenstein's followers - and especially, I would say, for the non-philosophers among them - his forbiddingly complex and beautifully written oeuvre represents a profound and sophisticated defense of the (or a) religious point of view.

And, because he didn't make explicit religious claims ('Whereof one cannot speak ...'), it is difficult to argue against his position.

I try to keep an open mind on these issues, but I do tend to the view that Wittgenstein's religious propensities are inextricably bound up with some very peculiar psychological imperatives and with his family and cultural background. His culture and most of his preoccupations are alien to us today. He was a member of one of the richest and most highly cultured Viennese families and grew up in the declining years of the once-glorious Austro-Hungarian Empire. The Romantic cult of death was in the air.

I have my doubts also about his followers. Finch sounds at times like a bit of an oddball. In an endnote on the discarding of "age-old machinelike aspects of the human mind", he mentions favorably the religious thinker Eric Gutkind (whom I have not read), and recalls attending in New York in October 1949 a talk by the architect Frank Lloyd Wright.

"He came out on the stage and began his lecture with these words, which are imprinted on my memory: 'The greatest man of our time has died today, and probably none of you has ever heard of him.' It was Gurdjieff ..."

If old Vienna was a weird and alien world, the bohemian milieu of mid-twentieth century New York might have given it a run for its money.




* Saul Kripke's work was very influential in re-mystifying the philosophy of language.