Lee Smolin's realism

Lee Smolin is a respected physicist who has always had strong philosophical interests and convictions. He recently articulated his realist views in a public lecture. What follows are my notes on his lecture mixed in with a few comments and observations.

Smolin is strongly opposed to postmodernists who reject the notion of objective truth and who see reality as a social or historical construct. He draws parallels between the anti-realism of postmodernists and the anti-realism of certain physicists associated with the development of quantum mechanics (QM) and the so-called Copenhagen interpretation.

Smolin claims (as Einstein did) that QM is an incomplete theory and so, in a real sense, wrong. The key problem with QM as Smolin sees it is the so-called “measurement problem”. It relates to the notion of wave–particle duality and the two laws or rules that QM provides to describe how things change over time. Rule 1 or law 1 says, in effect, that (except during a measurement) the wave evolves smoothly and deterministically (somewhat like a wave on water). This allows the system to simultaneously explore alternative histories which lead to different outcomes all of which are represented by the smooth flow of the wave. Rule 1 applies when you are not making a measurement. Rule 2 applies only when you make a measurement.

Smolin argues that the 2nd rule means that QM is not a realist theory. If we (or other observers) were not around, only rule 1 would apply.

One of the main developers of the theory, Erwin Schrödinger, was uncomfortable with the theory and its implications. He crystallized his doubts in the form of the famous live/dead cat-in-the-box thought experiment (which is explained by Smolin in his talk (starting at 39.54)).

Niels Bohr, in contrast to Schrödinger, embraced the paradoxical nature of QM, partly because it fitted in with ideas which he had developed previously. Bohr’s notion (or philosophy) of complementarity was shaped by these ideas and by the observed behavior of elementary particles. Sometimes such particles seem to behave as if they are waves, sometimes as if they are particles and, crucially, how they are observed to behave depends on the details of how we go about observing them.

Smolin takes an unequivocally negative view of Bohr’s metaphysical views as well as of the views of Bohr’s protégé, Werner Heisenberg. Here he is on the former:

“Now, of course, Bohr had a lot to say about things being complementary and in tension all the time and you always have to have two or more incompatible viewpoints at the same time to understand anything, and that especially goes […] for knowledge and truth and beauty. And he got off on the Kabbalah, of course. Anyway [long pause] … it doesn’t cut it with me.”

For Smolin, QM's incompleteness is intimately bound up with its incompatibility with realism.* QM is not consistent with realism because the properties it uses to describe atoms depend on us to prepare and measure them.

“A complete theory,” insists Smolin, “should describe what is happening in each individual process, independent of our knowledge or beliefs or interventions or interactions with the system.” He is interested in understanding “how nature is in our absence.” After all, we were not around for most of the history of the universe.

Smolin defines realism as the view that nature exists independently of our knowledge and beliefs about it; and that the properties of systems in nature can be characterized and understood independently of our existence and manipulation. Our measuring etc. “should not play a role in what the atoms and elementary particles are doing.” What he means, I think, is that our interventions should not play an essential or crucial role in the descriptions and explanations which our theories provide.

“A theory can be called realist,” Smolin explains, “if it speaks in terms of properties whose values do not require us to interact with the system. We call such properties “beables”.”

By contrast, a theory whose properties depend on us interacting with a system is called operational. Such properties are called “observables”.

Observables are defined as a response to our intervention. Beables, by contrast, are not defined as a response to our intervention. They are just there, it seems.

But how do we get to know the values of these properties unless we interact with the system? Also, there is the framework question. Properties and values arguably only exist within the context of a particular perspective or theory. In order for properties and values to be properties and values, we need to conceptualize them as such. I will ignore this broader question, however, and focus on what Smolin means by interaction.

Even ordinary observations (like seeing or hearing or recording something electronically) involve us or our measuring devices interacting in some way with the system we/they are observing/recording. Smolin appears not to be concerned with such interactions here because, although the nature of the observer’s perceptual apparatus and/or the nature and settings of the equipment being employed determine or pick out what is and what is not being observed or recorded, the results are otherwise quite independent. The type of datum is determined by the nature of the observer or the observing or recording process, but not the data themselves.

In the case of experiments with elementary particles, however, the situation is subtly – and sometimes dramatically – different. Interactions are such that they determine, or play an active role in determining, the values in question.

Arguably, ordinary cases of measurement and observation do not pose problems for the commonsense realist. But if our observations alter in a material way whatever it is which is being observed – as appears to be the case in respect of the quantum realm – problems arise.

Operationalism was first defined by the physicist Percy Bridgman (1882–1961). The book in which he elaborated his views, The Logic of Modern Physics, was published in 1927, the same year QM was put into definitive form. Bridgman’s philosophical approach has much in common with the instrumentalism which characterized the views of the majority of thinkers (physicists, logicians, philosophers) associated with logical positivism. Bridgman was in fact personally involved in the activities of the Vienna Circle.

It was the physicist John Bell who introduced the concept of beables. According to Bell – and according to Smolin – it should be possible to say what is rather than merely what is observed. This is all very well but – quite apart from philosophical arguments questioning the notion of a noumenal world – experimental results continue to come out against the realists. Experiments with entangled particles, for example, seem to exclude the possibility of any form of local realism. Some form of nonlocal realism is still very possible however.

Smolin is at his weakest when he talks history. The story he tells about the generation of physicists who grew up during the Great War is hard to swallow. It seems that they were predisposed to anti-realism by virtue of the unusual circumstances of their early lives. They had witnessed at an impressionable age the destruction of the social optimism of the 19th century, and so were skeptical of rationality and optimism and progress. They had lost older brothers and cousins and fathers and uncles and had “nobody above them ...” No wonder they didn’t believe that elementary particles etc. have properties which are independent of our interactions with them!

You would think that the fact that Niels Bohr, the father of the Copenhagen interpretation, was not a part of this generation would sink Smolin’s generational explanation from the outset. As would even a cursory knowledge of the history of 19th century thought which is shot through with various forms of idealism, anti-realism and radical empiricism. The phenomenalist philosophy of science of Ernst Mach (1838–1916) is a case in point. At the end of the 19th century, Mach articulated ideas which were later picked up by the thinkers Smolin is criticizing.

Smolin explicitly recognizes that Bohr’s main ideas were formed well before the development of quantum mechanics and that he was influenced by 19th century thinkers – including by Kierkegaard (whom Smolin clearly does not hold in high esteem).

Smolin quotes some of Bohr’s claims:

“Nothing exists until it is measured.”

“When we measure something we are forcing an undetermined, undefined world to assume an experimental value. We are not measuring the world, we are creating it.”

“Everything we call real is made of things that cannot be regarded as real.”

Heisenberg followed the same general approach:

“The atoms or elementary particles themselves are not real: they form a world of potentialities or possibilities rather than one of things or facts.”

“What we observe is not nature itself but nature exposed to our method of questioning.”

Bohr said: “We must be clear that when it comes to atoms, language can be used only as in poetry. The poet […] is not nearly so concerned [with] describing facts as [with] creating images and establishing mental connections.” What he meant, presumably, is that the normal referential function of natural language cannot be used in relation to the quantum world, and anything we say about that world (using natural language) will necessarily be a creative construct shot through with metaphor and paradox.

Maybe so. Or maybe not. It is not something we can know a priori. It all depends on how our models develop and on the results of experiments. But, until QM is subsumed into some (hypothetical) broader theory which allows us to envisage quantum processes in more intuitive or realism-friendly ways, Bohr's general views regarding the radical inapplicability of natural language and ordinary logic to quantum events or processes will remain plausible.



* There is also the question of gravity. Quantum field theory brings together QM and special relativity. QM and general relativity have yet to be satisfactorily reconciled, though a line of research associated with the so-called AdS/CFT correspondence – a string theory-based approach – has made considerable progress towards this goal.



This is a revised version of an essay published at The Electric Agora on June 4.

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.]

Frege on natural language

There was a discussion recently at The Electric Agora about Gottlob Frege's famous paper, 'On sense and reference', which brought home to me just how little progress has been made in the last century or so on this and other topics in an area often designated as the philosophy of language.

In fact, rereading Frege's piece, I was greatly impressed not only by its seriousness and intellectual fecundity but also by the careful and respectful way Frege – who was basically a philosophically oriented mathematician and logician – dealt with issues of natural language.

He did not draw easy conclusions but was often content simply to sketch out the semantic complexities involved in certain kinds of syntactic contexts, for example in relation to reported speech or subordinate clauses involving the subjunctive mood.

What has always been clear to me (and which this recent discussion only confirms and underscores) is that aspects of Frege's work have been appropriated and incorporated into a (philosophical) project and a narrative which is quite alien to what Frege – who identified as a man of science – saw himself to be doing.

The comment thread is interesting for a number of reasons but particularly perhaps for the contribution towards the end by someone who has recently translated some early work by Frege and who suggests – as I am suggesting here – that Frege would have been quite out of sympathy with most late-20th century philosophers of language, even those who claim him as a precursor.

I don't want to suggest that the science/non-science distinction is clearcut. It's not. For one thing, there are obviously huge differences between empirical work in different areas (between empirical work in physics and the study of natural language, for example); and also an important distinction between empirical work in general and the building of mathematical or logical or conceptual structures which may be intended (as Frege's were) for basically scientific applications.

But clearly certain kinds of discourse, such as aesthetic, moral and ideological discourse, while they may draw on scientific knowledge to a greater or lesser extent, are not scientific – and (contingent of course on one's conception of philosophy) not necessarily 'philosophical' either.

My first comment on the thread (which I quote here in a modified form) touched on this point.

[Quoting another commenter] "... So it seems Frege is really excluding discussions that clarify or debate sense [as distinct from reference] ... from logical analysis. (This is certainly in keeping with the agenda of Logical Positivism that followed after, which held that topics in aesthetics, religion, politics, etc., were philosophically moot.)"

Yes, this is a very important point. The references to Homer's Odyssey etc. in the Frege's paper seem to confirm what you are saying. Frege obviously respected poetry and fiction etc. but took discourse relating to these things, other hypotheticals and also political rhetoric as being in a very different category or set of categories from the kind of discourse and inquiry (scientific, philosophical) in which he saw himself to be engaged...

Frege's attitude to signs which have a sense but not a reference, which of course include not only the names of fictional characters like Odysseus but also many other kinds of expression and which he tentatively refers to as 'representations', is ambivalent. He accepts that they are an essential element of natural language-based communication, but sees them as operating beyond the scope of science and the sort of logical enquiry he is interested in, except in the sense that the latter may provide certain salutary lessons.

In the vast majority of cases the use of such 'representations' is perfectly fine, but sometimes problems can arise which the logician may be able to diagnose or at least see in a perspicuous way. Frege warns, for example, about political contexts in which expressions like "the will of the people" – which have a sense but not a reference (or at least not any clear or agreed one) – are used rhetorically for purposes of social or political manipulation.

Science as a way of seeing

Attitudes to science and attitudes to language are often related. Many science-oriented people are 'linguistic revisionists'. They have a low opinion of ordinary language (because of its vagueness and ambiguity) and seek to reform it or replace it wherever possible with various formalisms. Conversely, a negative attitude to science and mathematics and logic is often evident amongst lovers and respecters of natural language (especially in literary circles for example).

But there is no reason why one cannot combine a passionate commitment to a scientific (even scientistic) view of the world with a profound respect for natural languages – these curious products of biological and cultural evolution – as objects or systems and with a recognition of what these systems are uniquely equipped to do.

To complicate matters, it's also possible to combine a commitment to the formal sciences with a passionate hatred for the physical sciences. This is a not uncommon position, actually, but one I will not deal with here.

What follows, then, are some preliminary and loosely connected notes on the differences between broadly scientific and other modes of thinking, seen in relation to language.


Reasoning and deduction can, of course, be framed in formal terms, and even natural languages can, to an extent, be seen as interpreted formal systems.

Such formal logical approaches – which don't come naturally to most of us – represent a limited but (paradoxically) revealing perspective, rather like an X-ray image, or a monochrome drawing (a landscape, say).

They have their own beauty, these approaches, but it is a spare beauty which derives from abstraction, from leaving things out – like soft tissue in the case of the X-ray, or colour and smell and sound and movement and a third spacial dimension in the case of the drawing.

Revealing and beautiful – and also useful. It was this mode of thinking that gave rise to mathematics, science and technology. And, in the mid-20th century, habits of abstract and reflexive thought finally brought formal systems themselves to life in the form of the digital computer.

But computers, as embodiments of formal thinking, suffer the limitations of formal thinking, and are not well-equipped to deal with the rich parallelism of human perceptions or the tacit knowledge implicit in ordinary human actions and interactions and language use. Their strengths are our weaknesses and their weaknesses our strengths.

What is most notable about normal human brains – in stark contrast to machine intelligence – is their remarkable ability to deal with non-abstract things, and, in particular, with the hugely complex sensory and social realms; in conjunction, of course, with natural language, the bedrock of social life and culture.

Human languages are in fact quite remarkable in their capacity for expressing the subtleties of psychological and social experience. I don't much like the word 'literature'; it's a bit stuffy and pretentious but it's the only word we've got in English that picks out and honors, as it were, texts which explore and exploit this capacity.

The word 'letters' worked in compound expressions in the relatively recent past ('life and letters', 'man of letters') but is now quite archaic. 'Belles lettres' even more so.

The adjective 'literary' is, however, neither pretentious nor archaic, simply descriptive. It can be a neutral indicator of a specific context of language use. Or it can be used to designate (often pejoratively, it must be said) a particular style or register of language use (in contrast to technical or plain or straightforward or colloquial language, for example).

In the early 20th century, the linguist (and one-time student of Ferdinand de Saussure) Charles Bally saw the need to expand the scientific study of language to encompass the subjective and aesthetic elements involved in personal expression. His notion of stylistics was further developed by thinkers associated with the Prague school – most notably Roman Jakobson, who listed the 'poetic function' as one of the six general functions of language.

[I am always wary when scholars make numbered lists of this kind (suspecting that reality is rather less amenable to clearcut categorization than the scholars would wish).

Though his overview of linguistic functions is harmless enough, Jakobson did in fact have a tendency to drive his more technical insights too hard and too far. On markedness and binarism, for instance. But that's another story.]

On the question of the possibility of a satisfactorily scientific study of style I am undecided.

Certainly, the importance of stylistic elements in actual human communication is often underestimated and communication failures are often the result of stylistic rather than substantive issues. The aesthetic element is also important in its own right (as Jakobson saw).

But scientific approaches are characterized by their narrow focus and abstractness: by what they leave out. And what they leave out is generally the subjective or experiential side of things. Twentieth century phenomenologists and others tried – and failed – to reinsert into the scientific view what had been omitted.

A supposedly 'scientific' approach (phenomenological or otherwise) could never really replace, as I see it, the informal 'close reading' of a text or spoken exchange (for example) by a perceptive reader or listener who was well versed in the language and culture (or sub-culture) in question.

Was a particular characterization plausible or a given piece of dialogue convincing? Was a particular remark witty or just sarcastic or rude? Was someone being condescending in what she said, or kind (or both condescending and kind)?

Often the answers to such questions will depend not only on non-verbal and para-linguistic factors but also on the subtle connotation of a word or turn of phrase.

Logical languages (like the predicate calculus) strip these psychological and emotional and aesthetic elements away; and all scientific language – even in the social sciences – aspires to denotation, pure and simple.

As I started out by saying, that spare, direct approach has its own beauty which stems above all from its power to make us see in a more direct and culturally unencumbered way.

You can interpret the scientific way of seeing things (which goes beyond science as such) in an almost mystical way, in fact: as a means of 'cleansing the doors of perception', of temporarily sloughing off the necessary – and necessarily arbitrary – cultural baggage of social existence.

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.

The fading of philosophy

Last year, the well-known and respected philosopher Colin McGinn suggested that we replace the term 'philosophy' with 'ontics' to designate the area that academic philosophers – or 'onticists' – are engaged in. But, in my view, philosophy's problems are deep and long-term, and such talk of rebranding the discipline on the part of a leading practitioner only serves to underscore its parlous state.

My suggestion is not that we replace the term, but that we de-emphasize it, recognizing that it has gradually lost any substantive meaning as the designation for a stand-alone discipline.

When, in the early 20th century, metaphysics in general and philosophical idealism in particular fell out of favor, philosophy itself (of which metaphysics had traditionally been seen as the core) began to suffer a crisis of confidence and a fall in status. This trend was exacerbated as psychology and other social sciences established their scientific credentials, and severed their links with philosophy.

It's no wonder that the very existence of philosophy as an academic discipline began to be called into question, and, in the post-World War 2 period, it was seen by a significant number of its practitioners as being limited to serving a clarificatory function with respect to the sciences. It was seen as a handmaid to science in a similar way that, in the medieval period, it had been seen as a handmaid to theology.

Since the post-War period, things have gotten more complicated. There have been attempts to revive a more traditional and general role for philosophy, but, in my view, these attempts are fundamentally ill-conceived.

I would be happy to explain my case in detail to anyone who might be interested (a small and shrinking section of the population, I suspect), but for now will just say that I don't see whence such a discipline derives its authority.

Science derives its authority from established procedures generally referred to as 'the scientific method' which ensure that, to a large degree at any rate, human bias is filtered out: scientific findings are objective, and so authoritative. Mathematics incorporates similar procedures which allow results to be objectively assessed.

But nothing like this happens in philosophy. And, consequently, there is no convergence of opinion and slow building of a body of genuine knowledge such as occurs in the sciences.

This is not to say that science can play the role that religion played, that scientific knowledge can provide certitude, solace and a sense of purpose. It can't.

Nor can 'philosophy' of course. No discipline can.

There is – and always will be – a place, however, for reflective thinking. My point is simply that it doesn't constitute – and nor is it encompassed by – a single academic field or discipline.

Meta-thinking will always occur within and about the various physical, social, and historical sciences, and other disciplines, such as mathematics and logic. Such thinking can still be usefully described as the philosophy of physics, of biology, of history, of logic or whatever.

But reflective – and value-based – thinking about human life in general is more problematic. We all do it, but it does not – it cannot – be systematized. I have written before about my reservations about philosophical ethics, which I don't see as a viable area of research, or as something that constitutes a distinct and authoritative intellectual discipline.

What about reasoning in general (considered from a normative and pedagogical perspective)? Isn't this an area in which philosophers can claim expertise? Perhaps.

I do see a need to develop and promote logical thinking and skills related to reasoning and argument. But, though this is an area which philosophers are claiming as their own, I don't see it as necessarily being connected to philosophy at all.

In a recent discussion on a comment thread at Rationally Speaking, Paul M. Paolini argued (against me) that in areas beyond the scope of science and mathematics (like normative ethics) we have a stark choice between philosophy on the one hand and dogmatism or chance on the other. I made the point in response that defining philosophy in terms of rationality was inappropriate. Rationality is clearly a broader concept than philosophy, and there are many non-philosophical ways of dealing with general questions of human life and value which are compatible with reason.

In fact, ordinary educated discussion and deliberation may allow more scope for valuable, experience-based intuitive insight than the often stale, flat and superficially complex reasoning style of professional philosophers.

The careful use of language and sophisticated reasoning skills have traditionally been taught, directly and indirectly, in a variety of academic and intellectual contexts and subject areas. No knowledge of philosophy or philosophical logic is required to think and reason and argue well (which is not to say that a knowledge of informal and formal logic may not be useful).

On the question of logic, it is well to bear in mind that the crisp and complex grammars of ordinary human languages encapsulate the fundamental logical principles upon which formal logical systems are built. And ordinary language use is predicated on an understanding of these principles.

Philosophy and philosophers don't have a monopoly on reasoning or the teaching of reasoning, in other words, even if, historically, much cataloguing of logical fallacies and so on was done by philosophers.

Modern approaches will, of course, incorporate (but need not be restricted to) the findings of research in various branches of psychology concerning our brains' inbuilt biases of perception and reasoning.

Regarding the broader, more ambitious questions with which philosophy has traditionally dealt, we need to recognize that many of these questions are unanswerable, either because they are conceptually confused or because they are beyond the scope of current science (and perhaps also beyond our intellectual capacity).

It helps however – at least in my experience – to cultivate a sensitivity to, and a critical interest in, the fundamental media of our understanding: above all, ordinary language and its implicit logic; but also, if possible, mathematics and other formal systems.

The goal, as I see it, is clarity with respect to what we know, coupled with an awareness of the vastness of our ignorance and the need to remain alert to the possibility of new – and unexpected – perspectives.

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.

How we ought to think

'One of the great pleasures of the philosopher's life,' wrote Jim Hankinson in The Bluffer's Guide to Philosophy, 'is being able to tell everyone (and not just children and dogs) what they ought to do. This is Ethics.'

On this reckoning, logic should afford even greater pleasure to its practitioners than ethics does insofar as it purports - at least on some accounts - to tell everyone how they ought to think. For example, consider this (from a text book for undergraduates): 'Logic is sometimes said to be the science of reasoning, but that assertion is somewhat misleading. Logic is not the empirical investigation of people's reasoning processes or the products of such processes. If it can be called a science at all, it is a normative science - it tells us what we ought to do, not what we do do.'

Or, as Gottlob Frege put it: 'the laws of logic are ... the most general laws, which prescribe universally the way in which one ought to think if one is to think at all.' (The Basic Laws of Arithmetic)

Frege, in fact, was something of a proto-fascist, and the above statement could be interpreted as having an authoritarian, even totalitarian, tenor. It could also be interpreted simply as an honest statement of the constraints of thought, reflecting Frege's noble goal of defining the bedrock of human reasoning.

It's no surprise that most attempts to articulate logic's normative role run into trouble. For what authority can the logician appeal to?

Formal logical systems are often seen as part of an attempt to systematize thinking, to improve (as it were) on ordinary thinking and the ordinary language on which it depends. And it is certainly true that ordinary language often deceives us and obscures the underlying logic (or structure) of an argument. Translating an argument into a formal language can reduce ambiguity, but those who have sought through the study of formal logical systems to illuminate the laws of thought or their foundations have been disappointed. Doubts surround not only the putative authority of a logical system but the very meaning of its symbols.

Technically, the meaning of what Rudolf Carnap called the fundamental mathematico-logical symbols (now usually called logical constants) derives from the explicit rules we lay down for their use, but in fact the question of their meaning remains obscure. One thing is clear: the whole exercise is paradoxically dependent on a prior understanding of the basic logical operations. Ordinary language use is also predicated on such an understanding: anyone lacking it would not be able to use language in anything like a normal way.

The work of Frege and his successors led, of course, to the development of digital computers in the mid-twentieth century, and in this sense it was spectacularly fruitful and successful. But it has not really led to a new understanding of human reasoning or established clear guidelines - as Frege hoped - for how we ought to think.

In fact, the attempt to create formal systems which can do what natural language can do has led to a renewed appreciation of the complexity, power, elegance and logical depth of the latter. Wittgenstein was right to warn against thinking of our everyday language as only approximating to something better, to some ideal language or calculus.

We need formal systems for dealing with mathematics and science and technology, but, as far as the fundamentals of logic are concerned, it's all there - implicitly at least - in the language of a five-year-old child.

Gödel's magical mind

Kurt Gödel is one of the key figures in the intellectual history of the 20th century, but, like many people who are highly gifted in domains like logic and mathematics, he struggled to cope with mundane reality. He also had paranoid tendencies in his later years and suspected that people were trying to poison him. In the end he just stopped eating.

I was reminded of Gödel when I recently came across this paragraph in an article by Matthew Hutson about our deep-rooted tendency to think in terms of magical rather than scientific logic:

Another law of magic is “everything happens for a reason” — there is no such thing as randomness or happenstance. This is so-called teleological reasoning, which assumes intentions and goals behind even evidently purposeless entities like hurricanes. As social creatures, we may be biologically tuned to seek evidence of intentionality in the world, so that we can combat or collaborate with whoever did what’s been done. When lacking a visible author, we end up crediting an invisible one — God, karma, destiny, whatever.

Interestingly, Gödel took his teleological convictions as being simply and comprehensively true. His belief that everything happened for a reason led to some very odd conclusions and was a source of some amusement and no little concern to his friends.*

Gödel was a deeply religious man who believed in a spiritual realm and life after death. Hutson's article mentions our inability to accept - or even to conceive of in a deep sense - our own mortality as another example of magical thinking. (Gödel himself, as I recall, justified his own belief in an afterlife on teleological grounds.)

The paradox of this pioneer of mathematical logic being, in ordinary life, completely under the sway of magical thinking calls for some kind of explanation or comment. Was it that he sought to impose the strict and clear logic of his professional work onto a world which works in more complex (and random) ways? Was it that he put too much faith in the ability of his mind to intuit reality, seeing the mind as a spiritual thing rather than something arising from a bodily organ carrying the marks of a long evolutionary history?

Hutson's main point is that magical thinking is natural to us and can enhance our lives. On the other hand, he sees it (quite rightly I believe) as misrepresenting objective reality and as potentially dangerous. Gödel's case illustrates some of the dangers, but clearly he had specific psychiatric problems in his later years, and it would be simplistic to attempt some kind of comprehensive explanation of his fate as being occasioned by extreme teleological thinking or whatever.

Gödel remains a great thinker and was a man with many appealing qualities, not the least of which were gentleness and reticence. His later years, after the death of his best friend, Albert Einstein, were sad and ultimately tragic.

His religious - or magical - convictions were an integral part of the man and no doubt contributed to his greatness. And, one hopes, provided some comfort in the darkness of his final years.



* I recommend Rebecca Goldstein's concise and accessible account of his life and thought, Incompleteness: The Proof and Paradox of Kurt Gödel (Norton, 2005).

Apparitions

In David Berlinski's world, the great mathematicians and logicians of times past are alive and well, and make regular appearances in the here and now. Leibniz comes late one night to sit by Berlinski's desk and discuss his curious notion of an encyclopedia of human concepts, "his lush old-fashioned wig proving irresistible to my cats, who have come creeping from their tower to bat at it."*

And Gottlob Frege [1848-1925] somewhat surprisingly team-taught logic with Berlinski at an unnamed California college at an unspecified point of the later twentieth century:


Our classes were always well attended because logic was a prerequisite for an engineering degree, and they were, I must say, well received, Frege and I both receiving excellent if somewhat innocent standardized student evaluations, any number of students somehow saying the same thing, that while Mr. Berlinski should learn to match his ties and suits, Mr. Frege is very nice. No wonder they never complained about his clothes. Frege would dress severely, no matter the sunshine, which even in February seemed to light up every corner of the campus, wearing the same black frock coat and batwing collar that, no doubt, he had worn in Germany. You must imagine the man at the blackboard, the thick German chalk in his fingers, his back always toward our students and the logical symbols going up and down the board, the steps separated, when necessary, by heavily drawn lines.


Is Berlinski romanticizing the intellectual figures of the past in his literary fantasies? No doubt he is. But then perhaps Frege and other pioneers of logic were indeed special, and alive to the wider implications of their work in a way most contemporary logicians are not. This may be because they were wrestling with big ideas rather than merely technical elaborations of those ideas. Peter Smith has recently made the point that today's more 'advanced' logic is less philosophically interesting than the more basic stuff (in effect the work of the great pioneers).

Berlinski was taught logic by the legendary Alonzo Church, and so has in my mind a certain reflected glory, a certain aura, as he is a link to a great age of human thought. Like an old colleague and friend of mine who was taught by Willard Van Orman Quine, a fact which - quite irrationally - made me very forgiving of his many personal failings.**

One last quote...


Sometime in the fall after the spring in which Frege and I had taught logic together in California, my great friend, the logician DG took his life. He had loved someone a great deal and for a very long time, and when it was over he had only logic left and logic was not enough. He was cremated in Colma at the insistence of his wife; I watched as the conveyor belt took his coffin toward the winking red lights; there was a roar from far away as the gas-fired jets ignited, and two hours later, I was given a plain wooden box with his ashes.

I took the box with me to one of those sparse California hills, which are covered with chaparral and a few scrub oaks standing in copses.

I was about to scatter the ashes when I noticed that Frege had joined me. He was dressed, as always, in black. I opened the box and let the salt-smelling wind carry the ashes far away.

Frege looked into the middle distance. I thought he would remain silent.

"I always come for my own," he said, just before vanishing himself, leaving me alone with the smell of wild sage.




* All quotations are from Berlinski's The Advent of the Algorithm (Harcourt 2001).

** In truth, he is a good and intelligent man. (Hello John!)

Possible worlds and possible worlds

I have trouble seeing philosophy as an intellectual discipline. The gist of my thinking is that 'philosophy' is a word which has changed its meaning quite dramatically over the centuries as various sciences have split off from it and I'm not sure that it has much meaning left.

If one has a theological view of the world, philosophy's position will not be threatened as it can resume (or continue) its traditional role as a secular complement to theological discourse. But if one denies that there are truths we can intuit or know by non-empirical, non-deductive means, then, arguably, there is no place for a non-scientific intellectual discipline (unless it be seen as an art form or as a kind of game).

Of course, the study of formal deductive systems, logical or mathematical, is non-empirical, but it is continuous with science.

All that is left of philosophy for someone who rejects claims to substantive intuitive knowledge of a religious or moral kind are reflections on the various intellectual disciplines (physical, social and historical sciences, mathematics, logic, etc.). Such meta-thinking is best carried out (I would presume) by the practitioners of the various intellectual disciplines rather than by outsiders (whether or not they are designated as 'philosophers').

I do recognize, however, that much pure and applied work in certain disciplines (logic, mathematics, psychology and linguistics come to mind) draws strongly on philosophical traditions of thought, and raises issues which previously have been addressed by philosophers. An example of such work is the attempt (drawing on theoretical work in logic and mathematics as well as linguistics) to model the processes of natural language.

Computational linguistics clearly has great practical and commercial importance at the moment, but it can also be seen as a project the relative success [or failure!] of which has implications for the way we see human language – and ourselves.

My reading of the current state of play is that the formal approaches which followed in the wake of Chomsky's early attempts to give an explicit analysis of the syntax of ordinary language have not delivered as expected, just as early work in the field of artificial intelligence produced very disappointing results. Both of these research projects underestimated the importance of contextual factors and real world knowledge which is inevitably a part of intelligent human functioning and communication. Formal systems need in some way to be integrated into this real world context, but, even if they are, it is still possible that many important aspects of language and communication will remain out of reach. I am thinking in particular of aspects of language use which depend on social awareness, a sense of the sorts of things that people with autism spectrum disorders have trouble dealing with, including subtleties of tone and style.

There is a huge body of theoretical work in the syntax and semantics of natural language which shows, if nothing else, that there are countless ways of conceptualizing and formalizing (at least aspects of) natural language. In the light of this profusion, the key question – it seems to me – is not which theoretical approaches are true (whatever that might mean) but which are useful.*

We may want to postulate possible worlds and use set theory to model the semantics of natural language, including complex noun phrases and verb tenses and auxiliaries. But sets and 'possible worlds' are only one way (albeit a possibly enlightening one) of representing the way, for example, words like 'must' or 'could' or 'should' work. No claim need be made that such possible worlds exist. They are merely useful fictions.

Physicists, of course, also talk about other possible worlds, parallel universes and so on, but they are making ontological claims. Their concern is primarily with how the world (or the multiverse) is rather than with formal systems, though they use formal systems to model the operations of nature (as linguists may use formal systems to model the operations of natural language).

But the possible worlds of logicians and linguists are – notwithstanding some outlandish claims by certain logicians – merely formal constructs, to be judged entirely by their usefulness. The other worlds of the physicist may well prove in fact to be 'out there' – to exist in the normal sense of the word, though they may be inaccessible to us.

I am aware that the question of what existence consists in is a traditional philosophical one, but is it a serious or potentially productive question? I think not. Most of the confusions can be resolved simply by accepting that we use words like 'exist' in various ways.

The one area which does seem to raise important issues is mathematics. Just as there are possible worlds and possible worlds (the 'worlds' of the logician and the worlds of the physicist), so there are formal systems and formal systems, and, as we move from, say, the first-order predicate calculus to formal systems which can encompass arithmetic we cross a kind of threshold. Mathematics needs to be clearly distinguished from logic. But this is a topic for another time.



* This is not to say that the exercise of trying to create formal representations of natural languages may not reveal interesting things about natural language and provide new, more concise, more explanatory ways of understanding aspects of the grammar of those languages than traditional grammars provided. But, although such rarefied goals are not pointless, nor are they the sorts of goals for which society is likely to provide support. Traditional grammarians were, after all, essentially pedagogues and their grammars were pedagogical aids.

The gnome of logic

David Berlinski has written with gloriously overabundant and rich rhetorical flair on the history of mathematics and logic. Here he introduces Gottlob Frege, whom he calls "the gnome of logic":

His life was bleak. Frege was born in 1848 in Wismar, which lies in the province of Mecklenberg-Schwerin. Bleak enough. This is northern Germany, the land facing the Baltic Sea. Bleaker still. It is a countryside of dark and gloomy forests, hags and elves and goblins and toadish-looking men behind the sombre trees. At night, the horned owls hoot and black-footed wolves trot restlessly along the forest paths and hunchbacks gather in darkened glens to play the clarinet.

Frege spent his entire academic career at the University of Jena, trudging like Peano in Italy up the obligatory steps of the academic ladder: a Privatdozant in 1871, and so authorized to accept students without pay, an ausserordentlicher Professor in 1879, a Professor in 1896, and thereafter a Herr Professor, the open-voweled Herr followed in conversation by the three even beats of Professor.

He was married for many years - happily, so far as I know - die gnädige Frau Frege dying along with Europe during the course of the First World War, and so darkening a personality that was already dark, lonely, crabbed, solitary, and withdrawn.

And he seems to have been - in plain fact, he was - a ferocious anti-Semite, seeing in Germany's sad, doomed, cultured German Jews an alien and unwanted presence, and, no doubt, regarding the turbulent wave of eastern European Jewry, which had washed over Germany early in the century and with outstandingly bad judgement come to rest in Leipzig or Dresden or in Weimar itself, with feelings akin to frank revulsion. Disliking Jews, Frege disliked Catholics as well, the ink of his indignation ecumenical in its nature. He was deeply devoted to the German monarchy, its preposterous and dangerous kaiser receiving from Frege the respectful sentiments that he had nowhere else to discharge. With the exceptions of Bertrand Russell, Ludwig Wittgenstein, and, to a certain extent, Edmund Husserl - a not inconsiderable trio, of course - contemporaries could not fathom his work. It was ignored when it appeared, and if philosophers and logicians now agree that Frege was the greatest of mathematical logicians, if only because he was the first, their encomiums came too late to afford him solace. He died in 1925.

And he died alone.


[From The Advent of the Algorithm (Harcourt 2001), pp. 48-49.]