‘Brief and powerless is Man's life; on him and all his race the slow, sure doom falls pitiless and dark. Blind to good and evil, reckless of destruction, omnipotent matter rolls on its relentless way; for Man, condemned to-day to lose his dearest, to-morrow himself to pass through the gate of darkness, it remains only to cherish, ere yet the blow falls, the lofty thoughts that ennoble his little day; disdaining the coward terrors of the slave of Fate, to worship at the shrine that his own hands have built; undismayed by the empire of chance, to preserve a mind free from the wanton tyranny that rules his outward life; proudly defiant of the irresistible forces that tolerate, for a moment, his knowledge and his condemnation, to sustain alone, a weary but unyielding Atlas, the world that his own ideals have fashioned despite the trampling march of unconscious power.’

That is from Bertrand Russell's popular essay: ‘A Free Man's Worship’, written in 1910.

Of the many words he wrote, these are perhaps the most disdained by other philosophers: effusions of melodramatic materialism.

If Russell's body of work had mostly been of this ilk, he would not deserve, or have attained his place, far higher in our cultural pantheon than the peddlers on the other side the street, peddlers (for the most part) of blather about ‘spirituality’, ‘the meaning of life’, ‘transcendence’, etc., etc.

Bertrand Russell was a -- if not the -- leading figure in the rise of analytic philosophy. His best work was done before 1930; some would say 1920. Many philosophers would agree that if Russell had died about then, instead of lingering till nearly 100 in 1970, his stature would be undiminished, even enhanced. His Nobel Prize winning volume on the history of western philosophy came in the 30s; but it has been (a bit unfairly) denigrated as ‘Russell's Joke Book’. Russell shares with Sigmund Freud the distinction of winning a Nobel Prize for literature for writing neither poetry nor fiction.

Here I explain two of Russell's major ideas, ideas in the area of interplay among language, logic and metaphysics, interplay in a manner that Russell did much to inaugurate, the manner called the linguistic turn, the turn to philosophy of logic and language. To the chagrin of some and the rejoicing of others, analytic philosophy has dominated English-speaking philosophy for over a century now. Russell's influence was also great on European philosophers, mainly in Vienna, but also in Scandinavia and Poland. The Europeans who were most influenced, the logical positivists, fled Europe in the wake of Nazism and, for the most part, carried on in the United States and England.

The first idea I shall explain is a matter of Russell finding a new locale for philosophy's venerable concern with, and contrast between, Appearance and Reality. Russell introduced a distinction between the grammatical form and the logical form of sentences. Grammatical form is appearance; logical form is reality. The paper in which Russell inaugurated the distinction, written in 1905, is titled ‘On Denoting’. In this landmark essay he proposes his Theory of Descriptions.

His concern is with sentences such as:

Attend to the subject expressions, phrases of the form:

which are called definite descriptions. Russell reiterated his theory in a chapter headed ‘The’ in his Introduction to Mathematical Philosophy. A chapter devoted to the meaning of one such word is an emblem of analytic philosophy. Usually, if a philosopher writes profusely about one word, it will at least be a rather exciting word, such as ‘justice’ or ‘knowledge’ or ‘virtue’ or ‘beauty’, not the humdrum definite article.

Suppose I assert that the Prime Minister of Australia is a Christian. The subject of that sentence is ‘The Prime Minister’ and the predicate is ‘is a Christian’. Being a Christian is predicated of the Prime Minister. I have, we may think, predicated something of Tony Abbot, even though I did not, in the sentence, use his name. That is already to move from linguistic appearance toward logical reality. I spoke of Abbot using a definite description, took myself to be referring to him, picking him out, or, to use Russell's term, denoting him. With such a bit of language, we may take ourselves to be referring to a particular man, Tony Abbot; but, as we shall see, it is not so clear as it seems that the words I have spoken are really doing that. It is not so clear that when we use bits of language like ‘The………’, what we do is pick out an individual, despite the appearance that we do. Russell argues that if we must say what it is that what we say is about, we should say that it is about the world in general. It is, despite appearances, something general, not particular, that we are saying. Let me explain this further.

It seems all very well to think that what we say is about, or picks out, or denotes some particular individual so long as Abbot is around to be picked out and is, in fact (or not), a Christian. I mean it is all very well in the way of being true or false, and so in the way of making sense, being meaningful. We typically speak declarative sentences seriously and meaningfully when (and only when) what we say is true or false. Whether true or whether false, something has been asserted if and only if it is true or false.

It has long been taken (though not by all thinkers) to be a condition of a sentence being meaningful as opposed to meaningless, making sense as opposed to being nonsense, that the statement made with the sentence be either true or false. A fundamental logical truth, it is held, is that a statement must be either true or it must be false. The requirement is entitled The Law of Excluded Middle. There is no in-between. In recent times, this requirement is modified by saying that it is a condition of factual discourse that what is said be either true or false. If speakers say things with declarative sentences that are neither true nor false, they are not engaged in factual discourse, but are instead expressing emotions or attitudes in a misleading way. An example: while one appears to be stating a fact, e.g., ‘Adolph Hitler was a bad man’, one is really saying something such as ‘Bah to Adolph Hitler!’ or ‘Damn Adolph Hitler!’ The appearance is declarative, the reality expressive. Russell was not very happy with this deployment of his relocation of matters of appearance and reality. He acknowledged that he found great difficulty with the idea that to call something wrong or bad was only to express dislike or disapproval of it. But let me pass by this depressing development in twentieth-century philosophy and return to the business of sentences containing definite descriptions. I do not want however to move on without noting the irony. Russell inaugurates a striking new way of contrasting appearance and reality and finds it applied in a way he finds troublesome.

Instead of ‘The PM of A is a Christian’, consider ‘The King of France is bald’. If I say that, am I predicating of the French monarch that he is hairless? But France is no longer a monarchy. No such king is anywhere to be picked out and have predicates latched on to him, to have qualities attributed to him, as Tony Abbot was. We can speak of the subject of the sentence and of the predicate. But that is grammar. After all, if I had to say what I was predicating of what, with verbiage such as ‘The slithy toves did gyre and gimble in the wabe’, I could say that gyring and gimbling are being predicated of slithy toves. When I speak of subjects and predicates here I am speaking of the surface, of grammatical form (appearance), not at the deeper level of logical form (reality). We want to discern logical form, which is to get down to what goes into being true or false, not merely grammatically or linguistically – superficially – well-ordered. To say that the PM of A is a Christian looks like attributing a quality, being Christian, to Tony Abbot. But when it comes to slithy toves, there is nothing we can say we are attributing to anything. Nor is there anything we are referring to or picking out with the phrase ‘the slithy toves’.

Now consider the King of France. Russell was worried about the requirement mentioned above, that a sentence's being meaningful requires that speaking it constitute asserting or stating something true or false. This view about meaning and truth goes back to Aristotle. He also thought that anything you stated had to be one way or the other. If what you say captures neither things as they are nor things as they are not, then you have really said nothing; sound without sense, as Spinoza will later put it. Russell is worried about that with ‘The King of France is bald’ He first considers its surface appearance, suggests that we may think we understand it as telling us we will find the man picked out if we survey the class of bald people (if it is true) or if we survey the class of hirsute people (if it is false). He then notes that the monarch will not be found in either the class of bald men or in the class of hirsute men. In a jibe at Hegelians, he says that they, who love a synthesis, will declare that the king, being neither bald nor hirsute, must wear a wig. The sentence ‘The King of France is bald’ has the appearance of being about a particular man and a condition of his head. The sentence appears to attribute baldness to a man who reigns over France. But there is no such man.

So how can it be that the sentence, which is clearly not nonsensical, clearly is meaningful, manages to be either true or false? Russell shows us how it is false. He says that the denoting phrase ‘The King of France’ does not refer to or pick out, despite appearances, an individual. Rather the sentence, despite its appearance of being a singular statement, is really a general statement; moreover it is not just one general statement, but a conjunction of three general statements. It is logically, but not grammatically, a conjunction of three statements. And if any one of those statements is false, then the whole thing is false. It cannot be that ‘P and Q and R’ says something true if ‘P’ or ‘Q’ or ‘R’ says something false. That is the logic of the word ‘and’. If we want to ask what the statement made using the sentence is about, the answer is that it is about the world in general.

Here are the three sentences:

Lewis Carroll, who helped us with the slithy toves, can help us now to appreciate the force of this dethroning of the monarch as head of sentence. In Through the Looking Glass, a messenger arrives at court, out of breath from haste. The king is annoyed that the message is too late, and chastises the messenger for being late. The messenger replies: ‘But Your Majesty, I came as fast as I could and nobody passed me on the road’. The King sniffs and says: ‘Not so; if nobody passed you on the road, he would have got here before you did.’

The messenger might have fallen in with the king's foolishness and replied ‘Not necessarily so, your majesty, he might have passed me going the other way.’ When I taught at the University of London, my college, because demand was so great for philosophy, used entrance exams and interviews for those who applied. The test included the exchange between the king and the messenger and asked for comment. One woman's exam was very good, even brilliant, except for some obscurity in her comment on that passage. At her interview she was asked what, at first glance, she had thought of the exchange. She looked embarrassed and said: ‘I thought the messenger was using the word ‘nobody’ properly and the King was using it as though it were a proper name.’

This impeccable response delighted us; puzzled, we asked her why she hadn't said that in the exam. She replied: ‘I thought it was too obvious.’ Thus began her training in one of the philosophical arts, knowing when to say the obvious. Of course we accepted her. She achieved l^st Class Honours, went on to a doctorate, and teaches in England.

The three sentences with which Russell replaced ‘The King of France is bald’ have pronouns, somebody and nobody, as their grammatical subjects. They are general, not singular statements. The first is false. Nobody is King of France. The second and third are true. So the meaning, the logical reality of ‘The King of France is bald’, as Russell has analyzed it, is the conjunction of three statements and for a conjunction to be true, each of its conjuncts has to be true. ‘The King of France is bald’ is thereby false. Problem solved; the tight relation between meaning and truth or falsity is preserved. The same analysis would apply to ‘The PM of A is a Christian’, though it would come out true. Logical analysis has to be the same even when it so happens that there is an individual corresponding to the subject expression of the sentence. Logic, sense making, is what goes into making what we say ‘truth-evaluable’, that is, susceptible of either truth or falsity.

The Theory of Descriptions resolved other issues. Russell aided in the demise of the ontology of the German philosopher Alexius Meinong. Ontology is the (portentous sounding) study of being as such. An ontology is a stable of things that have being, or a stable of possible beings or a list of kinds of beings. Meinong was concerned with this. If you think that words and phrases having meaning is a matter of words picking out things then fantasy, fiction, and imagination become problematic. Meinong fretted over sentences such as ‘The golden mountain does not exist’. If to have meaning is to stand for something that exists, that sentence is implicitly contradictory. Meinong also worried about the more explicitly contradictory ‘The round square does not exist’. He decided that in order significantly to assert that the golden mountain and the round square do not exist, you had to allow that they enjoy some kind of being; he called it ‘subsistence’. A phrase like ‘The so-and-so’ that fails to latch on to anything existing has to latch on to something, some sort of being. Some phrases stand for things that only subsist, others for things that exist. Subsistence may be rather shadowy but there are all those imaginary or fictional or unreal things we speak of; they must have some sort of being. The words we use are not empty sounds or scribbles. This makes for a metaphysical clutter, which was dubbed Meinong's jungle. Russell cleared it up. What such phrases contribute to the meaning of a sentence is dissolved out of the subject and crystallized in the predicate. Their place as subjects, grammatically speaking, is taken over by the pronouns ‘somebody’, ‘someone’, ‘nobody’, ‘nothing’ etc. So, ‘The golden mountain does not exist’ gets analyzed as:

The apparent reference to the self-contradictory round square evaporates into:

It is only a joke to take the word ‘Nothing’ as picking out something. It takes on the burden of grammatical subject, and does so in a way that disinclines us treat it as a word picking something out.

Russell's’ accomplishment was logical analysis at its best, dissolving problems. Notice that the problem is not solved by answering a question, such as ‘Who or what does an expression of the form ‘The so and so’ stand for, unless it is an answer to that question to say ‘nothing’. The idea is to insist on looking at the entire sentence in which the phrase occurs and see how to locate its contribution to the meaning of the statement elsewhere than it appears to be located. Surface grammar misleads to unnecessary metaphysics; underlying logical reality restores sense and sanity. If Martin Heidegger had read Russell, would he still have written his famous piece of nonsense: ‘Das Nicht nichtet’ (The Nothing noths’)?

The second idea of Russell's I will discuss was mistaken, and I will again exploit Lewis Carroll to bring out what the mistake is.

Russell held that logical truths are among the highest levels of generality and necessity about the structure of reality. This might also be put by saying that the laws of logic stand above even the laws of nature. It is not so difficult as you might think to slip into this. When you are given a deductive argument that you see to be valid, there is recognition of compulsion: you have no choice but to agree to the conclusion if you have agreed to the premises. Wittgenstein spoke of ‘the hardness of the logical must’. And when you think of it that way, it can seem harder even than the ‘bound to be’ or ‘cannot but be’ of ‘The water must be boiling’ as the temperature hits 100C, if you are sea level, or ‘The glass cannot but fall’ as you release your grip on it.

I now offer a genesis of this illusion: we speak, initially harmlessly, of logical truth. The idea of laws of logic, which comes next, is already more problematic because of its assimilation of logic to physics, which is already an extension of ‘law’ from the social order, where it is most at home, to the natural order. But even ‘logical truth’ should be treated warily. Russell was not wary enough. His pupil, Wittgenstein, was, but that is for another day.

Russell fell into error because of his devotion to mathematics, the intellectual love of his youth. He was deeply impressed by the provability, certainty and the necessity of mathematical truth. Compared to facts we learn of by observation and experiment in everyday life and the laboratory, the ‘facts’ of mathematics look more firmly established. I think it is already an error to regard mathematical discoveries as findings of fact. To do that assumes that there is no difference between established truths and established facts, thus no difference between truths and facts. But there is a difference.

Here is a hint, but only a hint, that I am right about this. In the criminal justice system, we leave it to juries to decide matters of fact. We do not leave it to juries to decide matters of law or mathematics or morality. (A prospective juror who admits to holding that the relevant laws are themselves unjust will be disqualified.) It is bizarre to contemplate such a practice; but that is the hint. Still, it is only a hint and to make my point about facts and truths would also need another day.

Seventeenth-century philosophers distinguished truths of reason and truths of fact. A distinction is made between the a priori and the a posteriori, between what you can find out from just understanding what is said and what you have to make observations and devise experiments to find out about. Lurking in the background is the metaphysical distinction between the necessary and the contingent, which has nothing immediately to do with meaning and knowing, but is focused on whether a way things are could be or could have been otherwise.

Meaning, knowledge, understanding and truth are all stirred up in this mix. And no philosopher has yet baked a cake that pleases everybody The American philosopher, Willard Quine, rubbished the whole enterprise and said there was just truth, falsity and relative strength of belief. When you look at it naively, mathematical investigation is similar enough, experientially, to empirical investigation to incline one to treat the truths of mathematics as stating facts, indeed as facts more tightly stitched into the fabric of reality than the facts of astronomy, physics or chemistry This is especially striking when we think about numbers and not merely count with them. Suppose, having cottoned on to the idea of a prime number, a number divisible only by itself and 1, you are asked how many prime numbers there are between 10 and 20. It is easy to work out that there are, and can only be, four of them: 11, 13, 17, and 19. But now ask: how many between 100 and 200? Unless you are some sort of prodigy, you will have to do a lot of calculating. Some have even noted that, especially if you use a mechanical or electronic calculator to get the answer, you perform actions and wait to observe the results, rather like an experiment, not all that different from putting various stuffs in a test-tube, heating it up and waiting to see what colour the stuff turns or whether it crystallizes or explodes or whatever.

A nice example involves perfect numbers. 6 is a perfect number. What is perfect about it? It is divisible only by 1, 2, and 3; and 1, 2, and 3 add up to 6. The next such number is 28, which is divisible by 1, 2, 4, 7, and 14, which add up to 28. So a perfect number is a number that is the sum of the numbers, which divide evenly into it. Now I have not the remotest idea what the next perfect number is. For all I know there might not be anymore, though I reckon that is most unlikely. Indeed I incline to say I am certain there are more. (This shows, interestingly, that certainty can be justified or reasonable without thereby being knowledge.) I am sure that there is a neat formula for determining such matters.

While this activity of calculating is clearly different from the activity of ascertaining, say, how many guests are staying in Hilton hotels tonight, there is enough similarity to strike us that, in both cases, we are after the facts.

Suppose I am granted these points. But then suppose, like Bertrand Russell, you are sufficiently wondrous at the rigor, clarity, necessity and certitude of mathematics that you want to dig deeper, find out why the facts in this domain are so necessary and certain. The German philosopher Gottlob Frege and the American Charles Peirce, through striking intellectual effort, made stabs at reducing mathematics to logic, which means, roughly, establishing that mathematics just is logic. Russell famously criticized Frege's work but pursued the same goal himself. They both developed theories of language and logic which made it plausible to say that mathematical truth, with its necessity, was not a distinct kind of necessary truth, but was really logical truth.

If you can't do something like that, you will have to say that there are two distinct species of necessary truth, mathematics and logic. And in this region of thought, less is always more. Don't multiply necessities beyond necessity!

But suppose you do think of mathematics as not just a body of truths, but as a body of facts, facts which if not in physical space, are at least in logical or metaphysical space. The issue here also gets raised by worrying about whether numbers are entitled to be treated as objects, as some kind of substantial entities, as among the things that there are. If, in the grip of all this, you can reduce mathematics to logic, it provokes the idea that logic itself is a body facts, very deep down or very high up in reality, superfacts. Things could go the other way. If you are dubious about calling mathematics a body of facts, you may instead, to take one line, hold that mathematics is the devising of formulas and equations which can be applied to reality in explanatory enterprises. I lack the knowledge and understanding to explain this idea further. I think Wittgenstein was a proponent of such a view; he seems to have thought that mathematics was an activity of inventing new concepts.

Now, exploiting Lewis Carroll again, let me try to show why we should not construe logical truths as very high (or deep) level matters of fact.

The point summarily put is this: Logically valid arguments have premises and a conclusion. The conclusion has to be true if the premises are. The premises may be ordinary, unproblematic statements of fact. However, the principle of inference, which is in play to get the conclusion, must not itself be understood as further premise. It is a different creature than the things it is being applied to. Rather as a rule of chess is a different creature from a move in the game, e.g., ‘The bishop moves on the diagonal’. But since, like a rule, the principle (the logical truth) will be put in the form of declarative sentence, it is possible to be led into regarding it as a further premise. Lewis Carroll tells a tale of Achilles and the Tortoise. I won't use the same examples Carroll used, but I am sure he would not mind.

Achilles invites the tortoise to agree that the streets are wet. The tortoise wants to know why he has to agree to that since they are indoors and can't see the streets, though rain can be heard. Achilles then argues: it is raining; so the streets are wet. The tortoise says that he might very well agree that it is raining, but he still does not see why he has to agree that the streets are wet. Achilles asks the tortoise if he does accept that if it is raining, then the streets are wet. The tortoise acquiesces but still refuses to accept that the streets are wet. Achilles is writing in his notebook. He first has:

After the tortoise's first refusal, Achilles’ offers the hypothetical as the further premise that will force the tortoise to accept that the streets are wet. The tortoise says that if that is needed he wants it written down. Achilles than has in his notebook:

1. 1. If it is raining, then the streets are wet.

2. 2. It is raining.

3. 3. So, the streets are wet.

But the tortoise still want to know why, if he accepts 1 and 2, he has to accept 3. Achilles, after some admonitions about logic taking you by the throat, persists and says: Well, don't you see that the following is true: If it is true that (it is raining), and it is true that (if it is raining then the streets are wet), then the streets are wet.

The tortoise says he wants to see that one also written down. Now here we must pause and notice something. The three numbered sentences above, taken separately, are such that each could be false. Different from the tortoise, I assume that you will agree that if you accept first two, you will accept the third. But hold on a minute about this new, more complex one. The tortoise wants it written down as the new number 1. So we get:

1. 1. If it is true that (it is raining), and it is true that (if it is raining then the streets are wet), then the streets are wet.

2. 2. If it is raining then the streets are wet.

3. 3. It is raining.

4. 4. So the streets are wet.

If you treat the new complex arrival as just a further premise, there will be an infinite regress. If the tortoise can resist 4 having agreed to 2 and 3, he can surely muster the temerity to resist the new number 1 as making any difference. Before long, Achilles, resorting to shorthand, will have to write:

If 1,2,3,3, 5, 6, …………, then the streets are wet. However those increasingly complex sentences differ importantly from the others. They are making (have the appearance of making) statements that cannot be anything other than true; instances of a logical principle, the principle called modus ponens, schematically:

If, (if P then Q) and P, then Q.

That is called a tautology and not really a proposition but instead a rule of inference. You may call it a logical truth if you like, but what the tussle between Achilles and the Tortoise shows is that you had better not think of it as a suppressed or hidden premise in a deductive argument. It is rather the principle that impels the premises to disgorge their conclusion, not an additional premise. We can also see that it is just a statement of the argument itself, the argument that takes us from 2 and 3 to 4. Aristotle, in his Posterior Analytics had already made the point, in effect, that a principle of reasoning should not be treated as a further premise in the reasoning.

So logic should not be viewed as a body of supertruths or superfacts. There is a more plausible case for seeing mathematics as a repository of truths about the fundamental structure of things, but that takes me out of my depth. Galileo said that the book of nature was written in number. Plato said nearly that long before. Nobody ever said that about logic, which suggests that the attempts to reduce mathematics to logic should be abandoned. The debate about whether and how number is built into the deep structure of reality is still going on. But I don't think anybody anymore is trying to maintain that logic is a body of laws more prominent in the universe than even physical laws.

It is interesting to note that Russell, having made so much of the difference between grammatical form and logical form failed to follow to his own advice. The superficial linguistic rendering of logical principles as declarative sentences, which we typically use to state facts, seems to have helped seduce Russell into his mistaken view. Metaphysician heal thyself!!!!

Let me conclude with something about Russell's influence on Twentieth- and twenty-first-century intellectual life. Let me distinguish between soft scientism and hard scientism. Russell was softly scientistic. Scientism values science above all other forms of enquiry, at its hardest denies the legitimacy of any inquiry that cannot be somehow rendered a scientific inquiry. Russell wanted only that philosophy be more or less continuous with science and believed philosophical analysis would either undo philosophical problems as confusions and muddles or, when not, hand them over in better order to the sciences, participate in shaping them up to be scientific problems or questions, resolvable by scientific theorizing and empirical hypotheses. He allowed that the intellectual labor involved was not itself science, but worthy of doing because the muddles were real, somehow deep and troublesome, and not easily dispelled.

In this respect he was not all that different from his pupil, Wittgenstein, even though he came to denigrate Wittgenstein's later style of attention to ordinary language. But Wittgenstein also thought philosophical problems were confusions and that the job of philosophy was, as he put it: ‘to prevent the bewilderment of the intelligence by means of language’. Russell and the Logical Positivists were much firmer partisans of natural science than was Wittgenstein; but they were no less inclined than he was to think of their work as a sharp turn in philosophy, a turn to clarification and to the demise of metaphysics. One might even say deconstructive rather than constructive, but French thinkers have prior rights that word.

Finally, what I mean by hard scientism is the view that no reflective intellectual activity, no sort of enquiry or thinking, is really worth doing unless it takes the form of testable empirical hypotheses or theories which generate such hypotheses or satisfactorily explain data of observation and experiment. We find hard scientism in the writing of Richard Dawkins, who has said, astonishingly, that issues of the meaning of life and our identity belong in the biology classroom.

It may very well be, as Wittgenstein says, that there is no answer to questions about life's meaning; he says the riddle does not exist, that the solution to the problem of life lies in the vanishing of the problem. That is why, he says, those who have solved the problem never tell us the solution.

The nineteenth-century German philosopher, Arthur Schopenhauer was out after curfew in a park. A policeman accosted him and demanded: ‘Who are you; what are you doing here?’ Schopenhauer replied: ‘Those are the questions!’ Well, Dawkins surely can't think that either the policeman or Schopenhauer should enroll in a biology course. It may be that these worries are not real, as Wittgenstein wants us to accept; we should somehow come to see that the questions are muddles. But so long as human beings are inclined, even if only in certain moods, to ask them and their kin, philosophy will not be able to turn entirely away from metaphysics.