Previous Talks
BERTRAND RUSSELL
I
"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 most popular essay: 'A Free Man's Worship.'
Of all the many words he wrote, these are the most disdained by other philosophers. Effusions of melodramatic materialism.
If Russell's body of work had all or mostly been of this ilk, he would not deserve his place, far higher in the pantheon than the peddlers, on the other side the street, peddlers of anti-materialism, spirituality, and blather about the meaning of life.
Bertrand Russell was a, if not the, leading figure in the rise of analytic philosophy. His vital 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, his stature would be undiminished, even enhanced..
I will try here to explain to you two of Russell's main ideas, ideas in the area of interplay between logic and metaphysics, but interplay in a manner that Russell did much to inaugurate, the manner called the linguistic turn, the turn to the philosophy of logic and language. To the chagrin of some, and the rejoicing of others, the linguistic turn of analytic philosophy has dominated English-speaking philosophy for a century or so now. The influence was also enormous on European philosophers, manly in Vienna, but also in Scandinavia and Poland. The Europeans who most influenced, the logical positivists, deserted Europe in the wake of Nazism and, for the most part, carried on their careers in the United States.
II
The first idea is a matter of Russell finding a new place for the contrast between appearance and reality, the leading candidate for the title of oldest concern arising out of reflective thinking. Russell introduced a distinction between grammatical form and logical form. Grammatical form is appearance and logical form is reality. The paper in which Russell established this distinction, written in 1905, is titled 'On Denoting'. In this landmark essay he proposes his Theory of Descriptions.
He is talking about a certain sort of description, which we find in definite descriptive phrases, such as 'The Queen of England'. 'The King of France', 'The Prime Minister of Australia, 'The corner grocer', 'The local butcher', The man giving 2009's initial Blackheath Forum talk'
So we are thinking about phrases of the form 'The so-and-so'. In later writing, Russell reiterated his theory in a chapter called 'The' in his Introduction to Mathematical Philosophy. A whole chapter devoted to such a word is high point of analytic philosophy.
Suppose we say that the Prime Minister of Australia is a nerd. The subject, if I may remind you of your school grammar, is 'The Prime Minister' and the predicate is 'is a nerd'. We are told by grammar that being a nerd is being predicated of the Prime Minister. Note that we can be said to be predicating being a nerd of Kevin Rudd even though we did not, in sentence, use his name. To do that is already to move to logical grammar. We spoke of Rudd using a definite descriptions, or took ourselves to referring to him. With that subject expression, that piece of language, we naturally take ourselves to have been referring to a particular man, Kevin Rudd. But, as we shall see, it is not so clear as it seems that the statement we have made is just about him.
It seems all very well so long as Rudd is there to be referred to and is, in fact, a nerd. I mean it is all very well in the way of being true, or, it is also just fine in the way of making sense even if think it is false. We speak with full and unproblematic meaningfulness when what we say is true or false. Whether true or whether false, something has definitely has been said.
It has long been taken to be a condition of a sentence being meaningful as opposed to meaningless, having sense as opposed to being nonsensical, that a statement made with the sentence be either true or false. A fundamental logical truth, so it has been held, is that every statement must be either true or it must be false. There is no in-between. In recent times, this position is qualified by saying that it is a condition of factual discourse that what is stated be either true or false. If speakers appear to make statements that cannot be evaluated as true or false, it may be said that they are not engaged in factual discourse, but making value judgments ethical or aesthetic. Let us for today keep the lid on that can of worms.
Now instead of 'The PM of A is a nerd.', think about 'The King of France is bald'. If I say that, will I be predicating of the French monarch, that he is hairless? Alas, he is not around, not anywhere to have predicates latched on to him. We can speak of the subject of the sentence and of the predicate of it. But that is just grammar. After all, if I were pressed 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 gambling are being predicated of slithy toves. When I speak of subjects and predicates here I am speaking purely on the surface, of grammatical form, not at the deeper level of logical form. We want to deal with logical form, which is to get down to what goes into statements being true or false, not merely grammatically well-ordered. We speak of logical subjects and logical predicates, or of individuals (or things) and of properties or qualities. Logically speaking, to say that the PM of A is a nerd is to attribute a quality, nerdiness, or, if you like, nerditude, to Kevin Rudd. 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 with the phrase 'the slithy toves'.
Now back to the King of France. Russell was worried about the requirement I mentioned above, that a sentence's being meaningful requires that uttering it constitute a statement that is true or false. This view about meaning and truth goes way back to Aristotle, who said that to speak truly was to say of things that they are as they are and to speak falsely was to say of things that they are as they are not. He also thought that anything you stated had to be one way or the other. If what you stated neither captures things as they are or things as they are not, then you have really said nothing, sound without sense, as Spinoza will put such things.
Russell is worried about that with 'The King of France is bald' He first considers construing it as saying about an individual that he is thus and so, bald. He suggests we understand this as saying we will find this individual via a survey of the class of bald people and, if not there, via a survey of the class of hirsute people. He notes, however, that the monarch is not be found in either survey, or, as he puts it, the monarch is neither in the class of bald men nor in the class of hirsute men. In a sneer at Hegelians whose side he once belonged to, he says that they, who love a synthesis, will declare that the king, being neither bald nor hirsute, wears a wig. A joke not to be found in a survey of the class of good ones.
The sentence 'The King of France is bald' has the appearance of being about a particular monarch and a condition of his head. The sentence appears to attribute baldness to a man who rules over France. But there is no such man, even if Sarkozy conducts himself like Charles DeGaulle or Louis XIV.
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 argues that the denoting phrase 'The King of France' does not refer to an individual. Rather the sentence, despite its appearance of being a singular statement, is really a general statement; moreover it is not just one singular statement, but a conjunction of three general statements. It is, logically, if 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 either P or Q or R says something false. This 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 or about men in general.
Here are the three sentences that result form logical analysis:
Somebody is King of France
Nobody else is King of France.
Whoever is King of France is bald.
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. But it is too late for the message to do any good. The king is annoyed and says to the messenger that he is 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 now have fallen in with the king's foolishness and replied 'Not necessarily so, majesty, he might have passed me going the other way.' When I taught at the U. of London, my college, because demand was so great, had to use entrance tests and interviews for those who wanted to study philosophy. The test included the exchange between the king and the messenger with a question asking for comment. One woman's exam was very good, even brilliant, except for some obscurity in her comment on the messenger and king. At her interview one of us asked her what she had thought at first glance of the little dialogue. She looked embarrassed and said: "I thought the messenger was using the word 'nobody' correctly, and the King was using it improperly, as though it were a name or proper noun. "
This reply, absolutely correct, delighted and puzzled us and we asked her why she hadn't written it down in the exam. She replied: 'I thought it was too obvious.' She began her training, then and there in one of the philosophical arts, knowing when and where to say the obvious. Of course, we accepted her. She now has a Ph.D. and teaches in London.
The three sentences with which Russell replaced 'The King of France is bald' have pronouns, somebody, nobody, whoever, 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 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 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 nerd', though it would come out true; or, if false, false because the third conjunct is false. Logical analysis is the same even when it 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. I will mention one. Russell aided in the demise of the ontology of the German philosopher Alexius Meinong. Ontology is, so it is sometimes portentously put, the science of being as such. An ontology is a stable of things said to have being and/or existence. There is a debate as to whether having being and existing are the same thing. A paper was written some years ago, entitled: 'There are some things that do not exist'. Meinong was concerned with this sort of business. If you think that having meaning is, has to be, a matter of something words stand for beyond other words then fantasy and fiction, and imagination generally, 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 'The golden mountain does not exist' is implicitly contradictory. Meining also worried about the explicitly contradictory 'The round square does not exist'. He decided that in order significantly to assert that the golden mountain does not exist, you had to allow that it enjoyed some kind of being, which he called 'subsistence'. A phrase of 'The so-and-so' form which appears to fail to latch on to anything existing has to latch on to some sort of being. Some phrases stand for things that have being only as subsistence, others as existence. Subsistence may be a 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 do not seem to be utterly empty. This makes for metaphysical clutter, which came to be called Meinong's jungle. Russell cleaned things up. What such phrases contribute to the meaning of a sentence is dissolved out of the subject and crystallizes in the predicate. Its place as subject, grammatically speaking, is taken over by the pronouns 'somebody', 'someone', 'nobody' etc. So, 'The golden mountain does not exist' gets analyzed to mean simply:
Nothing is both golden and a mountain.
And supposed reference to the self-contradictory round square evaporates into:
Nothing is both round and square.
Once again, a pronoun 'Nothing' which it is only a joke to take as standing for something, takes on the burden of grammatical subject, and does so in a way that dispenses with any inclination to ask what it stands for.
Russell's' accomplishment was logical analysis at its best, eliminating 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 substantival phrase, grammatically speaking, occurs and see how to locate its contribution to the meaning of the statement elsewhere than it appears to be. Surface grammar misleads to mad metaphysics; underlying logical reality restores sense and sanity.
III
Russell's second important idea was, I think mistaken; later I will again exploit Lewis Carroll to bring out what the mistake is.
The idea is that logical truth is the highest level of generality about the structure of reality. More dramatically, this can be put by saying that the laws of logic stand above the laws of nature. It is not so difficult as you might think to slip into this illusion (as I think it is). When you are given a deductive argument that you see to be valid, there is a recognition of compulsion: you absolutely have to accept the conclusion if you accept the premises. Wittgenstein spoke of this as '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. Here in Blackheath, it requires a bit less heat, as anybody making adjustment for boiling eggs after life in Sydney know. You have to boil them longer!!!!
I now offer my genesis of an illusion: we speak, initially harmlessly, of logical truth. The idea of laws of logic, which comes next, is more problematic just because of how its assimilation of logic to physics. But even 'logical truth' should be treated warily. I don't think Russell was wary enough.
Russell fell into error, I speculate, because of his devotion to mathematics, the intellectual love of his youth. He was deeply impressed by the provability and certainty of mathematical propositions. Compared to facts we learn of by observation and experiment in everyday life and the laboratory, the facts of mathematics always 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 one 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 on matters of mathematics. It is bizarre to contemplate such a practice. but that only strengthens the hint.
Seventeenth Century philosophers registered a difference by talking of truths of reason and truths of fact. It, or its near kin, is registered, but I think clouded, as the distinction between analytically true statements and synthetically true statements, statements whose truth can be ascertained simply by considering what they mean as opposed to having to look beyond meaning to how things, empirically, are. A distinction is also made between the a priori and the a posteriori, what you can find out from just understanding what is said and what you have make empirical observations and tests to find out about. Lurking in the background is the metaphysical distinction between the necessary and the contingent, which has nothing to do immediately with meaning and knowing, but is focused on whether or not a way things are could be or have been otherwise, or could not be or have been otherwise.
It is some further help for me that major philosophers have differed as to whether mathematics is analytic or synthetic, though they have mostly agreed that it is a priori and necessary. Indeed, there are philosophers who think arithmetic is analytic while geometry is synthetic and others who hold the converse view. The overall issue is by no means settled. Meaning, knowledge, understanding and truth are all stirred up in this mix. And nobody has yet baked a cake that pleases everybody. It is easy to see why the American philosopher Willard Quine rubbishes the whole enterprise and says there are just truth, falsity and degree of belief.
When you look at it naively, mathematical investigation is so similar phenomenologically, experientially, to empirical inquiry, that it is very tempting to treat the truths of mathematics as stating facts, and indeed facts which are more tightly stitched into the fabric of reality than even the facts of physics or chemistry or biology. This is especially striking when we think about simple issues in number theory.
Suppose, having learned about the notion of a prime number, a number divisible only by itself and 1, you are asked how many prime numbers there are between 100 and 200. Unless you are some sort of prodigy, you will have to do quite 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. How is that so different from putting things in a test-tube, heating it up and waiting to see, e.g., what colour the stuff turns to?
An example I like even better arose when I learned what a perfect number is.
6 is the first perfect number. What is perfect about it? It is divisible by 1,2,and 3; and those three numbers 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 which is the sum of its factors, the numbers which divide into it evenly. Now I have not the remotest idea what the next perfect number. For all I know there might not be anymore, though I reckon that is most unlikely. I am pretty sure the powers that be will have devised a little program for determining such matters by a few presses on a few buttons.
While this activity of calculating is quite a bit different from the activity of ascertaining how many guests are staying in the Hilton 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 certitude of mathematics that you want to dig deeper, find out why the facts in this domain are so necessary and certain. Russell, like the German philosopher Gottlob Frege and the American Charles Peirce, through brilliant intellectual effort, made strong stabs as what is called reducing mathematics to logic. That is, they developed theories of language and logic which made it plausible to say that mathematical truth, with its necessity, was not a distinct species of necessary truth, but an instance of logical truth.
If you can't do something like that, you will have to say that we have two distinct species of necessary truth, mathematics and logic. And in this region of thought, less is always more.
But suppose you already think of mathematics as not just a body of truths, but as a body fact, 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 should be treated as things, or, to speak metaphysics, substantial entities. If, in the grip of all this, you can reduce mathematics to logic, it will be natural to think of logic itself as a body facts, very deep or very high up metaphysical facts.
Things could go the other way. If you are start out dubious about calling logic a body of truths or a body of fact and you can then show that mathematics is just logic, you will become reluctant to think of mathematical statements as truths or falsehood, but instead, to take one idea I have heard about, as the devising of formulas and equations which can be applied to empirical reality in explanatory enterprises. I wish I had the knowledge and understanding to explain this possibility further, but I don't. I think Wittgenstein was a proponent of such a view of mathematics; 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 high-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 are themselves statements of fact. However, the logical principle which is applied to get the conclusion must not itself be understood as further premise. It is a quite different creature than the things it is being applied to. Rather as a rule of chess is a radically different creature from a move in the game.
But since, like a rule, the principle (or the logical truth if you like) will be put in the form of declarative sentence, it is possible to be duped into regarding it as a further required premise for the argument to go through. Lewis Carroll tells a short tale Achilles and the Tortoise. I won't use the example of an argument that Carroll used, but I am sure he would not mind.
Achilles is trying to get the tortoise to accept that the streets are wet. The tortoise wants to know why he has to accept that since they are indoors and can't see outside. Achilles says that it is raining, so the streets are wet. The tortoise says that he might very well accept that is raining, but he still does not see that he is forced to accept that the streets are wet. Achilles asks if he does accept that if it is raining, then the streets are wet. The tortoise acquiesces in this but still feels unforced to accept that the streets are wet. As they carry on, Achilles is writing things in his notebook. So far he has
It is raining.
So, the streets are wet.
After the tortoise's first refusal, Achilles' offers the hypothetical 'If it is raining, then the streets are wet' as the reason why the further premise that will force the tortoise to accept that the streets are wet. The tortoise says that if that were the reason, he would like to see it written down with the other statements. Achilles now has in his notebook?
1, If it is raining, then the streets are wet.
2. It is raining.
3. 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 rhetoric 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 (if it is raining, then the streets are wet), and it is true (that it is raining), then it is true that the streets wet.
The tortoise says he wants to see that written down.
Now here we must pause and notice something vital. The three 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, very complex one. The tortoise wants it written down as the new number 1 I suppose. So we get:
1, if it is true that (if it is raining, the streets are wet) and it is true that (it is raining), then it is true that the streets are wet.
2. If it is raining, then the streets are wet.
3. It is raining
4. The streets are wet.
If you treat the new complex arrival as a further premise, there will be an infinite regress. If I or the tortoise can resist 4 having agreed to 2 and 3, I can surely muster the nerve 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, etc., etc., then ---------- (whatever number will now suit the blank.
However that complex sentence differs importantly from the others. It is not, while they are, capable of making a statement that is anything other than true; it is merely an instance of a logical principle, the principle called modus ponens, schematically:
If, (if P then Q) and P, then Q.
That is a tautology not so much a proposition as a rule of inference. You may call it a logical truth if you like, but what the struggle between Achilles and the Tortoise shows is that you had better not think of it as a suppressed premise in a deductive argument. It is rather the principle that links the premises to 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.
So logic should not be viewed as a body of supertruths or superfacts. There is probably a more plausible case for seeing mathematics as a repository of truths about reality, but I 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 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 law more strongly enforced by reality than even physical law.
Let me conclude with something about Russell's influence on 20th and 21st C philosophy. I want to distinguish between soft scientism and hard scientism. Russell was softly scientistic. Scientism values science above all other forms of enquiry. Russell wanted philosophy to be more or less continuous with science and believed philosophical analysis would either undo philosophical problems as confusions and muddles or, when not muddles, hand them over in better order to the sciences, participate in shaping them up to be scientific issues, 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 seem deep and troublesome, and not all that 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 muddles and that the job of philosophy was, as he put it: 'to prevent the bewitchment 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 the overcoming of metaphysics. One might even say deconstructive rather than constructive, but French thinkers have grabbed 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 a leading biologist, Richard Dawkins, who has said, astoundingly, that issues of the meaning of life our identity belong in the biology classroom.
Well, 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 19th C German philosopher, Arthur Schopenhauer was out after curfew in the park. A tall policeman accosted him and demanded: 'Who are you; what are you doing here?' Schopenhauer looked up and 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 riddles are not real, as Wittgenstein wants us to accept and we should somehow come to see that the questions are confused. But so long as human beings are inclined, even if only in certain moods, to ask them, philosophy will not be able to turn entirely away from metaphysics.
- Lloyd Reinhardt
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