Lecture at the 2015 Austrian Ludwig Wittgenstein Symposium

Absolute Pluralism and Degrees of Nonsense


Wittgenstein’s Tractatus was to an important extent a development of ideas first presented by Russell with his version of logical atomism. Russell himself reacted to the doctrines of the monism of British Idealists. The monists held the view that a singular judgement can only be partially true. Russell and Wittgenstein tried to show that judgements – or propositions – can be and must ultimately be independent and can thus be absolutely true without reference to other judgements. Whereas a proposition of the postulated ideal language depicts an existing or not existing state of affairs and is thus unequivocally either true or false, the propositions of everyday language are often vague and ambiguous or nonsensical. Everything that is not strictly true or false is to some degree nonsensical. This includes propositions following the law of induction or a lot of hypotheses of natural science that have heuristic value but are not and do not claim to be true.

1. Pluralism vs. Monism

In 1914 Wittgenstein makes the following remark in his Note Books:

A proposition like ‘this chair is brown’ seems to say something enormously complicated, for if we wanted to express this proposition in such a way that nobody could raise objections to it on grounds of ambiguity, it would have to be infinitely long. (NB 19.9.14)

Even an apparently simple proposition like this, he thought at the time, must be analyzed into really simple propositions, the elementary propositions that depict configurations of really simple objects by means of simple names. This view, of course, the picture theory of meaning, follows the doctrine of logical atomism that was first proposed by Russell:
The philosophy which I wish to advocate may be called logical atomism or absolute pluralism, because while maintaining that there are many things, it denies that there is a whole composed of those things. (Russell 1976, p. 108)

The philosophy Russell introduced was a direct reaction to the predominant philosophical tradition of the latter half of the 19th century namely monism as advocated by British Idealists as e.g. F. H. Bradley.

Russell rejected the view that knowledge alters the fact and the doctrine that every proposition attributes a predicate to a subject (Russell 1959, p. 32f). More specifically he rejected what he calls the axiom of internal relations. (Russell 1959, p. 43)

For the monist no proposition can be absolutely true, not even propositions of mathematics. The monistic view is ably expressed by Harold H. Joachim:

To the boy who is learning the multiplication table 32=9 possesses probably a minimum of meaning. It is simply one item of the many which he is obliged to commit to memory. Three times three are nine, just as three times two are six, or as H2O is water‚ or as *mensa* is Latin for table. These are ‘truths’ which he accepts and must not forget‚ but which he does not understand. But for the arithmetician 32=9 is perhaps a short-hand symbol for the whole science of arithmetic as known at the time. (Joachim 1906, p. 93)

No universal judgement of science “expresses in and by itself a determinate meaning. For every judgement is really the abbreviated statement of a meaning which would require a whole system of knowledge for its adequate expression.” (Joachim 1906, p. 96)

To give a trivial example: “There are eight planets in the Solar System.” This judgement was wrong 200 years ago, true 150 years ago, false 80 years ago and now it is true again. Obviously the truth is not only dependent of the nature (and our knowledge) of our Solar System but also on our definitions of the terms.

But when Russell and Moore led the rebellion against monism, they were sure they had common sense on their side. Truth in isolation must be possible. As Russell put it: „Some propositions are true and some false, just as some roses are red and some white.” (Russell 1904 p. 523)

It cannot be an essential, intrinsic property of Napoleon that he was admired by Stendhal. And so it must be possible to reach a verdict on the truth value without recursion to every object in the universe to which an object has some relation.

If it was clear what an alternative to monism must accomplish it was not easy to come up with a sound theory. There were two main obstacles. First, what was the nature of an object, if it could not be the sum of its internal and external properties? How do we refer to Napoleon at all, if every proposition about him should state a contingent fact? And second, what does a proposition refer to, in case it is wrong? Russell addressed both points with his theory of descriptions. The baldness of the current king of France is handled by introducing an otherwise unspecified x as subject of two propositions, that x is king of France and that x is bald. And a third proposition claiming that x exists. The important achievement is, of course, that by analyzing a proposition like this the ambiguity vanishes. And this meant that the way to reach the pluralistic goal was to be achieved by disregarding language of everyday life and postulating an ideal language, consisting of propositions pointing unequivocally to facts.

2. Wittgenstein’s Solution of the Riddle of External Relations

Unlike Russell Wittgenstein was not really interested in epistemology when he stated his own version of logical atomism in the Tractatus. So the first thing he would get rid of were logical objects, that according to Russell one had to be acquainted with e.g. to understand a multiple relation.

Instead Wittgesnstein postulated two realms, one ultimately consisting of objects one of names. These realms were isomorphic, meaning that every possible combination of objects, a state of affairs, had an exact counterpart in the realm of language, an elementary proposition (and vice versa, of course). The external relation between objects is what is contingent about the world but that the external relation is possible is guaranteed by the internal properties of the objects. To know an object I would need to know its internal properties, not the external. (T 2.01231) Whatever elementary proposition one utters (if it were possible in practice) would depict a possible reality. It would necessarily be true or false. In the realm of elementary propositions it is impossible to judge “a nonsense”. This, Wittgenstein says, is a condition that Russell’s theory does not satisfy. (T 5.5422) Everyday language is different, unfortunately. Language disguises thought, he said. It is impossible to infer the form of the thought beneath it. There are enormously complicated tacit conventions that make understanding everyday language possible. (T 4.002) And obviously, somewhere on the road taken to get from the form of thought to actual language nonsense emerges.

3. Kinds of Nonsense

The propositions of the Tractatus are nonsensical. The author himself said so, as if he were not sure that his readers would be able to make this observation. The ongoing argument now, of course, is whether they are “mere” nonsense or somehow “illuminating” nonsense. The suspicion that resolute readers try to discourage is that some kind of nonsense manages to somehow carry some meaning. Roger White gives a couple of examples of what he considers clear cases of nonsense that, nevertheless, get some meaning across. One example is Shakespeare’s “uncle me no uncle” another is a comment to a chess game: “Bj10 would have been even stronger” (than Bh8, that is). (White 2011, p. 38, p. 41) Not surprisingly, perhaps, resolute readers are not impressed. The examples, so Conant and Dain argue in their reply, are not nonsensical at all, since they have a “clear use” (Conant and Dain 2014, p. 70) And indeed since it is always possible to attach some meaning to everything and the examples clearly are understood, they cannot really be nonsensical. The suspicion arises that maybe nonsense might be found only in the Tractatus.

What is nonsense? The old fashioned approach would be to ask how the word is used. The first kind of nonsense is the one we associate with Lewis Caroll or Edward Lear or Monty Python or Mad Magazine. Here is an example by Christian Morgenstern: (Morgenstern 1963, p. 16f.)

Es war einmal ein Lattenzaun mit Zwischenraum hindurchzuschauen. Ein Architekt, der dieses sah, stand eines Abends plötzlich da und nahm den Zwischenraum heraus und baute draus ein großes Haus.
There used to be a picket fence with space to gaze from hence to thence. An architect who saw this sight approached it suddenly one night, removed the spaces from the fence, and built from them a residence.

It is very easy and maybe tempting to read in some deeper meaning into this but the fact remains, you cannot build a house out of spaces. It is nonsense, meant as nonsense and should be regarded as nonsense. We might call this fun-nonsense.

For some reason Russell and Wittgenstein seemed to worry about propositions like “Socrates is identical” or “this table penholders the book”. This is grammatical nonsense.

The third kind of nonsense is nonsense used as a term of abuse. For example when we say that Intelligent Design is nonsense. What is meant by this is that a proposition or an argument is not only false, but the underlying assumptions or the conclusions appear to be so devoid of rational substance that it would seem a waste of time to even enter a discussion with the believers. It goes without saying that the people holding nonsensical beliefs do think their beliefs make perfect sense. (With the notable exception of Tertullians’ Credo, quia absurdum est). Russell calls an early essay of his, still written under the influence of Hegel, “unmitigated rubbish” and “complete nonsense”. (Russell 1959, p. 32f.). Let us call this kind of nonsense rubbish nonsense then.

Religion offers a lot of propositions that seem nonsensical: “Jesus fed the 5000 with two fishes and five loafs of bread.” This makes perfect sense in a way. We can either believe it to be literally true by some sort of miracle or maybe somehow take it to be metaphorically true (although this is hardly possible, considering the twelve baskets full of crumbs, which remained at the end of the feast.) But what is not possible with this kind of proposition is to just regard it as false. This might be called nonsense by exaggeration.

Next: “Time wounds all heels”. This apparently is not nonsensical at all, and yet it has a nonsensical ring to it. It is a kind of parody of “Time heals all wounds”. This is a good example of a proposition that seems to be trivially true and obviously false at the same time. A great truth, Niels Bohr is supposed to have said, is a truth whose opposite is also true. That may be true but it is certainly the mark of nonsense. This is truly therapeutically nonsense. If someone is comforted by it, very good, if not, not much is lost.

“The surface temperature of an oxygen atom is 44°C.” This is similar to Wittgenstein’s “It is 5 o’ clock on the sun”. (PI, 350) An atom is just not the kind of stuff that can have a temperature, since its movements define what emerges as temperature at a macro level. What we have here is categorical nonsense. This, by the way, is a reason why one cannot talk about the existence of (Wittgensteinian) objects or the number of objects. Since the configuration of objects is the ontological foundation of any true proposition it does not make sense to build a proposition about objects. Now, Wittgenstein does talk about objects, being well aware that he is producing nonsense, but to paraphrase a well-known aphorism by Bradley: Where everything is nonsense it must make sense to avoid categorical nonsense.

To Leibniz the proposition that there is no finite speed was a universal truth, that is, a necessary truth, because in contrast to a contingent truth the proof of it requires only a finite number of steps. If, his reductio ad absurdum went, a point on the circumference of a rotating wheel were moving at the highest possible speed, then the diameter must only be enlarged to make the point moving with a greater speed. (Leibniz 1989, p. 25)

Something must be wrong with this argument, if the speed of light cannot be surpassed, as we now think. And indeed, the underlying concepts of space and time and mass have radically changed since Einstein. But the interesting question is the following: Can the configuration of objects somehow constitute a possible world in which there is no limit to speed? If not then Leibniz’ universal truth is not only wrong but nonsense. This would be metaphysical nonsense.

4. Degrees of Nonsense

So far I talked about different kinds of nonsense. But are there different degrees of nonsense? Imagine being a piece in a chess game, a pawn, for example. You could perceive the moves being made and you would know “by instinct” how to move, that is you would not do an illegal move. But everything else you are ignorant about. You do not know what the purpose of the game is (or that it is a game, to begin with) and you would have no idea of a world outside of the game.

Consider now the following propositions uttered by some pieces:

  • 1. Bc4 Bc5
  • 2. A Bishop always moves diagonally.
  • 3. Black and White move alternately, moving only one piece at a time.
  • 4. A pawn arriving at the last line is transformed into a Queen.
  • 5. Black pieces are better than white pieces.
  • 6. All pieces are equal.
  • 7. A Bishop is worth 3.5 pawns.
  • 8. The object of the game is to kill the opposing King.
  • 9. The object of the game is to make as many moves as possible without capturing an opposing piece.
  • 10. One should always make the best move possible.

The first proposition obviously makes sense. It describes in common notation the moves of the two Bishops. While they are not really elementary propositions since they depend on absolute space and so violate the independency requirement, they are as close as one can get to describing reality unambiguously.

The next two propositions are tricky. They follow by induction from the observed facts. But what is the status of induction? Wittgenstein says that the law of induction is “obviously a proposition with sense“ (T 6.31) and thus cannot be a logical law. Now, that is a rather lame argument, why does he not consider the possibility that it is nonsense? At least the propositions can be falsified, as (3) indeed is due to castling. Let us say these propositions are somewhere between sense and nonsense.

Proposition 4 is true on a meta level, it is just a rule, but from within the game, if it had never happened, there is no foundation for the claim, so it qualifies as rubbish nonsense.

Propositions 5 to 7 are nonsensical as long as there is no framework available that provides criteria for the claims. Such a framework could be given by the hypotheses of 8 and 9. These do not follow by induction. Even if it could be observed that the King gets trapped in every game, it does not follow that it is the object of the game to go after the opposing King. Hypothesis 9 is equally valid. Both are nonsensical assumptions, but without such an assumption it would not be possible to make a meaningful move. These hypotheses have a heuristic value. If proposition 8 were true then proposition 7 becomes immediately meaningful, and more it would be part of a heuristic method to evaluate the position of a game and would thus help into deciding which move to make.

If the pieces accept hypotheses 8 and if all the rules were known, they could in theory come up with a perfect game. But that would still leave the question unanswered why they should make the effort.

This brings us to proposition 10, which is nonsense of the highest degree. It does not gain sense on a meta level. But just because it is nonsense it does not mean that the pieces - or we for that matter - do not live by such a principle, even if only by implication.

5. Conclusion

Is it true what Wittgenstein says that we should only say what can be said? And is it true that natural science says only what can be said? (T 6.53) When Democritus suggested the existence of atoms, how could that not have been nonsense? When Pauli postulated the existence of the Neutrino, he had good reasons to do so, but in what sense was it not nonsensical? Many would agree that the Copenhagen interpretation is nonsense or the many-worlds interpretation but is it not science? The distinction between sense and nonsense is an important one, but in many cases it is impossible and also unwise to avoid making nonsensical assumptions.

6. Literature

Conant, James and Dain, Ed 2011 “Throwing the Baby”, in Rupert Read and Matthew Lavery 2011, 66-83.

Joachim, Harold H. 1906, The Nature of Truth, Oxford: Clarendon. Leibniz, Gottfried W. 1989, “Meditations on Knowledge, Truth, and Ideas” in: G. W. Leibniz, Philosophical Papers (eds. Roger Ariew and Daniel Garber), Indianapolis: Hackett, 23-27. Morgenstern, Christian 1963, Gallow Songs (trans. Max E. Knight), Berkeley: University of California Press. Read, Rupert and Lavery, Matthew (eds.) 2011, Beyond the Tractatus Wars: The New Wittgenstein Debate, New York: Routledge. Russell, Bertrand 1959, My Philosophical Development, London: Unwin. Russell, Bertrand 1976, “On Scientific Method in Philosophy”, in: Bertrand Russell, A Free Man’s Worship, London: Unwin, 96-121. Russell, Bertrand 1904, “Meinong’s Theory of Complexes and Assumptions (III)”, Mind 13 (1904) 509-524. White, Roger M. “Throwing the Baby Out With the Ladder”, in: Rupert Read and Matthew Lavery 2011, 22-65.


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