In Boltzmann’s case, even more so than in Mach’s, we can see his ideas about pseudo-problems developing over time. My treatment here will follow the course of that development, concentrating on a handful of Boltzmann’s most philosophical papers, all from his Populäre Schriften (and included in its partial English translation, Boltzmann 1905/1974).
‘The Second Law of Thermodynamics’ (1886)
Boltzmann begins his lecture ‘The Second Law of Thermodynamics’, an address to a formal meeting of the Viennese Imperial Academy of Science, by explaining that in choosing a scientific subject (rather than the more customary philosophical subject) for his lecture he does not want to provoke suspicion that he thinks topics of philosophical or metaphysical interest are insignificant or unimportant, compared with the special problems raised by the sciences. It is only the manner in which they have so far been treated, or in some cases the fact that they have been treated at all, that seems to him mistaken. This would have been quite a radical idea in 1886, since anti-metaphysical (we might even say anti-philosophical) thinkers like Mach and Gustav Kirchhoff were then still very much in the minority among scientists.
Boltzmann proposes that the methods of physics and chemistry are ‘the true means for unveiling the nature of things’, even though ‘many problems are like the question once put to a painter, what picture he was hiding behind the curtain, to which he replied “the curtain is the picture”’ (1905/1974, 15). The problems of philosophy, he is suggesting, are premised on the idea that a veil conceals the nature of things from us. But this is not so. His attitude is that while philosophers have either attempted to discern the nature of things but failed, or have declared that the nature of things is forever indiscernible, science can discern the nature of things.
Boltzmann sympathetically sketches Kirchhoff’s descriptivism, which portrayed physical sciences as purely descriptive and altogether renounced the task of explaining physical phenomena. But he then says:
If one seeks to explain motions from forces and these from the essences of things, that is phenomena from things in themselves, one always seems to start from the view that explanation requires reducing the explicandum to some quite new principle external to it. This view is alien to natural science, which merely resolves complex things into components that are simpler but the same in kind, or reduces complicated laws to more fundamental ones. If now this process is often successful it becomes so much a habit that we have no wish to stop even at its natural end (1905/1974, 16).
Here Boltzmann is setting himself against a metaphysical conception of explanation, a conception ‘alien to natural science’. The conception in question starts with legitimate scientific explanations, but becomes a metaphysical tendency when it turns, as it inevitably does, into a mental habit that overreaches. This is an important anticipation of Boltzmann’s later line of argument, and thus of Boltzmann’s anti-metaphysical stance.
The usual way of thinking about these matters, Boltzmann feels, is confused:
Usually one even regards it as a limitation of our intellect that, assuming we had succeeded in finding the simplest basic laws, we could then not explain or ground them further, that is resolve them into simpler ones; that as regards the existence of the most elementary constituents we are in any case unable to comprehend them, that is reduce them to simpler ones still. Are we not here once more placed in front of that painted curtain mentioned earlier? […] We shall be able to retain the word ‘explain’ if from the outset all such reservations are kept at a distance (p. 16).
What Boltzmann is renouncing here is the idea of explaining our ultimate explainers. But Boltzmann (unlike Kirchhoff) wants to retain the idea of explanation. Science can and does explain, but it can never meet the exaggerated and inappropriate metaphysical demand for explanation.
‘On the Fundamental Principles and Equations of Mechanics, I’ (1899)
More than a decade elapsed before Boltzmann returned to these fledgling ideas and elaborated them. In the first of his two lectures ‘On the Fundamental Principles and Equations of Mechanics’, delivered to an American audience, Boltzmann begins by mentioning recent controversies, especially in Germany, about the fundamental principles of mechanics, controversies of a philosophical or epistemological nature. Germans, he notes, have often been laughed at for their fondness for philosophical speculation, and in earlier times such a reaction was justified. But there does seem to be ‘an invincible streak in the human spirit, prompting it to analyse the simplest concepts and to render an account of the fundamental operations of our own thinking’ (p. 104). Instead of rubbishing this tendency or method of analysis, though, Boltzmann allows that it has been improved, so that today it is not nearly as empty as philosophy used to be, even if it is not yet of immediate practical use.
Boltzmann takes us through various reservations about the fundamental concepts of mechanics (space, time, mass and force) from ‘German’ physicists such as Franz Neumann, Heinrich Streintz, Ludwig Lange, and Mach. But the one he runs with is Kirchhoff’s objection to the very question ‘Does mass alone exist, force being merely a property of it, or conversely, is force alone truly existent, or must we assume a dualism of two separate existents (mass and force), force existing independently of matter and causing its motion?’. Why is Boltzmann so sympathetic to Kirchhoff’s rejection of such questions?
He is so because he has a general idea about our ‘conceptual signs’ (words and thoughts). The idea in question is that all our ideas and concepts are only ‘internal mental pictures’, and thus that the task of our thinking can only be ‘so to use and combine them that by their means we always most readily hit upon the correct actions and guide others likewise’ (p. 104). ‘The conceptual signs that we form thus exist only within us, we cannot measure external phenomena by the standard of our ideas’ (p. 104). He immediately takes this to mean that certain existence-questions are deeply problematic:
We can therefore pose such formal questions as whether only matter exists and force is a property of it, or whether force exists independently of matter or conversely whether matter is a product of force; but none of these questions are significant since all these concepts are only mental pictures whose purpose is to represent phenomena correctly (p. 104).
In other words we should not pose such questions. Boltzmann takes this to have been stated ‘with special clarity’ by Hertz in The Principles of Mechanics. What it rules out is not, as we shall see, only these most general questions of existence.Footnote 11 But it also ascribes to thought and language a strong pragmatic dimension, in a way reminiscent of Mach.
Boltzmann is soon led to a new criterion for the appropriateness of our scientific mental pictures: whether they represent experience as simply and appropriately as possible (pp. 105, 107). In considering how we reach such pictures, he contrasts the ‘Euclidean’ method of derivation, which has gradually been discredited, with what he calls the purely deductive method of representation (p. 107), which he takes both Hertz and himself to have used (pp. 108–109). What principally recommends the latter method to them both is the clarity it lends our pictures.
However, and again following Hertz, Boltzmann insists that the original question about the nature of matter, mass, or force is not solved by using the deductive method. Rather,
we have circumvented it by making a prior consideration of it quite superfluous. In our conceptual scheme these concepts are quite definite numbers and directions for geometrical constructions which we know how to consider and execute in order to obtain a useful picture of the phenomenal world. What might be the true cause for this world to run as it does, what is as it were concealed behind it and acts as its motor, these things we do not regard as the business of natural science to explore. Whether it might or could be the task of some other science, or whether following the analogy of other, sensible collocations of words we have perhaps merely strung together words that express no clear thought in these combinations, all this may be left entirely open here (pp. 109–110).
This paper, then, introduces the idea of questions that have no significance, identifying as such questions about the existence and the ‘nature’ of matter, mass, and force, along with questions of causes and hidden mechanisms. While trying his best to respect Hertz’s pedagogical concerns, notably by aiming at ‘perfect clarity’ (p. 108), Boltzmann generalises Hertz’s ideas considerably here, and he is more explicit than Hertz in declaring that questions about the nature of fundamental concepts can only be circumvented, not solved. He makes (but does not follow up) the suggestions that such questions are not within the purview of science, and that they might be combinations of words that express no clear thought. He also offers a new account of the nature of those problematic concepts as ‘directions for constructions’, although this is hardly fleshed out. All the time, I would suggest, Boltzmann is working with the idea of pseudo-problems, giving his most explicitly semantic diagnoses of them, and suggestions for their (non-) treatment.
One might also feel, though, that this paper is something of a strange and unsatisfactory half-way house. While it has a strong drift towards the diagnosis of pseudo-problems (rejecting certain metaphysical questions as insignificant), Boltzmann nevertheless thinks that the method of ‘analysis of the simplest foundations of knowledge’ (p. 104) has been improved, so presumably he is not proposing its outright rejection. And the ‘invincible streak’ he mentions, our psychological tendency to analyse even the simplest concepts, is not clearly resisted here, as we will soon see it is in his next papers. One might also want to know how Boltzmann might have squared his rejection of these questions with his scientific realism (that science can tell us the nature of things). We shall return to this issue below.
‘On the Principles of Mechanics, I’ (1900)
In his inaugural lecture at Leipzig, in 1900, a new element informs Boltzmann’s thinking when he produces a general diagnosis of how pseudo-problems arise:
Darwin’s theory explains by no means merely the appropriate character of human and animal bodily organs, but also gives an account why often inappropriate and rudimentary organs or even errors of organisation could and must occur. It is no different in the field of our drives and passions. […] Our innate drives often overshoot the mark as it were. The force with which for the sake of certain results they have linked themselves with our minds is so enormous that we cannot easily rid ourselves of it if these results are not achieved and the now habitual drive is superfluous or harmful (Boltzmann 1905/1974, 136).
He immediately went on to identify such errors in the history of the organism, in the mental sphere, and in philosophy. There, our tendency to judge the value of things according to whether they help or hinder our own existence becomes so habitual that ‘in the end we imagine we can judge as to the value or otherwise of life itself, and indeed whole books are written about this mistaken topic’ (p. 136).
This is not supposed to imply that life has no value (or meaning). On the contrary, the assertion that life has no value is, as it were, merely the null answer to the question of what value it has. What Boltzmann is proposing is that the question about ‘the value of life’ is nonsense, and thereby unanswerable, even by the null answer.
He also identifies other examples from philosophy, including the ‘antinomies’ in Immanuel Kant’s Critique of Pure Reason (p. 137), certain supposed ‘riddles of the universe’ (probably a reference to Ernst Haeckel’s 1895–1899 book Die Welträtsel (The World-Riddle)Footnote 12), and the question ‘Why is there something rather than nothing?’. He then suggests how we go wrong:
We must constantly dismantle concepts into simpler elements and explain phenomena by means of laws we know already. This highly useful and necessary activity becomes so much a habit as to produce the compelling appearance that the simplest concepts themselves must be dismantled into their elements and the elementary laws reduced to even simpler ones (p. 137)
This repeats his earlier diagnosis, in which our scientific tendency to ‘resolve complex things into their simpler components’ is pushed so far as to overreach itself. And it does look as if it might explain certain pseudo-problems. Some philosophers have, after all, tried to further analyse concepts which others have declared to be primitive and unanalysable, such as knowledge, goodness, and causation. But there is a problem with Boltzmann’s dialectic here: this diagnosis does not seem relevant to the pseudo-problem with which he began (of ‘the value or otherwise of life itself’), where the question of primitivity or analysability does not seem pertinent. However, Boltzmann does then give some examples where it seems a better fit:
Questions like what is the definition of the number concept, the cause of the law of causality, the nature of matter, force, energy and so on, always irresistibly recur, even to the person who is philosophically trained. He is convinced that these concepts are taken straight from experience and not explicable further, so that here the now irresistible mental habit of asking for the cause and definition overshoots the mark, but still he cannot overcome a certain residual dissatisfaction that such important concepts as number or causality defy all attempts at definition (Boltzmann 1905/1974, p. 137)
Here we also have two new ideas, firstly, that these questions are irresistible, even to trained philosophers. And secondly that we cannot be satisfied with the indefinability of the concepts in question. (It is worth noting, too, that Boltzmann has again here moved to something very like those ‘What is the nature of…?’ questions, maybe under Hertz’s influence).Footnote 13
Boltzmann then compares the situation here with optical illusions: ‘It is as when an optical illusion fails to vanish even after one has clarified its mechanical cause’ (p. 137). Even when we have realised that these philosophical questions are illegitimate, confused, unanswerable, we still feel their pull and we are still tempted to try to answer them—realising that they are nonsense does not free us from their grip.
This is worth comparing with Hertz who, as we saw, said that ‘our minds, no longer vexed, will cease to ask illegitimate questions’. Where Hertz holds out the hope for intellectual calm, Boltzmann at this point apparently does not. This is surely because of the biological/psychological slant to his thinking here—since we are always still subject to our bio-psychological drives, we can never (more than momentarily) escape the temptation to try to answer these questions.
Finally, he gives yet another example from philosophy: ‘that old aberration we now call solipsism’ (p. 137). Here, Boltzmann thinks, the perfectly legitimate idea that individual sensations can sometimes be explained without postulating an ‘outer’ object can, when over-generalised as far as possible, lead inappropriately to the solipsist conclusion:
By pushing this habit to excess and applying it even where it does not belong, one arrives at the notion that all our ideas are dreams and nothing exists except the person that has them, that is one single dreamer (p. 138).
The solipsist’s excess is to take a useful mental habit and, by fixating on it and failing to realise its limitations, misuse it. One can meaningfully ask whether each individual experience shows one what is real, or whether it is illusory. But one cannot meaningfully ask the same question about the entire totality of our experience.
Boltzmann, then, considers certain questions about totalities (in his examples: the entire realm of causality, the entire realm of life, and the entire realm of one’s experience) problematic, and problematic in such a way that they cannot possibly have answers. His idea seems to be that we ask ourselves such questions because our natural tendency to generalise overreaches itself, but that while we can legitimately ask certain questions about each member of a totality, we can’t meaningfully ask the same question about the entire totality.
‘On Statistical Mechanics’ (1904)
In the fourth paper in question, Boltzmann explicitly settled on describing the problematic intellectual tendency he had in mind as ‘overshooting the mark’ [über das Ziel hinausschießen]Footnote 14:
Many inappropriate features in the habits and behaviour of living beings are provoked by the fact that a mode of action that is appropriate in most cases becomes so habitual and second nature that it can no longer be relinquished if somewhere it ceases to be appropriate. I express this by saying that adaptation overshoots the mark. This happens especially often with mental habits and becomes a source of apparent contradictions between the laws of thought and the world, and between those laws themselves (1905/1974, 166).
He gives another example, of ‘the question whether cause and effect represent a necessary link or merely an adventitious sequence’, urging that one can meaningfully ask only ‘whether a specific phenomenon is always linked with a definite group of others, being their necessary consequence, or whether this group may at times be absent’ (p. 166).
This question of whether causality is a relation of necessity is certainly one that philosophers have asked. But it does not look like a question of any of the kinds Boltzmann has mentioned so far, and its status as introducing a pseudo-problem is surely far more contentious. Unfortunately, we hear no more of why Boltzmann counts it as such. Instead, he returns to his favourite examples from philosophy, the question of the value of life itself, our urge to resolve even the simplest existing concepts into yet simpler ones, and attempts to explain even the simplest fundamental laws. He then produces a very vivid general characterisation of the situation:
My present theory is totally different from the view that certain questions fall outside the boundaries of human cognition. For according to that latter theory this is a defect or imperfection of man’s cognitive capacity, whereas I regard the existence of these questions and problems themselves as an illusion. On superficial reflection it may of course be surprising that after recognition of the illusion the drive towards answering these questions does not cease. The mental habit is much too powerful to loosen its hold on us (1905/1974, 167).
Boltzmann’s declaration that these problems and questions are themselves illusory clearly places him in the pseudo-problem tradition, even though he never uses Mach’s term ‘Scheinproblem’. This passage also explains how that tradition is distanced from the more familiar, mainstream epistemic view that the questions in question do have answers, even if those answers are humanly unknowable. This was implicit in Mach, but Boltzmann makes it absolutely explicit.
Boltzmann again compares the situation with optical illusions, which ‘continue to exist even after their cause has been recognized’, but he then sounds a more personal note: ‘Hence the feeling of insecurity, the lack of satisfaction that grips the scientist when he philosophizes’ (p. 167). Philosophers themselves, though, are clearly on no firmer ground than scientists, in his view:
Only very slowly and gradually will all these illusions recede and I regard it as a central task of philosophy to give a clear account of the inappropriateness of this overshooting the mark on the part of our thinking habits; and further, in choosing and linking concepts and words, to aim only at the most appropriate expression of the given, irrespective of our inherited habits. Then, gradually, these tangles and contradictions must disappear (p. 167).
These passages do put the conclusion he drew back in 1900 in a more optimistic perspective. His view seems to be that although the questions that generate pseudo-problems are irresistible, and that we cannot help trying to address them, the illusions could eventually be made to recede, with the help of philosophy. This conclusion is not so different from that which Hertz drew. But how might philosophy perform these tasks?
If therefore philosophy were to succeed in creating a system such that in all cases mentioned it stood out clearly when a question is not justified so that the drive towards asking it would gradually die away, we should at one stroke have resolved the most obscure riddles and philosophy would become worthy of the name of queen of the sciences (p. 167).
I have argued elsewhere that one can see Ludwig Wittgenstein as responding to Boltzmann’s proposed ‘central task of philosophy’, and as trying to create something which would satisfy the perceived need for such a ‘system’ in his Tractatus Logico-Philosophicus (Preston 2017).
‘On a Thesis of Schopenhauer’s’ (1905)
Finally, in one of his very last publications, ‘On a Thesis of Schopenhauer’s’, Boltzmann really warms to his idea of overshooting the mark, and the notion runs riot. He uses examples of questions which overshoot the mark which we have seen before, such as the questions of whether life as such has value, and should be promoted or inhibited (pp. 192, 196), the question of why (that is, for what cause) the law of cause and effect itself holds (p. 194), the questions not only of why the world exists at all, but also of ‘why it is as it is, why we exist at all and why precisely now and so on’ (p. 194).Footnote 15
Again we see the idea that we have a need to ask the problematic questions (p. 196), that we are tormented by not finding answers to them, and that this torment ‘does not cease once we have recognized that the framing of the question is in itself misguided’ (1905/1974, 196). Confirmation that Boltzmann’s diagnosis is a bio-psychological one comes from his appeal to Darwin:
[P]recisely this phenomenon is perfectly explicable on Darwin’s theory; habit is simply stronger than recognition that the question is useless. Deceptions of the senses likewise do not cease even when they have been completely explained in terms of physics and physiology (p. 196).
And Boltzmann’s sarcasm about philosophy itself also gets an airing. Because we have such a strong instinct for classification, he thinks,
we take a lot of concepts to be clear or even a priori when they are really mere empty words. We imagine ourselves to be heaven knows how learned if without linking the words in question with clear concepts we ask whether something is synthetic or analytic, transcendental or empirical, real or ideal or material, quantitative or qualitative. About such questions philosophers are apt to write whole treatises; only, whether they are completely clear as to the meaning of their questions, about that they do not ask (p. 196).
The semantic aspect of Boltzmann’s conception grows more prominent, too. The question of whether life itself has a value he declares to be ‘one of those questions utterly devoid of sense’ (p. 196). His treatment here is not quite stable, though. He immediately goes on to contradict the idea that the question has no sense by saying ‘Life itself we must accept as that which has value, and whether something else does can only be judged relatively to life, namely whether it is apt to promote life or not’ (p. 196). But then, only a few lines later, we find him saying again that.
[I]f we ask whether life itself has value, this means whether life is apt to promote life, a question that has no sense. According to the definition we can ask only how life can be promoted. The valuable is simply what promotes life, the question as to the value of life itself is senseless, although according to Darwin’s theory it is readily explicable why it obtrudes itself. It is another mental habit that overshoots the mark (pp. 196–197).
In this article we also get an important and radical new theme. Previously we saw that Boltzmann had the idea that the problematic mental habits in question lead to apparent contradictions with, and among, the ‘laws of thought’ (that is, the laws of logic, as he conceived them). Here, that idea develops into the new theme that those laws themselves are such firmly established habits that they overshoot the mark (p. 195). Boltzmann introduces this theme via considering again how philosophy might help us avoid overshooting the mark:
The task of philosophy for the future is, in my view, to formulate the fundamental concepts in such a way that in all cases we obtain as precise instructions as possible for appropriate interventions in the world of phenomena. This requires first that if we follow different paths we never reach different rules for further thought and action, that is we never meet internal inconsistencies, such as if one path led us to the conclusion that matter was not infinitely divisible and another that it must be. That sort of event is always a sign that the laws of thought still lack the last finish, that we have placed our words badly. In that case we must alter the laws of thought that lead to such absurd consequences (p. 197).
Not only do philosophers overshoot the mark, then, the laws of logic themselves do so, or tempt us to do so. Boltzmann ends his article by suggesting that we should alter the laws of thought. In altering them, he suggests, we can get closer and closer to keeping our habit of overshooting the mark within proper bounds. The payoff he then describes thus:
[T]his would ensure cessation of the disquiet and the embarrassing feeling that it is a riddle that we are here, that the world is at all and is as it is, that it is incomprehensible what is the cause of this regular connection between cause and effect, and so on. Men would be freed from the spiritual migraine that is called metaphysics (p. 198).