Science, Speculation and Bachelard

I am presenting here a series of compressed notes on the French philosopher of science, Gaston Bachelard. I’ve recently begun the habit of writing down pen-and-paper notes for the books that I’m reading, and in this way I’ve accumulated a fair amount of notes reading Mary Tiles’ excellent book, Bachelard: Science and Objectivity. Before I read Tiles’ book, I read Gillian Rose’s excellent Hegel Contra Sociology. Having Rose’s work in mind put me in a Hegelian mode, and I was inclined to read Tiles’ Bachelard in part through Rose’s Hegelian lenses. Here I present the crux of my reading, taken from the first few chapters of Bachelard: Science and Objectivity. I hope to convert this set of notes, as the other sets of notes I have, into longform writing, so stay tuned.

Gillian Rose’s book is famously difficult, so I will not attempt to give an exhaustive précis. Still, I can give a brief overview. Rose’s book is an attempt to “retrieve Hegelian speculative experience for social theory.” ¹ Rose considers sociology as being divided into two antinomic paradigms, the Weberian and the Durkheimian. Each side is one-sided and cannot account for the latter, except in a derivative way. The reason for this is that they start from neo-Kantian premises, but they take a side between two starting-points.

The roots of this division she finds in the work of the nineteenth-century German logician and philosopher Hermann Lotze. Lotze was incredibly popular in the late nineteenth-century, both in Germany and in the English-speaking countries, though he is poorly-known today. Part of the reason for his fame comes from the eclipse of Hegelianism that occurred after Hegel’s death, which caused philosophers and scientists to retreat to a more Kantian mode of philosophizing. The emphasis on logic and idealism was retained from German Idealism by Lotze’s contemporaries like Friedrich Adolf Trendelenburg. It is a shame that they are not so well-known, both among analytic and Continental philosophers, because of the immense influence they exerted both on Continental philosophy (part of which Rose traces out) and on early analytic philosophy, especially in the area of logic.

The 'neo-Kantian paradigm' refers to those who attempted a new answer to the Kantian question of validity within the framework of validity and values first developed by Lotze. Within this framework the question of validity may be given priority over the question of values, or, the question of values may be given priority over the question of validity. ²

Validity (Geltung) refers to the reality that inheres to a proposition, a reality which is distinct from both things and states of affairs. “The reality of a proposition means that it holds or is valid, and that its opposite does not hold. For example, the proposition ‘x ist [is]’ is contrasted with the proposition ‘x gilt [holds or is valid]’.” ³ The feeling of value, on the other hand, is attached to our perceptions of things, and the connection between the two will remain inscrutable. “Our way of attributing value and meaning depends on judgements which do not conform to the principles of scientific understanding (Verstand), but are based on a ‘reason receptive to values’ (Wertempfindende Vernunft).” ⁴

However, it is Lotze's threefold distinction between validity, cognition of empirical reality and values which has been of importance, not the Leibnizian metaphysics which complements them… On the basis of Lotze's thought, critical, transcendental philosophy became transformed into the neo-Kantian paradigm of Geltung and Werte, validity and values. The three Kantian critical questions ‘What makes judgements of experience, of morality, of beauty objectively valid?’ become the questions ‘What is the nature of validity in general?’ and ‘What is the relation between validity and its objects?’ Logic is separated from cognition, validity from representation, but not from its objects. The result is a general but not a formal logic: a methodology. ⁵

The two great neo-Kantian schools are the Marburg school (validity over values) and the Southwest school (values over validity). This corresponds with the dual paradigms in sociology, the paradigm of Durkheim and of Weber. The problem is that they are caught within a series of antinomies, like individualism/holism, that they are not able to resolve. Ultimately we still have the dualism of bare facts and the force of values (Sollen). And we are stuck with an infinite labour that aims toward a goal that it can never reach, since the object of our cognition is posited only regulatively. The solution that Rose of course looks to is Hegel, who can think the unity of these dualisms, and hence the rest of her book is an explication of his work, especially his early critiques of the transcendental philosophy of Kant and Fichte in the social sphere.

So much for my excursion into Gillian Rose’s theses in Hegel Contra Sociology, which I hope acts as a useful introduction to my theses on the philosophy of science, which I suppose is in the grip of the same neo-Kantian structure. Historically speaking this is not so implausible given the influence that Lotze had on early analytic philosophy. Rudolf Carnap, who sets the tone for much analytic philosophy after him, was also brought up in the neo-Kantian mold, along with his phenomenologist opponent Martin Heidegger. ⁶

I think that the analogous division in the philosophy of science is between the context of justification and the context of discovery. While first named by Hans Reichenbach, the importance of this distinction must go back to at least Gottlob Frege’s critique of psychologism in logic and epistemology. I connect the context of justification to the pre-eminence of validity over values, and the context of discovery to the pre-eminence of values over validity. Due to their shared influence, analytic philosophy of science has historically been concerned with the context of justification. But there is no small amount of work done on the latter side, especially those concerned with historical analyses of rationality. I mention Larry Laudan, who thinks that “[i]nstead of defining progress in terms of rationality, we should define rationality in terms of progress.” ⁷

Both analytic philosophy of science and classical sociology provide “a transcendental account [that] necessarily presupposes the actuality or existence of its object and seeks to discover the conditions of its possibility.” ⁸ Classical sociology presupposes either the validity of social forms or indubitably presupposed values that act as a priori. There is an infinite regress which has to be stopped at some bedrock that cannot be analyzed any further for fear of a vicious circle. Analytic philosophy of science, in my opinion, is similar in that it presupposes the object of science, either as a body of statements with logical validity (Rudolf Carnap, W. V. O. Quine, their successors) or as a method presupposing various epistemic or other values (Karl Popper, Irme Lakatos, Paul Feyerabend, perhaps Thomas Kuhn). I am convinced that Bachelard is an improvement over analytic philosophy of science, and that he comes closer to Hegel, though ultimately in my view he is still very much a neo-Kantian.

Under this supposition, Bachelard takes the side of Weber in positing values over validity. Intriguingly, the titles of their most famous works (Le Nouvel Esprit scientifique, Die protestantische Ethik und der Geist des Kapitalismus) mention spirit, and I don’t think there is too far a distance between the spirit of some socio-psychological phenomenon and values. To be exact, scientific objectivity and progress play the role the values do in Weber. Just as “Weber granted the question of values priority over the question of validity and made values into the sociological foundation of validity (legitimacy),” ⁹ Bachelard gives the actual existent fact of progress in science over and above questions about the validity of science.

As Étienne Balibar mentions, “[Dominique] Lecourt has clearly shown that Bachelard's epistemology itself breaks with the idealism of all 'theory of knowledge' in that for it the objectivity of scientific knowledge is not a problem. Objectivity is not the name of a 'critical' questioning followed by the reassurance of a fictitious 'guarantee'. Rather it is posed initially, as a fact, not a simple fact but one which is not to be doubted of.” ¹⁰

The objectivity of scientific knowledge is what allows its history to be thought. The history of science for Bachelard has to be circular, because the history of science is retroactively transformed every time we as scientists today cross an epistemological obstacle. I note first of all that this only makes sense if we presuppose the givenness today of some determinate science such that I can regress to its conditions, much like the project of transcendental philosophy. This I cannot always secure, though, especially when it comes to a science like psychology, or even a data-rich theory-poor field like machine learning. It assumes the consistency of science in the present which does not really account for the possibility for a split within the current state of science between rivalling sides, and hence the appearance of the epistemological obstacle itself depends on the vantage point that I so “choose”. One can imagine how differently a Gouldian and a Dawkinsian might see the history of evolutionary biology, each identifying a different set of epistemological obstacles, which we have crossed to come to the point we are at today. But what point are we at today? This to me makes the notion of objectivity in Bachelard rather non-determinate.

Like Weber, Bachelard ends up working out an "empirical" sociology of validities of scientific knowledge. Hence his rather commendable interest in the history of science, in his attempt to show how the objectivity of scientific knowledge can be secured by giving a historical account of the epistemological obstacles that science has to cross. This is similar to the occasional exposition in textbooks as to the motivation of certain theories or formalisms. That the Fourier series first came out of attempts to understand the transfer of heat does not support or undermine the truth-value of whether you can decompose any periodic signal into a sum of trigonometric functions. Nevertheless, there is an objectivity to the problems faced by mathematicians of Joseph Fourier’s time, around infinite sums, continuity and so on, and the obstacles that they had to overcome, which lends objectivity in this broader sense to Fourier’s work. It shows not only that the formalism is correct but that there is an objective meaningfulness at play (value!).

The history of science is evaluative, and has to choose which elements of past science are genuine articles or epistemological obstacles that had to be overcome. These judgements of course are historically mutable (like the judgement of Einstein’s introduction and exclusion of the cosmological constant, taken as a presentiment of dark energy). The purpose of this is to rise from the “scientific spirit” to the resolution of the question of the validity of modern science. Bachelard himself thinks of scientific progress in a very neo-Kantian mode. The neo-Kantian interpretation of Kant’s famous Thing-in-itself as the regulative ideal of a final theory of our sciences, which our theories can approximate with increasing accuracy. For all of Bachelard’s instance that he has moved past the categories of classical philosophy, I think that he for better or for worse is still with them.

I note that there is no justification of the original value of science itself. I earlier quoted Balibar to the effect that Bachelard presupposes the objectivity of science. I do not think that Bachelard really is able to account for this. He has the inverse problem as his analytic opponents who in a similar fashion begin with the validity of logic and mathematics. There is a pseudo-ground where both can bottom it out in the pragmatic utility of science and mathematics, not to mention technology, but that is incredibly unsatisfying in that it does not take into account the truth embedded even in merely “pragmatic” activities (something I feel like Hegel understands very well).

To make a leap, I suggest that for Bachelard science and objectivity play something like the role of the inaccessible Thing-in-itself that society is for György Lukács. Bachelard posits a split between the epistemological obstacle (a picture-image that stalls science) and science proper, which proceeds through non-imagistic concepts. For example, we can assign to the former the billiard-ball and solar system models of the atoms that we are taught in school. The Bohr model of the atom is useful and allows us to understand the atom better, though it is inherently limited as a model, and has to be superseded with Erwin Schrödinger’s theory of the atom. Here we note that while we can clearly identify the imagistic nature of the solar system model of the atom, we have to consider the possibility that the Schrödinger theory too is an epistemological obstacle. This is the difficulty in providing a determinate distinction between concept and image.

There is some analogy with the account that Lukács gives of reification. Rose points out that he posits a dualism between the objective processes that take place in-between men (the total process of production), and the objectification of processes into social forms. For Rose, this account of reification, which has entered universal parlance, owes more to neo-Kantianism than Hegel. This in my opinion is analogous to the similar structure in Bachelard, the objective processes of science (or scientific concepts), and their objectification (actually, “imagification”) where the model or the image is confused for the concept. “Social forms are valid when viewed from the standpoint of their mediation by the totality, but not when viewed in isolation from the total process.” ¹¹ For Bachelard, read “models” or “images” for “social forms”, “mediation by the totality” as perhaps concepts, and “total process” as science as a whole. Of course, Bachelard cannot import Lukács’ politics into science and declare that the scientist is the subject-object of history who will finally extinguish reification!

Bachelard has to expect an infinite process that cannot be finished. So while he follows Descartes, he does not share Descartes’ single moment of the suspension of belief that grounds the cogito. Rather, Bachelard has to assume an endless number of reflective suspensions-of-belief. This might be what Hegel considers a bad infinity. The scientist as the Fichtean hero who is in constant struggle against the resistance put up by the Not-I of Nature? Regardless, Bachelard reads Descartes as assuming a perfect self-transparent cogito, into which Bachelard introduces unconscious sediments that act as epistemological obstacles. These sediments for him cannot be wholly extinguished. This conception of the distinction between the conscious and unconscious I think helps explain so much of his philosophy of mind. Compare with Jacques Lacan’s suggestion that the Cartesian cogito, the subject of science, is the subject which psychoanalysis intervenes on. Bachelard on the other hand has a Jungian conception of the unconscious.

Bachelard posits a dualism of intuitive and discursive knowledge. The former functions through images and the latter functions through concepts. I covered this with respect to reification and epistemology, here this is part of Bachelard’s more general psychology. From the standpoint of science, the former provide epistemological obstacles which are to be excluded. The four elements of alchemy are to be excluded by being placed in the former bin; Bachelard is not willing to countenance them even as proto-sciences. All we can say about them is that they are obstacles to scientific thought. From Lacan’s point of view, Bachelard has the Imaginary and the Symbolic, but not the Real. What he misses can be fleshed out through Anna K. Winters’ Hegelian notion of the meta-mysterian.

What we’re calling meta-mysterianism proceeds from this claim: that every “barrier to understanding” itself has a shape that can be understood qua barrier. In other words, the “mysterious” excess to what is understood to be “reason” can be raised to the level of reason’s own privileged object; the seemingly irrational, often unconscious byproducts of thought can be recognized to partake in an even more sublime form of reason, a properly speculative rationality refusing to abstractly oppose itself to the “irrational”. From this speculative standpoint, nothing is more self-defeatingly irrational than the claim that something is “irrational” itself, regardless of whether it is done in the name of reason or in the name of the rights of what it is thought to exclude. Irrationality is only the self-fulfilling prophecy of abstract opposition; but qua opposition, it cannot simply be wished away and must be recognized precisely in its irrationality as the bearer of a rationality of which it is not conscious. ¹²

Bachelard cannot think the logic of the image, and this is why he ends up having an oeuvre that is split between sober epistemology and “poetic” works on the four elements. And never shall the twain meet. This means that in my opinion that he cannot come to an account of the concept, or the concept of the concept. For Bachelard, science has to be parasitic on “common-sensical” forms.

Geometry did not start with lines and circles, for example. Geometry began with practices around land-measurement, surveying, and so on, which the Egyptians and Babylonians had carried out for a long time. It was only afterward that geometry appears, and when Euclid writes the Elements he is formalizing what has come before. The starting-point necessarily determines the content of science. That the Greeks started with straightedge and compass has determined much of our current geometry. But at the same time even if our geometry had begun from different premises, once someone could pose the question of the squaring of the circle, we should be able to find it impossible (according to the rules of straightedge and compass, of course). What Bachelard’s account of concepts misses is the autonomy or even the necessary concrete existence of concepts, such that they are already functioning in pre-scientific practice.

This is the fault of his constructivism, which subordinates concepts as merely inhering in the subject. (This is not so far from the analysis of the concept in Kant and his neo-Kantian successors). Unlike the mathematician and intuitionist L. E. J. Brouwer, Bachelard has an active constructivism in mathematics, according to Tiles. What in my opinion Bachelard misses about mathematics is that he makes mathematical objects purely subordinate to human constructions; that once we give some set of premises, everything is already given for us, even if we do not have logical omniscience. What Bachelard misses is the resistance that mathematical objects can pose to us (and so in his broader philosophy of science, scientific concepts), or even their givenness to us as something that is not merely under our construction. Tiles has an interesting discussion of Bachelard’s limitations in mathematics, which questions this feature of Bachelard.

It is perhaps worth noting that the point at which identification problems do arise within mathematics is in the discrete representation of the continuum. To get 'enough' real numbers one has to have more than those generated by law-governed sequences of rationals - one needs lawless sequences. But lawless sequences cannot be individuated on the basis of any finite number of terms. It is just this which is played upon in proofs of the independence of the Generalised Continuum Hypothesis and the Axiom of Choice from the other axioms of set theory and which thereby leaves their status indeterminate. It also means that the structures of constructive analysis mirror, in many respects, the epistemological situation of natural science. ¹³

Admittedly Bachelard does have an ingenious account of where resistance in mathematics comes from. It is from the interference of two different systems of axioms. In Greek mathematics, it is between arithmetic and geometry. While brilliant, I think that Bachelard still needs to account for the conceptual “background” for this happening in the first place, what allows two disparate sets of axioms to interfere with each other.

This brings my comments on Bachelard here to a close. I will have more to say on Bachelard, drawing on my notes, though not to this extent. Bachelard’s importance for me is his account of concepts (which as Mary Tiles convinces me, is richer and closer to the real work of science than that of Frege), his attention to the history of science, the importance he places on concepts rather than prediction or compression of experience. He has a rich account of science and an account of reason that is non-mechanically reflexive and critical in the Cartesian tradition.

What is the solution? For Gillian Rose, she can move on to the explication of Hegel’s social theory. Neo-Kantianism bars any access to the Absolute as being irrelevant to the social, or thinks the absolute as something other to the finite, something that is to be imposed onto the finite. Hegel, as Gillian Rose and Alexandre Koyré (in his famous essay “Hegel at Jena”) show, thinks the co-implication of the finite and the infinite. Hence Hegel can in the 1802/3 System of Ethical Life think both a relative and an absolute ethical life that is made actual in the community and the State.

Is there a solution in science? The neo-Kantian approach puts the object of science at an infinite distance, indeterminate. Perhaps what Hegel can apply in sociality (if he can even apply it in sociality) cannot apply to science. I think not, because of Hegel’s own concern with cognition, logic and science. Just as Hegel’s speculative method and absolute ethical life does not bring Utopia down from Heaven, but views it as being made actual in actual states, we might be able to find through speculation an analogue of absolute ethical life already present in science as it exists. Here I think that Bachelard shows us some of the way there.