Summary: The Philosophy of No (page 2)

Bachelard takes the example of a scientific concept — that of mass — to identify the different types of epistemological explanation that attach to it.

These different types of explanation trace an epistemological evolution that always moves towards greater rational coherence.

The first explanation of an object's mass is of the animistic type.

Reflecting a greedy grasp of reality, this view assumes that the biggest fruit is the best. As a result, the notion of mass materialises the very desire to eat ¹.

At this stage, mass is confused with volume.

This initial, unsatisfactory explanation is soon contradicted by experience — for, as Bachelard puts it, the first contradiction is, as always, the first step towards knowledge ².

This contradiction arises from the disproportion, in certain cases, between the "big" and the "heavy" (that is, between volume and mass). The "largest" is not necessarily the "richest." Bachelard offers the example of an empty shell. Thus emerges the concept of "intensity" — a kind of "intimate richness" through which the notion of mass becomes internalised.

This first contradiction leads the scientific mind to move beyond the visual aspect of an object (its volume) when estimating its mass. A tool is therefore required to establish mass more objectively: the balance. The mind then enters a second stage: empiricism (or realism).

To this simple and positive concept corresponds a solid, clear, positive, and immobile ³ empirical mode of thought. One might think the problem has been solved:

Such empirical thinking, anchored in peremptory experience, is called realist thinking ⁴.

However, the situation is not so simple. In fact, empiricism uses the instrument — the balance — before understanding the underlying theory — the principle of the lever.

It is at the next stage — that of rationalism — that the notion of mass becomes more complex. With Newtonian classical mechanics, we discover that this notion must be defined in relation to others: The notion of mass is then defined within a system of notions, rather than as a primitive element of immediate and direct experience ⁵.

The mass of an object is, in fact, defined by the ratio between its force and its acceleration.

These three notions are established correlatively, in a clearly rational relationship — one perfectly captured by the laws of arithmetic.

From a realist perspective, these notions appear highly diverse, and bringing them together within a single formula seems artificial.

However, rationalism surpasses itself, and we reach what Bachelard calls complete rationalism — complex rationalism — upon discovering that mass depends on velocity: The mass of an object is therefore relative to its displacement ⁶. This fundamental insight from Einstein's principle of relativity shows that the notion of absolute mass is meaningless.

Here again, we witness a complication of the notion of mass. This concept, initially simple, gives way to a complex one.

This complexity becomes total — in the sense that it is no longer intuitively graspable — at the final stage, which Bachelard calls dialectical rationalism, or surrationalism.

With regard to the concept of mass, we reach this final stage with Dirac, who demonstrates that there are two masses for a single object. The first is mass as understood by previous philosophies, from realism to complex rationalism. Although each of these epistemological approaches defined it differently, all took it as their object of study. But Dirac reveals that the second mass of an object is a negative mass!

While one half of Dirac's mechanics recovers and extends classical and relativistic mechanics, the other gives rise to a dialectic.

To a 19^th-century scientist, the concept of negative mass would have seemed monstrous ⁷. And so it seems to us too, prone as we are to remaining trapped within a realist conception of mass:

We, like everyone else, have our moments of realism — and even with a concept as sophisticated as mass, we are not fully psychoanalysed ⁸.

¹ chap.1, p.22
² ibid.
³ chap.1, p.26
⁴ ibid., p.27
⁵ ibid.
⁶ ibid., p. 31
⁷ ibid., p.37
⁸ chap.2, p.45