A short paper to commemorate Kant’s 300th birthday
"How Objects Conform to Knowing: Kant’s Example of a Line"
Marco Bettoni
1. Introduction
How do we know something in space, for instance a line? In 1787, at the core of his theory of knowledge, Kant mentions an example which answers this question in the following way (B 138) [1]:
“To
know anything in space, for instance, a line, I must draw it”
(original:
«Um aber irgend
etwas im Raume zu erkennen, z.B. eine Linie, muss ich sie ziehen“).
In other words, in order to know (see, feel) a line in space I must do something (for example look in a certain way) or, more precisely, I must perform certain mental operations, call them “line operations”. We will see later that by "I must draw it" Kant does not refer to a physical line in space affecting our sense organs but only to a mental act.This means that even if there is no physical line involved, whenever I perform those line operations, then as a result, I will know a line. By performing “line operations” in space we obtain as a result lines, we know lines. This means that the relation between objects and knowing is of the kind result-to-operation (Fig. 1).
Look now at Figure 2: the white circles on a black background represent schematically stars in the night sky. There are no drawn (physical) lines, but according to Kant’s example, you could nonetheless be able to know (see) some line: how?
Fig. 2 The night sky
(Ceccato 1980; Parini 1996)
If what we know in space depends on what we do, on the mental operations we perform, then, in the case of vision, what happens is that what we see depends on how we look. We can of course see Figure 2 as “chaos” but also see in it an ordered set of straight (Figure 3) or circular lines (Figure 4). And many other different ordered ways of looking at Figure 2 are possible (spiral lines, combined spiral and linear lines, etc.).
Fig. 3 Straight lines that Fig. 4 Circular lines that
can be seen in Fig. 2 can be seen in Fig. 2
2. Fundamental question and answer
In a famous letter to his friend Markus Herz (21.2.1772) Kant wrote that he was planning to publish a work in which he wanted to answer the question:
«on which ground is founded the relation between what we call 'Vorstellung' [knowledge unit, knowing] in us and the object» («auf welchem Grunde beruhet die Beziehung desjenigen, was man in uns Vorstellung nennt, auf den Gegenstand»).
Fifteen years later, in the second edition of his main work, the Critique of Pure Reason, Kant presents the answer to that question as the central hypothesis of his theory by saying that objects must conform to our knowing [2]. He also emphasizes that this "revolution" (so-called Copernican Revoltuion) constitutes the main purpose of the Critique (BXXII).
In order to understand Kant's "Copernican Revolution" (objects must conform to our knowing) and its consequences for epistemology in 2024, the real challenge lies in a critical reflection upon the specific components of Kant's hypothesis, which amounts at asking 3 crucial questions:
- What is Kant's conception of "object"?
- What is Kant's conception of "must conform to"?
- What is Kant's conception of "(faculty of) knowing"?
3. How a line conforms to our knowing
The basis for answering these 3 questions can be found in the Analytic of Concepts (Kant, B90 to B 169). As an example, consider, in the Deduction, Kant's summarized explanation of his hypothesis in the crucial § 17 in the B edition of the Critique [3] (B137, my translation based on Kemp-Smith):
“Understanding is, to use general terms, the faculty of knowledge. This knowledge consists in the determinate relation of given knowledge units to an object; and an object is that in the concept of which the manifold of a given intuition is united. Now all unification of knowledge units demands in fact unity of consciousness in the synthesis of them.”
The mechanism described in this passage is that of "Vereinigung" (unification) of what we call "Vorstellungen" (knowledge units). Kant specifies further that this unification mechanism should act when "Vorstellungen" are synthesized ("in der Synthesis") and that the result of its operation is an (experiential) object. From this I conclude that this description could be clearly interpreted as an operational explanation (a proposition of a generative mechanism, Maturana 1988) of the totally new conception of "object" that Kant needs in order to articulate his Copernican Revolution.
Tightly related to that explanation, a few lines further Kant gives the previously mentioned example of a line, one of his most famous (and rare) examples [4] (B138, translation Kemp Smith):
„To know anything in space (for instance, a line), I must draw it, and thus synthetically bring into being a determinate combination of the given manifold, so that the unity of this act is at the same time the unity of consciousness (as in the concept of a line); and it is through this unity of consciousness that an object (a determinate space) is first known. “
Here Kant wants to explain how we know a "line" and if we look at the functional side of what he writes we see that he presents an operational explanation. In fact, Kant describes here a "line mechanism" that, if you let it operate in your mind, gives you as result of your mental operations that "line" that he wants to explain.
What is exemplified here for the case of a line is also paradigmatically valid for any acquired experience-independent knowledge unit (a priori concepts like begin, end, singular, plural, unit, element, part, whole, space, time, number, here, there, now, etc.): we should try to develop also for them generative mechanisms which, if we let them operate in our mind, would deliver the acquired a priori concept that we want to explain.
4 Kant’s A Priori is not innate
Finally, I would like to conclude this short paper to commemorate Kant’s 300th birthday with a remark on Kant’s conception of the apriori.
As Michael Oberhausen (1997) remarks: "To simply consider Kant's apriori as innate still is a widespread cliché". This cliché is being disseminated not only by contemporary philosophers - with whom Kant is known to be in contradiction - but also by scientists when they approach Kant's work.
Indeed, this is not astonishing if we consider that Kant's doctrine of the acquisition of experience-independent elements 'up to now has been quite ignored by research' (Oberhausen 1997, p. 6).
Fortunately, we have now Oberhausen's comprehensive study which supplies the proof that Kant's doctrine of the acquisition of a priori constructs ('Vorstellungen') is not of no or only of secondary relevance but "lies at the center of critical philosophy". In his summary Oberhausen emphasises that Kant "in many different places of his work again and again explicitly explained that both space and time as well as pure concepts are acquired ..." (Oberhausen 1997, p.6).
5 Conclusion
What are now the implications of such considerations for us in 2024? I think that they can help to answer the crucial question of experience (learning): What do we contribute of our own to our knowledge?
In the light of Kant's explanations, the answer is that what we
contribute of our own are the mechanisms and operations of acquisition,
generalisation and application of acquired experience-independent elements
('reine Verstandesbegriffe a priori') that implement the unity of
experience (categories) and are the conditions of possibility of experience.
Acknowledgments
I am very grateful to Kant for his life and for his work! His life is an example to me and his work gives me hope. Hope that we can find support in mastering the difficult task of making human beings out of ourselves, i.e. coming closer to the ideals of freedom, equality and fraternity than has been the case up to now.
That's why I'm so very grateful to Kant and why it has been my pleasure and duty to remind ourselves with a short text that we still urgently need Kant's philosophy in 2024.
Notes
