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Friday, July 15, 2022

The Correct Starting Point for the Philosophy of Arithmetic: the Pure Activity of Thinking Used to Combine Concepts

    

Photo by Jean-Pierre Dalbéra of 12th Century Mosaic in Palermo




   Enumeration requires collecting aspects of the world into groups. In order to approach the most fundamental activity of combining and collecting aspects of the world into groups, there must be an area in reality where such a combining activity can take place. There must also exist a power that can manipulate the contents of this area where combining takes place. Furthermore, if such a power and the contents of this area are to become conscious, an observing activity must also take place. This region is the world of concepts, the power that combines is thinking activity, and the observer who reflects on this combining activity and its contents is the self-conscious thinking activity of the I AM.


   In the still too influential Critique of Pure Reason of Kant, we read the following passage: 


"...We can represent nothing to ourselves as combined in the object without having previously combined it ourselves. And among all representations, the combination is the only one that cannot be given through objects, but rather can be achieved only from the subject itself, because it is an act of its spontaneity." Version B, paragraph 15. 


Husserl uses this passage in his Philosophy of Arithmetic to provide evidence from Kant to demonstrate that sets do not exist in sense perception but only in thinking activity.  According to Husserl, we do not see multiple objects in pure perception, but only combine them in thinking activity or what he calls categorial intuition. Husserl sees his ideas with more clarity and directness than Kant permits, but that is not the main issue here. 


Nevertheless, Kant has made some errors in his presentation, which however appropriate for his time period, must be corrected in our own time, and experienced through our own self-conscious thinking activity. The real situation is correctly stated as follows: 


       I can represent nothing to myself as combined in an object or a group of objects without the work of thinking activity, which has combined them in concepts before I have represented the combination to myself as a personal subject. This collecting or combining activity cannot be accomplished or given through the objects themselves, but is rather achieved only through the activity of pure thinking. In fact, the notion of object is never perceived in our sense experience as such, but is only separated into its own 'room' through thinking activity. This activity of pure thinking is the creator of the ideas of object and subject in the first place, as well as the idea of parts, subsets, or organized aspects of such objects. The will in thinking activity, led by the laws of universal, meaningful, logical, and harmonious organization, draws together groups of concepts into temporary sets according to their content, and then it stops thinking and temporarily freezes this particular organization (Aristotle indicates this for the first time in his "On the Indivisible Line"). Such a temporary stopping of thinking activity on a frozen organization of concepts is counting or enumeration. Such a organization of different ideas or groups of the same idea can be displayed in a particular mental picture for my personal subjectivity. For example, I can represent the idea of the number five as the quincunx arrangement of the game die in the way that is shown on the mosaic of the Palermo chapel in the photo above. 

    Because the sense of my own self arises through the fact that my personal subject remembers all of these particular representations that have arisen through thinking activity combined with perceptual grasping, I become conscious of myself. Then, this permanent element arising through perception and memory can be taken up into pure thinking activity, where a new Self-consciousness arises as the I of pure thinking. 


      Rudolf Steiner makes all of these issues crystal clear in his Philosophy of Freedom, Chapter 4: 


"It must, however, not be overlooked that only with the help of thinking am I able to determine myself as subject and contrast myself with objects. Therefore thinking must never be regarded as a merely subjective activity. Thinking lies beyond subject and object. It produces these two concepts just as it produces all others. When, therefore, I, as thinking subject, refer a concept to an object, we must not regard this reference as something purely subjective. It is not the subject that makes the reference, but thinking. The subject does not think because it is a subject; rather it appears to itself as subject because it can think. The activity exercised by man as a thinking being is thus not merely subjective. Rather is it something neither subjective nor objective, that transcends both these concepts. I ought never to say that my individual subject thinks, but much more that my individual subject lives by the grace of thinking. Thinking is thus an element which leads me out beyond myself and connects me with the objects. But at the same time it separates me from them, inasmuch as it sets me, as subject, over against them."