Based on the notes and summary of the Second Investigation, there are several points to bear out:
1. The bridge between the properties of things is a bridge of qualific similarity that may be called categorical.
2. Part of the reason of experience is the relevance of the outward to the inward, implying an imperative that experience cohere to a kind of aesthetic of the mind.
3. Individuals, defined as identities with roles, find value within this afforementioned field of qualities, even if indirectly, by apprehending objects which to the extent that they have value, cohere to such a system.
4. There is a relationship amongst properties through which there is a common sense of place, justice, beauty, usefulness, ethics, intelligence, and identity. Thus the aesthetic or composition amongst these properties may provide a map of other sorts of relationships.
Although I have written of the field of categories before (the Motist manifesto provides a means for discovering such relationships, which are many and varied), I'm taking this opportunity to chart new territory, thus I am focussing not on specific truths as the methods may formulate, but rather more general rules or speculations reflective of over-arching themes.
I haven't written much before on the qualities themselves, although this is implicit in the method. I myself have difficulty finding the place in my thought where I apprehend with deep feeling, other than by awe or fear. As I continue the trends of the investigations, I am seeking the life of the thought, not as fossilized categories, but fields or vessels within which tranformation may take place.
From the first statement is implied that there is a sense of layers; property : quality : category. One may shift while another remains unchanged. For example, if I substitute property for symbol, quality for qualifier, and category in terms of a field of dichotomic opposites, what may be compared is for example CIRCLE : UNIFIED : NOT DISPERSED. If NOT DISPERSED is defined more accurately within the same field as UNIFIED, creating two other intermediate categories, we may then elaborate on it within the axial definitions of the two terms.
Unified may be defined as ALL CONTAINING, therefore its opposite would be the opposite also of ALL and CONTAINING. Since DISPERSED would thus be defined as NOTHING OUTSIDE, we have two new categories, one defined in terms of ALL OUTSIDE, and another in terms of CONTAINING NOTHING. A deeper interpretation yields that CONTAINING NOTHING = SPACE, while ALL OUTSIDE = POINT. So both a circle and its opposite are defined in terms of space and point. Interestingly, I have already defined the opposite of a circle as a cross, in my pages on mystical geometry at
Cross as Polygon Type 2Obviously this sort of determinative logic has already proven that it has some legitimacy.
Focussing on the second point, the question in a categorical aesthetic is for special situations that have particular value, that can't be dismissed as coincidences or incidentals. What are some names of special convergences of categories?
Paradox: a paradox is always a convergence of two things which appear true, which can only be solved in a special case, or not at all. The paradox provides two truths, or categories, within which a solution must adhere to each: the solution must be categorical, but it must also be a special case. Since I have suggested that categories are important, this seems almost like an archetypal representation of "special convergences of categories", especially in an axial system of opposites.
Another is analogical, like
CIRCLE : UNITY : NOT DISPERSED :: CROSS : DISPERSED : NOTHING OUTSIDE
However, not every case is categorical. We might say that BLUE : GREEN :: SEA : TREES, but this might be reduced to COLOR : COLORED; overall the property defined is color, whereas in the case of "circle : cross" different symbols are being compared, hence axially different properties are produced. The first is a more discerning case, in part because an analogy was necessary simply to define circle as "unified". However this is not to deny that it is a property of circles, thus by extension there is a categorical logic operating. When we cannot deny a property, we cannot also deny that a true opposite has a truly opposite property. This is the strictest sense I have found that an analogy may be categorical.
If it can be proven that the opposite does not have an opposite property, the opposition comes into question. If the opposition cannot come into question, then the property of the first object comes into question. When the opposite of the property of the first object is a property of the opposite, this is evidence that it is a true opposite of the first object.
Returning to the notion of paradox, there are ways in which the relationship amongst categorical parts of an analogy may be paradoxical. In what case is a cross a circle? In what case is a point space? It seems that this could be solved through considering categorical relationships.
The properties of space in the context of circle and cross are CONTAINING and NOTHING, while the properties of point are ALL and OUTSIDE. Thus both the situation in which a cross is a circle and the case in which a point is space are situations where CONTAINING is OUTSIDE and ALL is NOTHING. However, in this example, nothing is what space contains and containment is what a circle does. Therefore we may interpret it to mean that a cross is a circle when there is a circle outside, and what the circle contains is space. In the point-space example, the circle must be zero or one; it is a matter of whether it contains a point. However this suggests a valuation of points that is not spacial; for when a circle is complete with a single point in it, it is as though the circle is a point, suggesting that space and points do not exist without infinity.
If the axis of point-space is infinity, and the axis of circle-cross is ascriptive in the sense that it implies manifestation (signifier or nature, represented by the cross) is possible within certain limits or boundaries (the outer circle) whereby there is a relationship, a higher paradox is formed between infinity and the ascriptive, which may be seen in terms of qualities of each.
If infinity is the opposite of ascription, a compromise or amelioration may only be found through the ascription
of infinity. Either what is ascripted perpetuates within infinity, or infinity may be ascripted within a finite context. One way to interpret is that these are the same.
Bearing on the third point of objects conceived within this system that may ameliorate by paradox, it is a case in which independent of the personal valuation of the perceived object (an object I will assume exists in any perspective regardless of the nature of the object, since such an object is required as a context to understand that change is possible and in this sense prefigures time) there is a correspondence between the unity of the perceptive framework and the nature of the object perceived.
For example, within time any object may be perceived as a trend (relating to Aristotle's concept of ~Talos). When a given condition has a beginning, middle, and end there is a way where it may be defined in terms of the presence or absence of its former and future qualities. In most cases the future condition is not the same as the past condition, thus the present may be defined in terms of the opposite past and future cases. When the present, or more specifically the object's state in the present, is defined in those terms, its nature may be seen as an interpretation of meeting potentials and seeking potentials, a sort of volitional dynamics.
If the present case is an individual person, these might be seen as accomplishments or resources, and a capacity to meet future conditions such as through wilful action or preparedness. However, in a more abstract sense the focus may as well be on opposites, but not of dynamic situations. What Aristotle calls the soul of a thing may as easily result from unchanging conditions; oppositions which exist already, or simply opposite potentials. Life becomes a potential to make the most of a figure ground, or at least travel within the realm where this ground moves. So long as language consists of opposites they may be compared.
Even if there are disagreements as to what opposes what, their compromise is different insofar as their terms are different. Therefore these are really two different fields; one where one thing opposes another, and a second case in which a third thing opposes the first. Because the parsing is different, they cannot be considered as though they are the same. The question is not "what is the opposite", but how to solve the problem as one means to approach it.
The fourth point I'll touch on briefly here by saying that notions of general concepts such as justice, beauty, usefulness, ethics, intelligence, and identity may be assembled in terms of parsing oppositions from different standpoints. A categorical context for one of these might be compared to another, in such a way as to lead to a broader, richer view of the meaning of each. For example, there may be a relationship amongst the beauty of machines, the usefulness of machines, and the ethics of machines, such that it is understood that the mechanics is in fact something apart from, but operative within, each of those zones.
Or there may be zones of experience in which the archetypes of those machines belong, a sense in which zones are related categorically through the categorical relation of the machines themselves: their role and meeting of a more universal notion, for example, the beauty of usefulness (technological perfection), the ethics of beauty (a positive psychological role), and an ethics of usefulness (an efficiency in meeting the overall needs of a given system or population; also archetypal value in meeting its place within the categorical framework, partly following from the previous two, or other combinations).
Of course, here I am considering machines in a broad sense, as a metaphor applicable to visible or invisible systems (in part, notions of conceiving), as well as the aforementioned objects considered as expressions of identities with roles, or simply a circumstance considered dynamically as a place where opportunity and sustenance are reliable.
I will clarify and expand on this in my following Notes & Summary.
