Chapter 10

Comprehending and Indicating Thinking

We established previously that the act of perception establishes a relationship between the thing-point and the self-point. But this relationship presupposes something deeper: the relatedness of each point to reality.

Now we must examine this relationship more carefully. Consider a crucial property we have overlooked: the connecting line between self and thing is not merely a line but a directed line. This direction has its determination through its relationship to at least one other direction.

Just as finding a line implies finding its direction, and this includes its directional difference from another line, so too is the directionally determined relationship only established in relation to a directionally different relationship.

This seemingly simple observation has profound consequences. It means that no act of comprehension occurs in isolation—every grasp of an object involves at minimum a directionality distinguishable from some other directionality. Understanding always operates through contrast, through differentiation of mental directions.

Because this directional nature was overlooked, past research on understanding exhausted itself for centuries—especially since Kant—in fruitless variations on the theme: subject and object, consciousness and being, thought and being, consciousness and something, idea and reality, I and not-I.

These formulas, multiplied almost indefinitely, offered one and the same dichotomy in ever-new attire as the ultimate solution to the problem of discovering the world.

But consider what our schema reveals: the relation of the objective point to the perceiving point requires at least a second objective point. The division of subject-object, or self and thing, is actually a high-level abstraction from the repeatedly experienced basic situation in which the self relates to a particular thing.

Everyone realizes: it is not "the thing" that is experienceable, but a thing among other things.

Even the individual thing is already distinguished by its being grasped from its properties, states, and the processes taking place on or through it—finally from its location in space and duration in time.

We think of each concept as somehow opposite to a complementary concept, such that none could be thought at all without the directional determination thereby established: individuality—connectedness, unity—plurality, property—process, state—process, space—time. Further: quantity—quality, size—degree, sameness—difference, equality—diversity, whole—part, inside—outside, cause—effect, and so forth.

Language preserves unmistakable knowledge of this. We not only "direct" our thoughts, attention, efforts, and feelings toward something, we not only speak openly of "drive direction" and "will direction," but we even call every selective peculiarity of belief, conviction, approval, disapproval, and action a "direction": taste direction, attitude direction, political direction, belief direction, progressive direction.

Traditional logic represented concepts through circles whose size indicated scope, and whose positions indicated relationships. This old circle schematism completely fails to recognize that the geometric location of all concepts without exception is comprehending consciousness.

Exclusively concerned with scope relationships and always in danger of reifying concepts, this approach overlooks the basic fact that concepts are nothing other than fixed directional determinations of comprehension.

It could not even raise—much less solve—the question of what in the mental direction belongs to life, what belongs to mind, what is merely intended through them, what is conceptualized.

If the mental act cannot set the point except as an ordering location, then with the setting, a mental direction is inevitably fixed, and with the point, necessarily a place is comprehended. The conceptualized therefore belongs to the special position that the mental gaze is forced to take in order to find the place.

We must accordingly distinguish in the conceptualized: its character of unity and the ordering location of the relevant unity in otherwise varied intersecting series.

But just as a place does not change its nature because it stands at the intersection of several series—and through participation in many series gains no increase in similarity with the coherent means it divides—so also with the concept: the direction of relationship is not understood as the associated section of reality, but only the fact of its difference from sections of other directions.

A concept marks a position in a network of directional contrasts. It is where one mental direction distinguishes itself from another.

If the point-like nature of thought objects led us to the fundamental contrast between boundary and continuity, their positional nature leads us to the fundamental contrast between conditionality and unconditionality—or, as it is misleadingly termed, the "relative" and the "absolute."

A possible object of thought is formed only by the relationship of two directions. The reality that conditions this relationship is indeed experienced and intended, but not comprehended.

We would not have the concept of redness if there were not also the concept of blueness. With the concept we comprehend the difference of red from blue. But we mean thereby—and are able to, thanks to the directional determination of our relatedness to the impression content of red—something that everyone must admit cannot be touched, let alone grasped, by specifying its difference from even hundreds of thousands of other colors.

Consider this carefully: One can easily make a person born blind understand that red is different from blue. One can instruct them in the laws of optics. One can give them an idea of the character difference between the two colors by comparing them to the difference between a high and low tone. But one cannot bring any single color to their perception with all that.

If we mean, as no one will doubt, with the concept of redness also the perceptual content of redness, we clearly mean something undefined and incomprehensible, which is only thought of with the conceptualized. The direction of relationship to red forms an imaginary angle with the direction of relationship to blue—but neither direction captures the experience of redness or blueness itself.

The "gaze" of our mind actually goes in another direction when we think of redness than when we think of blueness. But what is comprehended—grasped, mentally possessed—thanks to such a "gaze" is merely the relationship of two directions to one another, not at all the phantasm of redness and the phantasm of blueness.

These phantasms, comparable to neither a point nor a direction, are received by living soul and can completely disappear in the thought process as soon as the direction of mental gazing caused by them has once solidified.

We must sharply distinguish in the thought process: the act of fixing and the process of representation that sometimes helps but often disturbs it—commonly called "imagining."

In most cases, there is no representation of the objects of thought during thinking. It is a question that must be repeatedly raised and is sometimes extremely difficult to decide: what exactly and how much is represented?

Thinking consists of continuous transition—or rather leaps—from one direction of view to another. It is essentially a constant change of attitude of the mind.

Consider particles and conjunctions, these indispensable parts of speech. We mean something different with "although" than "nevertheless," quite different with "if," different with "until" than "before." While "and" corresponds to a gliding forward movement of the mind, "but" is comparable to a reversal and mighty swing of the pendulum. Yet it causes us the greatest difficulties to determine whether something is being represented and what it is.

The mental act operates primarily through directional shifts, not through image manipulation. We change our mental stance more than we picture objects.

We have now completely clarified what prompted us to designate the concept with the dimensionless point. It is not about the point itself, but about the direction to be determined by it. The indivisibility that initially recommended the point to us is not the indivisibility of the atom, but of direction.

Certainly, we cannot avoid placing a point at a certain distance behind the intended experience content, as otherwise the relatedness of the experienced could not be schematically visualized. But this is an expedient for provisionally avoiding the question of how that relatedness comes about in the first place.

The direction itself points lengthlessly into the "infinite," thus figuratively confirming the timelessness of the object of thought. By extracting the direction—the side it shares with the metaphor of "gazing"—from the metaphor "beam" as actually existing, we demonstrate that for any conceivable judgment, the origin must be traceable to the content of experience, or more precisely to the medium of spatiality inseparable from any experience content.

Instead of saying every concept means something comprehensible as well as something incomprehensible, we now have these two sentences:

All comprehension consists in the precise awareness of the imaginary angle of two directions of the mind—it does not consist in grasping the experience contents that intersect them.

Just as surely as nothing other than a direction is understood—namely in relation to a second one—so surely can the direction also mean a reference to the occasion of its emergence: the never comprehensible experience content.

We use this insight to refute the logician's objection.

If the logician counters that even the non-objective is a concept content and thus a product of thought, we reply in a much deeper sense: no object of thought is found without the related foreground of an experience content, which, although intended with its help, can never be comprehended.

There could be no talk of uniformity if an indivisible continuity were not involved, in view of which sameness only gains meaning.

We do not deny that "reality," "happening," "experience," "continuity," "incomprehensibility" are concepts and thus recognition markers for objects of thought. However, we now show how they differ from concepts like unity, number, uniformity, point, thing.

If the relation to the object includes a relatedness to the non-objective, we can make each concept a carrier of our judgments in a dual aspect:

First, for the purpose of unfolding the comprehended, by relating concept to concept, object of thought to object of thought.

Second, for the purpose of pointing to the incomprehensible, which we had to disregard for the sake of comprehension.

We distinguish in each concept its function of comprehension from its function of indicating.

Consider what happens when I say "this table here." I distinguish the intended from the intended in "that table over there," and thus have expressed unrestricted comprehension that two different tables are in question.

However, in the meaning content, these phrases do not present the slightest of the sensory images that would appear if I were to alternately point with my finger at physically present tables—nothing of the factual situation without which the conceptual indication would lack its experienced cause.

If one understands the indicative function of concepts as the conceptual difference of each intended object from other objects, then it would be merely the function of comprehending in another light. However, if one understands it as the necessarily assumed cause of conceptual differentiation, then it is essentially different from comprehending and is meant to link the object of thought with a reality that can never be comprehended.

Then it becomes clear: we can utilize all concepts for dual purposes—to order the objects of thought with each other, or to illuminate their dependencies on the experienced cause of objectification. Thus two fundamentally divergent directions open for all thinking and research.

Even brief reflection on arbitrarily chosen names reveals that in concepts, sometimes the comprehending, sometimes the indicative note prevails.

Consider these words: equality, difference, sameness, unity, plurality, number, point, line, thing, weight, possibility, impossibility. One gets the impression that what is meant by them is always something entirely comprehensible, penetrated by mind, completely "definable."

In contrast, consider: night, spring, youth, cold, darkness, glow, roaring, miracle, chance, mystery, reality, event, experience, infinity. Even the least trained person can feel that the difficulty of defining these concepts is significantly greater—what is meant by such names contains more indefinable than definable elements.

The former serve especially comprehending and ordering thinking, while the latter serve indicating thinking. The former primarily relate the thinking mind to the unexchangeably "fixed" object of thought, while the latter predominantly use the object to relate to non-objective realities.

The former are meaning-poor concept words, while the latter are concept-poor meaning words.

We attribute the distinction between a comprehending and pointing side of thinking to the significance of a logical discovery—one that puts an end to the millennia-old dispute over the possibility and value of truth.

All objects of thought are indeed fictions, insofar as one believes to have comprehended reality in them. But no object of thought needs to be a fiction if one distinguishes what is actually comprehended in it from what it can only point to as something incomprehensible.

It is the comprehending function of thinking that allows us to grasp objective time and sharply distinguish it from objective space—to establish the ordered, bounded, point-like structures through which understanding operates.

It is the indicating function of thinking that allows us to mean, with help of the same concept, the content of experience: the incomprehensible real time as well as the incomprehensible real space.

Comprehending thinking gives us the network of directional contrasts, the system of fixed positions, the calculable relationships. Indicating thinking points beyond this network to the living reality that occasions it—the flowing, continuous, never-graspable experience that comprehension must arrest to function, but which remains the ultimate reference of all our concepts.

Truth lies not in choosing between these functions but in recognizing their distinction. Understanding falsifies when it believes its comprehensions capture reality. Understanding serves truth when it recognizes that its fixed directional determinations merely indicate—point toward—the incomprehensible flow of experience they can never contain.