Bruno Campello

Quid est veritas? This is the most serious and most frivolous of issues. It depends, of course, on the intent of the questioner. Some admit that the meaning and value of human life depends on the existence of some eminently certain and reliable truth that can serve as a measure of the validity of our thoughts. Others feel that life can go on without any truth and without any foundation. Among these was, of course, old Pilate. By exclaiming — “What is the truth?” — he was not asking a question himself, but expressing with a shrug his unwillingness to ask the question seriously. The prospect of no truth that would lead to despair for those who think life needs it to be justified was for Pilate a relief and consolation — a guarantee that he could continue to live without worry. Some bet on the existence of truth and cherchent en gémissant. Others turn their backs and wash their hands. The verbal formula with which they express themselves is the same: Quid est veritas? But in the difference of its nuances lies the entire distance from the tragic to the comic. The frivolous or comic school is widely dominant today, whether in universities or in culture in general. Even those who seek to believe in an effective truth surround it with all sorts of limits and obstacles, for example by reducing it to the kind of partial and provisional truth given to us by some experimental sciences. Others cling to faith, saying the truth exists, but it is beyond our comprehension. In any debate about the problem of truth in our day, the program almost invariably consists in shuffling again and again the remarks that philosophers, from Pyrrho to Richard Rorty, have made about the limits of human knowledge. These limits, taken together, set up a formidable mountain of obstacles to any claim to know the truth. And this mountain is soaring, with a peak that goes farther and farther as we climb it. For example, from the Pyrrhonist school’s simple objections against the validity of knowledge by the senses to the enormously complex constructions with which psychoanalysis denies the priority of consciousness or Gramsci reduces all truth to the expression of ideologies that follow one another through history, much has evolved the discouraging injection machine into the seeker of truth. Not surprisingly, many of the builders of this machine, when they add a new piece to it, instead of regretting the increase in human helplessness, bring a smile similar to Pilate’s lips. The inexistence of truth, or the impossibility of knowing it, is a comfort to them. We will see below what are the deeper reasons for this strange satisfaction. For now, let’s set these creatures aside and raise the question of truth on our own. Since we do not yet know whether the truth exists or what it claims, we have to appeal to a provisional formal definition, which makes it possible to start the investigation without prejudging its outcome. This provisional definition, to meet this requirement, must express the mere intentional meaning of the term, as it appears even in the mouth of those who deny the existence of any truth, since to deny the existence of something one must understand the meaning of the term that designates it. I say, then, the truth which we do not yet know whether or not it exists, the truth whose existence and consistency will be the object of our inquiry as it has been of so many investigations before us, is the permanent and universal cognitive foundation of validity of judgments. If we say, for example, that the sole ground of the validity of our judgments is their usefulness, we deny the existence of a cognitive ground, that is, we deny the existence of truth by negating one of the elements that make up its definition. The same goes for saying that all valid judgments are based on faith. If we claim, however, that there are no valid judgments of any kind, then we deny the existence of any foundation, cognitive or otherwise. If we affirm that judgments are valid only for a certain time and place, we deny that the foundation is permanent. If we affirm that judgments are subjectively valid only to the one who utters them, we deny that the foundation is universal. If we say that the foundation of the validity of judgments is only logical-formal, without any scope on the real objects mentioned in the judgment, we deny that this foundation has cognitive significance. All these denials of truth presuppose the definition of truth as the permanent and universal cognitive foundation of the validity of judgments. Similarly, if we say that there is truth, that it is knowable, that on the basis of it we can build a valid set of knowledge, we will have nothing added or removed from this definition, but we have only stated that the object defined therein exists. Our provisional definition, and therefore compatible with the two maximally opposing currents of opinion which dispute over the issue, is a superior and neutral ground from which investigation can be initiated without prejudice and in all honesty and rigor. We thus start from a consensus. The next step of the inquiry is to ask whether or not the truth thus defined may be the subject of radical questioning. By the term radical questioning I mean that kind of questioning which, assuming ex hypothesi the nonexistence of its object, — as for example has so often been done with the existence of God, innate ideas, or the outside world — ends in either favor of that very nonexistence, whether of existence. The radical questioner of God, innate ideas, or the outside world, can question them because he places himself out of divine, innate, or mundane ground from the beginning, that is, he reasons as if God or innate ideas or the world not existed. As his investigation unfolds, he will either come to the conclusion that his premise is absurd, which will therefore lead him to admit the existence of which he had not postulated, or, conversely, to the conclusion that the premise holds perfectly well and that what was supposed to nonexistent doesn’t really exist. The most classic example of using this method is that of Descartes. It presupposes the inexistence of the outside world, the sense data, its own body, etc., etc., and continues to reason in that line until it finds a limit — the cogito ergo sum — that forces it to retreat and admit the existence of all when he had initially denied it. The radical questioning is the hardest test that philosophy can submit to any existing idea or entity. What we must ask, therefore, shortly after we have obtained the formal definition of truth, is whether the truth thus defined can be the object of radical questioning. The answer, which may seem surprising to many, is a stinging no. Truth cannot be object of radical questioning. No inquiry into the truth, however radical, can give as presupposed that there is no permanent and universal cognitive foundation for the validity of judgments and continue to reason consistently with this premise until it reaches some result, positive or negative. And it cannot for a very simple reason: the assertion of the absolute absence of any permanent and universal cognitive foundation of the validity of judgments would itself constitute the permanent and universal cognitive foundation of subsequent judgments made in the same line of inquiry. The investigation would be paralyzed as soon as formulated. Let us briefly examine some of the classic truth-denying strategies that the questioner might resort to in order to escape this cul-de-sac. Let us try, for example, the pragmatist strategy. It asserts that the validity of judgments rests on their practical utility, that therefore the basis of this validity is not cognitive. If we were to say that the absence of a universal and permanent cognitive foundation of the validity of judgments is not itself a universal and permanent cognitive foundation, but only a practical foundation, of both there can be only one right answer: either this practical foundation would in turn have to be universal and permanent, or it would be only partial and provisional. In the first hypothesis, we would have two problems: on the one hand, we would fall into the paradox of universal utility, that is, something that could usefully serve all practical purposes, even the most contradictory ones. It would be the universal means of all ends or, even more clearly, the universal panacea. On the other hand, we would have to ask whether belief in this panacea would in turn have a cognitive foundation or whether it would be merely a practical utility, and so on infinitely. In the second hypothesis — that is, in the event that the questioner admits that the assertion of the absence of truth is only a partial and provisional foundation for the validity of subsequent judgments — then, of course, there would always remain, unabated, the possibility that outside the judgment ground thus delimited could exist other universal and permanent cognitive foundations to validate a multitude of other judgments, and the investigation could go on and on, jumping from provisional ground to provisional ground, without ever being able to be based on its own assumption, that is, in the radical absence of truth. Let’s try a second strategy, that of subjectivist relativism. It proclaims with Protagoras that “man is the measure of all things”, which is commonly interpreted as “every head, a sentence”, that is, that what is true is true only from the point of view of the thinker, and may be falsehood from the point of view of all the others. Can this statement form the basis of a radical questioning of the truth, such that the denial of the existence of any universal and permanent cognitive foundation for the validity of judgments does not in itself become the universal and permanent cognitive foundation on which the validity of judgments rests subsequent judgments in the same line of inquiry? In other words, and simpler: can relativism deny the existence of valid judgments for all men without this negation itself becoming a valid judgment for all men? To do so, it would have to deny the universality of this denial, which would result in admitting the existence of some or a few or a multitude of judgments valid for all men. Thus relativism would itself be relativized and would end up in a platitude without any philosophical significance, that is, in the statement that some judgments are not valid for all men, which implies the possibility that other judgments may be so. No, the subjectivist relativism cannot carry out a radical questioning of the truth as pragmatism could not. Can historicism do it then? It declares that all truth is merely the expression of a temporally localized and limited worldview. Men think this or that not because that or this imposes itself as universal and permanent mandatory truth, but only because it imposes itself in a limited place and time. In proclaiming these limits, can historicism prevent the affirmation of these limits from becoming itself the universal and permanent cognitive foundation of the validity of judgments? To this end, it would have to be admitted that there may be some ground that denies this statement; but if this foundation exists, then there is some truth whose validity is unlimited in time and space, some truth whose validity escapes historical conditioning — and historicism would be reduced to the miserable realization that some fundamentals of validity are historically conditioned, and others not, without even being able to apply this distinction to concrete cases without affirming in the same act the invalidity of the historicist principle taken as a universal rule. I will spare the reader the enumeration of all possible subterfuges and their detailed impugnation. He can perform them himself as an exercise if he so wishes. I even suggest it do it. And as many times as he will do so, he will always end up returning to the same point: it is not possible to deny the existence of a universal and permanent cognitive foundation of the validity of judgments, under any pretext whatsoever, without having this negation, together with its respective pretext, to assert itself as the universal and permanent cognitive foundation of the validity of judgments, thereby paralyzing the next denial by which research should, if it could, be pursued. Truth as we define it cannot, in short, be the subject of radical questioning. Nor can the possibility of knowing it. Denied that it is possible to know any universal and permanent cognitive foundation of the validity of judgments, either this impossibility would become such a foundation, affirming in the same act its own lack of any foundation, or else, in order to not assume this vexing role, it would have to be limited to say that some judgments are unfounded and others probably aren’t, a statement that is within the reach of any schoolboy. Unable to achieve the desired aim point, the enemy of truth is therefore condemned to gnaw it around the edges, eternally, without ever getting to the vital center of what he would desire to destroy. He will sometimes deny one truth, sometimes another, sometimes under one pretext, sometimes under another, varying the strategies and directions of the attack, but can never be rid of his fate: every denial of one truth will be the affirmation of another, and so much that negation as well as this statement will always result in the affirmation of truth as such, that is, of the actual existence of some universal and permanent cognitive foundation of the validity of judgments. This explains, at the same time, the continuous, limitless and unbroken proliferation of denials of truth, and their complete impossibility of sweeping from the face of the earth the belief in the existence of truth, the belief in the possibility of knowing the truth, the belief in the present and full possesion of some truth capable of giving universal and permanent ground to the validity of judgments. That is why the number and variety of attacks on the truth, from Pirro to Richard Rorty, far outnumber the number and variety of defenses that formally present themselves as such: it is that they themselves, albeit to the disgust of their authors, always end up as defenses and praises of the truth, not only sparing the apologist work, but vivifying themselves what they would wish to bury and honoring what they would wish to humiliate. This is also why the novice, impressed by the variety and continuing resumption of attacks on the truth that is observed in the history of philosophy — at a noticeably increasing speed these days — soon adheres to skepticism so as not to feel a member of a isolated and weakened minority, but, by continuing his studies and surpassing the first impression based only on apparent quantity, he cannot maintain this position and finds that the strength lies not in the number of those who deny it, however impressive it may be, but in the quality of those happy few who serenely affirm the truth. The impossibility of radical questioning, which we found in the previous chapter, leads to the conclusion that truth can be attacked only in parts, but that each negation of the part reaffirms the validity of the whole. In other words: what can be questioned are truths. “The” truth cannot be questioned, and indeed never has been, except in words, that is, by a pretense of denial that ultimately turns out to be a statement. But that takes us one step further in the investigation. A venerable tradition, begun by Aristotle, states that the truth is in the judgments, that it is the property of the judgments. Some judgments “possess” the truth, others do not. We call the first true judgments, the second false judgments. The set of true judgments is therefore a subset of the set of possible judgments. Possible judgments, in turn, are a subset of the set of human cognitive acts, these are a subset of the set of mental acts, these a subset of the set of human acts, and so on. The territory of truth is thus a small cut-out area within the vast world of thoughts, deeds, and beings. Is this really possible? How could truth be both the foundation of the validity of all judgments and a property of some of them in particular? Isn’t this a stark contradiction or at least a problem? To equate and solve it, a distinction must be made here between truth and veracity. Truth is the universal and permanent cognitive foundation of the validity of judgments. Veracity is a quality that is observed in some judgments, according to which its validity has a universal and permanent cognitive foundation. Once this is understood, it strikes the eye that truth is a foundational condition of truthfulness, not the other way around. If there were no universal and permanent cognitive foundation for the validity of judgments, no judgment could have a universal and permanent cognitive foundation. If, however, a particular judgment has this foundation, nothing in the world can determine that it alone has it, that the existence of the foundation depends on the existence of that particular judgment. Already this particular judgment could not exist and be true if there were no truth. The truth is therefore logically prior to truthfulness and constitutes its foundation. But, being the foundation of truthfulness, truth is also the foundation of untruthfulness, because false judgments are false only insofar as they can be truthfully challenged, either by their simple denial — veridical in itself — or by the statement of the contrary veridical judgment. Being the foundation not only of the truthfulness of the true judgments, but also of the untruthfulness of the false judgments, if truthfulness is present only in true judgments, and cannot be present in false judgments, truth, in turn, must be present in both as the basis of the truth of the former and the untruth of the latter. The territory of truth, therefore, is not identical with the set of possible true judgments, but encompasses this and that of possible false judgments. Does truth, the foundation of all judgments, necessarily have to be a judgment? Can only one judgment be the foundation of a judgment? The answer is yes and no. Yes, if by foundation we mean, restrictively and conventionally, the premise on which the proof of judgment is based. But the premise states something about something, and that something, in turn, is not judgment but its object. I say, for example, that turtles have shells. I base this judgment on the definitions of turtle and shell, which are judgments, but I ground these definitions in the observation — which is not judgment — of turtles and shells, which are not judgments either. Should not this observation also be true, capturing traces truly present in true objects? Or will I appeal to the subterfuge that observation has to be only accurate, not applying the concept of “true” to it? But what does “exact” mean, if not anything that informs me beyond or below what was truly observed in what an object truly showed? And besides, is it an authentic accuracy or just a simulacrum of it? There is no escape: either there is truth in the observation itself, or it cannot be exact, correct, adequate, or sufficient, nor have any other quality to recommend it except if that quality is, for its part, true. Thus, the foundation of the truth of a judgment lies not only in the truth of the judgments that serve as premises, but also — in the case of judgments concerning objects of experience — in the truth of the data from which I draw these premises and in the truth of what I know from experience. Moreover, if the foundation of judgments had to be itself always a judgment, the first foundation of all judgments would itself be a judgment without any foundation. Aristotle, led to this dead end, stated that knowledge of the first principles is immediate and intuitive. But by that only meant that these principles had no proof, not that they were without foundation. The principle of identity, for instance, as expressed in judgment A = A, has no judgment behind it that can serve as a premise for its demonstration, but it has an objective foundation in the ontological identity of every being with itself, which is not judgment. Now what can be intuitively known is this ontological identity, not the A = A judgment that only manifests it. The intuition of the first logical principle is not in the form of judgment, but of immediate evidence which is not judgment in itself. There can be no judgment without signs that turns this immediate evidence into a verbum mentis, a conscious assent, which, without being yet a proposition, a statement in words, is no longer merely a simple intuition but a mental reflection of it and therefore, a derived cognitive act and second, not first. Thus, if the territory of logical premises begins in the judgments that affirm the first principles, this territory does not even cover the whole field of cognitive foundations, which, on the contrary, extends into the realm of intuitive perception, either of objects from experience, either from the first principles. With this, the falsity of the image in which the truth is a small area cut out in the vastness of the territory of possible judgments becomes evident. All judgments, true and false, are a modest cut in the immense territory of truth. By this we are led to understand that truth, being the criterion of validity of judgments, can neither be an immanent property of the judgments themselves, nor be something wholly external to judgments from outside judging them; for this would turn in judgment. If I say the chicken has laid an egg, where can the truth of this judgment lie? In the judgment itself, regardless of the chicken, or in the chicken, regardless of the judgment? The absurdity of the first hypothesis led Spinoza to proclaim the inanity of judgments of experience, which are never valid or invalid in themselves and always dependent on something external: a true judgment, for him, would have to be true in itself, regardless of what it was, for example A = A is independent of what is A and any other external verification. But the identity of A with A is not only in the judgment that affirms it, but in the consistency of A, whatever it may be. There is no purely logical judgment that can be true or false in itself and without reference to something that is what the judgment speaks of. Even a judgment that speaks only of itself unfolds into the affirming judgment and the judgment from which something is affirmed, and this one is certainly not that. To say that a judgment is true in itself cannot mean total alienation from the world, which is supposed to be the very possibility of making a judgment. Escaping into the domain of formal identity does not solve the problem at all. Will we then say, with an old tradition, that the truth lies in the relationship between judgment and thing? Now this relation is in turn affirmed in a judgment, which in turn must have a relationship with its object (the affirmed relationship), and so on infinitely. The other hypothesis, that the truth of the judgment the chicken laid an egg is in the chicken regardless of the judgment, would lead us to equally insurmountable difficulties. It would result in saying that the truth of the judgment does not depend on whether that judgment is issued, that is, once the chicken has laid an egg, the judgment that affirms it is true even though, as a judgment, it does not exist. Edmund Husserl would subscribe to this without blinking: the truth of judgment is a matter of pure logic, which has nothing to do with the merely empirical question of whether a particular judgment is once affirmed by anyone. The confusion between the sphere of truth of the judgments and the sphere of their psychological production did indeed much harm to philosophy, and Husserl undid this confusion definitively. But if the chicken has laid an egg and no one has said anything about it, the truth of the matter is not in the judgment but in the fact. The judgment that has not been issued cannot yet be true or false, it can only have the conditions to be so; if it is true that the chicken has laid an egg, the judgment that affirms it will be true if formulated, while the truth of the fact is already given with the appearance of the egg. But if the truth of the judgment the chicken laid an egg is neither in the judgment independently of the chicken, nor in the chicken regardless of the judgment, nor in the relationship between chicken and judgment, where on earth can it be? Now we have just seen that, regardless of the judgments that affirm them, the objects intended in the judgments can also be true or false, regardless of the judgments that may be made about them. The chicken laid an egg is opposed to the chicken not laying an egg, regardless of whether or not someone says it. There is contradiction and identity in the real, regardless of and before a judgment affirms or denies anything about it. Or, what is the same: truth exists in reality and not only in judgments, or else it could not exist in judgments at all. There is truth in the fact that the chicken has laid an egg, there is truth in the judgment that affirms it and there is truth in the relationship between judgment and fact as well as in the judgment that affirms the relationship between judgment and fact: truth cannot then be in fact, neither in judgment nor in relationship, but it has to be in all three. Moreover, if it is in all three, it must also be in something else, unless we admit that a single fact, the judgment that affirms it, and the relationship that binds them, together, may be true in the hypothesis that everything else is false. But this “everything else”, which is contained neither in fact nor in judgment nor in relation, necessarily includes the very existence of facts as well as the logical principles implied in judgment and in relation. If there are no facts or logical principles, the chickens will uselessly lay eggs in the realm of non-fact, and a relationship between fact and judgment in the realm of illogism will be futile. Therefore, the truth of one fact, one judgment and its relation implies the existence of truth as a domain that transcends and encompasses at once facts, judgments and relations. Searching for truth in fact, in judgment, or in relationship is like searching for space in bodies, their measurements, and their distance from one another; just as space is not in bodies, neither in measurements nor in distances, but bodies, measurements and distances are in space, so the truth is not in fact, in judgment, nor in relationship, but all are in truth or they are nowhere, and even this “not being anywhere”, if it really means anything and is not just a flatus vocis, has to be in the truth. Truth is not a property of facts, judgements, or relationships. It is the realm within which facts, judgements and relations occur. At this point, the kantian temptation is practically unavoidable. As a condition for the possibility of facts, judgements and relationships, the truth is effectively an a priori condition. But is it an a priori condition for the existence of these three things or only for the “knowledge” we can have of them? This problem is solved in a simple and brutal way: if we say that the truth is an a priori form of knowledge and intend this statement to be true, then knowledge must be in the truth and not truth in the knowledge, because what is a priori cannot be immanent to something which it itself determines. To be an a priori condition of knowledge, truth must necessarily be an a priori condition of something else that is not knowledge, but rather its object. Knowledge, like facts, judgements and relationships, is within the realm of truth, and that is so independently of knowledge being considered exclusively in its eidetic content or as a fact: the truth of what is known, the truth of the knower, and the truth of knowing are all aspects of truth, and truth is not an aspect of any of them. After all there is no kantian way out. Either knowledge is in the truth or it is nowhere.

The point is the traditional symbol of Being, or Unity. The simplest and most fundamental of symbols has been the one on which the greatest number of mistakes and paradoxes has accumulated, both in elementary geometry and in the psychological study of symbolism. Of these paradoxes, the most surprising is the one that, having affirmed that the point has no dimension, declares that the lines and planes, like all geometric figures, are composed of points. How could anything be composed of something that, having no dimension, could be added to itself indefinitely without ever exceeding the zero dimension? School geometry escapes this problem through the decree that point, line and plane are “intuitive” notions, implying therefore something like the popular notion about the “mysteries” of the Church, which although we cannot understand in any way we must accept willingly (as if it were possible to accept — or reject — a sentence whose meaning we do not entirely know). In the case of Catholic mysteries, however, dogma leaves the door open to another form of understanding, stating that through faith and grace we will be able to assimilate a food that reason has in the account of indigestible; while the geometer assumes reason as the end point, recognizing no form of intellectual intuition as superior to this, and leaving no other option but to accept paralogism as the basis of logic and madness as the foundation of reason. The irritated haste with which the geometry teacher slips over this point, repressing as impertinent the student who wishes to deepen it, is an invitation to the premature stupefaction of intelligence, which will be driven to be insensitized by daily coexistence with the mystery rendered harmless. We all know that school prizes go to those who do best in the skillful handling of mechanisms whose meaning they are totally unaware of and who will, in fact, maneuver with greater development and proud sufficiency the less they suspect the existence of a meaning, as this suspicion could bring it returns to the question of the fundamentals of reason, and to end in the paralyzing terror of the mysterium that extends beyond the utilitarian and self-complacent operationalism in which the “mathematics” of modern teaching are summed up. Either we recognize that all essential knowledge is intuitive and immediate, with science being only the deductive application of intuitive principles to particular cases — with which we return to the medieval concept of science as art, or “application of doctrine” — or we accept that all science rests on an initial absurdity, to which it must periodically return, after a brief tour of particular phenomena and sensitive experience, to be devoured in the labyrinth and darkness as the ritual victims of a new Minotaur. By diverting the students’ attention to the purely operational aspect — technical or pyrotechnical — of mathematics, and turning their ears to the appeal of its primordial, metaphysical and symbolic aspect, modern education becomes a self-indulgent and irresponsible dance on the abyss, preparing young people to get drunk later in the curious mixture of rationalistic pride and dark despair, which constitutes all the characteristic stench of modern cultural life. The ancients, on the contrary, never failed to recognize that reason has its foundation and root in an intuitive form of knowledge, not, however, understood as a vague and indigestible obscure and infra-rational “mystery”, which we pass through quickly and in fear, like a thief in the night, to steal some axioms and run towards the technical and practical applications that constitute for us, today, the only clear and safe domain where we take shelter; intuitive form of knowledge understood, I mean, not as a blackness of the incomprehensible, but as a clear sky of contemplation (contemplatio, theoréin); beatitude of knowledge that was the ultimate goal of all pedagogy, all technique, all science, all rationality. For the ancients, the “first principles”, known by intuition, were the origin, but also the goal of knowledge; but not in a circular, self-repetitive and dark process as in the case of the modern Minotaur, since the origin, the path and the end occurred in different planes. The “origin” designated not only the logical or temporal beginning, but, on the contrary, the supra-temporal plane of archetypes or eternal possibilities The path was, on the one hand, temporal existence and, on the other, the reason as a guiding thread or a map of return to the world of archetypes. Philosophy — science as such — was an activity aimed at correcting the deviations of the human mind, shaping it by the infallible certainty of archetypes, symbolized in numbers, musical harmonies, geometric figures and planetary spheres. Reason, therefore, led man to the portal of mystery. But this mystery differed profoundly from the abyss of perplexity that is the starting and ending point of modern logic and mathematics First, if reason was not the end point, but only the means or the path to lead to something else, the ancient philosopher would have no more reason to be frightened when he reached the border of the non-rational than would have been an traveler who, having taken a train to go to a certain city, saw the end of the journey approaching. Far from seeing this perspective as the end of the world, he would see it simply as the transition from the provisional to the definitive, from the middle to the end. In fact, the very name of philosophy presupposes the existence of knowledge superior to philosophy itself, that is, of a terminal, definitive wisdom, “after the obtainment of which there is no more knowledge to be obtained”. Outside this hypothesis, it must be admitted that philosophers defined themselves from the beginning as lovers of the non-existent. The passage from philosophy to wisdom is well marked in the structure of the Platonic dialogues, where the dialectical, — preparatory or properly philosophical — part always follows the mythical account, that is, the symbolic transmission of an effective and conclusive knowledge of a sapiential nature. Second, the word “mystery” only very recently — from the Renaissance, as far as I know — came to mean the unintelligible. Before, it designated precisely something through which knowledge was revealed, became visible. If not, how can we explain that this word was used as the name of a theatrical, pedagogical and popular genre, such as medieval “mysteries”? Before that, however, the term mystery properly designated a phase of wisdom teaching — the “Little Mysteries” referring to the teaching of the laws of the cosmos and becoming, the “Great Mysteries” to the knowledge of God and eternity. When it comes to teaching, it is evident that neither the small nor the great Mysteries had anything “mysterious” in the current sense of the term. Thirdly, the cyclical return to the mysteries did not have the aspect of endless repetition, in a closed circle that rightly could be considered an image of hell, because it was precisely a question of returning from manifest, and therefore finite, reality to the world of archetypes, and therefore of eternal possibilities, and from there to the Absolute, leaving definitely the whole cycle of transformations (samsara). The return to principles thus had the function, on the one hand, to reassure the submission of the parties to a central and superior nucleus of principles and, on the other, to allow that central intuition to radiate again over the whole field of particular knowledge and applications, fertilizing it and renewing them. Each return brought, therefore, a regeneration of the world, and, in this sense, the periodic return of science to its principles had a function analogous to the rites of renewal of time that all Traditions have always performed at the end and opening of each time cycle and of which the current year-end festivities represent a cartoon residue. The point, it is said, is that which has no dimension or extension of any kind. Now, a dimension is nothing more than a system of directions that defines the various extensions according to which a figure admits to being measured. Depending on the minimum number of directions that define a figure, such will be its dimension. A line is defined by a single direction (two directions); one plan, for two; one solid, for three. Euclidean geometry admits only these three dimensions, but we can use geometric, or spatial, symbolism to represent realities that are not in themselves spatial or geometric; for example, when we use the movement of a watch’s indicators to mark the time; in these cases, the geometric representation will imply more than three dimensions, although in the drawing they have to remain implicit, so to speak. It is clear that no symbolic system can account for the totality of reality, and that is why the ancients articulated several symbolisms to each other, by attaching, for example — in the quadrivium — music to geometry; in fact, a watch is a simultaneously geometric, musical and astronomical representation of time; and anyone can verify that the absence of any of these three representations would make the existence of this symbolic synthesis called clock impossible. Any symbolic system is thus implicitly multidimensional, and geometry would have no way of escaping that, whether modern geometrists admit it or not. Now, a point, if it has no extension, has, however, dimension, contrary to what is believed, because it has to be in some direction, under penalty of not being anywhere, that is, of not existing. Well, in how many directions is a point? It is in all directions at the same time, because any line that you imagine, in any plane that is, will always have a parallel that necessarily passes through that point. The point is thus the figure that, having no extension, is simultaneously in all directions and therefore has the totality of dimensions In this sense, the point represents the logical and ontological principle from which the figures emerge, and not just a constitutive “element”; because an element, in order to contribute to the formation of the figure, should be added or articulated to other elements of the same genre, with which we would fall into the already mentioned nonsense, of the sum of inextensive elements ending up producing extension; whereas a formative principle necessarily contains the key to all the phenomena it produces, not needing to be added to whatever is of a different and superior reality to that where these phenomena occur. Thus, having all directions and dimensions, the point also contains the formative key of all figures. These, therefore, cannot be formed by adding points, but, on the contrary, by suppressing the directions and dimensions of the point. A line will thus be defined as one of the many directions that cross a point; one plan, like two; space, like three. The various directions and dimensions can thus be considered as points of view according to which the point can be focused; and geometric figures, as combinations and articulations of these points of view. If a point, considered in itself, has all directions, considered as an “element” of a line it will have a single direction, precisely because of the unidirectional limitation that defines that line. The dimensions and figures are, in this way, and so to speak, “subjective” in relation to the point, as they constitute only ways of looking at it, while the point is totally objective, therefore, containing in itself all points of view, does not depend on any of them to exist. With that, we get rid of the pejoratively “abstract” character of geometry and restore its organic link with normal human perception, since, in the sensitive reality, we cannot “see” a point, except as intersection of lines, even so that we cannot “see” an object “in yes”, that is, in the simultaneity of all its dimensions, but only according to one or a few points of view, which will be precisely those for which we face it. The point’s invisibility is the invisibility of any object framed — and therefore limited — by a given system of perspectives. So that the apparent paradoxes about the point are found in any sensitive object, and it is not appropriate to attribute to the geometric objects a character that is neither more nor less “mysterious” than to all the others. Thus, as the figures are formed by particularization — and therefore limitation — of the possibilities of the point, it is clear that the totality of the possible figures will be an integral manifestation of these properties and, therefore, the equivalent, in the order of manifestation, of what the point is in the order of principles. This is symbolized in the relationship between center and circumference, since the circumference represents, in the plane, the same as the sphere in space. We know that the curve is determined by its tangents; the tangent, being a straight line, contains a direction (two directions). Therefore, the circumference, being the only figure that is defined by having an “infinite” (or rather, indefinite) number of tangents equidistant from the center, has, at its own level, one of the properties of the point, which is that of having a ‘“infinite” number of directions; the difference is that the circumference has “infinite” directions in the plane, while the point has them in space, being itself thus the principle of space. As for the sphere, it has an indefinite number of tangent lines and planes in all directions, and could be considered totally equal to the point, if these tangents were also tangent to the center; now, the distance from the center to the tangent plane of the sphere — the radius — is not in itself a tangent to the sphere, and therefore the sphere has all possible directions minus the directions of the rays, and is therefore more limited than the point. There is a homologous relationship between the point and the sphere to that which exists, in metaphysics, between “Absolute” and “Totality”; the totality implies a quantitative consideration, (to which the Absolute is transcendent) and therefore, although representing the Absolute, it is not. Of all the figures, the most similar to the point is therefore the sphere, because, the figures differing by their number of directions, both the point and the sphere have an indefinite number of directions. The same could be said of the circumference, in a flat symbolism. The line, on the other hand, is the most different figure from the point, because it is the most limited in terms of the number of directions. The point and the line therefore form the two ends of a “scale” within which the various geometric figures are distributed according to the number of their directions. As the point, however, is not exactly a figure, but itself is the principle of the figures, it can be said that it is outside and above that scale and that therefore the first figure — the most multidirectional of the scale — is the sphere, thus being the sphere and the line the two extremes. In a decreasing sense, this scale would go from the sphere, through curved solids — topological surfaces — to regular polyhedra, from these to flat figures and from these to line segments and lines, more or less like this: Scale of figures 1st Sphere 2nd Solids of curved surfaces with tangent planes not equidistant from the center. 3rd Polyhedra with n sides 4th Polyhedron with n-1 sides 5th Polyhedra with n-2, n-3 … sides 6th + 1 Flat figures with curves 7th + 2 Regular flat figures with n sides 8th + 3,4,5, … n Flat figures with n-1, n-2, n-3 … sides 9th + n Line segments 10th + Line This scale is the symbol of the totality of the states of being, according to its progressive “removal” from the pure Being. The line symbolizes the principle of division — the substance — and the point of the principle. An indefinite number of lines can pass through a point. Each segment of these lines has a type of double and simultaneous reality: it can be seen as part of a line or as part of the total plane, which is the emanation of the point and in which the line to which this segment belongs is but a point of view between many. In the same way, each entity can be seen either as a member of its own species, or simply as an entity, that is, as something existing. Now, given a straight line and, in it, a segment, this segment cannot be measured — compared — with a segment of another straight line unless we suppose the existence of a common plane to both. (Here it is necessary to open parentheses to explain that two parallels could not, by themselves, determine a plane, because either there is a distance between them, or there is not; in the latter case, both are the same line, and a single line does not determine a plane ; in the previous case, it is necessary to assume between them an indefinite number of straight line segments of equal length, perpendicular to both, and thus it is not just two lines that determine the plane, but it plus at least one more segment. Thus, two lines determine a plane as long as they are not parallel). Now, if we talk about plane, we immediately report to the point of origin and crossing of the lines. Thus, the measurement — comparison — of segments presupposes the existence of the plane and the reference of all lines to the point, that is, of all those related to an Absolute. Thus, each segment belongs, simultaneously, 1st to the point that originates the line to which it belongs; 2nd to this line; 3rd to the total plan; 4th to each of the straight lines that cross the point and spread across the plane, because, if the segment belongs to the totality of the plane, it also belongs to each of its parts, since these have nothing but the totality. Therefore, we have a symbol of the simultaneous participation of the entities in various states of existence (represented, in this case, by the directions). The entity participates in its own state through the direction it is in and, therefore, the distinction between that direction and the others; this distinction is made from the point. But it participates in the whole through the union of all directions at the point. And it also participates in each of the other directions through geometric figures that establish relationships between the various segments. The symbolism of the circle and the line contains, in summary, all the cosmology. As the symbol of the Absolute, the point evidently represents the essential side, and the circumference, as a symbol of totality, the substantial side of the manifestation in particular, the point — representing the totality of possibilities, will pass, quite naturally — through the inversion that always occurs in the change of plane — to represent the substance of which the figures are made, and the line the essence, that is, what determines the particular quality of these figures. In fact, this is clear from the fact that, on the one hand, what defines the figures, when rectilinear is the direction and number of their edges, and, when curvilinear, the direction of their tangents; in both cases, they are lines or line segments that will determine the shape — that is, the nature, quality or essence — of the figures. On the other hand, since figures are nothing more than “points of view” about the point, as we have seen, it is clear that the figures are made from the point, from the point that is its substance, being more accurate to say that than to affirm, in the plural, as is generally done, that they are made “of dots”, which, in addition to leading to the contradiction that we have already noted, contradicts the unity of the substance on the cosmological plane. So it is that, again by inversion, the rectilinear and regular figures will serve as a symbol of the incarnate Logos — the cross — while the circle will be the symbol of the transcendent Logos. Christ in human form is crucified; dead and transfigured, the “Sun of Justice” is in heaven. For the same reason, rectilinear and regular symbolism will evoke the essential side of nature, its “divine” or heavenly aspect — for example, the three-dimensional cross that evokes Universal Man from the directions of space — and the curvilinear and irregular symbolism its substantial, “descending” aspect.