c) If we take the judgements of mathematics and those of fictional literature one by one, we shall see that in each of them that of which one judges is "something real". The concepts, the fictions, and the percepts are simple apprehensions; they express what the real "might be", i.e., they are formally and explicitly inscribed within reality itself. But in reality itself not qua terminus of a concrete content but qua it "might terminate" therein; that is, they express not what it "is" but what it "might be". Therefore we say that this simple apprehension expresses something unreal. I need not emphasize it more since it was discussed above. Now, the {131} judgements of mathematics or fictional literature do not concern something formally "unreal", but something unreal though "realized"; they consider that the reality terminates in fact in this or that thing. I use a word from mathematics to refer in a unitary sense to this "concrete" termination, namely 'postulating'. The unreal, without ceasing to be unreal, acquires a postulated reality. When the mode of realization or "making real" is construction, then we have the reality both of mathematics and of fiction. The affirmations of mathematics and fictional literature thus refer to something unreal which is realized (made real) by constructive postulation, whether in the form of construction according to concepts (mathematics) or construction according to percepts and fictions (fictional literature). The intelligence is thus not limited to apprehending what "is already" in it, but also realizes (makes real) its concepts, its fictions, and its percepts in it, or rather, before it. What is intellectively known "is" not then before the intelligence but is something "realized" by the intelligence before itself. To be sure, one can realize without constructing; this is the case with the majority of judgements whose content is realized in the real but without construction. What one cannot do is to construct without realizing. Whence the inevitable consequence that the real, when realized by postulation-despite being so according to concepts or fictions or concrete percepts-may then have, as we are going to see, more notes of its own than those formally included in the concepts, in the fictions, and in the percepts. It is from this reality realized

Thus every judgement, every affirmation, is about something real presupposed as such. When things are real in and by themselves, that presupposition {132} is formally the primordial apprehension of reality. When the things are real, but realized constructively, then the presupposition is formally postulation. Postulation is possible only by being intrinsically and formally grounded in the primordial apprehension of reality. Therefore the primary and radical structure of judgement is to be an affirmation of a thing already apprehended as real (in primordial apprehension) but according to its formal moment of being in a field. In virtue of this, a judgement is not an immediate intellection of something real, but an intellection modalized from that apprehension, that direct and immediate intellection; it is intellection in returning from a stepping back. What is judged in this intellection?

Stated negatively, the reality of the mathematical is not like that of a stone, for example, because the stone is something real in and by itself. On the other hand, a mathematical space is not real in and by itself, but it does not therefore become not-real. The fact is that, as we have seen at length, reality and content are not the same. In the differential actualization of the real, the moment of formality of reality in a field is formally distinct from the moment of content. Nonetheless, that formality is always physical; the same formality of reality can encompass different contents, not just simultaneously but also successively. Thus, if the color of this stone changes, the content of its apprehension will also change; but its moment of reality has been conserved as numerically the same. Whence it is revealed to us that in these conditions "the" physical reality is a moment which perhaps does not have such concrete content. Reality within a field is in fact, as we saw, the autonomized "de suyo". It is not a kind of ocean in which things are immersed; {134} rather, it is purely and simply the field moment proper to the formality of reality of each real thing. And we have just seen that according to this moment, each real thing is more than it is by virtue of its content. This moment of the "more" is reality itself. Reality itself is therefore a physical moment and not just a conceptive one. And precisely because it is "more" it is possible for it not to have such-and-such a concrete content, i.e., it can have some other. Under these circumstances (1) the "more" is actualized in concepts, in simple apprehensions; and (2) these concepts are then realized as content of the "more". The unity of the these two moments is, as we saw, the unreal object expressed in the "might be". Now, when one postulates that the object "is thus", then one has passed by postulation from the "might be" to the "is". We have reality itself actualized in intellection, and the realization of what is conceived, but realized as a free thing. A free thing is the physical reality with a freely postulated content. Such are the objects of mathematics, for they are real objects constituted in the physical moment of reality itself in a field, the same reality according to which things like this stone are real. The moment of reality is identical in both cases; what is not the same is their content and their mode of reality. The stone has reality in and by itself, whereas the circle has reality only by postulation. Nonetheless the moment of reality is identical. The reality of mathematical objects is the "more", that same "more" of every real thing in and by itself. And precisely by being a "more" it is extended to have a free content by postulation. How mathematical objects are constituted in their postulation I shall explain forthwith.

For now I should like to recall what I explained in Part One, {135} viz. that reality is not synonymous with existence. Existence and notes pertain only to the content of the real; on the other hand, the formality of reality consists in this existential content and these notes being such de suyo. An existence which did not de suyo concern what is existent would not make of it something real, but rather something which is a phantom. Existence and notes, I repeat, pertain only to the content of the real. Now, the moment of reality in a field is the moment of formality of the "de suyo" autonomized when things are apprehended some among others; i.e., the moment of reality is the ambit of reality, an ambit strictly and rigorously physical. Reality itself in a field is "physical" but not formally existent. Certainly if the content were not existent what was apprehended would not be real; but neither would it be real if it did not have such-and-such determinate notes. That is, there is no reality without content (existential and notes). What happens is that there is "field reality", i.e., reality in a field, a field which is de suyo, but without this particular determinate content, i.e. without such-and-such determinate notes and their determinate existence. The field moment is the de suyo, but in a form such that the "suyo" [itself] of this "de suyo" remains free. Both the notes and their existence remain free, but the de suyo persists as the formal moment of reality. The impossibility that if there is no existence there is no reality does not mean that reality is existence; it only means, as I just said, that while reality is a formality, there cannot be a de suyo without a content of notes and existence. These notes and this existence are what a postulate postulates for reality: they are notes and existence realized only by being postulated in reality itself. In virtue of this, the notes or properties, like their existence, are notes and existence as postulated; but these notes and this existence are real only {136} by free postulation in reality itself, in the de suyo. For greater clarity let me add that when, in mathematics, an existence theorem is formulated (e.g. the existence of a root of every algebraic equation, or of an integral in an ordinary differential equation, or the non-existence of an algebraic equation having e as a root), existence means the naked realization of a note in virtue of the realization of other notes. Since the naked realization of these notes involves a postulated existence, the naked realization of the content is what, with full justification, one calls mathematical existence. It is always a question of realization, but not in the sense of identifying reality and physical existence in and by itself.

The mathematical mode of this postulation is what I here term 'construction'. Geometric space is not a system of objective concepts; rather, the construction realizes, by postulation, these objective concepts. Constructing is not only making something an intentional and unreal terminus (that would be a question of simple content); rather, it consists in projecting this {137} unreal part of the concept onto reality itself "according to concepts". Therefore construction is a mode of realization; it is realizing according to concepts.

Gödel calls 'constructing a group' the operation of generating it via the iterated application of certain operations axiomatically defined in the Zermelo-Fraenkel axioms. One must emphasize this: we are dealing with operations "defined" as such and not with the procedure to bring them about. These groups are what Gödel called constructables. His disciple Cohen (1963) based himself upon non-constructable groups in this sense. The elements of every group in fact have two classes of properties. Some, the specific ones, correspond to the postulates and operational axioms to which I have just referred. Others are generic, in virtue of which they form a group leaving indeterminate the specific properties, which would "force" the generic properties to be specific. The groups thus obtained having only generic characters are by definition non-constructed. Cohen bases himself (for his sensational discovery of the falsity of Cantor's continuum hypothesis) on these non-constructable groups. This seems to contradict what I just said about all of mathematics being constructed. Nonetheless, the contradiction is only apparent, because what I here call construction is something different. In the first place, this is so because what Gödel and Cohen construct is ultimately the objective concept both specific as well as generic. But in contrast the construction to which I refer consists in realizing before my intelligence a concept {138} already objectively constructed (whether constructable or not). And in this sense the realization itself can and ought to be called construction. It is then something very different from construction in the sense of Gödel and Cohen. Both the constructable groups and the non-constructable ones are constructed in the sense of things realized before my intelligence. Secondly, this realization is the construction of a content in physical reality; it is an intellectively free realization in "the" physical reality. It is, precisely, postulating. And this construction thus postulated is construction of the content in physical reality. The groups of Gödel and Cohen are constructed (in my concept of construction) in physical reality. So the construction itself does not formally concern concepts, nor is it a "conceptive" construction; rather, it is a realization in "the" physical reality, but "according to concepts"-two completely different things. And in this sense every mathematical object is constructed by being postulated. It is for this reason that the object thus constructed is a strict reality which can have properties or notes "of its own", or "proper", and not just properties "deduced" from the axioms and postulates. This does not refer to deduced properties but to properties which are already formally in the object. Mathematical objects have their properties de suyo, i.e., they are real. The fact is that the real object made real by being postulated according to concepts has, by being realized, more notes or properties than those defined in its postulation. On account of this and only on account of it are problems posed which may not be solvable with the finite system of axioms and postulates which defined its realization. What is constructed in reality itself is, by being realized, something more than what was postulated when realized. This, as I see it, is the thrust of Gödel's theorem. It does not refer to a limitation intrinsic {139} to affirmations based on axioms and postulates qua affirmations-that is the usual interpretation of the theorem-; rather, it leaves the character of reality of what is constructed according to the axioms and postulates in question to be revealed before the intelligence. It is not, then, the intrinsic inadequacy of a system of postulates, but the radical originality of what is constructed by being real, a reality which is not exhausted in what has been postulated about it. This object is not a real thing in and by itself as is this stone. But neither is it only what "might be real"; rather, it is what "is real" by being postulated and constructed. That, in my judgement, is the interpretation of Gödel's theorem. The judgements of mathematics are then judgements of something real, judgements of the "postulated real". They are not judgements about the "possible real" but judgements about "postulated reality".

This conceptualization of mathematical reality by construction is not, then, a type of formalism, but neither is it in any sense what has been set forth in rigorous opposition to such formalism, viz. intuitionism, especially that of Brouwer. That is the other concept of construction which it is necessary to eliminate in this problem. For intuitionism, mathematical construction is not the same as defining and constructing concepts. Intuitionism rejects the idea that mathematics is grounded upon logic; a demonstration which appeals to the logical principle of the excluded middle is not, for Brouwer, a mathematical demonstration. Mathematics is not a system of defined concepts and operations. An operation, if it is to be mathematical, has to be an operation actually carried out, i.e., one comprised of a finite number of steps. To be sure, mathematics is not interested only in finite groups; for example, it concerns itself with the infinite digit strings making up real numbers. It is true that {140} mathematics cannot actually carry out all the operations necessary to obtain an irrational number, because the number of steps would be infinite. But they can be given, and are given, in a rule or algorithm in which the operations are continued "indefinitely". The object of mathematics, then, would be finite groups as the terminus of operations carried out on them. Intuitionism is a radical finitism. The majority of mathematicians therefore reject Brouwer's ideas despite its applications to topology, because to amputate the infinite series would be for them to nullify an enormous part of the mathematical edifice. Brouwer, they tell us, if forced to be consistent with himself, would be compelled to abandon as invalid an enormous portion of infinitesimal analysis [calculus]. But let us not be concerned with this aspect of the question because in our problem the essential part is that intuitionism claims to be opposed to formalistic axiomism or formalism by putting forth actually carried out operations as opposed to axiomatic definitions. At bottom it is an idea of Kronecker in action: God created the whole numbers and man created the rest. The whole numbers would be a datum of intuition, and therefore constructing would be reduced finally to counting what is given. Defining does not suffice.

In the first place, Brouwer's finite group is not intuitive. Leaving aside for now the problems posed by intuition, let us say that intuition is the "vision" of something given immediately, directly, and unitarily. {141} In inituition I have the qualitative and quantitative diversity of the given, but never do I have a group. There are no strict intuitive groups, because in order to have a group I must consider, separately so to speak, the moments of the intuitive diversity as "elements". Only then does their unity constitute a group. A mathematical group is always a group of elements, and only that. But then it is clear that no group, not even a finite one, is intuitive, because intuition gives only "diversity of moments", never a "group of elements". In order to have a group it is necessary to have a subsequent act of intellection which makes the moments to be elements. It is then necessary to have a construction. The so-called finite construction, presumably given in intuition, is nothing but the application of the group already intellectively constructed to the diversity of the given. This application is just a postulation: one postulates that the given is resolved in a group. Therefore rigorously speaking one cannot call Brouwer's mathematics intuitionism. Brouwer's group is not intuitive; it is the objective content of a concept of group which is "applied" to the intuitive.

In the second place, the very construction of the group is not, ultimately, a system of operations actually carried out. I say "ultimately", because the carrying out of operations is not the primary component of what I have termed "construction". The finite group is the content of objective concepts. Therefore the operations carried out on this content are operations, however much executed one may like, but always executed on objective contents of concepts. Finite or not, the groups with which Brouwer's mathematics is concerned and the operations carried out on them are conceptive groups and operations. And therefore they are inadequate, {142} as I see it, to ground mathematics: mathematics does not deal with "objective concepts" but with "things which are thus". What I understand by 'construction' is something different. To be sure, it is not a construction of objective concepts by mere definition; but neither is it a series of operations carried out in Brouwer's sense, because his operations are operations on objective concepts. And on this point Brouwer's mathematics does not differ from that of Gödel and Cohen. What I am referring to is that constructing is not carrying out objective operations but projecting before my intelligence that objective content in "the" physical reality. And this reality is not given in intuition but in the primordial apprehension of reality; it is given impressively. As this reality does not have determinate content, I can freely project upon it the content of what is objectively constructed operationally. This projection and not the operation is mathematical construction. The mathematical object, even if it is finite, and even if the operation which objectively produces its content is carried out, nonetheless has a radical proper reality, the physical reality impressively sensed in primordial apprehension. And this is construction. Brouwer's finite group not only is not intuitive, it is the result of a double postulation: the postulate that groups are applicable to what is intuitively given, and the postulate of conferring upon reality itself the content of the objective concept (operationally constructed) of group. A mathematical object is not intuited but apprehended in a primordial apprehension-two completely different things, as we shall see. Free creation, projected in this double postulation, is intrinsically and formally sentient. Only a sentient intelligence can, for example, {143} not sense the content of a continuous group, i.e. the group of irrational numbers, and nonetheless freely realize this content (conceptualized either by mere definitions, or by operations actually carried out) in a sentient way. A mathematical object, even though finite, and even though the operation which produces it is actually carried out, has, I repeat, its own reality, the physical reality impressively sensed in primordial apprehension. And this is its construction.

Mathematical construction is thus always an act of sentient intelligence. And therefore the mathematical object has postulated reality. It is not an objective concept of reality but rather is reality in concept. It is, I repeat, the reality itself of any real thing sentiently apprehended, but with a content freely constructed in that reality, according to concepts. What is postulated, I repeat, is not logical truths nor operations actually carried out, but the content of the real (already defined or carried out) {144} in and by postulated construction. The mathematical object is not constituted by the postulates; rather, what the postulates define is the "construction" before the intelligence of that whose realization is postulated, and which acquires reality by this postulation.

As the moment of reality is just the "more" of {145} each real sensed thing, it follows that every mathematical object is inscribed in the formality of reality given in impression. That is, it is the terminus of a sentient intellection. This does not mean that a geometric space or irrational number is sensed like color is sensed; the former objects are clearly not sensible. Rather, it means that the mode of intellection of an irrational number or a geometric space is sentient. And this is so (1) because they are intellectively known by being postulated in a field of reality, i.e. in the formality given in the impression of reality, and (2) because their construction itself is not just conceptuation but realization, i.e. something brought about sentiently. Without sensing the mathematical, one could not construct mathematics. Here we put our finger on the difference between sensible intelligence and sentient intelligence about which I spoke at length in Part I of this work. Sensible intelligence is based on the senses; sentient intelligence intellectively knows everything sentiently, both the sensible and the non-sensible. A mathematical object is real with a content which is freely constructed in the physical reality given in impression, and its construction is postulation.

Mathematics itself has produced, among other things, two theorems whose essence, as I see it, is what I said previously, viz. the anteriority of reality over truth. Gödel's theorem, according to which that constructed by postulation has de suyo more properties than those formally postulated, in my view expresses that what is postulated is reality before it is truth. And Cohen's theorem (let us call the non-Cantorian theory of groups that): groups are not just systems of elements determined by postulation; rather, prior to this, there are groups which he terms "generic" and which as I see it {146} are not generic but the simple realization of the group, without the specific properties determined by postulation. The postulated properties themselves are then real prior to being true. The specification here is not a logical difference but a real determination. It is the reality of the group prior to the axiomatic truth postulated. In my view, this is the essential meaning of the theorems of Gödel and Cohen: the priority of the real over the true in mathematics.

In every judgement, as we have seen, one judges about something real, and does so in reality itself. I said that affirmation is a dual intellection because the same real thing is intellectively known twice: once, as that of which one judges, and another, as that which is affirmed about it. This duality of affirmative intellection is based upon a deeper dimension. Since every real thing has a moment of individual reality, and a moment of reality in a field, when a real thing is intellectively known "among" others, these two moments are differentiated and in a certain way "distanced", i.e., stepped back from; this is a dimension of the duality of what is intellectively known itself. What impels us and puts us into the field of reality itself is just the primordial apprehension of reality of that about which one judges. And it is in this field that intellective movement takes place. That about which one affirms in this movement is the real thing already apprehended in the primordial apprehension of reality. That in which the affirmation moves is reality itself (it is the medium of affirmation). So in contrast to what is usually said - or rather repeated monotonously - judging is not affirming reality itself but rather affirming "in" the reality. Prior to judging and in order to be able to judge, we are already intellectively in reality itself. The function of reality itself is not to be a constutitive part of the judgement itself, because reality itself is also, as we have seen, a moment of simple apprehension. Reality itself is prior to every {148} intellective movement, both simple apprehension as well as affirmation. Reality itself is not, then, a correlate of affirmation, but the formality of every intellective apprehension whether it is judgmental or not. Judgmental intellection is an intellective movement, and this intellective movement in reality itself is a "realization". Upon judging one realizes reality itself in a real thing already apprehended, i.e. one judges about the termination of reality itself in this thing; he judges that which is the real. Now, with this reality itself is reintegrated, in a certain way against every stepping back, to the real thing, to its individual formality of reality. Therefore this reintegration is the formal establishment of the unity of being in a field and being individual. And this formal unity is just what a thing already apprehended as real is "in reality", viz. its "this, how, and what". Therefore that which is judged is what a real thing, already apprehended as real, is in reality. Judging is affirming what a thing already apprehended as real is in reality.

The poorly named "subject" of judgement is that real thing {149} about which one judges. It is not properly "subject" but "object" of judgement. What one judges is the realization of a simple apprehension in an object, i.e. in the real. Judging is not then attributing one concept to another but realizing a concept, a work of fiction, or a percept in a real thing already apprehended as real in primordial apprehension. Affirmation is the phase of intellective movement opposed to retraction. In retraction one goes inside the real which is given toward the unreal apprehended in simple apprehension, toward what the real thing "might be" to what it "is". Now one is not dealing with a realization in constructive postulation but with a realization in simple apprehension as such in primordial apprehension. This realization is the judgement. Judging is not, for example, apprehending that this thing which we call a man is real; nor is it apprehending what this man is (which is but apprehending what this thing "might be"). Judging is affirming that what it "might be" to be a man is realized in this real thing which we call a man, i.e., that this real thing which we call "man" is in reality what we understand by man. And this is not a tautology, because the concept of man is not univocal but depends upon that aspect, freely selected, from which one starts in order to conceive it. Starting from the zoological ladder is not the same as starting from the capacity to make tools (for example, from homo australopithecus or from homo habilis). Similarly, starting from social organization is different than starting from the modes and general forms of the real. Thus, what this thing is in reality which we call a man, by being the realization of a concept, is once again known intellectively with respect to the primordial apprehension of reality in each case.

Every affirmation is a dynamic intellection, by returning {150} from stepping back, of something already apprehended in a primordial apprehension, a dynamism which cuts across reality itself, and whose terminus consists in intellectively knowing what that which we have intellectively known as real is in reality.

When speaking about judgement, I am not referring to the classical division of judgements into quality, quantity, relation or modality, which is the division canonized by Kant. And this is because all these kinds of judgement are but forms of a single kind, viz. judgement as predication. Now, affirmation as such is not predication. There are, as we shall see, forms of judgement strictly pre-predicative. In predicative judgement, that about which one judges has a clear function: to be subject of the judgement. But that is not the only nor even the primary function of the reality about which one judges. Here I use the term 'forms of judgement' to refer to the diversity of judgements according to the function carried out by that which is judged; i.e., the diverse forms according to which a thing already apprehended is the terminus of affirmative intellection. The predicative function is just one of them. There are others, for example judgements in which the thing judged is proposed to the affirmation but not as a subject of it; these are propositional judgements but are pre-predicative. There are also judgements in which the thing judged is not proposed but only placed before the judgement. In these judgements the affirmation is not just pre-predicative but also pre-propositional; they are merely positional judgements. Each of these forms is based upon the previous one: propositional affirmation is based upon positional affirmation, and in turn predicative affirmation {152} upon propositional affirmation. What is the structure of these three forms of affirmation?

1. Above all, judgement is what I call a positional affirmation. Let us begin by posing some examples. I open the window and shout, "Fire!", or perhaps, "rain, sun", etc. Here there is something apprehended in the primordial apprehension of reality, viz. what I apprehend upon opening the window. And I apprehend it in all its notes, in primordial apprehension, as something real and in all of its richness and variety of notes. But I do not intellectively know what it is "in reality". Intelletively knowing it as fire, rain, etc. is just the proper affirmation of the judgement, viz. what I have apprehended is in reality. These names, as mere names, are simple apprehensions (percepts, fictional items, or concepts). But in affirmative connotation they express that what is simply apprehended is realized in what I have apprehended primordially, and is what this latter is in reality. If I did not have these simple apprehensions there would be no judgement and I could not say, "Fire!"; I would have only the primordial apprehension of this igneous reality which, without knowing what it is in reality, I apprehend primordially upon opening the window. In this sense I say that that affirmation is positional, because the thing which I judge is not previously apprehended in turn in a simple apprehension which qualifies it, as is the case in other forms of judgement. If I say that the fire is burning, the subject is already qualified as fire in a previous simple apprehension. But when I shout, "Fire!", what I apprehend is not intellectively known previously as fire. Precisely on account of this, what I see upon opening the window is not designated by any previous denomination because every denomination is a denomination of something already simply apprehended. Here what is apprehended upon opening the window is the terminus of a primordial apprehension {153} of reality, but without qualification, without previous denomination. In every judgement the primordial apprehension of that of which one judges is anterior to the judging itself. But this does not mean that a real thing was already previously qualified in some previous simple apprehension. In positional judgement the real is not already qualified by a simple apprehension; rather, there is a single simple apprehension, say that of fire, which forms a part not of the subject but of the predicate, and whose realization is affirmed so to speak globally. It is for this reason a positional judgement. On one side I have the primordial apprehension of reality; on the other, the denomination. Its identification in what is in reality what I have primordially apprehended is just positional judgement. It is because of this that there are not two denominations as in other types of judgement, one of what I see and another of what I affirm as realized in what I see. There is here but a single denomination, and what is denominated is posed as reality. There is but the total, global realization, of this unique single apprehension in the primordial apprehension of reality. It is, to speak a bit loosely, the identity or identification of with simple apprehension; or from the standpoint of simple apprehension, the integral realization of it in the real. I repeat that I am not saying "this is fire" but simply "Fire!". The positional judgement is, in a certain way, not the denomination but the denominative affirmation of the real apprehended in its totality. When I say "Fire!" I clearly have a simple apprehension, that of fire. Otherwise I could not say "Fire!". But that which I see upon opening the window is posed directly as global realization of this simple apprehension, without it having been {154} previously qualified by another simple apprehension. Here the function of the real thing of which one judges is to be "posed" for my denomination or identification as real.

2. There is a second form of judgement, viz. propositional judgement. {155} In it the real already apprehended is not apprehended only as real, but is also apprehended as something which for its part is already qualified from a simple apprehension. Let that of which one judges be A. A is not just something which I apprehend as real, but as something which is already A. And therefore, when it becomes the terminus of an affirmation, this A is not simply "posed" for the judgement but "proposed" to it, i.e., posed "as reality" for a subsequent position of what it is "in reality". A proposition is a special form of position; it is the propositional judgement. Permit me to explain.

In this affirmation what is affirmed clearly has two moments. One, the moment pro-posed A. This moment is not only real, but moreover its reality is already qualified and proposed as terminus of a subsequent position. There is, in addition, that of which this real thing is affirmed B. In itself B is not something real, but rather {156} a simple unreal apprehension. But upon becoming the determination of the thing already real, of A, B is realized in and by A. That is, the reality of B has been posed qua that of A, or what is the same thing, the reality of A has been posed not in itself (since it has been proposed as something already real), but qua B. For this reason it is, I repeat, a position which is pro-positional. What is this position of B in A? That is the essential question.

c) This B is not only determined intrinsically by the reality of A; rather, the determination itself, i.e. B, has reality but "in the reality of A". That does not just refer to the fact that a woman by her own nature determines changeability, but to the fact that what is {157} determined-this changeability-is a moment of feminine reality itself: B is a moment of the reality of A.

The expression of a propositional or constitutive judgement is a nominal phrase. It suffices to return to the (Latin) examples given earlier to discover in them two essential aspects. The nominative phrase, {158} above all, lacks a verb; it is an a-verbal affirmation, having only nouns. This does not refer to a verbal ellipsis but to a particular and originary mode of "averbal" phrase. But in contrast to positional affirmation which only has a noun, the nominal phrase always has at least two nouns. These two nouns do not designate a subject and predicate, but a single constitutive reality. The nominal phrase is propositional, but it is pre-predicative. On the other hand, this phrase expresses the affirmative moment of a mode which is proper to it, in the "pause" between the two nouns. The pause is the expression of the constitutive affirmation as such. It is not merely a position, nor is it copulative attribution; this aspect is what the pause expresses. The nominal phrase is generally used in invocations, but not exclusively there. The problem which interests me here is not the when and where-something that varies from language to language-but the nature of the affirmation enunciated in such sentences; this is a propositional affirmation.

3. The third form of judgement, I repeat, is predicative judgement. For the moment, borrowing some terminology from classical logic, let us say that it is the judgement whose scheme is A is B. It is because I have referred to classical logic that I have termed the two previous forms of judgement pre-predicative. The linguists call everything said of something a 'predicate'; the predicate here {159} would be is B, and A would be the subject. But this, while it may be true, nonetheless cloaks the proper character of what is affirmed in a judgement. For one of the essential moments for this judgement is that the affirmation be made using a verb, which in the foregoing scheme is the verb "is". And there is another moment which must be pointed out. Ultimately we are dealing more with a copulative affirmation than a predicative affirmation; the verb to be, in fact, discharges the function of a copulative. Whence there is some justification in calling only B the predicate, in respect of which A would be the subject. Given this initial clarification, to which we shall shortly return, and without making the notions more precise at the moment, let us speak somewhat loosely about predicative judgement in the sense of copulative affirmation.

Up to now, the predicative affirmation has only been a propositional affirmation. But the role of the predicative affirmation {160} is in the mode of position of A as B, or what comes to the same thing, of B in A. With which position are we dealing?

Modification of predication consists in B being grounded on A, but in such a way that this foundation of the reality of B in A is not necessarily-as in the case of propositional affirmation-the very "nature" of the reality of A. Rather, it consists in that B, though being in A, is so only in the sense of "merely being". Here "being" is used in the sense of "realizing" something, independently of the character of of this realization. In propositional judgement what is affirmed is that this realization is what is in the "nature" of something. But here we are dealing with a realization in which we disregard its mode, whether necessary or not necessary. A and B each have their own entity, and their unity consists in B being realized in A. In this fashion the reality of B in A, or the reality of A as B, involves two moments. On one hand, B is in fact in A. But on the other, B is something which, although it takes its reality from being put in A, nonetheless its reality is maintained in a certain way as its own reality inside the reality of A; and therefore {161} even though it is in A, it is, in a certain way, different from A. Therefore between A and B there is a unity to be sure, but a unity which, within A, maintains a certain distinction between the reality of A and the reality of B. Hence it is not a simple constitution. The constitution not only puts B in A but puts this B in the very "nature" of the reality of A, whereas now B is put in A though as something formally distinct from A. A is certainly B, but does not consist in being B, nor does B consist in being A. This is no longer constitution; it is what I shall term connection. There is a great difference between constitution and connection. Connection is union as well as distinction; union and separation are the two aspects of the unity of connection. This connection can have various characteristics; it can be either necessary or de facto. But one is always dealing with a connection "derived" from the reality of A. On the other hand, in the unity of constitution, rather than a "necessity of A", one deals with the very "nature" of A. The constitution is thus more than necessary; it is in a certain way constituting. When one says, "femina, variabile", one affirms that a woman is changeable by virtue of being a woman. Similarly, when one says "this paper, white", that about which one is thinking, to wit, "this paper", is white precisely because it is "this", i.e. one thinks in a certain way about the nature of "this". But when one says "this woman is changeable" or "this paper is white", one does not affirm that "this" woman consists in being changeable nor that "this" paper consists in its whiteness. In propositional judgement one thinks more about the nature of A than in the reality of the "other thing", B. In predicative judgement there is the reality of A and the realization of B in A, but in an A which as such has its nature independent of B; it is for that reason that there is connection. It is no longer AB but rather A-B. This is the connective or copulative affirmation. {162}

In the first place, what is affirmed? The connective unity of B and A. That is, in what is affirmed A and B enter, and what is affirmed of them is their connection. We have, above all, A and B. Some think that A and B are two variables of the same type and that their difference is merely functional: A carries out the function of subject, and B that of predicate. For just this reason it is possible to switch their functional positions, making B the subject and A the predicate. This is the so called "conversion" of propositions in formal logic: "All men are mortal", {163} and by conversion, "Some mortals are men". Apart from the quantifiers, A and B do not differ in the two cases other than by their functional position. But this is actually not correct. Strictly speaking, A is not a part of what is affirmed; rather it is simply "what" is proposed to what is affirmed. Hence, rather than being a part of the judgement, it is assumed by it. This assumption is usually called the "subject"; but strictly speaking it is not the subject but rather the "object" (sit venia verbo) about which one judges. The function of that which is already apprehended is now being pro-posed as "subject". This interpretation of what is proposed to the judgement as its subject is certainly a very debatable one. It depends upon the concept one has of the structure of the unity of things and their notes. Conceptualizing a thing as the subject of its inherent accidents is nothing but a theory. In my view, this theory is unacceptable. But that is not what interests us at the moment. Rather we are concerned not with the ulterior concept of connection, but the connective character of B with A, whether or not it has the character of a subject. And only in order to clarify the expression will I call A the subject; it is in fact the reality already apprehended as something which is not the "subject of" B, but the "subject to" a connection.

On the other hand, B is not something which is on a par with A, so to speak, because in itself B is a term proposed not as real, but as something unreal, as terminus of a simple apprehension (percept, fictional item, or concept). Hence its connection with A has all the character of "realization" of B in A. To identify A and B with two interchangeable magnitudes, as if they were homogeneous terms, is to speak nonsense. The subject is reality and the predicate realization. They do not function on the same level. Even when I carry out the so-called "conversion" of a judgement, the essential difference is not in the quantification of A and B, {164} but in the fact that in the second judgement A is by itself now a simple apprehension realized in B, which is the reverse of what happened before. Thus A and B are not, formally, on the same footing. The difference between them is not a difference in location in the judgement, but an essential difference. A and B can be interchanged so that A is sometimes the subject and other times the predicate. But their formal difference is always essential not interchangeable. The subject is always a proposed reality and the predicate is always something unreal which is realized. It is the same thing which happens in the case of all propositional judgements: it doesn't make sense to convert the nominal propostion, "all women, changeable" into "something changeable, woman".

What is affirmed of A and B is their "connection". We have already seen that this conection is not a relation; rather, the "relation" is something consequent upon the "connection" and grounded upon it. The connection establishes A in B. The relation between B and A exists, but only after B is established in A, i.e., after the connection. The relation-if one desires to speak of relations-is what results from the realization of B in A, i.e., it is the result of the connection. The formal conceptualization of A and B refers to this relation, which presupposes its essential connective difference. Therefore the so-called formal logic is based upon the relation resulting from the connective affirmation. Now we see that this logic is not what is primary, because the formal relation between A and B is grounded on the affirmative connection of realization of B in A. That is, every formal logic is grounded upon a more radical logic, the logic of affirmation. "Formal logic" is the play of two homogeneous variables, whereas the "logic of affirmation" is the intellection of the realization of something unreal (B) in something already real (A). And this is the essential point: the logic of the affirmative intellection of the real. As our subject is not logic, {165} it suffices to have pointed out this idea which I deem essential; we are not seeking to invalidate modern formal logic, only to ground it in the logic of affirmation.

The grammatical expression of this predicative affirmation requires some special consideration. It is the expression by the "is". This "is" discharges, as I see it, not two but three functions: {166}

To summarize, affirmation is a moment of intellective movement which intellectively knows what a thing, already apprehended {169} as real, is "in reality". Moving in the field of reality itself, the intelligence steps back from a real thing in a retraction in which it intellectively knows what the thing "would be" in reality. This is simple apprehension (percept, fictional item, concept). Now, following in the field of reality itself, the intelligence turns therein to a real thing in order to intellectively know, in this stepping back, what the thing is in reality. And that intellection is, as we have seen, affirmation. Affirmation is the "distanced" intentum of a thing, i.e., in a stepping back. That about which one judges is something already apprehended as reality, and that which one judges of the thing is what it is "in reality". For it, the thing of which one judges can have three functions: mere position, pro-position, and subject of predication. And each of these functions constitutes a form of affirmation.

This difference among the three functions of the real in affirmation has a formally sentient character. Only because there is an impression of reality is there a field of reality, a field of the de suyo. The three functions are grounded in and established by the impression of reality. It is sentiently as if I see myself having stepped back from what something, already apprehended as real, is in reality; and it is sentiently I find myself retained by the real as apprehended and returned to it: this is sentient logos. In this reversion, the logos intellectively knows the realization of the simple unreal apprehension, and intellectively knows it by a determination of what has already, previously, been apprehended. This determination is, to be sure, anchored in the fact that it is my intellection which, by being sentient, is distanced or stepped back from, and which by being so returns to the real in three different forms: positional, propositional, and predicative. But it is because the real, when impelling me impressively to step back, opens to me {170} the three possibilities of determination: positional, constitutive, and connective. They are thus three ways of traversing the distance from the unreal to what the real is in reality (through stepping back and returning). They are three forms of intentum. A non-sentient intellection cannot step back, and therefore it cannot have the three functions: positional, constitutive, and connective; nor can it intellectively know in the corresponding triple intentionality: positional, constitutive, and connective. The logos is born from the impression of reality and returns to it in these three forms, grounded upon the three forms determined by the real as apprehended primoridially. Now, in what, formally, lies the difference between these three functions? To intellectively know what something is in reality is to intellective know the unity of the field moment and the individual moment of the real. These two moments are moments of the formality of reality impressively given in it. Whence it follows that the three functions are three forms of the unity of what is of the field and the individual, i.e., three forms of unity of the formality of reality. In this unity something which we may call "the force of reality" is made patent; not in the sense of force of imposition of the real, but in the sense of force of unity of the moment in a field and the individual moment, i.e., force of realization. The strongest unity is positional form; it is the supreme form of intellectively knowing with the logos what something is in reality. Less strong is the propositional or constitutive form; it affirms unity as constitution. Weakest, finally, is predicative affirmation, which affirms the unity of the real as connection. Altogether, then, there are three degrees of force of realization, three degrees of intellectively knowing what something is in reality.

But in each of these three forms of affirmation there can be distinct modes. The problem of the forms of affirmation {171} thus leads to the third problem. After having examined what affirming is, and after examining what the forms of affirmation are, we now have to confront the problem of the modes of affirmation.

Above all it is, as I said, an intellection in movement, a movement which consists in intellectively traversing the distance in which we are with respect to what a thing is in reality, i.e., in stepping back from it. This intellective movement is, then, dual. By being so, the intellective movement which is intellectively knowing that a thing is real, is not intellectively knowing yet what this real thing is in reality. In this sense, the intellective movement is above all an absence of intellection of what the thing is in reality. But it is not just a movement characterized by this absence, because it is the movement of a dual intellection, in which the movement is directed towards a fixed point, toward what the already real thing is in reality. The duality thus stamps the movement with its own character, in the sense that what is not intellectively known is going to be so, or at least is intended to be so. Whence it follows that this movement is not just an absence but something essentially different, a privation. {173} Privation is the character which duality stamps on intellective movement qua movement. This intrinsic unity of movement and duality is what constitutes expectation. The movement of privation as such is what constitutes expectation. Conversely, expectation formally consists in privational intellective movement. Expectation is the intellection of the other in its first presentation as "other". This concept already greeted us some pages back when we spoke of the concept of intellective movement.

This "expectant" movement takes place in stepping back. And in this being moved back a step, the intellection has, as we saw, its own character: intellective intention. It must be stressed that every intention-in order to be such-is in itself formally and constitutively expectant. I deem this concept essential. It does not refer to the fact that one must expect an {174} affirmation, but to the fact that the intention itself is the proper and formally intellective moment of expectation. If it is necessary to intellectively know that A is B, not only do I have the intentionality of B in A, but precisely because I start from A this point of departure constitutes an expectation of what the intentionality of A is going to be. Every intention is, then, formally and constitutively expectant. Conversely, every expectation, as the character of intellective movement, is formally and constitutively intentional. Intellective movement is a movement "from-toward". In this movement I can consider only that "toward" which one is going. That is the only thing which up to now has generally been considered; in the classical concept of intention, one considers only the fact that the intention "intends" its end, an end which therefore is usually termed "intentional". But I believe that this is inadequate. The fact is that one can and should consider the intention itself not only as "going toward" but also as "departing from". And then the intention is expectation. Expectation and intentionality, then, are but two intrinsically unified aspects of a single intellective movement, which is therefore "expectant intention" or "intentional expectation". Whence it follows that the intellective movement in which we intellectively know what a thing already apprehended as real is in reality is, I repeat, intentional expectation or expectant intention.

Granting this, we must ask ourselves how this intentional expectation is resolved. Resolution is the affirmation in which expectation is molded; it is intellection itself as affirmation. But let us not get confused. There is on one hand the intellective intention itself qua intention; and this intention is intrinsically expectant. But on the other hand, there is the affirmation in which this intention is molded. {175} Since it is molded intention, I have called it and will continue to call it affirmative intention. Let us not confuse, then, the intellective intention with the affirmative intention. This latter is the resolution of the first, the resolution of the expectant intention. So how is intentional expectation resolved into affirmative intention?

a) Above all, it is an intellective actualization of the real, but of the real as already apprehended as real; it is therefore reactualization. And this reactualization is such with respect to the simple apprehensions with which we seek to intellectively know what the real is in reality. We are dealing, then, with the realization of a simple apprehension in what has already been actualized as real. Now, this realization depends first of all upon the characteristics, the traits, which are already given in the primordial actualization of the thing as real. I speak of the traits as "given". This phrase is chosen for now to be deliberately neutral, because the real qua reactualization poses two questions. The first is, What is the mode by which such-and-such real thing determines the realization in it of simple apprehension? The second is that of ascertaining in what the determining itself consists, in what the real qua determining principle of this reactualization in all its modes consists. We shall concern ourselves with the latter question in Part Three. For now let us fix our attention on the first, {176} in the diverse modes through which the real determines its reactualization, i.e. the diverse modes through which the given traits of the real determine the realization or non-realization of what is simply apprehended. And it is because of this that I speak about the fact that the traits are given in reactualization. To simplify the terms, in place of reactualization I shall speak simply about the actualization of traits given in the realization of simple apprehensions. Do not confuse the actualization and the realization of traits of what is simply apprehended in reality itself with this actualization of a real thing in simple apprehensions and with the realization of these simple apprehensions in the given thing. Now, the simple apprehensions are realized in different ways depending upon the nature of the actualization of the real.

First, all these modes of affirming depend essentially and constitutively upon the modes of reactualization of the real in the order of simple apprehensions. {177} Ambiguity, for example, is a mode of this actualization. It is the real itself insofar as it actualizes its traits in an ambiguous way with respect to simple apprehensions, with respect therefore to what the real is in reality. It is a characteristic prior to any affirmation; it is, let us repeat, the mode of actualizing the traits of the real with respect to what this particular thing is in reality, with respect to the simple apprehensions at my disposal.

In the second place, these different modes of actualization define different modes of affirmation and of affirmative intention; for example, ambiguous actualization of the real determines dubitative affirmation or dubitative affirmative intention-doubt properly so-called. In these modes, for example the doubt-mode, we are not primarily dealing with a state of insecurity in which we are assaulted by ambiguity, in contrast to other states, such as that of security. We are not talking about states, but formal modes of affirmative intention. We do not mean that when one affirms that something is ambiguous he finds himself in a state of doubt; rather, we mean that doubt is the ambiguous affirmation of the ambiguous qua ambiguous. It is the affirmative intention itself which is intrinsically and formally doubting. The ambiguous is not just that to which affirmative intention refers, nor it is only a characteristic of what is intellectively known; rather it is at one and the same time a characteristic of intellection and the affirmation itself. Doubt is not just an "affirmative intention about the ambiguous" but an "affirmative ambiguous intention in itself, determined by the ambiguity of the actualization of some real thing. Doubt is then a mode of affirmation, not a state consequent upon affirmation; and the proof is that both moments can be quite disparate. I can be in a state of insecurity with respect to a doubting affirmation. In such a case, I am sure that the affirmation {178} is of doubt; I am sure that the thing is in reality doubtful. The same applies mutatis mutandis for certitude and all other modes of affirmation, as we shall see forthwith.

In what does this modality as such consist? We have already seen that affirmation is a sentient intellection at a distance, the result of "stepping back". And its sentient nature reveals that the return to the real has the character of a force, the force of realization. This force has three different degrees depending upon whether one is dealing with positional, propositional, or predicative affirmation. And this force not only has degrees, but also a quality which we might term firmness. It is just what the term and concept 'a-ffirmation' refer to. "Grade of realization" and "firmness" are not the same thing. Each of the three degrees of force of realization can be exercised with different firmness. For example, the difference between doubt and certainty has nothing to do with the force of realization, but rather with the firmness with which this force operates. I can doubt or be certain that "every woman, fickle", or that "A is B". The first phrase is nominal (a constitution), the second predicative (a connection); they are two degrees of the force of realization. But doubt and certainty are in the firmness with which the constitution or connection is realized. Every logos is sentient, and is so in two moments. First, because I sentiently intellectively know what something is in reality as a force of realization; and second because I sentiently intellectively know with a certain firmness. That is, there is force and there is firmness. The firmness is the very mode of affirmation. Now, the differences of firmness are the different modes of affirmation. {179}

b) With respect to these simple apprehensions, the traits of the real are actualized in different ways; this is the moment of reactualization. These traits, as moments of the real and simply real, are what they are in and by themselves, and nothing more. But with respect to simple apprehensions, they can take on a different mode of actualization. A far-off figure is apprehended in the primordial apprehension of reality as a far-off figure, and nothing more; in itself it is something actualized as real and nothing more. But if I am to intellectively know what this figure is in reality, I draw upon my simple apprehensions, for example that of shrub, man, dog, etc. Is this figure a shrub, a man, a dog, or what? With respect to these simple apprehensions, and only with respect to them, do the traits of the far-off figure acquire a reactualization, because the fact is that I seek to intellectively know if this figure realizes the characteristics of the simple apprehension of a man, {180} a shrub, a dog, etc. It is then a second actualization but-I must again insist-only with respect to the realization of simple apprehensions. Reactualization is intellection brought to fullness in the light of simple apprehensions. Reactualization is a second intellection; and this second intellection is distinguished from the first by being intellection in the light of simple apprehensions. Herein consists the "secondarity" of second intellection: in being an intellection qualified by simple apprehensions. Simple apprehensions are not merely the terminus of an intellection, but are also and formally an intrinsic qualification of intellection. Simple apprehension is the "quali-ficating" moment of second intellection itself. Second intellection is intellection at a distance, from stepping back, and in virtue of that one knows intellectively only in the qualified light of simple apprehensions. A perfectly determined trait in primordial apprehension can be, as we shall see, only slightly determined with respect to the realization of a simple apprehension, because reactualization is actualization of the real as realization of a simple apprehension. And this reactualization is what has different modes: the unknown shape can reactualize the characteristics of a shrub, of a man, of a dog, etc. and actualize them in a more or less vague way, and so forth.

c) I intellectively know these diverse modes of reactualization, and I affirm them with respect to realization itself; this is the moment of affirmative intention, the moment of affirmation. Depending on what the modes of reactualization have been in the second moment, affirmation takes on different modalities because every affirmation is in itself modal. To be sure, this modality has nothing to do with what in classical logic is referred to as modality, viz. the difference in connection {181} of subject with predicate according to whether it is contingent, necessary, etc. Here we are not talking about the connection between subject and predicate, but about the mode in which the actualization of the notes of the real are affirmed.

The study of this structure can be made from different points of view. These modes, in fact, are mutually dependent. And this dependence is of the greatest importance in our analysis. But it is essential to delineate carefully the ideas involved, because this dependence can be of different types. "Dependence" can mean the mode in which an affirmation depends upon others with respect to its production in the mind. The dependence is then a psycho-genetic fact. But it is not this connection which is of concern to us here. The only decisive thing is the internal structure of each mode of affirmation. And it is this structure which is found to be dependent, qua structure, upon other affirmations. Thus it is possible that an affirmation might be doubtful as compared with a certain affirmation, for example. But this can mean two things. It can mean that the affirmation began as something doubtful and that doubt has given way to a certain affirmation. This is the psycho-genetic connection. But it can also mean that as a mode of affirmation the structure of the doubtful affirmation occupies a well-defined place with respect to a certain affirmation. This is a structural nexus or dependence. The two types of dependence are quite different. Our certain affirmation almost never comes preceded by a doubt, but is generated in other ways. Nonetheless, in every case the structure of certainty, the structure of what certainty is, is dependent constitutionally upon the structure of what doubt is. What we are here trying to conceptualize is not a psychogenesis {182} of our affirmations, but the intellective spectrum, so to speak, of its diverse structures. And it is only to this dependence of structural nature that I refer when I speak of the fact that some modes of affirmation are dependent upon others.

Let us return once again to our modest point of departure. We have an intellection of a certain real thing and we seek to know intellectively what it is in reality. Intellection is {184} then a movement of intentional expectation, which has to be resolved. And the resolution of this expectation has three moments.

Let us recall what it is to intellectively know what something is "in reality". Every real thing apprehended in its formality of reality has two moments, that of individual reality and that of reality in a field. And it is precisely their intrinsic unity which formally constitutes what the real thing is "in reality". Now, as I have already said, when one intellectively knows something real "among" others, these two moments are {185} in a certain way functionally differentiated, since the field encompasses not one but many things. Whence the unity of being in a field and being an individual is not apparent. It is rather mediated by simple apprehensions in the field of reality itself. It is the realization of these simple apprehensions which fills the field moment and its unity with individual reality; mediation is the actualization of a real individual thing in simple apprehensions. Now it can happen that individual reality is not actualized in any of the simple apprehensions we have had. In that case there is a unique actualization, viz. the actualization of the real thing as in a field, but an empty field. The real thing thus is inscribed in the "hollowness" of the field. Whence it follows that the unity of the individual thing and the field remains in suspense. That is, what this thing is in reality remains in suspense. This suspension is not just an absence, nor some lack of determination; rather, it is a positive mode of actualization, viz. privational determination. It is the positive actualization of the "in reality", but in a privative mode. It is then the privative actuality of a hollowness; and this privational actuality is precisely the "indetermination". Indeterminate, then, does not here mean indefinite, because being indefinite is a mode of determination. Indetermination means rather "un-defined". "Un-defined" is not the same as "indefinite". In virtue of that, the ambit of the indeterminate is constitutively open without limits; it is open to everything else. "Everything else" does not refer to other things, but to what the "un-defined" thing might be in reality. It is the "everything else" of the "in reality". What is un-defined is the mode of unity of the individual and of the being in a field, i.e., what the thing is in reality. As it is the {186} un-definition of something already definite as real in primordial apprehension, it follows that this un-definition is privation. Privation is the actuality of the "hollowness" of the individual in the field; it is the "in reality" in suspense. Simple apprehensions are what determine the actuality of the indeterminate.

c) This actuality of the indeterminate, this actuality of the "hollowness" of the field of individual reality, in turn defines its own mode of intellective affirmation because it defines its own mode of realizing something in simple apprehension. Every intellective movement is, as we have seen, intentional expectation. And therefore, qua mere intellection, that movement is a privational intention; it is in just this respect that its expectant character consists. This intentional privational expectation is resolved in an affirmation whose mode is determined by the mode of the actualization. When the actualization is a privational "hollowness", the affirmation takes on a special mode. Every expectant intention is in itself privational; when the actuality of the expected is indetermination (in the sense explained), it follows that intentional privation becomes the character of the affirmation; it is the privational aspect of intention molded into a mode of affirmation. It is not privation of intention; that would be just an intellective deficiency. Nor is it intention {187} itself as deprived of a positive terminus, because that would be just some manifestation. It is an intention which consists in the very mode of affirming; it is the affirmation itself as privational. Privationality of the act of affirmation is vacuous affirmation. Now, this mode of affirming is precisely what constitutes ignorance. Ignorance is affirming "privationally" the "in reality". It is an affirmation suspended in itself as affirmation. It is a positive mode of affirmation. A mode of affirmation such that the affirmative intention is as if folded back upon itself is a proper intentional hollowness; the empty affirmative intention as a mode of affirming is what ignorance consists in. It is like a shot in the dark. It is, then, in the first place a hollowness, but in the second a hollowness of what the real is in reality. Hollowness is then a positive affirmative ambit; a positive affirmation in hollowness, an indeterminate affirmation. The expectant privational intention is folded back upon itself, molded into a suspended affirmation. It is being suspended as a mode of affirmation itself, not merely a suspension of what is affirmed. Such is the essence of ignorance: a suspended vacuous affirmation, of the indeterminate as such.

The realization of simple apprehensions is therefore {188} not a simple task. Insofar as this realization progresses, real things actualize their traits in a more definite way; this is the structural emergence of other modes of affirmative intellection.

b) This mode of actualization and realization moulds the affirmation in accordance with a particular mode of intention, viz. the affirmative intention of the hint as guess. {189} A guess is a mode of affirmation. This does not refer to guessing an affirmation, but to affirm by guessing, so to speak. The emptiness of intention, i.e., of ignorance, now gives way to that of guessing the intention. This is the intellection of the first pointer to the determination of what a real thing is in reality. One guesses only what the thing is in reality, because it is actualized for us as a hint.

This intellection naturally admits of various degrees. Merely pointing to a determination can be a pointing which tends to make itself clear. But it is a pointing quickly revoked. This mode of hint is what I call clarescence, the breaking of the dawn of clarity. Guessing the affirmative intention of the clarescent is glimpsing, the glimpsing of the clarescent. The hint can be more than just clarescence. In the revoked pointing of the hint, not only may the light which is dawning be actualized, but some traits of the thing as well. But these things, now revoked, actualize the thing as something which is in reality poorly drawn or sketched. This actualization of the hint can be called blurred. Something blurred consists in traits being actualized sketchily with respect to what the thing is in reality. It does not refer to a type of mix of traits, but to a rigorous sketching. Sketching is not the privation of figure, but neither is it a precise figure. "Sketching" here refers to the revoking, which actualizes the traits as not being determinately of the thing such as it is simply apprehended. And this "not" actualizes the thing not as indeterminate but as sketched. The revoking sketches the traits of the thing actualized in simple apprehension. Nothing is blurry in itself but only is so with respect to {190} simple apprehensions. And the blurred formally consists in this sketching. Now, affirmative intention, the realization of the blurred qua blurred is confusion. This does not refer to some confusion of "ideas" or anything of that sort; rather, it is a mode of affirming, affirming confusedly that something is in reality blurred. We dimly perceive what that thing is in reality. Finally, in the repeated appearance and disappearance of actualized traits, there are some which do not point to something else, which remain as definitively revoked; whereas others continue to point insistently. The blurred thus continues to manifest vaguely its traits. So the hint is more than what is sketched of the blurry; it is realization as indication. It is a "pointing manifestation", but one which is revoked as soon as it points. Therefore we say that its traits are only indicated. There is only an indication of what the thing is in reality. Now, affirmative intention of something indicated, realized as such, is what we call suspicion. It is a mode of affirmative intention: one suspects something which is only indicated. It is a suspicion of what the thing is in reality.

3. In fact the peak of the indication conduces to fixing a set of traits with respect to simple apprehensions. {191} In them a real thing is actualized in a way different from and superior to the hint, and this actualization determines an affirmative intention superior to the guess.

Here we have the traits of a real thing actualized now with respect to simple apprehensions. But it remains to go {192} one step further. These traits are sustained, but by whom? By the real thing itself. It isn't enough to say that traits comprise a bounded and definite multiplicity; rather it is necessary to say in what the sustaining itself consists. The sustaining is thus the mode of actualization of a real thing with respect to the simple apprehensions of dog and shrub. Hence what must be said is in what the sustaining consists as actualization. When something actualizes its traits in a sustained manner, we do not say that the thing could be one thing or another indifferently, but that it could be one thing as well as another. Sustaining is not mere insistence, but that mode of actualization of the "either one". Now, these traits pertain to the real thing. It is the real thing which sustains the traits of the dog or of the shrub. And then this thing is no longer either indeterminate nor a hint. It is no longer one or the other, but as much one as the other: it is ambiguous. The mode of actualization of what a real thing is in reality now has the mode of ambiguity. In the sustaining of multiple traits of a bounded and defined multiplicity, a thing is in reality ambiguous. What is bounded and defined of the multiplicity concerns the traits; the ambiguity concerns its sustaining, its actualization; it is an intrinsic mode of actualization. Together with the mode of actualization of indetermination and hint, we now have a third mode of actualization: ambiguity. It is a real thing itself which in reality is actualized ambiguously with respect to simple apprehensions.

b) Now, actualization of a real thing as ambiguous is molded into its own form of realization of affirmative intention; this is doubt. Doubt is formally the affirmation of the ambiguous real qua ambiguous. Doubt is etymologically a mode of duplicity. But here we are not dealing {193} with the duality of intellection by stepping back, at a distance, but the dual character of the actualization of the real. It is this special mode of duality which constitutes ambiguity. Let us remark in passing that when speaking of doubt and ambiguity, it is not necessary that there be only two terms (dog, shrub); there could be a greater number. But for the sake of clarity I limit myself to those cases where there are two. And this is the essential point. Doubt is not grounded in disjunction; it is not grounded in the fact that a real thing is in reality either a dog or a shrub. Doubt is grounded, on the contrary, upon a conjunction, namely that something can be as much dog as shrub, i.e., upon an ambiguity. And as a mode of affirmation, doubt is not a type of oscillation or vacillation between two affirmations. It is on the contrary a mode of affirming what a real thing is ambiguously in reality. We vacillate because there is a doubtful affirmation; but there is no doubtful affirmation because we vacillate. Doubt is a mode of affirmation, not a conflict between two affirmations. We affirm yet with doubt the ambiguity of what something real is in reality. It is not a not-knowing where to turn, but knowing that the thing is in reality ambiguous. It is of course understood that the thing is really ambiguous with respect to my simple apprehensions; nothing is ambiguous in itself.

Here we have the third mode of affirmation: doubt. It constitutes a structure erected upon the structure of ignorance and of conjecture. The emptiness of indetermination is molded into the conjecture of the hint. And this conjecture or guessing grows: the glimpse of the clarescent becomes the confusion of the blurred; and this confusion is pinned down in the suspicion of the indicated. Now, the suspicion of the indicated is pinned down in the doubt of the ambiguous. In the reduction of {194} indetermination to hint and hint to ambiguity, one is so to speak stretching the circle of what the real thing is in reality. One more step, and this circle takes on a qualitatively different mode, which in turn determines a different mode of affirmative intellection.

a) As actualization with respect to simple apprehensions, a real thing is closer to one than the other. What is this proximity? In ambiguity one deals with a multiplicity which is bounded and limited. But now a new characteristic appears, that of "weight", pondus. Actualization has a certain weight; it is not just a metaphor introduced ad hoc. It is something extremely precise which is expressed in a term, pre-ponderance. The intrinsic character of actuality is more than simple ambiguity; it is preponderance. What is preponderant is the actualization of the traits with respect to a simple apprehension. Approximation pertains intrinsically to the actualization of a thing; and this intrinsic approximation is what constitutes preponderance. In virtue of that, the actuality of a thing includes, just as in the case of ambiguity, two terms 'bounded' and 'defined'; but it sustains one more than the other. Therefore the thing is no longer "one as much as the other" but "rather more one than the other". The "rather one than" is the preponderance. In ambiguity this character of preponderance is cloaked, so to speak. From such a point of view, {195} ambiguity would be an equi-ponderance. But the converse is not true: ambiguity is a mode of actuality which is intrinsically distinct from and independent of all ponderance. The continuity of the transition is a mode of actuality to the other; its intrinsic irreducibility cannot be reduced.

As a mode of affirmation, opinion can have different characteristics depending upon the weight of the traits actualized. Preponderance, preponderant actuality, can at time be only a light tilting or attraction. It is a kind of inchoate gravitation. The affirmative intention {196} of the actual as tilting or attraction is that intention we call inclination. This is an expression which is most definitely ambiguous. It can suggest, indeed, the idea of a tendency or something like it, as happens when one speaks of good or bad inclinations. But here it means only inclination as an intrinsic mode of affirming. The same thing happens with this expression as with the word 'intention'. From meaning the intention of an act of will it came to mean the intentionality proper to intellection. I believe that it is necessary to bring about the same thing with respect to this expression as happened centuries ago with the word 'intention'. Inclination is a modalization of this intention; it is the mode of affirming, of realizing actuality as tilting or attracting.

Just one more step and the form in which the preponderant traits are actualized will no longer be merely tilting or attracting; rather, those traits will "carry" more on one side than the other. We may term this mode of actuality gravity, a gravitation not merely inchoate but in a certain way macroscopic. The affirmative intention of the preponderant with gravity is probability. Here I refer to probability as a mode of affirmation, not of probability as a characteristic of physical reality. What physics understands by probability is as I see it what we might call the measure of possibility. All physical states of the electron described by its wave function are possible. But all are not equally possible. The quantitative structure of this of this possibility is what as I see it constitutes real probability. But here we are not dealing with that. We are not dealing with the measure of the real but with modes of affirmation; I affirm probably that a thing is such or such in reality. The modalization of the preponderance {197} according to gravity constitutes a probable intention as a mode of intention.

a) What is this mode of actuality? A dim figure in the distance has all the traits proper to a dog. Here, then, we are not involved with any ambiguity at all, nor with any preponderance. The traits are neither ambiguous nor preponderant; they are on the contrary univocally determined. We say, then, and with reason, that we see a dog. {198} But is this the same thing which occurs when I see a dog in my house? I also see the dog in my house; but there is an essential difference between these two apprehensions. In my house, I see something which in fact "is" a dog, whereas that which I see in the distance, although it has all the canine characteristics perfectly defined and delineated, nonetheless only "has" them. This "having" indicates precisely the difference in actualization of the real with respect to the traits of simple apprehension of the dog. What is this having, in what does it consist, and what is the mode of actualization of a real thing with respect to it? These are the important questions.

In the first place, the "having" designates a certain difference between what a real thing is in reality and its traits. Otherwise the verb "to have" would lack meaning. This does not refer to ambiguity or preponderance, because ambiguity and preponderance concern the traits of a thing and here these traits are univocally determined. The difference marking off "having" has to do with a different dimension, the effective volume of a thing. Permit me to explain. Actualized traits are univocally determined, but only constitute what is superficial-the super-facies-or the surface of the thing's real volume. Now, the volume qua circumscribed by these "facies" or faces has that mode of actuality termed aspect. Here, 'aspect' does not mean something which is only more or less precise, variable, or ephemeral and circumstantial. On the contrary, aspect is here something perfectly precise; and in its precision it pertains intrinsically, really, and determinately to the thing. But it does so in a special way. Aspect is only a mode of actualization of what a thing is in reality. It does not refer, I repeat, either to ambiguity or preponderance of traits; rather, it refers to the fact that, in its own precision, this group of traits {199} comprises the aspect of what the thing is in reality. What the dim distant figure has is precisely the aspect of a dog.

In the third place, "What is the mode of actualization in aspect and manifestation of what a thing is in reality? When I apprehend a dog in my house, I apprehend the dog and in it the manifestation of its traits, its aspect; I therefore say that it is in fact a dog. But when I see at a distance a figure which has the aspect of a dog, I do {200} the inverse operation: I apprehend the aspect and intellectively know in it the actualization of what the thing is in reality; I go from the aspect to the dog. The first thing which strikes me about this actualization is the dog's aspect. And this "striking me" is what, etymologically, comprises obviousness. In the obvious a real thing is actualized, but merely as aspect. And upon going from aspect to thing, it is obvious that the latter has been manifested in aspect: a thing is obviously what is manifested in its aspect. Precisely on account of this it never occurred to anyone to say without further ado that what is apprehended is a dog. But it is a dog only obviously. The obvious is on one hand the aspect as being "of" a thing; on the other hand this "of" admits of degrees of pressure. And in virtue of this the aspect is, in a certain way, "attached" to the a thing but with laxity. Laxitude is the formal character of merely "having". Laxitude of determination is univocal, but the "of" itself is lax; strictly speaking a thing could be in reality different than its aspect. Actualization has, then, a precise mode: it is the aspect which manifests as obvious what a real thing is in reality. Obviousness is the new mode of actualization. Like all the rest, this mode is so only with respect to simple apprehension. Nothing is obvious in itself, but only with respect to a simple apprehension. The realization of the simple apprehension as aspect is only now obvious.

b) Now, the actualization of a thing as something obvious determines a proper mode of affirmative intention of realization; it is plausibility. Plausibility is formally affirmation of the obvious. It is a mode of affirming, viz. affirming plausibly that a thing is in reality such as its aspect manifests it. Plausibility is a mode of affirming, and that which is affirmed in this mode is the obvious. But since {201} the obvious is what strikes us, it follows that plausibility is the form in which intentional expectation of intellection at a distance is molded. Simple apprehension is plausibly affirmed as realized in a thing. The plausible, just by virtue of being so, is what a thing is in reality, as long as the contrary is not evident. This "as long as" expresses at once the character of the obvious reality from the aspect and the plausible character of its affirmation.

This idea of the obvious and the plausible is, as I see it, what constitutes Parmenides' doxa. The mind is borne to what strikes it when it apprehends things in accordance with their form and their names. Onoma and morphé are the mode in which things strike us; náma-rupa say some of the Upanishads. Forms and names are the obvious aspect of a thing. And affirming that things are thus in reality is just the plausible, the doxa. It is not a question of mere phenomenological appearances, nor of sensible perceptions, much less of concrete entities as opposed to being as such. As I see it, the question is one of obviousness and plausibility. All affirming of the concrete multiplicity of things is simply affirming the obvious, affirming that things are in accordance with the aspect which strikes us. Therefore that affirmation is only plausible. For Parmenides, the philosopher goes beyond the obvious and the plausible, to the true being of things. For Parmenides and the most important philosophers of the Vedanta, our science and our philosophy could only be science and philosophy of the aspectual. This mutual implication between aspect, obviousness, and plausibility is, as I see it, the interpretation both of Eleatic philosophy as well as some Vedantic thought. {202}

In the second place, precisely on account of this, the actualization {203} means that it is the thing itself and not only its manifestation which realizes my simple apprehension. This simple apprehension is not actualized only in the aspect; it is not an aspectual actualization but an actualization of what a thing is in reality. That is, what is realized from a simple apprehension constitutes a moment of the real thing itself in its reality. That is the constitutional character of this new actualization. Here, constitution is not a character of the reality of a thing, but only of the intellective actualization of what that thing is in reality. 'Constitutive' here means what pertains to what the thing is in reality; it is not a character inside of the real thing by which one distinguishes other characteristics of it, for example those which are adventitious. A trait which belongs to what a thing is in reality is a trait which constitutes this "in reality" of the thing. Here the genitive "of" does not mean "having" but "constituting". The simple apprehension of the dog is not "had" by this thing; rather, it constitutes what the thing is in reality: a dog. Laxity has given way to constitution.

Corporeity, constitution, and effectivity are three concepts which, {204} upon reflection, if not perfectly identical in this problem, at least are three concepts for which the words expressing them are ultimately synonymous. For better understanding, I shall call this mode of being actualized 'effectivity'.

Here we must pause briefly. These ideas of constitution and corporeity may seem to be the same as those characterizing the primordial apprehension of reality. A real thing apprehended in and by itself is compact; it seems, then, that what we call the actualization of a real thing in intellective movement is only a new designation for compaction. But this is not at all the case, because affirmative intellection is an intellection at a distance (by stepping back) of mediate character; it is not intellection of a thing in and by itself. In intellective movement we have distanced ourselves from a thing and we return to it in order to intellectively know it in a reactualization. This reactualization, however much it may be actualization, is only "re-". What does this "re-" mean? To be sure, it is not compaction in any primary sense. What we have called 'constitution' is not compaction but something similar to this; it is rather a re-constitution. When we step back from a real thing, not only my intellection of reality, but also my intellection of what the real thing is in reality, is distanced. The compaction is broken into incompaction. Now, in effectivity, in the constitution of actuality, what a thing is in reality is actualized not in a compact mode, but in a reconstituted mode. Seeing this white paper is a primordial apprehension of reality. Actualizing it as a piece of paper which "is white" is a reconstitution. In virtue of being so, the constitution is subsequent to the compaction. It is, if one wishes, the mode in which the non-compact becomes in a certain way compact. This becoming is reactualization. {205}

b) This mode of actualization determines a mode of affirmative intention, viz. certainty. The in fact-ness of constitution determines the certain firmness of affirmation. Certainty, radically considered, is not a mental state of mine. We are not talking about being sure but rather that the thing apprehended is thus with total firmness. The word 'certainty' [certeza], then, is taken in its etymological sense. That is certain which is already fixed; it is the fixedness of a thing. 'Certain' [cierto] is an adjective derived from the verb cernir which means to choose with firmness, to screen. In Spanish we have the derivative acertar which does not mean "to be sure" but "to hit upon precisely that which one aimed at"; "to be now sure of" something is not a type of security but a goal reached. Whence the verb acquired the meaning of encountering. Certainty is thus the supreme degree of firmness of intention. By the same token, we can say that it is unqualified firmness, as opposed to other modes of affirmation such as doubt or probability. Certainty is not the maximum probability, as is often said; rather, it is another mode of affirming with a different firmness. In certainty we have firmness par excellence. Here I again emphasize the difference between a judgement which is certainly firm and the primordial apprehension of reality. In the primordial apprehension of reality there is, if one wishes, a primary firmness of an intellection of the real in and by itself; this is the mode of intellection of the compact. But strictly speaking primordial apprehension does not have firmness; that rather is the exclusive province of certain judgements. In certainty, one deals, so to speak, with {206} a "con-firmation" of what was the firmness of the primordial apprehension.

All these modes are so many modes of resolution of the intentional expectation in affirmation. They are {207} modes of firmness. And these modes depend upon the diverse modes in which the real is actualized differentially in intellective movement.

But this poses a decisive question for us, because all these modes of affirmation-as we have just seen at great length-are modes in which the real determines affirmation in its dimension of firmness. But now we have to ask ourselves not what they are nor in what the modes of determination consist, but rather what is the determining itself. The study of what affirmation is, of what its forms are (force of realization), and what its modes are (modalities of firmness), has been the study of the structure of affirmation. Now we have to delve into this other important question: the real determinant of affirmation, the medial structure of the sentient logos. {208}

firmation. {210} The study of intellective movement in its two phases has been carried out in Section 2.

NOTES