The *second task* consists in distinguishing the mode of knowing operative in ontology as science of Being, and this requires us to *work out the methodological structure of ontological-transcendental differentiation*. In early antiquity it was already seen that Being and its attributes in a certain way underlie beings and precede them and so are *a proteron*, an earlier. The term denoting this character by which Being precedes beings is the expression *a priori*, *apriority*, being earlier or prior. As *a priori*, Being is earlier than beings. The meaning of this *a priori*, the sense of the earlier and its possibility, has never been cleared up. The question has not even once been raised as to why the determinations of Being and Being itself must have this character of priority and how such priority is possible. To be earlier is a determination of time, but it does not pertain to the temporal order of the time that we measure by the clock; rather, it is an earlier that belongs to the "inverted world." Therefore, this earlier which characterises Being is taken by the popular understanding to be the later. Only the interpretation of Being by way of temporality can make clear why and how this feature of being earlier, apriority, goes together with Being. The *a priori* character of Being and of all the structures of Being accordingly calls for a specific kind of approach and way of apprehending Being―*a priori cognition*.The basic components of *a priori* cognition constitute what we call *phenomenology*. Phenomenology is the name for the method of ontology, that is, of scientific philosophy. Rightly conceived, phenomenology is the concept of a method. It is therefore precluded from the start that phenomenology should pronounce any theses about Being which have specific content, thus adopting a so-called standpoint." ―Martin Heidegger, from_The Basic Problems of Phenomenology_
Because they are assertions about Being in the light of time properly understood, all ontological propositions are Temporal propositions. It is only because ontological propositions are Temporal propositions that they can and must be *a priori propositions*. It is only because ontology is a Temporal science that something like the *a priori* appears in it. *A priori* means "from the earlier" or "the earlier." "*Earlier*" is patently a *time-determination*. If we have been observant, it must have occurred to us that in our explications we employed no word more frequently than the expression "already." It "already antecedently" lies at the ground: "it must always already be understood beforehand": where beings are encountered, Being has "already beforehand" been projected. In using all of these temporal, really Temporal, terms we have in mind something that the tradition since Plato calls the *a priori*, even if it may not use the very term itself. In the preface to his *Metaphysische Anfangsgründe der Naturwissenschaft [Metaphysical principles of natural science], Kant says: "Now to cognize something *a priori* means to cognize it from its mere possibility." Consequently, *a priori* means that which makes beings as beings possible in *what* and *how* they are. But why is this possibility labeled by the term "earlier"? Obviously not because we recognize it earlier than beings. For what we experience first and foremost is beings, that which is; we recognize Being only later or maybe even not at all. This time-determination "earlier" cannot refer to the temporal order given by the common concept of time in the sense of intratemporality. On the other hand, it cannot be denied that a time determination is present in the concept of the *a priori*, the earlier. But, because it is not seen how the interpretation of Being necessarily occurs in the horizon of time, the effort has to be made to explain away the time determination by means of the *a priori*. Some go so far as to say that the *a priori*―the essentialities, the determination of beings in their Being―is extratemporal, supratemporal, timeless. That which does the enabling, the possibilities are characterized by a time-determination, the earlier, because in this *a priori* nothing of time is supposed to be present, hence *locus a non lucendo*? Believe it if you wish."―from_The Basic Problems of Phenomenology_
On the other hand, it is also characteristic of the state of philosophical inquiry today and has been for a long time that, while there has been extensive controversy about whether or not the *a priori* can be known, it has never occurred to the protagonists to ask first what could really have been meant by the fact that a time-determination turns up here and why it must turn up at all. To be sure, as long as we orient ourselves toward the common concept of time we are at an impasse, and negatively it is no less than consistent to deny dogmatically that the *a priori* has anything to do with time. However, time in the sense commonly understood, which is our topic here, is indeed only one derivative, even if legitimate, of the original time, on which the Dasein's ontological constitution is based. *It is only by means of the Temporality of the understanding of Being that it can be explained why the ontological determinations of Being have the character of apriority*. We shall attempt to sketch this briefly, as far as it permits of being done along general lines.We have just seen that all comportment toward beings already understands Being, and not just incidentally: Being must necessarily be understood precursorily (pre-cecently). The possibility of comportment toward beings demands a precursory understanding of Being, and the possibility of the understanding of Being demands in its turn a precursory projection upon time. But where is the final stage of this demand for ever further precursory conditions? It is temporality itself as the basic constitution of the Dasein. Temporality, due to its horizonal-ecstatic nature, makes possible *at once* the understanding of Being and comportment toward beings; therefore, that which does the enabling as well as the enablings themselves, that is, the possibilities in the Kantian sense, are "temporal," that is to say, Temporal, in their specific interconnection. Because the original determinant of possibility, the origin of possibility itself, is time, time temporalizes itself as the absolutely earliest. *Time is earlier than any possible earlier* of whatever sort, because it is the basic condition for an earlier as such. And because time as the source of all enablings (possibilities) is the earliest, all possibilities as such in their possibility-making function have the character of the earlier. That is to say, they are *a priori*. But, from the fact that time is the earliest in the sense of being the possibility of every earlier and of every *a priori* foundational ordering, it does not follow that time is ontically the first being; nor does it follow that time is forever and eternal, quite apart from the impropriety of calling time a being at all.” ―from_The Basic Problems of Phenomenology_
As a method however, the *method of ontology* is nothing but the sequence of the steps involved in the approach to Being as such and the elaboration of its structures. We call this method of ontology *phenomenology*. In more precise language, phenomenological investigation is explicit effort applied to the method of ontology. However, such endeavors, their success or failure, depend primarily, in accordance with our discussion, on how far phenomenology has assured for itself the object of philosophy―how far, in accordance with its own principle, it is unbiased enough in the face of what the things themselves demand. We cannot now enter any further into the essential and fundamental constituent parts of this method. In fact, we have applied it constantly. What we would have to do would be merely to go over the course already pursued, but now with explicit reflection on it. But what is most essential is first of all to have traversed the whole path once, so as, for one thing, to learn to wonder scientifically about the mystery of things and, for another, to banish all illusions, which settle down and nest with particular stubbornness precisely in philosophy.There is no such thing as *the one* phenomenology, and if there could be such a thing it would never become anything like a philosophical technique. For implicit in the essential nature of all genuine method as a path toward the disclosure of objects is the tendency to order itself always toward that which it itself discloses. When a method is genuine and provides access to the objects, it is precisely then that the progress made by following it and the growing originality of the disclosure will cause the very method that was used to become necessarily obsolete. The only thing that is truly new in science and in philosophy is the genuine questioning and struggle with things which is at the service of this questioning." ―from_The Basic Problems of Phenomenology_
Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..."Klapaucius thought, and thought some more. Finally he nodded and said:"Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit.""Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming:Come, let us hasten to a higher plane,Where dyads tread the fairy fields of Venn,Their indices bedecked from one to n,Commingled in an endless Markov chain!Come, every frustum longs to be a cone,And every vector dreams of matrices.Hark to the gentle gradient of the breeze:It whispers of a more ergodic zone.In Reimann, Hilbert or in Banach spaceLet superscripts and subscripts go their ways.Our asymptotes no longer out of phase,We shall encounter, counting, face to face.I'll grant thee random access to my heart,Thou'lt tell me all the constants of thy love;And so we two shall all love's lemmas prove,And in bound partition never part.For what did Cauchy know, or Christoffel,Or Fourier, or any Boole or Euler,Wielding their compasses, their pens and rulers,Of thy supernal sinusoidal spell?Cancel me not--for what then shall remain?Abscissas, some mantissas, modules, modes,A root or two, a torus and a node:The inverse of my verse, a null domain.Ellipse of bliss, converge, O lips divine!The product of our scalars is defined!Cyberiad draws nigh, and the skew mindCuts capers like a happy haversine.I see the eigenvalue in thine eye,I hear the tender tensor in thy sigh.Bernoulli would have been content to die,Had he but known such a^2 cos 2 phi!
Furious, the beast writhed and wriggled its iterated integrals beneath the King’s polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann’s Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier-—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, “Hurrah! Victory!!
So they rolled up their sleeves and sat down to experiment -- by simulation, that is mathematically and all on paper. And the mathematical models of King Krool and the beast did such fierce battle across the equation-covered table, that the constructors' pencils kept snapping. Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F_1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, "Hurrah! Victory!!