We could say that Heidegger’s introduction to Being and Time is rigorous and formalized to the extreme, like any other great (self-satisfied) German philosopher. Yet Heidegger also denounces any smack of self-satisfaction that would creep up in a philosophico-ontological investigation. What I want to do here in this short essay is to illuminate how Heidegger formulates the question of Being through Dasein, what this has to do with the ontological tradition and its destruction, and also what Heidegger thinks this has to do with the foundations of any science whatsoever. Due to the shortness of this essay, I will attempt to articulate these concerns simultaneously (bear with me).
Heidegger mentions that the structure of an explicit questioning does not become explicit until all the constitutive factors have become transparent (5). It is in this sense that Heidegger analyzes the Being of Dasein insofar as the latter is equivalent with the inquirer par excellence. Thus the elucidation of Being requires that the entity with a pre-ontological understanding of Being (Dasein) be analyzed explicitly. Heidegger will also talk about this as the existential analytic of Dasein or as the hermeneutic of Dasein, since this hermeneutic is the possibility for any ontology or any analytic of the existentiality of existence (38).
However, this question cannot become explicit until a few fundamental concerns are addressed. For example, Dasein’s pre-ontological understanding of Being is only possible because of the former’s being-in-the-world. In other words, for the existential analytic of existence to become fully transparent, Dasein’s ontical constitution (i.e. it’s being in a world) must be taken as the standpoint from which any ontological relevance is to be fathomed. This is why he claims that the roots of the existential analytic of Dasein are existentiell/ontical. Only through existence itself (our existentiell belonging to a world) can existentiality be analyzed into existential data (suitable for the foundation of a real ontology).
Some of Heidegger’s claims become more understandable when we present them in this way. For example, he argues that this analytic of Dasein is only possible through a “radicalization…of the pre-ontological understanding of Being” (15). In other words, since the world is reflected ontologically in Dasein, the latter’s everyday experiences in the former (its ontical constitution) must be taken as data from which to set out upon our quest to rigorously found an ontology. Another way of saying this is to claim that the question of Being must become historiological (42).
What does historicity/historiology imply though? In a sense, if historicality is the basis of any history whatsoever, historiology is involved with the way in which history is passed down through tradition along with the way in which this passing becomes concealed or self-evident in its movement from generation to generation. This is precisely where the question of the destruction of the ontological tradition comes to bear its philosophical fruits. For example, when Heidegger claims that ontology must be self-critical, he is not saying this in an arbitrary way, but he means that for any science whatsoever to evolve in its field, it must takes its problematic historiologically, i.e. it must become suspicious about the traditions that promote it so as not to lose sight of the fundamental question of Being that gets so easily concealed (36). Another example—which is really not an example but a way of reading Heidegger’s project through his reading of others, here Kant—becomes more clear when we read that Heidegger faults Kant for merely presupposing the relations between time and the “I think,” which he has inherited from Descartes. Kant’s procedure is not historiological since it doesn’t question the sources from which he obtains his arguments about the subject, nor does he make Being into a question (this is obvious). Where we see Heidegger actually formulating his own project is when he argues: “[Kant] failed to provide an ontology with Dasein as its theme or (to put this in Kantian language) to give a preliminary ontological analytic of the subjectivity of the subject” (24). If we look at the Kantian exposition of Heidegger’s task, we will see that he relates the problem at hand as one of the analytic of the subjectivity of the subject. This may be another reason why Heidegger begins with being-in-the-world.
What does this tell us about Heidegger’s stance on science? When we quoted the passage where he claims ontology must be self-critical, we were not arbitrarily providing an assertion out of context. Heidegger argues that the basic concepts undergirding any science whatsoever have to be taken as clues from which these sciences can be founded. He argues that the “real ‘movement’” of the sciences is determined by “how far it is capable of a crisis in its basic concepts” (9). It is in this strict sense that Heidegger envisions the destruction of the ontological tradition to be productive and positive, not simply negative. For as a science, ontology must be able to treat its own fundamental concepts—res cogitans, cogito ergo sum, etc.—as material to be reworked in order to make the real problem of Being transparent. It is also in this vein that Heidegger asserts that “ontological science is primary to ontical science” (11). This is why he claims that ontology is fundamental, whereas physics or biology deal with regional, ontical questions, i.e. questions concerning particular entities. However, since the Being of these entities has not become transparent until the advent of universal phenomenological ontology, science has to be subordinated to philosophy (in Heidegger’s view of things). My question is: does this not perpetuate the perennial struggle between science and philosophy? How is it that philosophy can have the pretentiousness to claim to ground real science, when, from the scientists’ point of view, philosophy is the mere recycling of concepts that do not have any factual basis in scientific inquiry? In other words, Heidegger continues the war between science and philosophy, even if he claims the latter is the most universal of sciences. How can we introduce democracy into thought and put science and philosophy on the same footing without claiming to give one or the other any sort of precedence? How can we break down the hierarchy that establishes itself in thought, i.e. how do we establish a peace treaty between philosophy and science, especially from the former to the latter?
Fractal Ontology 
Do you think Badiou’s self-satisfied? –All kidding aside: what would Heidegger think of Badiou?
Nice to see you putting the Laruelle to work, by the way!
I was paraphrasing Laruelle, and I’m tickled that you cought me in the act. I want to become more explicit about this relationship between Heidegger and Laruelle, and so I will try to devote a separate post for it.
Is Badiou self-satisfied? Great question, and I have to tell you that re-rereading Being and Event may give that assumption (at least in the introduction). However, I don’t know if I would go so far as to claim that he would be self-satisfied: perhaps his prolific nature proves otherwise (or, taking the case of Heidegger with his 100+ volumes, and keeping in mind that Heidegger “scholar” Graham Harmann notes that the latter is a wonderfully redundant thinker, maybe not…)
What would Heidegger think? I’m not so sure…he seems to be suspicious of mathematics…he notes a crisis in mathematics in the introduction to Being and Time, and later he says something that is reminiscent of a proto-critique of Badiou: “In our exposition of the problem of worldhood, we suggested the importane of obtaining proper access to this phenomenon. So in criticizing the Cartesian point of departure, we must ask which kind of Being that belongs to Dasein we should fix upon as giving us an appropriate way of access to those entities with whose Being as extensio Descartes equates the Being of the ‘world’. The only genuine access to them lies in knowing [Erkennen], intellectio, in the sense of the kind of knowledge [Erkenntnis] we get in mathematics and physics. Mathematical knowledge is regarded by Descartes as the one manner of apprehending entities which can always give assurance that their Being has been securely grasped. If anything measures up in its own kind of Being to the Being that is accessible in mathematical knowledge, then it “is” in this authentic sense. Such entities are those which always are what they are. Accordingly, that which can be shown to have the character of something that constantly remains (as remanens capax mutationum), makes up the real Being of those entities of the world which get experienced. That which enduringly remains, really “is.” This is the sort of thing which mathematics knows. That which is accessible in an entity “through mathematics,” makes up its Being. Thus the Being of the ‘world’ is, as it were, dictated to it in terms of a definite idea of Being which lies veiled in the concept of substantiality, and in terms of the idea of a knowledge by which such entities are cognized. The kind of Being which belongs to entities within-the-world is something which they themselves might have been permitted to present; but Descartes does not let them do so. Instead he prescribes for the world its ‘real’ Being, as it were, on the basis of an idea of Being whose soure has not been unveiled and which has not been demonstrated in its own right–an idea in which Being is equated with constant presence-at-hand. Thus his ontology of the world is not primarily determined by his leaning towards mathematics, a science whih he chances to esteem very highly, but rather by his ontological orientation in principle towards Being as constant presence-at-hand, which mathematical knowledge is exceptionally well suited to grasp. In this way Descartes explicitly switches over philosophically from the development of traditional ontology to modern mathematical physics and its transcendental fundations.”
Ok, so not a refutation, but taking into account Badiou’s rejuvenation of Cartesianism, it made me think…
Although, to really do that long quote justice, we’d have to go into Heidegger’s distinction between presence-at-hand and ready-to-hand…
Joe, being a mathematician, wouldn’t you agree that a proof or an equation, an algorithm or a logarithm have as much readiness-to-hand as a hammer? The mathematician speaks softly and weilds proofs like a hammer…
Nietzsche writes somewhere in Daybreak that he suspects we can only think what we have words “at our fingertips” to express. Mathematical functions produce a break which forces thought, and precisely as you suggest seem to act more like abstract machines, or perfectly generic “tools” which may function at several layers simultaneously. But do they penetrate the real essence of being? And what would this mean, anyway? For some reason I’m reminded of D+G’s description of math as a “monster slang”… but also of Levinas’ wry comment that a proof of transcendence necessarily contains a contradiction!
Speaking to Joe the mathematician, would you not agree that mathematics is more the antithesis of, as you quote Deleuze and Guatarri, a, “monster slang,” as what exists more enquisitive of quidditative originarities and the Ontic as its vulgar and constituent exactitudes, respecting rigorously invariably univocity as existent of the ideo-language semiotic contextualizations of which constitute common notions of language? Is not mathematics a disillusionment with the philosophical neologistic mania which had by the later half of the nineteenth century been recognized as such by serious logicians keen to the capacity of truth to be found by means of analysis devoid of the vagarious fictives composed by individuals conflating affects and senses of truth with truth as such? Mathematics, being the study of coextensionalities and equivalences among variously intensionally defined sets, must be that conceptualizative field designated for the realization of univocity in an eradication of otherwise adulterating plurivocity, a designation for which I see few others of the sort superior in fitness with respect to apprehension of truth. Thus mathematics would seem, considering its description provided, as the optimal route to truth. Yet one may suggest to look again at the stipulations superiority with respect to which, on occasion of the comparative operand’s being mathematics, was said to be a predicate incapable of veridically-disposed concatenation unto any existent: to be of an enquisitivity of quidditative originarities and the Ontic as its vulgar and constituent exactitudes possessive, all whilst respecting rigorously invariably univocity as existent for the ideo-language semiotic contextualizations of which constitute common notions of language. Let us now examine these stipulations for consistency when posed in conjunction with each other and so as definitions for a conceptualizative field.
It should first proceed a disambiguation of that meant precisely by, “the Ontic as its vulgar and constituent exactitudes.” Indeed Heideggarian notions of the Ontic might coincide in convenient congruities with those I have formulated for this notion as denotatum for, “onticity” existent, but this should not preclude propriety of my explicating precisely the characters providing identity to the latter. “Onticity” in my neologistic assignment of definitions refers, in my phenomeno-ontological system founded upon a conceptualization of ipseicity as occurs in a Universe of Consciousness, to the state of Being genitively related to that ipseic-al state in which ipseicity reigns in a dominion consisting as an uncompromising partiality to the vapid and vulgar corollaries in a pseudo-dialectic existent for ipseity. This “pseudo-dialectic” exists as the conceptual schematic of the relationship among the various ways by which may exist the essential finitudinousness of ipseity. In speaking of ipseity’s “finitudinousness” one speaks of that the ipseity constitutes a sort of fundamental vacuity consisting as the ascription to an essence’s subsisting in the ontological deserts of the antinomous logical relativity as which exists ontical reflexivity. This relationship of self-sameness is an intension-ality of null extensional corollary (it should be noted here I am not referring to the intension, “yields veridicity on occasion of being predicatively related to operand denoted as follows, “is identical to itself””; rather I am referring here to the antinomous proposition yielded from a certain concatenation of operands which might be made clear by pointing to that ontical reflexivity is of this vacuity of which I speak due to the fact that it is a relation between operands existent as elements of the void when operating in ipseico-existential contexts; it is thus yielding of a propositional antinomy; it is this antinomy of which I speak when invoking an intension-ality (though it should be noted that ontical reflexivity is itself indispensable in the explication of the vacuity as it is the relativity of specificity to ipseics as it is the relativity in-volved in the contrivances, later to be explained, ultimately yielding of an imminently mentioned ousia-less-ness)), and as such obligating of a transcendental self-iteration to yield some salvation from its true vacuity. This vacuity founds the existentiality of ipseity in that the ipseic’s essence is nothing save for some ousia-less-ness, which is its existence. This is to say that the ipseic exists nothing of axiomatical substantiality save for its brutally given factical substratum; the ipseic founds an essence for itself by contriving its own existence, a notion (existence) derived from assigning fallaciously the hyper-realisticities proper to subsistence unto a vacuity of ontical reflexivity; this is the primordial originarity genitively related to ipseity and subjectivity and thus existentiality and existence (existence is precisely antithetical to essence as existence is the antinomous property of occasion of subsistence-without-essence; this is the essence of ipseics and conscious subjects (I employ the term, “ipseics” as to adhere to principles of univocity: Why contextualize an abstract class into a multifarity of supposedly real distinctions when this does nothing save for obfuscate potentially clear truth?; thus I’ve elected to denote with, “ipseics” as it denies such obfuscatory agents the effecting of improper contextualities; indeed one must treat the subject not as axiomatically distinguished from other existents, but as qualifieds of the intension of a set of existents of certain logical properties), or essence-less-ness (one might indulge the articulation)). This finitudinousness is essentially the defining character of the properties about the collectivity of the axiomatical substantiality of one’s factical substratum and the ousia-less-ness of one’s existence. Both serve to perturb the ipseic into exacerbated cognizance of the quidditatively factical inexistence of the haecceity as which one ipseic has contrived itself, but in distinct ways the distinctness of which absolutely must be explicated. It is only upon reflection of the singularity of one’s factical substratum’s being of axiomatical substantiality and as one (this is to say generically one thing, as opposed to one factical substratum) of an ipseic, and thus to conceive an alterity existent between such and one’s essence (as one’s own existence), that an ipseic’s factical substratum may provide such a perturbance. But then what of the said ousia-less-ness’s provision of such a perturbance? Is not the just-explained conceptualizative procedure whereby one’s factical substratum comes to be that providing of this perturbance formally equivalent to cognizance of the here concerned ousia-less-ness? Indeed both cognizances are equivalent and equal in providing of this ipseico-haecceitive perturbance ablatively respecting of the designation of privitious exclusion from the non-solicitudes of quidditatively fintudinal quantitativity. But what’s this? It seems now that it may be possible to analyze the perturbing effects of the axiomatical substantiality of one’s factical substratum as such, rather than as a re-articulation of another perturbing effect. Here we may meet the notion of “finitudinality”, which is an essential quidditativity of the ipseico-haecceitive procedure whereby an ipseic classifies certain facticalities as elements of its haecceitive constitution, thus posing it to potential molestation by the non-solicitudes aforementioned. The ipseic may either provide sanctuary of the ipseico-haecceitive privities it has conceptually harvested from its factical substratum through non-reflection or singular adherence to the vulgarly fruitless of the sort, or the ipseic may elect to such reflection, upon such an occasion dissolving the sanctuary the ipseic once provided them. I will not here speak elaborately on the originaries proper to the finitudinal quantitativity’s essential non-solicitude with respect to ipseico-haecceitive privities as conceptually counted as such from their former being but a constituent of an ipseic’s factical substratum, but I can say that this is perhaps more easily intelligible through reference to that the perversities inherently by metricity intended treat such privities with respect but to their thingliness or onticity. Thus it should be clear now that the finitudinousness of ipseity, abominably abbreviated explanation of which is above, may not by dialectical means be schematized as to congrue with conceptual palatability. And indeed it should be known now that partiality to the vapid or vulgar corollaries of this pseudo-dialectic constitutes submission to the brutalities of the stipulativity of reality, or treatment of ipseico-haecceitive privities as things to be measured metrically (naturally (I apologize for the potential redundancy)) by satisfaction of stipulations posed by reality; this is a sort of characterization of the Ontic as occurs in my neologistic vocabulary, and thus it may become more clear what is meant by “Ontic as its vulgar and constituent exactitudes”;
Now how may the Ontic so characterized be compatible with conjunction with the other provided stipulation and so posed as definition of a conceptualizative field? The other stipulation speaks of enquisitivity of quidditative originarities. This latter stipulation speaks indeed of a route to truth devoid of the vulgarities proper to the more common ipseic-al state genitively related to the Ontic, and thus I concisely state their incompatibility as co-operatives in a definition of a conceptualizative field.
Thus, no, mathematics indeed would not be the optimal route for truth, as its principles are inconsistent with each other. I say that invariable respect to univocity as existent for the ideo-language semiotic contextualizations of which constitute common notions of language is essentially of co-occasion with enquisitivity of quidditative originarities, but is impossible to maintain when one treats the Ontic as its vulgar and constituent exactitudes. This is due to the fact that the two activities are specific to mutually exclusive corollaries in the pseudo-dialectic concerning ipseic-al finitudinousness an abominably abbreviated explanation of which I provided above.
Now what is left to verify that mathematics is indeed not so lofty as to be the optimal route to truth is demonstrating that mathematics is indeed founded upon the principles I provided as stipulations satisfaction of which may oblige subsequent consideration of a certain conceptualizative field as mathematics. This is not intended to be extremely convincing or scientifically substantiating, but I do conceive that on the first stipulation’s satisfaction, as concerns mathematics, one may speak of the early twentieth century inquisitions concerning the foundations of mathematics and proceeding development in mathematical and metamathematical analysis for attestation. The stipulation that the conceptualizative field be rigorously adherent to univocity so specified is clear as what is much of mathematics but a formalization of natural language incapable of without ambiguities and occasionally at all the proper synactico-denotative system for specification of all the multiplicities which may exist in the world? The stipulation having that the Ontic be treated as its vulgar and constitutive exactitudes is satisfied by mathematics in a fashion less easily apparent. Indeed as opposed to philosophical enquiry capable of more primordial recognitions, mathematics does not have at disposal equipment for address of such, to the field, arbitrary and fruitless concerns such as that of the definition of number or some of the most basic elements manipulated in field-work, if you will. Mathematics rather treats what is empirically observed as qualified in being, say, number without specifying the intension of the set as an element of which did the mathematician just qualify the object he observed as such. In this respect mathematics is a vulgar practice inconsiderate of the originarities some sub-fields of it claim to be rigorously pursuing. Indeed thus the mathematician is analogous to the brutal stipulativity of reality, classifying observed objects not by expressible intensions more considerate of quidditative factors, but by mere measurements of stipulative qualifications. This constitutes the non-inquisitiveness proper to an ipseic succumbed to the dominion of ipseicity and who thus may have as option but an uncompromising partiality to the Ontic corollary of the ipseico-finitudinous pseudo-dialectic.
I may write more on the vulgarity of fintitudinality and the primordial originarities of numericity and the mathematicity of concern for such things as number not as such but as objects empirically qualifying as some unspeakable thing the quiddity of which one should not with very much expectation of rigorously harvested fruits investigate , but I believe I’ve already exhausted that supply allotted to one in my circumstances in the limits of which appropriate elaboration is possible, and for which the implied co-extension is veridical for the negations of the respective predicates.
I do hope that this post is not excessively inappropriate, as it is primarily an explication of the non-primacy of mathematics as a conceptualizative field (a point which could be said as aligned with Heidegger’s thoughts on the ontic and the excesses of arid and occasionally depriving logic in his day).