There is no epistemic representation through mental images in the circumspection that brings the ready-to-hand closer to the agents of average everydayness. Circumspective making-present in a given environment of practices includes in itself retention of the whole environment in which the practitioners are awaiting an actualization of possibilities for further instrumental dealing with entities ready-to-hand. Awaiting and retaining are ingredients of the present brought into being by a circumspective making-present. From a phenomenological point of view, awaiting and retaining are projecting a horizon within which the present, actualized by a circumspective making-present, can conform to a current equipment-world (including its public environment) that belongs to this world. All readiness-to-hand within this world is bound to (and bounded by) the horizonal unity of awaiting, making-present, and retaining.

Against the background of these considerations, there is a trivial way of explaining the existential genesis of the theoretical attitude. According to it, when a utensil (equipment) ceases to serve its traditional functions, one discovers its unusability by examining both the practice in which one uses it and its instrumental properties. In establishing the kind of unreadiness-to-hand in that practice, one tries to eliminate the troubles by replacing the equipment with another utensil or by changing the context of its use. The dysfunctional entity is still not completely devoid of readiness-to-hand. Yet if one does not succeed in “saving” the meaning of the utensil within the equipmental world, then one begins to look at it with the intention to establish its physical properties as belonging to something present-at-hand. The thing is not only decontextualized, it is completely demundanized (i.e., detached from the equipmental world), thereby getting the status of a theme of investigation. In order to delineate the theme, however, one needs to project a formal structure by means of which all relevant things present-at-hand become objects of inquiry. Thus, the deworlding of the readiness-to-hand implies an objectifying thematization. A practitioner who is able to carry out such a thematization becomes an epistemic subject whose basic characteristic is the theoretical attitude toward the objects of inquiry. This explanation of the genesis of science’s theoretical attitude is trivial since it does not take into account the horizonal temporality of the equipmental world.

The existential conception of science puts forward a much more sophisticated explanation. The development of this conception in Heidegger’s Being and Time ([1927] 1962) is guided by the aim of illuminating the “temporal constitution of being-in-the-world.” In Heidegger’s jargon, when practical dealing with the ready-to-hand holds back from any kind of manipulation, then the entities excluded from instrumental-practical circumspection are no longer bound to the temporal-horizonal unity of making-present, awaiting, and retaining. Heidegger describes the first step in the genesis of science’s theoretical attitude as a modification of circumspective deliberation into a discovering of entities by merely looking at them, thereby detaching them from particular practices of everyday life but not from the world as a horizon of everydayness. This “merely looking at” is the kernel of the theoretical attitude. The modification of circumspective deliberation takes place when deficiencies in the use, manipulation, and production of the ready-to-hand are no longer eliminable within practical contexts.

Roughly speaking, the genesis of the theoretical attitude is rooted in dysfunctions within the equipmental world that reduce the making-present in circumspective deliberation to a pure seeing of a presence-at-hand. The latter is described with respect to its properties that are achieved through “theoretical seeing.” The very description is not spoken within the horizon of awaiting and retaining an equipmental totality serving everyday practices. In this nontrivial version of the existential conception of science, the disappearance of praxis, which provokes the genesis of the theoretical attitude, is due to an atemporalization within the temporal horizon of being-in-the-world—an atemporalization that is itself a kind of temporalizing of the ecstatic temporality. In other words, the theoretical way of making-present as objectifying thematization by no means puts into play simply an isolation of the horizonal scheme of the present from what Heidegger calls “ecstatical unity of temporality.” The making-present that belongs to scientific research is, rather, “the kind of discovering which . . . awaits solely the discoveredness of the present-at-hand” (Heidegger [1927] 1962, 415). This is why the existential conception of science cannot be disentangled from Heidegger’s doctrines of the temporalizing of ecstatic temporality and the transcendence of the world.

Yet in Being and Time Heidegger is after an explanation of science’s objectifying thematization, in which the atemporalization of the theoretical way of “making-present” replaces the transcendence of the world by a mathematical projection. The explanation leaves more questions open than it is able to resolve. All practices involved in objectifying thematization are within-the-world, thereby presupposing the transcendence of the world. For a replacement of the latter by a mathematical projection, one can speak only with regard to science’s ontic knowledge. The talk of an “ontological replacement” is obviously non sequitur since the mathematical projection is grounded upon the transcendence of the world.

The notion of the “mathematical projection of nature” plays not only a central role in the existential conception of science, but it is also of essential significance for the development of Heidegger’s ideas about science after Being and Time. It refers to the mathematical idealizations (and the corresponding idealized theoretical objects) by means of which a research domain is disclosed a priori and made-present for empirical investigation. In fact, it is the projection of a mathematical structure (e.g., a system of differential equations) that makes present actual and possible empirical objects of inquiry in a given domain. The mathematical projection is mediated by the constitution of theoretical models that translate the language of a mathematical structure (involving a set of idealized objects) into the language of empirical objects. In other words, the mathematical projection discloses a domain of empirical objects of inquiry through the theoretical models it imposes. The domain’s empirical scope is defined by the totality of theoretical models’ possible empirical interpretations. Thus, for instance, the models of classical genetics make present the transmission of genes as an empirical object of inquiry. By the same token, the models of special relativity make present the possible objects of the space-time of a non-Euclidean four-dimensional world that can be empirically investigated. The models of synthetic theory of evolution (especially Dobzhansky’s version of it) make present the maintenance of evolutionary mechanisms of phylogenetic alterations grounded on the advantage of heterozygotes and the coadaptation of chromosomes.²

The notion of the mathematical projection of nature is closely related to several other important notions of the existential conception of science. As I mentioned, it is closely connected with the notion of objectifying thematization, which refers to the transformation of readiness-to-hand within-the-world into presence-at-hand, on the one hand, and the formation of epistemic subject out of prescientific environments of practices, on the other. The mathematical projection of nature has also much to do with the notions of “deworlding” (Entweltlichung) and “delimitation of a domain of entities present-at-hand.” The former refers to the disappearance of any situatedness (or place) in what becomes mathematically projected and disclosed for an empirical investigation. Situatedness makes sense only within the interrelatedness of contexts of equipment (Zeugzusammenhänge). In a mathematically projected domain of scientific research, the situatedness of something that is ready-to-hand becomes a “spatio-temporal position, a world-point, which is in no way distinguished from any other” (Heidegger [1927] 1962, 413). The delimitation of a domain (as a further specification of its mathematical disclosedness) is due to the formulation of symmetry groups that remain invariant with respect to all possible transformations of spatiotemporal positions. The delimitated domain is constituted by all possible theoretical models that translate a basic mathematical structure into empirical objects of inquiry.

The most important merit of Heidegger’s attempt to develop an existential conception of science is the way in which he is figuring out relations between the existential finitude that implies the transcendence of the world (the finitude as situated bondage to an “always already” projected horizon, Horizontgebundenheit), the ecstatic unity of temporality, and the cognitive structure that objectifies and regionalizes the reality within-the-world. Nevertheless, Being and Time does not offer a coherent conception of the mode of being-in-the-world-by-thematizing-the-world-objectively in terms of hermeneutic ontology. There are several reasons for this failure.

As pointed out, Heidegger’s conception addresses the constitution of regions of scientific research as a result of the transformation of everyday practices into theoretical exploration. To be sure, this subject is too complex to be reduced to the disappearance of praxis. Its handling requires developing a picture of that cognitive structure in which objectifying thematization takes place. Prima facie the doctrine of mathematical projection, which discloses a region of scientific research, bears resemblance to the paradigm of constitutional analysis, which characterizes the existential analytic as hermeneutic phenomenology. One can even admit that Heidegger elaborates on this doctrine by extending the paradigm of meaning constitution. According to the latter, the constitution of meaning within-the-world is due to the interpretative appropriation (or “articulative interpretation”) of possibilities projected as a horizon of understanding.³ The constitution of regions of inquiry is, in turn, also due to a projection that releases things ready-to-hand within-the-world from their environmental confinements, and delimits a region where possibilities of applying a formal apparatus are discovered. Following this line of reasoning, the mathematical projection seems to open possibilities for empirical interpretations of theoretical structures. (For instance, by projecting the structure encoded by partial differential equations that establish relations connecting space, time, and the electromagnetic field-magnitudes, one opens possibilities for studying all phenomena the region of classical electromagnetism potentially contains.)

Yet the analogy with the paradigm of meaning constitution is misleading. Heidegger’s existential conception of science does not treat the mathematical projection as a horizon that promotes a meaning constitution within new (scientific) contexts of practical comportment. By contrast, it argues that this projection leads to a deworlding that forecloses all possibilities of a circumspective constitution of meaning. This way of treating the mathematical projection implies a kind of mathematical essentialism concerning the nature of scientific research. Paradoxically enough, the conception of the existential genesis of science’s theoretical attitude is essentialist in terms of the constitution of the domains of scientific inquiry. All possible entities, events, and processes—so Heidegger’s argument goes—that can be discovered in a mathematically determined region of inquiry are already projected by a formalism that remains invariant with respect to a group of transformations (e.g., the Galilean transformations) or other principles of invariance.⁴

By postulating this sort of essentialism, Heidegger contradicts his own view that scientific research as a secondary mode of being-in-the-world (founded upon the primordial average everydayness) is a modality of “authentic existence” since it “has its existentiell basis in a resoluteness by which Dasein projects itself towards its potentiality-for-being in the truth” (Heidegger [1927] 1962, 415). For reasons spelled out within the existential analytic, it is impossible that a mode of being-in-the-world, determined by a hypostatized essence, should bear a character of “authentic existence” and “resoluteness.” Heidegger’s claim that “science has its source in authentic existence” is ruled out by his own doctrine that only the existence that takes over its “anticipatory resoluteness” is able to understand its finitude authentically, thereby drawing all moral consequences of that understanding. In its anticipatory resoluteness, authentic existence is freed from hypostatized authorities.

There are several other shortcomings of Heidegger’s existential conception of science that are informed by its mathematical essentialism. Among those I will discuss in the chapters to come are: (a) the underdeveloped picture of science’s cognitive structure; (b) the willful neglect of science’s intrinsic circumspection; (c) the heavy dependence on the dichotomist interpretation of ontico-ontological difference;⁵ (d) the missing links between scientific thematization that objectifies and the solution to the problem of transcendence; and (e) the lack of an appropriate approach to the intrinsic horizon of the temporality of scientific research. (The making-present of thematic objects is a process distinguished by its own temporal dynamics. Heidegger conflates in an inappropriate manner two essentially different issues: the atemporalization of what is made-present in objectifying thematization, and the proper temporality of scientific research as a specific mode of being-in-the-world.)

Now, let me return to an aspect of the existential conception of science I already mentioned by the by. Heidegger observes that the mathematical projection discloses a domain of inquiry. (Phrased differently, the mathematical projection discloses a structure of world-points that is a priori.) This is a transcendental claim: The mathematical projection provides the conditions of possibility for articulating thematic objects within the domain that it delimitates and delineates. The articulation is carried out by executing research practices like observation, calibration, calculation, experimentation, instrumentation, measurement, and so on. For Heidegger, these practices are only a specified continuation of reading theory’s mathematical formalism. They are procedures serving the “theoretical seeing.” The transcendental conditions govern the construction of theoretical concepts (and models) and their empirical interpretations, the choice of themes, the design of methods, the possibility of epistemic truth and objectivity of what is thematized, and the epistemic rationality of all practices employed in the articulation of thematic objects. By fulfilling the conditions posed by mathematical projection, scientific research objectifies.

The starting point in overcoming mathematical essentialism is the elaboration of a hermeneutic view about a scientific domain’s disclosure. This view has to replace the claim that a domain gets disclosed by an idealizing mathematical projection. Furthermore, the projection of mathematical idealizations is the upshot of a particular readable technology that belongs to a cluster of such technologies on which the reading process of articulating a domain of research is based. One would make a mistake if assuming that the disclosure of a domain of scientific research is a “procedure” prior to the constant reading of experimental results, measurement data, diagrams, computer simulations, formal apparatuses, systems of differential equations, patterns of dynamic behavior, and so on. In this formulation, reading is both production and reproduction of what is being read; creating texts and disseminating them in deferring spaces of representation; construction and deconstruction of textual structures. Like the configurations of interrelated scientific practices, the readable technologies are working in concert. Presumably, a juxtaposition of such technologies corresponds to a configuration of practices. I will take up the discussion of scientific research in terms of a reading process in the third section of this chapter. Before that, let me address a central question I have carefully avoided so far.