A Kantian Defense of Ptolemy

There is, apparently common to humanity, a strange and somewhat inexplicable desire to get things right. A fundamental trouble with this desire is that, in the course of a human life, getting things right seems to be the thing we are least capable of. Any psychoanalyst worth their salt would describe this condition as hysteria—under the influence of which we create desires in principle unsatisfiable for ourselves. Nonetheless, this condition is, I contend, the origin of much of the history of philosophy and science. A brief but important chapter in this history implored us to abandon the desire in its unsatisfiable form, and it is the claims of that chapter, of an early Kantianism, with which the following essay will be concerned.

It is often said that the aim of the sciences is to ‘get us closer to truth’ or to ‘approximate truth.’ A corresponding thesis is that scientific progress consists in the process of more and more closely approximating the truth. While this sounds eminently reasonable, what exactly it means is rarely asked. So, we’ll start by asking it: what, exactly, does it mean to approximate truth? The language is at least suggestive of truth as a quantitative notion—arriving at truth is asymptotic. Four-fifths is closer than two-thirds to one, and nine-tenths closer than that, and so on, until we approach one by infinite steps.

This seems wrong, as there aren’t a simple number of feature to correctly represent of the world, one by one getting them right as we get closer to exhaustive understanding—some features of the world are deeper, more fundamental, more significant, relevant to its nature and to a comprehension of it as a whole, and our representations of these features may be of differing quality. A better, but admittedly less precise comparison would be that of a sketch artist attempting to best capture a scene, or the drawing of a portrait. While more troubling cases can be conceived, it’s true that if a portrait were a sketch of an apple this would be further from a genuine representation of its subject than if it were a generic sketch of a human being. Nonetheless the closer our attempts to sketch the subject reach infinity, by way of cautious and anxious trial and error, careful comparison with other sketches and their features, examination and reexamination, eventually we might reach an indistinguishably true picture of the subject (such a picture, if progress is to be approximating it, must at least be posited as an ideal). Enter hysteria.

It’s the insights of a chapter in the history of philosophy that I’d like to recover, a chapter which problematizes at least one interpretation of the ideal scientist as an ideally skilled sketch-artist. And so, to clarify a more fully developed sense of what it means for something to be approximately true, or what it means to get closer and closer to truth, I’ll start with an antiquarian discursion into this and its preceding history.

While it’s well understood that modern metaphysics saw perhaps its most fundamental transformation in Kant’s critical turn, a significant part of this transformation is often neglected: the early modern concern with the “objective reality of ideas,” or with the “clarity of perceptions,” is replaced with a concern for the “objective validity of judgements.” I want to say that this transformation, when understood, calls by analogy for us to abandon perfectionism in science, and that furthermore this comes at no cost but peace—perfection was never really what we were looking for. It also suggests an alternative: a universal and necessary justificatory order that is as human as the judgements it takes as its objects, that holds all actual and possible scientific investigation to assessment in light of binding, rational standards, and which nonetheless relates itself to some of the highest-order truths—those about ourselves.

The early modern concern with assuring that our ideas are as real as they can be, or our perceptions as clear as they can be, in the face of which Kant issues his famed farewell, I take to be the epistemic predecessor of our contemporary colloquial perfectionism. In certain ways, it seems to me, the seventeenth century perhaps had a stabler and more mature account of ‘the whole truth’ to which we should aspire, and a more developed sense of what it means to approximate it—that’s where we’ll begin.

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The way of the predominant early modern philosophy, in its Cartesian inception, was the ‘way of ideas.’ Ideas are “images of things,” representations corresponding to objects thought or perceived. The way of ideas is a method: in the attempt to understand how knowledge is possible, we look to the nature of our representation of things, and we come to knowledge when our representations really are what the object is, that is, when they really present it. The method rests on some clear presuppositions: (1) there is a way objects really are, (2) what we have direct access to, thought or perceived, is representations and not the objects themselves, and (3) representations are the means by which we apprehend the way objects really are. The ultimate end of this epistemological project is the assurance of the reality of our ideas.

Descartes distinguishes two senses of this reality. The formal reality of ideas may be satisfied simply in the idea being conceived—a unicorn has a formal reality in the sense that it is indeed an idea. It is so far as it is an idea. The objective reality of ideas, on the other hand, lies in the representational content of ideas, it is satisfied in the degree to which our representations present their corresponding objects. It is so far as it is the object. 

The end of the Cartesian way of ideas as a project of assuring the reality of all finite ideas is crucially premised on our clear understanding of the ens realissumum, the most real being; we “clearly understand that there is more reality in infinite than in finite sub-stance, and that hence the perception of the infinite is in some way prior in me to that of the finite, that is, the perception of God is prior to the perception of myself.” Our understanding of the ens realissimum is epistemologically prior to our understanding of any finite thing precisely because all finite things are defined by limitation of the infinite. Furthermore, the degree of the objective reality of our cognitions can only be defined in terms of limitation or privation of those cognitions of the infinitely real cognizer (whose cognition causes its object and creates the universe of all really existing things), God. It might appear now that the Cartesians are speaking spooky, but without such a conception, they would be speaking non-sense, approaching an ideal with no conceivable referent. The priority of the divine intellect, and the ideal of a God’s eye view of the object, suggests for us derivative laws governing our cognitive activity, and suggests as our ideal the assurance of the absolute reality of our ideas.

While this approach was modified by succeeding philosophers, it was substantially maintained, and expressed arguably in its highest empiricist and rationalist forms by Locke and Leibniz. For each also, suppose, their reason for concern with the reality of ideas rests in the relation of their reality to the ens realissumum. For each, our cognition is compared to God’s cognition (the intellectus archetypus), the cognition for which there is no distinction between synthetic and analytic representations (this was the Leibnizian solution to the trouble of Cartesian dualism). For Locke and Leibniz, we can approximate this divine cognition of things with more or less arbitrary precision, depending on either how immersed we are in experience or how far we purify our logical analysis, respectively. For Locke, the normative status of logic, prescribing rules for the direction of the mind (and its inquiries), presupposes a particular empirical psychology, and for Leibniz a particular rational psychology. It’s with Hume that we recognize a great and shared justificatory problem: though we are enticed by the prospect of reaching toward divine a priori certainty with respect to our representations of objects, the fact that on the one hand all objects presented to us through experience are a posteriori, and the fact that on the other all objects merely considered logically don’t reach out to that which they represent, forecloses the possibility of such a project’s success, leaving us only able to claim that we just happen to be subjectively constituted (whether it be by a given rational psychology or a given empirical psychology) such that we are inclined to reach toward an inaccessible reality of ideas. Hume thus held that the early modern philosophical project has attempted to establish a priori concepts by no more than the subjective re-ordering of a posteriori concepts.

Early modern philosophy has, in dealing with the reality of ideas, addressed only a quid facti (‘by what facts?’) concerning our possession of knowledge of certain logical rules and how we must be so subjectively constituted for us to possess them, but not the quid juris (‘by what right?’) concerning the very legitimacy with which specific logical rules can possibly serve as the criteria for the formal assessment of our thought and inquiry. These two questions correspond to different methods: the former, a psychology of human reason (empirical or rational), the latter, we will explore in more detail as the essay progresses. Yes, we are so inclined to perfectionism, we desire to see all sides of the object as God would, and yes, there are facts about our constitution that produce this inclination, and yes, if one seeks perfection, this likely suggests a notion of objectivity and accompanying norms of thought and inquiry that apparently instrumentally tend toward the perfect. Is this pursuit (unsatisfiable as it is), or the norms derived from it, ever justified beyond observation of facts about our subject constitution, rational or empirical?

The character of this epistemological project, I want to say, is in important respects analogous to the contemporary treatment of the sciences as theoretical representations of physical objects, where we seek to revise our theory in light of its capacity to as closely as possible represent the character of the theory’s object as it is in itself. While representationalist pictures of perception and an understanding of the ‘mind as a theatre,’ in which objects and notions dance across the stage, has been thoroughly questions and examined—it is significantly less controversial that scientific theories are representational—we introduce, define, and relate technical notions in an attempt to model targeted features of the world. The perfect scientific theory, the ideal toward which such revision is in the first place motivated, represents the object of inquiry in its entire and true nature. Perfection is the central normative notion for early modern epistemology, and a perfection of the same kind appears to be the central normative notion for a philosophy of science which takes as science’s aim perpetual approximation of the whole truth. The difference, however, is that this new form, the form of contemporary scientism, lacks for its motivation the archaic notion of the ens perfectissumum. At least early modern philosophy had to fall to Hume’s critique—the contemporary analogue falls far before that. We cannot rely, in the contemporary scientific version of the early modern project, on an understanding of God as the ideal theorizer, an understanding prior to any of our own particular theorizing. Lacking such motivation, the death of God (or at least a more steadfast recognition of His incomprehensibility) plunges us headlong to hysteria—a desperation consequent of the feeling of having had and lost something infinite. We now lack any substantial conception of what we are even after (and it’s no wonder we never get there), let alone foundational justification for why we are after it.

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“Metaphysics is not a philosophy about objects, for these can only be given by means of the senses, but rather about the subject, namely, the laws of its reason. We have laws for the use of our reason a posteriori, these cannot be applied to concepts, but rather only to objects of experience. Metaphysics thus treats only the subject dogmatically, but it treats the object, with regard to synthetic judgements, problematically.”

Kant, in his pre-critical period, shared the spirit of the early moderns, and his Inaugural Dissertation was a final contribution to philosophy in the way of ideas. Perfection as approximation of the divine intellect, cast in Kantian flair as “noumenal perfection,” remained the central normative notion: “God, as the ideal of perfection, is the principle of cognizing, He is also, at the same time, in so far as He really exists, the principle of the coming into being of all perfection.” That Kant’s critical turn is a turn away from the straightforward ideal of the ens perfectissumum is clear in a famous letter to Marcus Herz, in which he is seen in a state of motivated anxiety after awakening from his dogmatic slumber:

If that in us which we call ‘representation’ were active with regard to the object, that is, if the object itself were created by the representation (as when divine cognitions are conceived as the archetypes of things), the conformity of these representations to their objects could be understood. Thus the possibility of an intellectus archetypus (an intellect whose intuition is itself the ground of things) is at least comprehensible. However, our understanding, through its representations, is neither the cause of the object, nor is the object the cause of our intellectual representations in the real sense [i.e. objects of the intellect are not affected in the same way as is sensation].

It is in Kant’s critical turn that we recognize that having any positive conception of the ens perfectissimum whatever is impossible. We can have no possible concept of God’s cognition in general (it is “nothing to us”), let alone one that we could, with our finite cognition, seek to approximate. To treat God as a thing about which we may have a concept is to reduce him, and his intellect, to the finite, and so to fall into transcendental illusion.

The central early modern concern for assuring the objective reality of ideas, in lieu of a substantive conception of the ens perfectissumum, is supplanted in the critical turn with a concern for assuring the “objective validity of judgements.” Objectivity now modifies a different predicate, and consists no longer in the extent to which one’s mental or theoretical representations approximate a God’s-eye view of the object. Ideas themselves were only units of normative significance considered in relation to and limitation of perfection—when the latter notion is dissolved, ideas alone may no longer be subject to norms. An idea, such as a representation of a chair, or any given perception, does not fall short or stand tall, its just what it is. What can be subject to norms, Kant realizes via Hume, is relations of ideas, whose character may be lawful or unlawful, valid or invalid. A judgement, for Kant (following the Port Royal logicians), consists in nothing more than a relation of concepts: our judgement that “the tree is green” relates our concept of “tree” with our concept of “green” by way of the copula. Indeed, a concept is a concept “only because other representations are contained under it by means of which it can be related to objects. It is therefore the predicate for a possible judgement…The understanding can make no other use of concepts than that of judging by means of them.”

The objective validity of judgements, the lawfulness of their character, consists in their conforming to certain universal and rationally, publicly accessible principles, namely, some synthetic principles a priori that structure and constitute domains of their respective forms of judgement. The ultimate conclusion of the Critique lies in the claim that synthetic principles a prior (in metaphysics, mathematics, and natural science) spell out the criteria of objectivity for all a posteriori judgements, and that furthermore these principles are constitutive of the forms of judgement (our forms of judgement) concerning the given domain. On the other side of the coin, the justification for these synthetic a priori principles can be nothing other than the objectivity of judgements a posteriori.

Instead of attempting to answer the question of how far are our representations from the complete and true nature of the object, and instead of suggesting an ideal that we perpetually strive for the clearest perception, the greatest representational reality of our ideas, we are now directed to an apparently more fundamentally human, justificatory question: are we entitled to relate our concepts to their objects and to each other, and what are the criteria for assessing that entitlement, for the warrant in throwing our weight behind certain judgements a posteriori?

We ask for these criteria and at the same time a justification of their legitimacy, and their justification is, reflexively stated above, nothing other than the objectivity of the thought they govern. In scientific practice, this ought to model a cyclical kind of reform, a feedback loop in which our principles are not only constitutive of the practices which are born of them, and our practice is held liable to assessment in light of them, but also in which the results of our practice may demand the re-conception of our principles. That is, if the articulated criteria of objectivity in a particular domain yield practices of inquiry which return results suggesting the contradiction of those very practices or criteria, this gives us prima facie reason to call into question the justifications of the contradicted practice and criteria (this is apparently quite rare, but e.g. quantum theory’s potential to call into question event-causation—a theory which arose in the assumption of an event-causal structure, but may suggest its violation). Herein is a radical kind of openness, which permits, under the articulated conditions, the revision of even the most fundamental rules of inquiry, but does not sacrifice absolutely binding rational standards for scientific practice. This is no contradiction (as explained in the coming discussion), but it does call attention to a tension at the heart of what it means to be a finite reasoner.

As we are not creatures whose intuitions are the grounds of their objects, as we had to accept that our finite cognition is not of a kind that makes approximation of God’s cognition in principle possible, so must we come to grips with the fact that we are not the kinds of creatures who will, even in our best efforts, ever offer a scientific theory that contains the perfect comprehension and presentation of its object—we will not articulate a perfect theory of everything, worse still, we will not articulate a perfect theory of anything. Obscurity necessarily accompanies finitude, and the sooner we recognize this, the sooner we will come to ideals fitting of the obscure nature of our finite rationality, the sooner we will abandon indicting ourselves for not being what we never were: gods.

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We proceed with an initially puzzling conclusion: How can we have rational standards that are absolutely binding on our judgements, which are themselves subject to revision? This appears to be a contradiction only if one thinks that because a standard happens to be false, that it therefore is not necessarily binding. Perhaps this is true on the perfectionist model, where we are bound by our ideal to get it right, and getting it wrong constitutes a deviation from our ideal cognitive activity. But, a philosophy that takes seriously the finite nature of our rationality not only accepts the possibility that standards which legitimately and justifiably bind us are potentially to be eventually abandoned, it also accepts that we can be bound to get things wrong, that is, we can provide the utmost justification for the entitlement (and indeed the necessity) to make judgements whose contents are in fact false. To reasonlessly believe, in the first century, that the Sun was in the center of the solar system, was not only true, it was irrational, and one would be a blameworthy inquirer for believing it. Elementary observations by the naked eye, all we had, suggest the centricity of the earth: celestial objects always rise in the east and set in the west around the same points on the horizon, and the earth always seems still beneath our feet. Further, in accordance with the rest of our best (Aristotelian) astronomical theories, the geocentric model was dramatically more predictive and simpler. To believe it was not only false, but necessitated by basic principles of our finite reason.

When we abandon perfection, when we abandon concern for the objective reality of ideas, and embrace in finite rationality, what we come to care about is whether we can in fact legitimately make judgements about the world and which those are, about the objects of experience or knowledge whatever they may be, judgements which may be objectively valid, i.e. which are held liable to assessment in light of rational standards universal and necessary for their corresponding modes of inquiry, that are essentially communicable and thereby public, and that are by this nature amenable to the kind of reciprocal accountability fundamental to the social form of all inquiry. What we care about is inquiring in the right way, as that which we are, thrown into the world the way we so are, and not about getting closer to the chimerical perspective of a universal eye that sees all and knows all. The latter is not what it really means to be objective. Ptolemy was not a fount of subjectivism just because he got it wrong. The objective scientist should feel perfectly comfortable dying as Ptolemy—and indeed, she should aspire to no more than this. Take a breath, and do the best you can, there really is nothing else for us.