Between Old and New Teleology. Kant on Maupertuis’ Principle of Least Action

In the Appendix to the Transcendental Dialectic, Kant formulates teleological principles, or rather ideas, and explicates them referring to concrete examples of natural science such as chemistry, astronomy, biology, empirical psychology, and physical geography. Despite the increasing interest in the systematic relevance of the Appendix to the Transcendental Dialectic and its importance for Kant’s conception of natural science, the numerous historical sources for the regulative use of reason have not yet been investigated. One that is very central is Maupertuis’ principle of least action. In 1781, Kant transformed teleology into heuristics and methodology, but in doing so, he partially develops a teleology which was disqualified by Maupertuis because its starting point lies in the construction of animals or plants, the structure of the earth, and the immensity of the celestial bodies. Based on Maupertuis’ principle of action, it can be shown that the Appendix forms a systematic interface between Universal Natural History and Theory of the Heavens and Critique of Judgement which allows the reconstruction of Kant’s regulative use of reason and its specific status in the context of natural science and his critical appraisal of Maupertuis.


Introduction
In the Transcendental Analytic of the Critique of Pure Reason¹ and subsequently in the Metaphysical Foundations of Natural Science, Immanuel Kant clearly distinguishes his critical project from teleological thinking² and the closely related physicotheology. At the same time, in the Appendix to the Transcendental Dialectic, he explicates the "systematic unity of a teleological connection,"³ referring to concrete examples from natural science such as chemistry, astronomy, biology, empirical psychology, and physical geography. In doing so, the decisive point of reference is Pierre Louis Moreau de Maupertuis, although he is not mentioned by name. With his principle of least action, introduced in the 1740s,⁴ Maupertuis significantly changed the debate about the status of final causes and the possibility of teleology in natural science. Fully aware of the central importance of his principle, he defended his conception as a new teleology against the old forms.⁵ In terms of the principle of least action and its specific status in Maupertuis' theory, both continuities and breaks in Kant's concept of teleology can be reconstructed. Starting with the Universal Natural History and Theory of the Heavens, Kant develops an old teleology which was disqualified by Maupertuis and defends it based on the solar system. In the Appendix to the Transcendental Dialectic, Kant transforms teleology into a heuristic and a methodology, but develops systematically incompatible approaches: on the one hand, Kant reduces the regulative principles to mere auxiliary means of the principles of understanding, thus taking away their transcendental dignity; on the other hand, he mixes two concepts of final causes which were strictly differentiated by Maupertuis as old and new teleology. Not until the Critique of the Power of Judgment will these contradictions be resolved, but without dropping the claim made against Maupertuis. Despite the increasing interest in the systematic relevance of the Appendix to the Transcendental Dialectic⁶ and its importance for Kant's conception of natural science,⁷ the numerous historical sources for the regulative use of reason have not yet been investigated. One of these sources will be examined in the following sections on the basis of the principle of least action, in order to discuss a systematic problem which lies in the possibility or the status of teleology within the framework of the first critique. Research has already drawn attention to the mixture of various teleological approaches in the Appendix to the Transcendental Dialectic.⁸ On that basis, the status of the regulative principles or ideas is controversial and discussed as categorial, system, and recently also as an ideational interpretation.⁹ The references to Maupertuis make it possible to develop an historically based criterion by which it becomes clear that all three positions in the question of the status of teleological principles have not only text-immanent proofs but also a systematic explanation deficit. For this reason, it can be shown with reference to the principle of least action where Kant's so-called unsolved problem¹⁰ of the Appendix to the Transcendental Dialectic lies and why, in the 1780s, it "still remains a problem worthy of investigation"¹¹ for him.¹²

Teleology and Critique of Pure Reason
In the Critique of Pure Reason, Kant explicates the principles of understanding to develop transcendental conditions of experience of an object in general. Accordingly, the Transcendental Analytic formulates  des corps (1740) and the paper Accord de différentes loix de la nature qui avaient jusqu'ici paru incompatibles, which was presented at the Paris Academy in 1744. For the history of the development of the principle, see Terrall,Man,270;and Storni,"Principle,. For a formal description of the principle and the relationship to L. Euler, see Pulte,Prinzip,75;Radelet De Grave,"Moindre,Hecht,Pierre;Leduc,"Métaphysique,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]and Lyssy,"L'économie,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]Versuch,20. 6 For an overview of the current controversies concerning the Appendix to the Transcendental Dialectic, see Willaschek,Kant,Ypi,"Deduction,Thöle,"Einheit,Meer,Grundsatz,[3][4][5][6][7][8]Grier,Doctrine,and Klimmek,System, 7 See in particular Kitcher,"Order,Marcucci,"Aspetti,Watkins,Kant,[70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89]McNulty,"Use,[1][2][3][4][5][6][7][8][9][10]and Massimi,"Thing,Thöle,"Einheit,Horstmann,"Idee,Horstmann,"Anhang,McFarland,Concept,Ginsborg,Role,and Kitcher,"Order,. However, the theoretical scientific background of this confusion has not been taken into account. 9 This outline of the state of research is proposed by McNulty, "Use," 1-15. 10 Kant, Theoretical Philosophy after 1781, 153 [4:364]. 11 Ibid.,151 [4:362]. 12 In the Prolegomena, Kant refers explicitly to the first part of the Appendix to the Transcendental Dialectic. In the second part, the references to natural science are less concrete. At the core are the concept of God and an examination of its deistic and theistic interpretations. However, questions concerning natural science are also developed, especially when Kant explicitly refers to the history of the earth or physical geography and physiology of physicians (Kant,  general laws of nature that are prescribed by understanding.¹³ In the Metaphysical Foundations of Natural Science, the principles of understanding are schematized based on the concept of motion,¹⁴ through which Kant deduces the "universal laws of material nature."¹⁵ In addition to these laws, in the Transcendental Dialectic, in particular the Appendix, Kant develops regulative principles of the "systematic unity of nature."¹⁶ Through these, a "purposeful unity of things"¹⁷ is created which "opens up for our reason, as applied to the field of experience, entirely new perspectives for connecting up things in the world in accordance with teleological laws."¹⁸ In order to establish science as a "whole of cognition ordered according to principles"¹⁹ and not merely as an aggregate, Kant refers in the Transcendental Methodology, and, in particular, in the Metaphysical Foundations of Natural Science, to the concepts of reason by which natural science is determined as "rational"²⁰ and, with this, is set apart from a mere "historical doctrine of nature."²¹ In addition to the "nexus effectivus,"²² according to which the connections between causes and consequences are clarified a priori by the principles of understanding, a "nexus finalis,"²³ through which the relationship to a unity is reflected, also plays a crucial role in Kant's theoretical philosophy. In contrast to the antinomy and its resolution in the Critique of the Power of Judgment, in the Critique of Pure Reason, there is no explicit clarification given to the function of the concepts of reason and their importance with respect to the principles of understanding or the relationship between teleology and mechanics:²⁴ in the Transcendental Analytic as well as in the subsequent examinations of the Prolegomena, Kant formulates the principles of understanding as forming necessary and sufficient conditions of experience²⁵ and does not develop the regulative use of reason in the Metaphysical Foundations of Natural Science as an immanent principle. At the same time, however, the regulative use of reason is introduced as "indispensably necessary,"²⁶ and "lacking that, no sufficient mark of empirical truth"²⁷ would be possible.²⁸ Consequently, the principles of understanding are necessary but not solely sufficient conditions for experience and depend on the regulative use of reason. Based on this indeterminacy of the necessity of teleological connections in the context of the first Critique, the respective research positions are also controversial. Sketched out in schematic form, it is possible to distinguish three interpretations, i.e., a categorial, a system, and an ideational interpretation. Following the categorial reading, all laws that are presented in the form of necessity are indirectly related to the principles of understanding. Systematicity is therefore only an additional auxiliary means for laws of experience, which however does not have an independently founded status.²⁹ Following the system  Ibid.,183 [4:468]. On the relationship between the Kantian classification of science in the Metaphysical Foundations of Natural Science and the Critique of Pure Reason; see in particular, Van den Berg, "Conception," 11-6, but also Plaaß, Theorie, 38; Pollok, Anfangsgründe, 58-9; Watkins, "Structure," 568; and Sturm, "Kant on the Ends," 1-3.  89-90, 96, 110-1 [4:294-5, 302, 318]. 28 Following Kant, "all human cognition begins with intuitions, goes from there to concepts, and ends with ideas" (ibid., 622 [A702/B730]), and has in "regard to all three elements sources of cognition a priori" (ibid., 622 [A702/B730]). 29 See Friedman, "Laws," 161-99; Friedman,Kant,Friedman,"Regulative,and Pollok,Theory,109. reading, the connection of concepts, in a hierarchy of scientific judgments and their approximation to an ideal, forms its own source for necessary laws.³⁰ Thus, it is to be explained independently of the principles of understanding. Following the ideational reading, the ideas gained via the transcendental principles of reason are apodictically applied in the sense of an as-if and form their own source of a priori laws.³¹ The categorial, the system, and the ideational readings thus form three different interpretations of the status of regulative principles and their relationship to constitutive onesa problem that remains unresolved in the Critique of Pure Reason. This ambiguity has its origin in the fact that Kant does not strictly separate various historically established teleological concepts, but rather mixes them in his own elaboration in the Appendix to the Transcendental Dialectic.
3 Historical sources for Kant's concept of teleology 3.1 The principles of the philosophers More so than in other passages of the Critique of Pure Reason, in the development of the systematic unity of nature in the Appendix to the Transcendental Dialectic, Kant refers to concrete results of natural science: "For even though it is not actually expressed this way, it is still very easy to discover the influence of reason on the classifications of students of nature."³² And even more concretely, Kant writes: "We also find this transcendental presupposition [of the "systematic unity of nature"] hidden in an admirable way in the principles of the philosophers, although they have not always recognized it [in nature] or admitted it to themselves."³³ Accordingly, this precondition forms a scholastic rule or logical principle, without which there could be no use of reason, because we can infer from the universal to the particular only on the ground of the universal properties of things under which the particular properties stand. But that such unanimity is to be encountered even in nature is something the philosophers presuppose in the familiar scholastic rule that one should not multiply beginnings (principles) without necessity (entia praeter necessitate non esse multiplicanda). It is thereby said that the nature of things themselves offers material for the unity of reason.³⁴ In this passage, Kant explicitly refers to the principle that became known in early modern times as Occam's razor.³⁵ The actual point of reference, however, is Maupertuis, although he is not mentioned by name.³⁶ Kant studied Maupertuis' Essai de cosmologie from 1751, which was translated into German as Versuch einer Cosmologie (1751), even before he published the Universal Natural History and Theory of the Heavens.³⁷ With the principle of least action presented in the Essai, Maupertuis developed a mathematical reformulation of the scholastic principle of parsimony.

Maupertuis and the implementation of a new teleology
In the eighteenth century, the debate on Descartes', Leibniz', and Newton's natural philosophy led to an increasing skepticism toward teleological explanations.³⁸ At the same time, a multitude of teleological approaches can be found that differ in their argumentation and objectives.³⁹ This results in intensive debate about the status and function of the concept of purpose in physics and leads to the question of the position of final causes in relation to efficient ones.
Maupertuis' principle of least action represents a decisive turning point in the development of eighteenth-century teleological thought. According to the highest principle, when bodies collide with each other, the "movement is distributed such that the quantity of action, required for the change that has taken place, is as small as possible."⁴⁰ This describes the physical quantity of the action which is necessary during the transition from one point to anotherthe actual transition is realized on that path which assumes the least action.
According to Maupertuis' conviction, the principle overcomes the assumption of primary forces by contrasting the concept of efficiency with a final approach. The goal is to reduce physics to the collision of bodies, which can be derived from the principle of least action.
The bodies of animals and plants are too intricate machines, their last parts escape our sensations too much, and whose application and intention we know too little to be able to judge the wisdom and power which was necessary for their construction.⁴⁶ As Maupertuis indicates, this criticism is directed explicitly against the cosmogony of Descartes and the physicotheology of Newton. With regard to Descartes, Maupertuis writes: Some philosophers have been daring enough to explain all the mechanism of the world and even its first formation from these single laws. They have said, give us matter and motion, and we shall make the world such as it is. An enterprise truly extravagant!⁴⁷ Maupertuis alludes in this quote to Voltaire's characterization of Descartes' cosmogony, according to which he hypothetically tries to develop the world starting from chaos and based on natural laws.⁴⁸ In addition to this excessive Cartesian attempt, Newton is also guilty of a teleology based on individual cases, when he "seems to have been more moved by the proofs found in the contemplation of the world than by all the others he could have taken from the deep insight of his mind" and thereby mistakenly concludes that these are "nothing else but the effect of the will of a supreme being."⁴⁹ Following Maupertuis' criticism of these varieties of an old teleology, a justified version of teleology cannot be based on individual phenomena but rather must be based on general laws of nature. "A true philosopher must neither be blinded by those parts of the world from which order and agreement shine forth, nor swayed by those which he does not discover."⁵⁰ The supreme being is therefore "not to be sought in the separate and small parts of the world, whose relations to one another we know too little."⁵¹ It is found in the "first laws" and "general rules," and "not in phenomena which are nothing but too complicated consequences of these laws."⁵² Thus, in his new teleology, Maupertuis proceeds from general laws of nature  46 "Les corps des Animaux et des Plantes sont des machines trop compliquées, dont les dernières parties échappent trop à nos sens, & dont nous ignorons trop l'usage & la fin, pour que nous puissions juger de la sagesse & de la puissance qu'il a fallu pour les construire" (Maupertuis, Essai, 32-3)/"Die Körper der Thiere und Pflanzen sind allzu verwickelte Maschinen, deren letzte Theile unsern Empfindungen allzu sehr entwischen, und deren Gebrauch und Absicht wir allzu wenig wissen, als daß wir von der Weisheit und Macht, welche zu ihrem Bau nöthig gewesen ist, sollten urtheilen können." (Maupertuis,Versuch,31). 47 "Quelques Philosophes ont été assez téméraires pour entreprendre d'en expliquer par ces feules lois toute la Méchanique, & même la premiere première formation: donnez nous, ont-ils dit, de la matiere matière & du mouvement, & nous allons former un monde tel que celui-ci. Entreprise véritablement extravagante!" (Maupertuis, Essai, 112-3)/"Einige Philosophen sind verwegen genug gewesen, aus diesen einzigen Gesetzen die ganze Mechanik der Welt und sogar ihre erste Bildung erklären zu wollen. Man gebe uns, haben sie gesagt, Materie und Bewegung, so wollen wir eine Welt machen, wie diese ist. Eine in der That ausschweifende Unternehmung!" (Maupertuis Versuch,59). 48 Voltaire,Eléments,34;Sala,Kant,22;and Waschkies,Physik,571. 49 "Newton paroît avoir éte été plus touché des preuves qu'on trouve dans la contemplation de l'Univers, que de toutes les autres qu'il auroit pû pu tirer de la profondeur de son esprit. Ce grand homme a cru, que les mouvemens des corps célestes demontroient démontroient assez l'existence de celui qui les gouverne." (Maupertuis, Essai, 10-1)/"Newton scheint durch die Beweise, welche man in der Betrachtung der Welt findet, mehr gerühret gewesen zu seyn, als durch alle andere, welche er aus der tiefen Einsicht seines Geistes hernehmen können.
[…] Newton hat geglaubt, eine solche Einförmigkeit könne nichts anders, als die Wirkung des Willens eines höchstens Wesens seyn." (Maupertuis,Versuch,23). 50 "Le vrai Philosophe ne doit, ni se laisser éblouïr par les parties de l'Univers où brillent l'ordre & la convenance, ni se laisser ébranler par celles où il ne les découvre pas." (Maupertuis, Essai, 46-7)/"Ein wahrer Philosoph muß sich weder durch die Theile der Welt, aus welchen Ordnung und Übereinstimmung hervorleuchten, blenden, noch durch diejenigen, wo er dieselben nicht entdecket, wankend machen lassen." (Maupertuis,Versuch,36). 51 "Ce n'est donc point dans les petits detailsdétails, dans ces parties de l'Univers dont nous connoissons trop peu les rapports, qu'il faut chercher l'Etre suprème" (Maupertuis,Essai,./"Man muß also das höchste Wesen nicht in den voneinander getrennten und kleinen Theilen der Welt, deren Verhältnisse gegen einander wir allzu wenig kennen, suchen" (Maupertuis,Versuch,39). 52 "[C]herchons le dans les premieres premières lois qu'il a imposées à la Nature; dans ces regles règles universelles, selon lesquelles le mouvement se conserve, se distribue, ou se détruit; & non pas dans des Phénomenes Phénomènes qui ne sont que des suites trop compliquées de ces lois." (Maupertuis, Essai, 61-2) "Laßt es uns in den ersten Gesetzen suchen, welche es der Natur gegeben hat, in den allgemeinen Regeln, nach welchen die Bewegung erhalten, vertheilet oder zernichtet wird, und nicht in Erscheinungen, welche nichts, als allzu verwickelte Folgen dieser Gesetze sind." (Maupertuis,Versuch,41). and formulates an instrumentalist standpoint. The principle of least action builds a second-order law that allows him to derive other specific laws which are known and confirmed by experience.⁵³ 4 Kant's examination of Maupertuis' principle of least action 4.1 Universal Natural History and Theory of the Heavens In the Universal Natural History and Theory of the Heavens, Kant agrees on the one hand with Maupertuisʼ criticism of the old teleology. In this sense, he shares Maupertuis' doubts about developing a teleology in the field of biology: in the question of the creation of a single plant, a caterpillar,⁵⁴ or even a single snowcrystal,⁵⁵ there is far too little concrete evidence for a well-founded teleology. On the other hand, the book from 1755 represents a large-scale attempt to rehabilitate the old teleology criticized by Maupertuis in the case of the solar system. Among all "things in nature whose first cause we can investigate, the origin of the world system and the generation of the heavenly bodies together with the causes of their motions is the one which we might first hope to understand thoroughly and reliably."⁵⁶ Accordingly, the Universal Natural History and Theory of the Heavens can also be read as an alternative to the principle of least action, as becomes clear when Kant claims, with regard to Maupertuis' criticism of the old teleology, "I shall destroy this difficulty,"⁵⁷ and outlines his own project as follows: It seems to me that in a certain sense one could say here without being presumptuous: Give me matter and I will build a world out of it, that is, give me matter and I will show you how a world is to come into being out of it.⁵⁸ Kant implicitly quotes here Maupertuis' reference to Voltaire's parody of Cartesian cosmogony. Thus, he positions his natural history in the context of a thinker who is directly attacked by Maupertuis. Furthermore, with his writing from 1755, Kant addresses a case in relation to which Maupertuis believes that he has demonstrated in Newton the limitations of old teleological thoughts. Although Kant proposes a different solution than that of Newton,⁵⁹ he positions his concept again in the context of a thinker attacked directly by Maupertuis. In this sense, Kant not only conceives the Universal Natural History and Theory of the Heavens as an old teleology, but also defends it explicitly before the president of the Berlin Academy.⁶⁰

The Appendix to the Transcendental Dialectic
The Universal Natural History and Theory of the Heavens represents, if not a counterexample, at least an alternative to Maupertuis' new teleology. The book also forms the starting point of a defense of a teleological 59 According to Kant, the laws of action (attraction and repulsion) are inherent to matter. The natural order necessarily unfolds in accordance with these laws. They are sufficient for the production and preservation of the orderly and functional constitution of the world (ibid., 199 [1:228]; see Janiak, Newton, 102-12). 60 In contrast, Tonelli, Elementi, 51-61; Tonelli, "Conditions," 126-44; Waschkies, Physik, 573-6 finds in the Universal Natural History and Theory of the Heavens a defense of Maupertuis' principle. However, this is an interpretation that is strongly influenced by The Only Possible Argument in Support of a Demonstration of the Existence of God and goes back to basic considerations of Cassirer, Erkenntnisproblem, 586-600. See also the remarks of Sala, Kant, 27-8, who also argues with reference to the book from 1763. Buchdahl, Metaphysics, 493; and Pulte, "Teleologie," 82-3 argue in a similar way. For the relationship between the book from 1755 and 1763, see Kreimendahl and Oberhausen, "Einleitung." concept based on individual cases that can be traced throughout Kant's entire writings, although it is in a state of constant transformation.
Despite the increasing discrediting of teleology in the context of physics toward the end of the eighteenth century, the question of its function and structure remains an unresolved problem for Kant. The difficulties that arise from the status of final causes are made clear by a very complex formulation in the Appendix to the Transcendental Dialectic, compressed into one sentence: What is strange about these principles, and what alone concerns us, is this: that they seem to be transcendental, and even though they contain mere ideas to be followed in the empirical use of reason, which reason can only follow asymptotically, as it were, i.e., merely by approximation, without ever reaching them, yet these principles, as synthetic propositions a priori, nevertheless have objective but indeterminate validity, and serve as a rule of possible experience.⁶¹ Using the word concern in the introductory formulation of this quotation suggests that Kant does not necessarily intend to present certain results of his considerations apodictically, but rather sketches a problem that is found in the following juxtaposition: the principles of reason form "synthetic propositions a priori,"⁶² serve "as a rule of possible experience,"⁶³ and thus seem to be "transcendental."⁶⁴ At the same time, however, they represent "heuristic principles"⁶⁵ in the treatment of possible experience, by which the empirical use of reason is guided, but follows "only asymptotically."⁶⁶ Based on this juxtaposition and the fact that a transcendental justification of concepts is merely feasible with reference to the manifold in time and space,⁶⁷ Kant comes to the conclusion that a "transcendental deduction is always impossible in regard to ideas."⁶⁸ Nevertheless, he claims that the principles of reason have "objective but indeterminate validity"⁶⁹ or, as Kant formulates it in the following paragraph, "some objective validity."⁷⁰ The strangeness mentioned by Kant results from an ambiguity in the task and function of teleological explanation in nature. Kant's approach oscillates between a reduction of systematicity to a mere auxiliary means of the principles of understanding, and a purposeful explanation of individual natural phenomena and nature as the lawful connection of our ideas, i.e., between an abolition of final causes and the old and new teleology characterized by Maupertuis.

Final causes of specific phenomena
The ideas or principles of reason are developed in the sense of an old teleology when they become "a rule of possible experience."⁷¹ Kant writes: "It is thereby said that the nature of things themselves offers material for the unity of reason."⁷² Based on this consideration, "systematic unity, as pertaining to the objects itself, is assumed a priori as necessary."⁷³ Thus, purposiveness is not a second-order principle of the cognition of understanding but is developed based on individual cases and likewise applied to them. Thus, in Kant's argumentation so far, it "cannot even be seen how there could be a logical principle of rational unity among rules unless a transcendental principle is presupposed."⁷⁴ In the first part of the Appendix to the Transcendental Dialectic, Kant contrasts the apodictic use of reason with a hypothetical one: in the latter, the particular is the certain and the universal is "assumed only problematically."⁷⁵ In the course of the hypothetical use of reason, "several particular cases"⁷⁶ are tested by a general rule "to see if they flow from it."⁷⁷ Thus, the intention is "bringing unity into particular cognitions."⁷⁸ If all particular cases can be explained by this rule, "then the universality of the rule is inferred, including all subsequent cases, even those that are not given in themselves."⁷⁹ A similarly formulated mental figure can also be found in the second part of the Appendix to the Transcendental Dialectic which refers to the ideas of God, world, and soul. Starting from the field of possible experience, an "object in the idea"⁸⁰ is concluded by means of a process of abstraction. This object in the idea "serves only to represent other objects to us, in accordance with their systematic unity."⁸¹ Thus, it is possible to derive "the object of experience, as it were, from the imagined object of this idea as its ground or cause"⁸² in the form of an "as if."⁸³ With the object in the idea, "we think a relation to the sum total of appearances, which is analogous to the relation that appearances have to one another."⁸⁴ For this reason, Kant concludes that there is "not the least thing to hinder us from assuming these ideas as objective and hypostatic."⁸⁵ In both parts of the Appendix, Kant formulates a reciprocal inference, in which he combines the inference of induction, subsumption, and analogy.⁸⁶ With induction the first, Kant explicates an inference from the manifold (the particular) to a unity (the universal) based on the principle of "universalization,"⁸⁷ with the second one, how specific cases are subsumed under general rules, and with the third one, an inference "from many determinations and properties, in which things of one kind agree, to the remaining ones, insofar as they belong to the same principle."⁸⁸

Final causes of general laws
In contrast to all forms of old teleology, Kant points out in the same passages that it is not "merely a few parts of nature, e.g., the distribution of dry land, its structure and the construction and situation of mountains, or even only the organization of the vegetable and animal kingdoms"⁸⁹ that can be seen as purposive. Such argumentation is disqualified as "lazy reason (ignava ratio)."⁹⁰ On the contrary, "we make a purposiveness in accordance with universal laws the ground."⁹¹ In this context, Kant always speaks in analogy of understanding and reason. In accordance with the "analogy of a causal determination,"⁹² the different laws should be systematically connected through reason. As understanding "unites the manifold into an object through concepts, so reason on its side unites the manifold of concepts through ideas."⁹³ In this sense, purposiveness becomes a kind of second-order principle and differs from that of the Transcendental Analytic because it is regulative and not constitutive. This approach becomes most clear, when Kant writes: Reason never relates directly to an object, but solely to the understanding and by means of it to reason's own empirical use, hence it does not create any concepts (of objects) but only orders them and gives them that unity which they can have in their greatest possible extension, i.e., in relation to the totality of series.⁹⁴ Thus, the concepts of reason become "maxims"⁹⁵ based solely on the "speculative interest"⁹⁶ of reason, "even though it may seem as if they were objective principles."⁹⁷ In this sense, the regulative use of reason reflects the laws which are determined by the principles of understanding.

Critique of the Power of Judgment
What Kant lacks in 1781 is an explicit choice between the various functions and forms of teleological thinking and, associated with this, a clarification of the relationship between final and efficient causes. In the Critique of the Power of Judgment,⁹⁸ however, he has already clarified this ambiguity in the form and structure of final causes in natural science. Thereby, the reflective power of judgment forms a capacity that is not directed to a certain cognition but to cognition in general. It reflects the conditions under which specific cases can be the object of human cognition, although they elude the objective cognition of the principles of understanding. "As for what occasions it, this principle [of purposiveness] is of course to be derived from experience,"⁹⁹ but "cannot rest merely on grounds in experience."¹⁰⁰ It must have "as its ground some sort of a priori principle, even if it is merely regulative and even if that end lies only in the idea of the one who judges and never in any efficient cause."¹⁰¹ Thus, the need to recognize the manifoldness of specific phenomena becomes the occasion for the power of judgment to reflect the relation and possible purposiveness of the capacities. In this sense, the reflecting power of judgment "attributes nothing at all to the object (of nature), but rather only represents the unique way in which we must proceed in reflection on the objects of nature with the aim of a thoroughly interconnected experience."¹⁰² Individual phenomena are therefore the starting point for teleological reflections and do not assist an understanding of nature in the sense of the old teleology.

Unsolved problems of the Critique of Pure Reason
Maupertuis' differentiation between an old and new teleology allows the analytical separation of various incompatible elements in Kant's conceptions of teleology. However, it is important to note that this distinction is not an unrestricted standard for Kant: as he constantly undermines it. At the same time, it becomes evident that in 1781 Kant lacks a critical examination between the various forms of teleology and the "choice among these proofs"¹⁰⁷ which was explicitly demanded by Maupertuis. Regardless of the methodological transformation of teleology in the Appendix to the Transcendental Dialectic, Kant's approach oscillates between three extremes: firstly, Kant reduces the regulative principles or ideas to mere auxiliary means of the principles of understanding and thus deprives them of their independent dignity within the framework of natural philosophy. Secondly, the regulative principles or ideas are developed for a systematic unity and therefore as a second-order condition, whereby the specific laws of understanding are subject to the more general laws of reason. Thirdly, Kant develops the regulative principles or ideas as a systematic unity of nature in the empirical use of reason, whereby these can be understood in a specific way as belonging to the objects.
It is remarkable, on the one hand, that the latter two interpretations renew and reproduce Maupertuis' old and new teleology as shown above. On the other hand, the ambiguities in Kant's teleological concept are reflected in the current research question concerning the necessity of regulative principles and ideas, i.e., the categorial, the system, and the ideational reading. It becomes clear that all three positions in the question of the status of teleological principles have not only text-immanent proofs but also a systematic explanation deficit.
The categorial interpretation is based entirely on the core function of the Transcendental Analytic. In this passage, Kant characterizes the principles of understanding as necessary and sufficient conditions for experience. This interpretation takes into account the fundamental role of the principles of understanding within the framework of the Metaphysical Foundations of Natural Science, according to which the "concept of matter had therefore to be carried through all four of the indicated functions of the concepts of the understanding."¹⁰⁸ In addition, in the Appendix to the Transcendental Dialectic, Kant disparages the function of regulative concepts by formulating that they "cannot do us any harm."¹⁰⁹ For then nothing more can follow from it in any case than that where we expected a teleological connection (nexus finalis), a merely mechanical or physical one (nexus effectivus) is to be found; in such a case we only miss one more unity, but we do not ruin the unity of reason in its empirical use.¹¹⁰ In this way, the natural scientist is instructed to follow the mechanical connections as far as possible and to regard teleological connections only as temporary auxiliary means. However, if the independent necessity of the regulative use of reason is disputed in relation to the constitutive principles of understanding, the central claim of the Critique of Pure Reason in regard to the Universal Natural History and Theory of the Heavens would become invalid, i.e., the differentiation between the principles of understanding and the principles of reason.¹¹¹ In the framework of the Metaphysical Foundations of Natural Science, the reduction of all necessary laws to the principles of understanding leads to the problem that Kant's differentiation between proper and improper science cannot be maintained.¹¹² In this sense, for example, the lawfulness of chemistry would also have to be indirectly attributed to the principles of understanding. Moreover, the hierarchically organized distinction between rational science, which is legitimized by the systematic unity of the ideas of reason, and proper science, which in turn is legitimized by the principles of understanding, becomes questionable.¹¹³ The system interpretation, in turn, corresponds to the concept of the principle of least action as introduced by Maupertuis. Accordingly, the "law of reason"¹¹⁴ permits a "coherent use of understanding";¹¹⁵ the principles of understanding, however, make experience possible in the first place. The systematic unity forms, in this sense, a second-order condition to the principles of understanding and has, in analogy to the validity of the constitutive principles, "objective but indeterminate validity."¹¹⁶ In contrast to Maupertuis, however, in the Appendix to the Transcendental Dialectic, Kant renounces a uniform principle of all-natural research, whereby the systematic unity becomes variable. Accordingly, there is a separate supreme touchstone in chemistry, biology, astronomy, and empirical psychology. However, what remains unexplained in the system reading isin contrast to the categorial and ideational readings (and also the teleological judgment)how the insights through the regulative use of reason have an effect on the constitutive one.¹¹⁷ Consequently, it remains open how the ideas of reason that have been developed regulatively or hypothetically as the supreme touchstone of truth can be applied concretely.
The ideational interpretation already points clearly toward the solution of the teleological judgment. Kant introduces final causes starting from special cases, moving from these to a general rule or object in the idea, in order to explain cases which are not given. Based on the actual scientific handling of empirical material and its classification, the Appendix to the Transcendental Dialectic pursues the claim to argue in a pragmatic manner and in a practically well-founded way. In the development of systematic unity, Kant refers to chemistry, physiological anthropology, astronomy, and empirical psychology¹¹⁸ to make the possibilities of teleology plausible, even if not purely argumentative. In doing so, the circular, elliptical, parabolic, and hyperbolic movements of the planets,¹¹⁹ the elements of pure earth, pure water, pure air, etc.,¹²⁰ the ladder of continuity among creatures,¹²¹ a single radical or absolutely fundamental power,¹²² as well as "wise intentions of a world-author" in "regard to the shape of the earth, the mountains, the seas, etc."¹²³ are concluded, determined, and apodictically applied in the sense of an as-if. However, within the framework of the Critique of Pure Reason such an argumentation stands in contradiction to Kant's claim of a sufficient and necessary validity of the principles of understanding.

Conclusion
Maupertuis' philosophy of nature, and in particular his foundation of mechanics via the principle of least action, forms a central reference point for Kant's thinking, which can be traced from the 1750s through the Critique of Pure Reason to the Critique of the Power of Judgment. In all three stages of development, Kant attempts to establish his own philosophy of nature with reference to, but also in critical dissociation from, Maupertuis. Remarkably, Kant's entire philosophical writing thus pursues a teleology that starts out from distinct phenomena but reconciles it in a specific way with the question of the connection between human cognition and capacities.
In the Appendix to the Transcendental Dialectic, this leads to a blending of systematically incompatible concepts: on the one hand, Kant reduces the regulative principles to mere auxiliary means of the principles of understanding, so that consequently, they do not have a transcendental status; while on the other hand, he also mixes two concepts of final causes differentiated by Maupertuis as old and new teleology. Based on this ambiguity, a final clarification of the relationship between nexus effectivus and nexus finalis is not possible in the context of the first Critique. At the same time, this offers an explanation for the different interpretative approaches in to the status of regulative principles, i.e., the categorial, system, and ideational interpretations as discussed in the research on the Appendix to the Transcendental Dialectic. Kant's analysis lacks a critical examination between the different forms of teleological thinking. He has not yet decided which form of teleology the critical project is compatible with. Probably, he had exactly this difficulty in mind when he wrote in the Prolegomena that there is an unsolved problem in the Appendix to the Transcendental Dialectic.