Friday, November 9, 2012

Treatise on the Speculative Nature and Origin of Life
by Ryan Haecker

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I. The Abstract Nature of Life
Life is generically defined as the set of those things which may move, metabolize, grow, die, reproduce, and possess complex internal structures that are passed on to their children.[1] This definition of the positive biological sciences obscures more than it clarifies, for it affirms a multitude of powers that Life may possess without explaining why it is that Life must possess them: that is to say, it abstractly affirms the modally possible powers of Life, and yet neglects to negate among these modalities to distinguish the individual that is necessary to concretely unite them all. The powers listed are thus, simply by themselves and collectively among themselves, conceptually inadequate to define, not merely the order and various relations of each, but moreover the inner necessity from which all of these powers emerge and have their being. Thus Socrates objects to Meno's list of virtues in Plato's Meno: "Even if [the definitions of virtue] are many and various yet at least they all have some common character which makes them virtues... we have discovered a number of virtues when we were looking for only one." (72c/74a) If Life is a real universal natural kind and not merely a conventional name given to many kinds, it must, as Socrates implores, be one common and necessary concept that unites, within itself, all of the many powers and adaptations found amongst the stupendous heterogeneity of living things.

[1] Weber, Bruce, "Life" Stanford Encyclopedia of Philosophy, 2011: "Living entities metabolize, grow, die, reproduce, respond, move, have complex organized functional structures, heritable variability, and have lineages which can evolve over generational time, producing new and emergent functional structures that provide increased adaptive fitness in changing environments... Something that is alive has organized, complex structures that carry out these functions as well as sensing and responding to interior states and to the external environment and engaging in movement within that environment... living systems may be defined as open systems maintained in steady-states, far-from-equilibrium, due to matter-energy flows in which informed (genetically) autocatalytic cycles extract energy, build complex internal structures, allowing growth even as they create greater entropy in their environments, and capable, over multigenerational time. of evolution."

In the history of Western Philosophy there have been three prevailing opinions on the nature of Life: Mechanism, Vitalism and Hylomorphism. mechanism supposes the effects of movement in all parts of living things to be caused through a linear succession of externally related transitive movements in the manner of the winding cogs in a clock. Vitalism supposes that all of the parts of living things are moved by some external 'vital force' just as a gale of wind propels a sand storm. Hylomorphism contends, contrary to both, that the substance of a living organism, by its very nature, synchronously moves all of its parts in a reciprocating cycle according to their various relations to the whole. Mechanism and Vitalism, hence, both suppose the cause of movement in Life to be extrinsic to the part that it effects, while Hylomorphism supposes the cause to be intrinsic to the relations of the parts and the whole. The distinctive feature of Hylomorphism is, thus, the recursive and cyclical movement of cause and effect between the parts and the whole of the living organism. 

'Hylomorphism' is a Greek term used by Aristotle to describe substance as the composite of form and matter. Form and matter are each abstract concepts related to one another as ethereal order is to the ground of being: each is an abstract concept as it is conceived, not as it exists in the world, but only as it may be thought of in our minds prior to any existing thing. Essence and existence are similar to form and matter, according to their mutual relations, and yet they differ according to the aspects of concretely existing things. The being of matter and form differ from the being of existence and essence as abstract being is to concrete being. The term 'substance' will be used to describe a individuation of concrete being which unites within itself the posterior concreta of existence and essence with the prior abstracta of matter and form. Form and matter are abstract concepts for-us prior to the existence of a thing, while essence and existence are concrete concepts of the thing as it is in-itself. Thus, form and matter are conceived of a priori, while essence and existence are conceived of a posteriori. Essence is the opposite of existence, just as form is the opposite of matter; while form and matter are the existential privation and subaltern negation of essence and existence. The mutual negative oppositions of existence, essence, form, and matter admit of the possibility of representing their four-fold relation from the standpoint of each corner of a square of logical opposition: 

From the standpoint of existence (Figure 1): all existence grounds existence (All S is P); no essence exists without existence (No S is P); some matter is abstracted from existence (some S is P); some form is not abstracted from existence (Some S is not P).

From the standpoint of essence (Figure 2): all essence orders existence (All S is P); no existence orders existence without essence (No S is P); some form is abstracted from the order of existence (some S is P); some matter is not abstracted from the order of existence (Some S is not P).

From the standpoint of matter (Figure 3): all matter is prior to and grounds existence (All S is P); no form orders existence without matter (No S is P); some existence is concretized from the matter of existence (some S is P); some essence is not abstracted from the matter of existence (Some S is not P).

Finally, from the standpoint of form (Figure 4): all form is prior to and orders existence (All S is P); no matter grounds existence without form (No S is P); some essence is concretized from formal order of existence (some S is P); some existence is not abstracted from the formal order of existence (Some S is not P).

The abstract a priori concepts of form and matter are implicitly and potentially what the concrete a posteriori concepts of essence and existence are explicitly and actually.  The a priori concepts of form and matter are prior to all intuition of existence and thus prior to the a posteriori concepts of essence and existence in the way of knowing, via cognoscendi; while the a posteriori concepts of essence and existence are posterior to all intuition of existence and thus prior to the a priori concepts of form and matter in the existing the way of being, via existentiae: the abstract apriori concepts are first known for-us as the potentiality of being, while the concrete a posteriori concepts are first in existence as actuality of thing-in-themselves. These two ways of approaching this four-fold distinction offer distinct avenues of examining the essence of life: according to (I) the  abstract and a priori way of knowing, or according to (II) the concrete and a posteriori way of existence.

Beginning a demonstration under the intention of avoiding dogmatic presuppositions is a nigh-impossible task, for the idea of a presuppositionless science must, in its infinite self-determination, possess neither a determinate beginning nor end; yet written propositions follow a linear and determinate sequence that altogether implies that the latter propositions depend for their soundness and validity upon the former propositions. As Hegel describes in the introduction to the Encyclopedia of Philosophical Sciences, a demonstration for human understanding must render the infinitude of the concept in a finite sequence of propositions so as to burst open the self-resolving gateway of science:

"We can assume nothing and assert nothing dogmatically; nor can we accept the assertions and assumptions of others. And yet we must make a beginning: and a beginning, as primary and underived, makes an assumption, or rather is an assumption. It seems as if it were impossible to make a beginning at all... In this manner philosophy exhibits the appearance of a circle which closes with itself, and has no beginning in the same way as the other sciences have. To speak of a beginning of philosophy has a meaning only in relation to a person who proposes to commence the study, and not in relation to the science as science." (§1/17)

The purpose of a demonstration is, in the unfolding of a sequence of propositions, to arrive at the final moment of thought wherein the potentiality of the abstract concept comes to be known for-us in the complete identity of its concrete actuality. Hence, demonstration proceeds according to the way of knowing as a sequence of conceptual moments, from the universal to the individual, and from the most general and abstract concept to its concrete specification. This treatise on the origin and nature of Life will bracket, from itself, the fundamental questions of first philosophy and presume a broadly Aristotelian metaphysic of the four-fold opposition of abstract form and matter to concrete essence and existence; of the implicit potentiality of abstract concepts for-us to the explicit actuality of the concrete existing things-in-themselves, to demonstrate the essence of Life in existence as these concepts unfold according to their corresponding logical relations. The method of the demonstration is intended to be neither a linear sequence of the formal entailment of fixed propositions, nor the dialectical circle of speculative propositions that unfold according to the emergence of their intrinsic contradictions, but rather a middle-way between the line of didactic entailment and the circle of dialectical emergence: the demonstration will analogically approach the dialectical circle of coincident concepts, in which the former becomes explicit in the latter as the latter is implicitly presupposed by the former, even while maintaining the possibility of a subsequent formal demonstration as a linear sequence of propositions in which the conclusion is validly entailed by the premises. In short, the demonstration will presuppose Aristotelian metaphysics, proceed in a quasi-dialectical sequence of coincident conceptual moments, and culminate in an idea of the essence of Life that may be manifested as an argument of formal logic. The demonstration of the essence of Life will thus proceed from (I) the  abstract and a priori way of knowing to (II) the concrete and a posteriori way of existence; from the pure forms of (I.A.) particularization, (I.B) motion, and (I.C) teleology; to their hylomorphic instantiation in the concrete specification of (II.A) reproduction, (II.B) conception and (II.C) the self-identity of essence, in the living organism. The presentation of (I) the abstract nature of Life will thus consist in the three conceptual moments of (I.A) the particular substance, (I.B) motion as a succession of the presence and absence of being, and (I.C) the teleological purpose of parts to the whole.   

A. The Particularization of Self-Enclosed Substance
The Pre-Socratic philosopher Anaximenes, the later Stoics, and Spinoza held the doctrine of Hylozoism in which the entire universe is a living substance. Aristotle proposed the doctrine of Abiogenesis in which life is, on the contrary, generated from non-living substances. Hylozoism attributes life to all existence, while Abiogensesis distinguishes some existence as living and others as non-living. The principle problem of Abiogenesis is that of accounting for the origin of living substances from non-living existence. Just as being may not be generated from non-being, so may life not be generated from what is not life. The division of some finite living substance from the whole of non-living existence is the particularization of the universal. The concept of particularity is produced from the negation of being which is of non-being: non-being determines a limit to being, in which non-being circumscribes and demarcates being-in-itself from being-in-another. The concepts of particularity and limitedness are required for the reciprocating movement of the organism, to conserve the organism's dynamic inertia as it moves itself within the its own self-limiting domain. For example, an asteroid is a limited and self-enclosed substance that, in its separate particularity, may move with relative indifference
among its material surroundings.  

B. Motion as the Succession of Absence and Presence of Being
A living thing is that which moves itself: rather than needing movement to be imparted upon it from without to subsequently move according to the propensity of this force, the living thing imparts motion to itself by its own native power of motion. An organism is defined as a living thing whose reciprocating operations causes the effect of its own self-movement, in which some parts move other parts in a continuous cyclical interplay of self-mediated motion. In a self-moving organism, the operation of movement remains immanent within the (I.A) limits of the organism, and, in most cases, does not escape from the organism. Finally, all particular organisms must first have motion imparted to it from without, for nothing that is limited may be either absolutely self-subsistent or self-moving. For example, the Sun is a self-moving substance because it moves the parts of its corona as a result of the heat generated by nuclear fusion in its core. Yet even the Sun is not the first movement of movement, for its very matter was collected from surrounding gaseous nebula and compacted into a singular sphere through the attractive forces of universal gravitation. Hence no merely finite substance may be absolutely self-moving, for each has movement first imparted to it from without.

In the Phaedrus, blessed Plato introduces the doctrine of an organism as self-moving as the notion that living things, possessing souls, are to be defined by their self-motion:

"since that which is moved by itself has been seen to be immortal, one who says that this self-motion is the essence and the very idea of the soul, will not be disgraced. For every body which derives motion from without is soulless, but that which has its motion within itself has a soul, since that is the nature of the soul." (Phaedrus, 245e)

 In the Sophist, Plato further defines motion as the succession of presence and absence of being and non-being, in which non-being is ontologically derivative from being:

"Then we must admit that motion is the same and is not the same, and we must not be disturbed thereby; for when we say it is the same and not the same, we do not use the words in the same sense. When we call it the same, we do so because it partakes of the same in relation to itself, and when we call it not the same, we do so on account of its participation in the other, by which it is separated from the same and becomes not that but other, so that it is correctly spoken of in turn as not the same." (Sophist, 256a-b)

Erudite Aristotle defines substance as a composite of form and matter. In the Physics, Aristotle defines life as self-movement of a thing in which one part moves another in a succession of moments of the absence and presence of being. This movement imparted from without, via some exterior source of motion (e.g. the Sun, hydrothermal vents, gestation etc.), nonetheless persists within (I.A) the self-enclosed limits of the substance as an immanent motion. Aristotle writes:

"[H]ow can anything of continuous and naturally connected substance move itself? In so far as a thing is one and continuous not merely in virtue of contact, it is impassive: it is only in so far as a thing is divided that one part of it is by nature active and another passive... If, then, it is moved in virtue of some part of it being moved by that part itself, it is this part that will be the primary self-movement, since, if this part is separated from the whole, the part will still move itself, but the whole will do so no longer." (Physics VIII)

Aristotle termed the principle of self-movement in the organism the essence; the formal aspect of substance or substantial form; which produces motion as it is united with substance in the concrete organism. The substantial form is, not as might be thought, any additional substance or 'vital principle' that is added to the sum of the organism's matter. Rather it is the totality of all of the formal relations of all parts to the whole and the whole to all parts within the self-moving organism. Essence may thus be said to be the total 'whatness', qualitas, or quality of a thing that makes a thing what it necessarily is in-itself. 

C. Speculative Conception of the Potentially Infinite Motion of Teleology
This doctrine of organism as self-movement persisted unmolested in Western science until sublime Immanuel Kant issued his critique of any possible knowledge of organic substances. Kant adopted a modified Leibnizian account of Aristotle's doctrine of essence, in which  the essence of life was described as the principle of self-organization through which a substance imparted self-movement to itself according to its own intrinsic form of finality, final purpose, or telos. Kant distinguished mechanisms from organisms according to their possession of extrinsic and intrinsic purposes: mechanisms were artificially constructed and thus given a purpose by their artificer, while organisms were generated from within each other and thus possesses their purposes intrinsically within themselves. Kant writes in the Critique of Judgment: 

"In a thing that we must judge as a natural purpose (an organized being), we can no doubt try all the known and yet to be discovered laws of mechanical production, and even hope to make good progress therewith, but we can never get rid of the call for a quite different ground of production for the possibility of such a product, viz. causality by means of purposes. Absolutely no human reason, in fact no finite reason like ours in quality, however much it may surpass it in degree, can hope to understand the production of even a blade of grass by mere mechanical causes... there can never be a Newton for even a blade of grass." (§ 65)

However, Kant disagreed with Aristotle on whether this Principle of Self-Organization could ever be constitutive of natural science because Kant, following David Hume's phenomenalism, held that the reality of a thing, the thing-in-itself, was ultimately unknowable. Due to his Humean skepticism of the intelligibility of real things, or particular substances, Kant critiqued the Aristotelian doctrine of substantial form as a hypostatization of form and matter, in which the form of life that subsists in the living organism and the substance of the organism were, each singly and both together, mistakenly imagined to subsist as separate substances, as a thing-in-itself. Contrary to this hypostatization, Kant distinguished between the regulative principle of teleology; that may be postulated to guide scientific inquiry; and the constitutive principle of teleology; that, as a thing-in-itself, could not ever become an object of genuine knowledge. The regulative principle was merely postulated to explain any possible organism, while the constitutive principle was the equivalent of the substantial form, the essence, which Kant sought to banish beyond the outer-most walls of all possible cognition: the first could be known as nothing more than a postulate of reason, while the latter subsisted, if at all, beyond the intelligible phenomenal realm of space and time. 

If the Kantian critique of the Aristotelian hypostatization of teleology, as the substantial form in organism, is correct, then there is no place for the concepts of (I.A) substance, (I.B) organism, and (I.C) essence and teleology in the natural sciences, and nothing can be known about the origin and nature of life. This negative moment in the intellectual history of the concept of Life is important because it continues to inform the practice of the positive biological sciences: Kant's Humean skepticism both produced and gives credence to theories in which the essence and teleology of Life is reductively conceived as a Cartesian Mechanism; and thus reducible to its material parts; or as merely a set of semantic terms which can a most describe a theoretical postulate. Whether it comes in the guise of 'teleonomy', 'teleomentalism' or 'adaptive function', the positive sciences have ran and hidden from any constitutive account of essence and teleology, as the organism really is in-itself, so as to evade all questions, concerns and responsibility for first philosophy. The post-kantian successors of Immanuel Kant were, however, neither so narrow-minded nor so shallow-spirited. The Philosophy of Nature has long-since repudiated Kant's Humean critique of the Aristotelian doctrine of organism and teleology, by grounding the original identity (whether in Fichte's self-positing Ego or in Schelling's Absolute) of reality and ideality, the thing-for-us and the thing-in-itself. The following will demonstrate the possibility of knowing the essence and teleology of living organisms. 

a. Apparent Causal Loops of Teleology
The concept, of the purposeful directedness, or telos, of all parts according to a superintending substantial form, or essence, is the most difficult of all to educe because it appears to defy our common understanding of linear causality. As Kant described in the Critique of Teleological Judgment, according to the concept of teleology, the logic of telos, the conditions that are prior to and causing of the substance that is conditioned are themselves determined by events that are posterior. This inversion of the priority of cause  and the posteriority of effects contradicts our common understanding of the linear succession of causes to effects (e.g. if A then B, if B then C etc.) by proposing what appears to be a recursive causal loop in which posterior effects determine prior causes (e.g. if A then B, if B then A etc.). For example, Alaska Salmon will travel miles upriver to lay their eggs, even as they individually receive no tangible benefit and may even perish in the endeavor. The laying of eggs benefits the collective species of Salmon rather than the individual Salmon. Nonetheless the Salmon are apparently caused to undertake this arduous journey on behalf of the effect of perpetuating the species that is entirely posterior to the cause itself. This is the mystery of purposiveness, final causation, or teleology

The concept of teleology is that the whole organism acts as a cause to determine the operations of its parts. It is commonly thought that parts cause the effects of the whole. The parts causing the whole may be thought of as bottom-to-top or upward causation, while the whole causing the parts may be thought of as top-to-bottom of downward causation. Cartesian Mechanism affirms upward causation, from the material parts to the whole, while Vitalism affirms downward causation, from the vital principle of life to the parts. For Aristotelian Hylomorphism the concept of teleology includes both upward and downward causation: the parts cause the whole simultaneously as the whole cause the parts. 

The organism is self-caused because the upward and downward causation are simultaneous and synchronous in time: there is neither a linear temporal sequence of the prior cause of parts to the posterior effect of the whole, nor from whole to parts; but rather a synchrony of both the prior causes of parts to the posterior effect of the whole, and from the whole to the parts; such that upward causation conditions downward causation and downward causation conditions upward causation. Hence the linear sequences of upward and downward causation are for Aristotelian Hylomorphism held to be mutually conditioning; neither simply anteceding nor consequenting the other, but rather each are, at once, simultaneously the antecedent and the consequent; the cause and the effect; the condition and the conditioner of the other. Kant describes this in the Critique of Judgment:

"In such a product of nature, every part not only exists by means of the other parts, but is thought as existing for the sake of the others and the whole – that is, as an (organic) instrument... Only a product of such a kind can be called a natural purpose, and this because it is an organized and self-organizing being." (§ 65)

This synchrony of cause and effect, in which each linear sequences of causes mutually conditions the other, appears to contradict any conception of a linear sequence of cause and effect in time: for, when the procession of time is conceived in an irreversible course or prior causes and posterior effects, there can never be a posterior effect that causes its own cause and thus acts as a cause unto itself. For this reason, the simultaneous mutual conditioning of upward and downward causation in Aristotelian Hylomorphism has the apparent unacceptable consequence of backward causality, or causal loops, in naked defiance of the linear procession of time. While a linear procession of discrete causes and effects has a finite quantity, causal loops presents the mind with an infinity of causes and effects that may never come to rest in any determinate quantity of causes or effects, which become one and the same in a continuous loop. The difficulty here is that we cannot comprehend, with any finite enumeration of causes, how - like a snake that consumes itself - any substance might affect its very own cause and thereby act as a cause unto itself. Such a comprehension of a teleological organism requires an infinite enumeration of the successive causes of parts in relation to the whole. Kant held that, because any such infinite enumeration of causal relations is beyond the powers of our finite discursive understanding, we could never come to know an infinite causal loop of teleology in an organism. For this reason, also, the concept of teleology, and by extension of essence also, could never be constitutive of human understanding, but must forever remain a mere postulate of theoretical reasoning: teleology may be postulated to explain an organism but teleology could never be certainly known to actually constitute an organism. What is impossible for the understanding is, however, possible for the imagination. 

Anaximander described how the infinite (apeiron ἄπειρον) is prior to and immanent in all things. The Pythagoreans similarly affirmed that the infinite was, like all numerical and geometric forms, apprehended directly by the intellect. Plato and Aristotle distinguished between two kinds of infinity: potential and actual. In the Physics Aristotle denied that we may know actual infinities but affirmed that we may know potential infinities:

For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always different... Our account does not rob the mathematicians of their science, by disproving the actual existence of the infinite in the direction of increase, in the sense of the untransversable. In point of fact they do not need the infinite and do not use it. They postulate only that the finite straight line may be produced as far as they wish." (Physics III)

An actual infinity may be understood as a set S of some thing P with no end, or limit, to either the number of its members or the multitude of its instances (i.e. S = { ∞P}). A potential infinity, however, merely requires some set S to possess a finite number of P members, to which there is afterwards ceaselessly added new members at regular intervals (e.g. S = {P1, P2, P3}, |S|+ Pn, if S then n+1). Potential infinity is called 'potential' because the quantity of its members may progress onward to ever greater sums, while always remaining a finite set. A set that thus remains finite and only potentially infinite, may never become a true and actual infinity. 

 The distinction between potential and actual infinity corresponds to the Kantian duality of the phenomenal thing-for-us and the noumenal thing-in-itself because, while the extension of space and the duration of time may, without contradiction, be infinitely divisible for noumenal things-in-themselves, our apperceptive cognition is limited to intuitions of phenomenal things-for-us which may only ever be composed of finite sets that are potentially infinite. To know the infinite is, for Kant, to know the nounemal thing-in-itself, whether of God, being or numbers. On this account, the Kantian limitation of cognition to potential infinities is nothing less than a denial of the possibility of knowing reality as it is in-itself. The consequences of an absolute bifurcation of enumerated reality, whether as the Kantian duality of phenomenal and noumenal realms or the Aristotelian distinction between potential and actual infinity, is thus an inescapable anti-realism, subjective idealism, and self-destructive solipsism.

 "words are signs of ideas, and ideas the similitude of things, it is evident that words relate to the meaning of things signified through the medium of the intellectual conception. It follows therefore that we can give a name to anything in as far as we can understand it. Now it was shown above (12, 11, 12) that in this life we cannot see the essence of God; but we know God from creatures as their principle, and also by way of excellence and remotion. In this way therefore He can be named by us [analogically] from creatures, yet not so that the name which signifies Him expresses the divine essence in itself [i.e. univocally]." (ST Q13, A1)

c. Principle of Analogy and Doctrine of Double-Negation
The problem of solipsism, or subjective idealism, in the dualisms of Kant was recognized and resolved by the post-Kantian Philosophy of Nature. The question of infinity later arose in Patristic and Scholastic Theology concerning divine names, or the possibility of predicating any finite term of the infinite being of God: negative or apophatic theologians such as Dionysius of Areapagite and Maimonides contended that all predication of God must be equivocal; which is to be predicated in one sense for finite creatures and in another sense for the infinite being of God; while the positive or cataphatic theologians such as seraphic Saint Bonaventure and subtle Duns Scotus contended that predication of God may be univocal; which is to predicate in one sense for all being. Equivocal predication absolutely bifurcated what may be spoken and judged of the real between the finite terrestrial realm of man and the infinite heavenly being of God, while univocal predication flattened the distinction between God and man into a single uniform existence with the consequent dilemma: if for negative theology nothing could be predicated or judged of God, then God could not be known; while if for positive theology God could be predicated and judged just as finite creatures are known, then God may be exhaustively known as an object of thought so as to eliminate all divine transcendence, mystery and infinitely surpassing excellence. The equivocal bifurcation of the finite terrestrial realm of man from the infinite heavenly being of God anticipated not only the Kantian bifurcation between the phenomenal realm of things-for-us and the noumenal realm of thing-in-themselves, but also the Vitalist notion of a super-sensual vital force that pervades uniform matter; while the univocal flattening of all distinctions between God and man into a uniform being anticipated not only the homogeneity of matter in Scientific Materialist, but also the transitivity of motion through linear causal series in Cartesian Mechanism. 

The solution provided by the angelic Saint Thomas Aquinas was to propose a Doctrine of Analogy as a middle-way to mediate between the dualisms of matter and form, finite and infinite, univocity and equivocity, and negative and positive theology. The Doctrine of Analogy holds that God may be predicated indirectly rather than directly through a negation of the mode of predication in the very act of predication: (α) the universal predicate of a creaturely thing is abstracted from an individual creaturely thing; then (β) the abstract universal is negated in the mode of its finite creaturely individuality; so that (γ) it may be predicated of God. The (α) finitude of the predicate is (β) negated and made infinite, so that it may be (γ) predicated of the infinite being of God. Thomas Aquinas writes in the Summa Theologiae:

 "words are signs of ideas, and ideas the similitude of things, it is evident that words relate to the meaning of things signified through the medium of the intellectual conception. It follows therefore that we can give a name to anything in as far as we can understand it. Now it was shown above (12, 11, 12) that in this life we cannot see the essence of God; but we know God from creatures as their principle, and also by way of excellence and remotion. In this way therefore He can be named by us [analogically] from creatures, yet not so that the name which signifies Him expresses the divine essence in itself [i.e. univocally]." (ST Q13, A1)
A similar operation of analogous predication may be applied, in the activity of thought, to the potentially infinite apparent causal loops of teleology, for whether terms are predicated of God or organisms, judgment must escape from the finitude of the understanding. The encyclopedic philosopher G.W.F. Hegel applied the homologous Principle of Double Negation to the dialectic of all concepts. Hegel's Principle of Double Negation is neither an argument nor a method, but rather a principle to regulate reasoning that is abstracted from the triadic logical relations intrinsic within Hegel's philosophical science: it cannot be completely formalized without negating its immanent relation within the philosophical science, but may nonetheless be exemplified in formal logic. The Principle of Double Negation may, for example, be described to hold that an (α) intuited concept becomes (β) qualitatively and not merely quantitatively different when some part of itself negates another part of itself (¬ Pα); after which this concept that has itself been negated (β) has some further part of itself negated (¬ ) by itself; and finally both the concept before (α) and the concept after (β) the negation are, each having some of part of themselves negated ((α & ¬ Pα) & (β & ¬ Pβ)), (γ) re-combined to produce a new synthetic concept (e.g. where Pα is a part of α, and Pβ is a part of β: α , if α then ¬ Pα , if α & ¬ Pα then β, if β then ¬ Pβ, if ((α & ¬ Pα) & (β & ¬ Pβ)) then γ, γ). Aquinas's Doctrine of Analogy can thus be understood as a instance of the Principle of Double Negation, in which this Principle of Double Negation is applied to judgments about God. Hegel's expresses as much in the first paragraph of the Encyclopedia of Philosophical Sciences when he writes: "The objects of philosophy are the same as those of religion: the object is Truth, in that supreme sense in which God and God only is the Truth." When the Principle of Double Negation is applied to question of predication, the (α) initial mode of finite creaturely predication is (β) negated by the concept of infinity (i.e. of non-finite), so that the predicate may (γ) then be applied in an infinite mode, e.g. to the infinities of God, reality and number. The philosophy of Hegel systematically employs Principle of Double Negation to negatively deconstruct and synthetically reconstruct organic and teleologically-oriented concepts that are constituted by potentially infinite being.  

Reasoning from analogy according to the Principle of Double Negation allows the mind to indirectly know actual infinities through the knowledge of a progressing series of potential infinities; a potentially infinite series of potential infinites; in which the potentiality of each is itself negated so as to be reunited in the infinite synthetic concept. As potentiality is the privation or negation of actuality, so the potential infinitude of potential infinities is nothing other than the negation of negation, the double negation of the potentially infinite concept. In the Science of Logic Hegel argues that this dialectical procession, via the Principle of Double-Negation, allows the mind to adequately - albeit indirectly - know the infinitude of the Absolute Idea, the ultimate synthesis of all potentially infinite concepts, that approaches the absolute knowing and transparent omniscience of God. In his Jena lectures on the "Foundations of Transcendental Philosophy" J.G. Fichte described how Zeno's paradox presents an exemplary lesson in conceiving of infinities: Zeno of Elea proposed there to be an infinite number of discrete spatial and temporal moments in the procession of any movement, such that no movement could ever reach its completion. According to Zeno's paradox, an infinite number of discrete moments, immanent in all movements, must presumably have the consequence that all movement must remain merely potential and never become actual. There is, however, no real difficulty in either perceiving or imagining a movement that contains within itself an infinity of moments. While we cannot understand each discrete moment of an infinite motion in its distinct duration, we must, to begin swimming, nonetheless dive into the water. Where the understanding stumbles bewildered and drowns in finite moments, the imagination and swims amongst infinite ideas. 

While infinite concepts may ostensibly defy our understanding of finite enumerated series, the Doctrine of Analogy and the Principle of Double Negation illustrate how infinite concepts may come to be known in a progressing series of potential infinities. According to Aristotelian Hylomorphism, organisms are self-moving substances in which the movement of parts to the whole is mutually conditioned and reciprocally caused by the teleological movement of the parts to the whole and the whole to the parts. This mutually inter-conditioning and reciprocal causation of parts and the whole (I.C.a) appears to result in a causal loop, of posterior effects to prior causes, in defiance of the finite discursive powers of the understanding. The infinitude of the apparent causal loop is, however, (I.C.b) negatively reconceived as either a potential infinities that may be known or as an actual infinities that may not. The (I.C.c) progressive knowledge of potential infinities, via the Doctrine of Analogy and the Principle of Double Negation, allows the mind to imagine the infinite causal looping of teleology. The 19th Century German mathematicians Bolzano and Cantor challenged the Aristotelian dictum against the possibility of knowing infinities - Infinitum actu non datur - with the creation of a mathematic of infinite sets, in which an infinite set could be infinitely greater than another infinite set so as to subsume the latter infinities within former infinity. Cantor identified the infinite that subsumes all infinities within itself with the absolute Infinitude of God. The mathematics of infinite sets is thus also a theology of potentially infinite concepts. Hegel's systematic employment of concepts of potential infinity thus anticipates Cantor's formal mathematics of infinite sets. This knowledge of the potentially infinite movement of substances progresses beyond all finitude to mediate between the Kantian dualisms, of the finite concept-for-us and the infinte thing-in-itself, to collapse both in the potentially infinite movement of speculative reason. There is thus no longer any persisting duality between the regulative and constitutive principles of teleology, for the progressing series of potentially infinite concepts constitutes knowledge of the infinite teleological movement of all organic substances, which is biological science. By postulating an original identity of thought and being, and by reasoning according to the Doctrine of Analogy and the Principle of Double Negation, Schelling and Hegel collapsed all of the Kantian dualisms; of the phenomenal thing-for-us and the noumenal thing-in-itself; to overcome Kantian solipsism and know the infinite concepts immanent in the realities of nature. The boundaries of finite understanding are broken open as the progressing knowledge of infinite concepts guides thought to a progressing knowledge of the infinite movement of organic substances, and the essence of Life. The pieces of living nature that the understanding had shattered may thus be resurrected in the idea of a Philosophy of Nature.

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