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The Inroad of the Irrational into Reality

The Boundary between Nature and Culture as a Locus of Freedom

Lecture held before the Junge Akademie of the Berlin-Brandenburgische Akademie der Wissenschaften

Anyone under the illusion that the world is not only caused biologically, so through matter alone, but also through a spirit; anyone, therefore, who asserts the duality of the world, is held to have a genetic defect – the claim that my mind is different from my body (which is obvious to me and to everyone, after all) supposedly stems, it is openly taught today, from a “genetic default option”.1
When biologists dress up an assertion, for which there is neither proof or probability, this is done in the interest of a theory and of its desired affirmation, but not in the interest of the truth. Epistemologically, doctrine relieved of proof is simply no longer scientific and indicates that a theory is being elevated to faith. Even worse, faith that is not based on facts and cannot be accessed by science – unlike Christianity – is not religion, but esotericism. It is religious to admit a lack of knowledge and to reveal it as faith. It is esoteric to offer ignorance as knowledge and matter-of-fact and to react indignantly to epistemological queries. Yet the evolutionists’ biometaphysical perspective, which gives biology the capability of terror, is not new. It provided the scientific justification for the mass murders of the Third Reich.7b
The alternative to biological fundamentalism, which shapes reality according to its notions and ultimately justifies the killing of people, is not a better knowledge, but the freedom to admit ignorance and open oneself to the obvious appearances of reality and to an ethos that forbids killing.

1. Are we sacrificing Enlightenment and freedom to evolutionism?

The dogmatic lengths to which Christian fundamentalism must go, in order to make God directly responsible for everything in His creation, are not all that different from the lengths to which popular monism must go, in order to turn the aspect theory of evolution into a universal concept of the human world. Evolutionism, according to an example by Hubert Markl,2 declares the “obvious awareness of freedom of will” to be a reduction of definition of conduct to improvement of competitiveness and, as a result, to be a freedom that is compelled to serve evolutionary success – a contradictio in re. A dogmatic faux pas, which surely would not have happened if Hubert Markl had studied theology and familiarised himself with theodicy, therefore with the contradiction that needs to be solved between the freedom of man and the omnipotence of his origins.
Evolution, of course, is not opposed by religion. A theory that explains the development of what already exists, but does not explain the origins, is not in competition with a doctrine that, according to today’s concept of the Church, does not explain the development, but the origins of what exists. The real competitor of evolution theory based on the eternal pro­gress of nature is dualism, which has as its object the permanence of principles and the freedom of man. It is only when evolution is elevated to the cause of existence and becomes evolutionism, that it comes into conflict with religion. However, this difference is currently thoroughly academic. In debate, evolution is almost always consonant with materialism, as though, with the evolution theory, matter were automatically defined as the (likely) cause of life. As a result, the freedom which man apparently possesses is, of course, also extinguished.
According to Immanuel Kant, man is faced with the choice of either following his nature and emerging from his tutelage, or not. In his manifesto, “What is Enlightenment” he conceded that many people did not make use of this privilege.3 Man’s freedom to decide for or against his nature is the metaphysical core of the Enlightenment.
By contrast, the justification of reality being 100 percent biological is a materialism unbound from all intellectual notions. Karl Marx declared that the history of the world was no other than “the development of nature for man.”4 Culture as the sum of human conduct, then, is reduced to nature. The theme of our conference, the nature/culture boundary, becomes a failed hypothesis in biological interpretation. Biological reductionism, escalating to a closed worldview, becomes as dogmatic, illiberal and anti-Enlightenment as Christianity is popularly accused of being. The result is maximum simplification. Hubert Markl: “Evolution explains the creative freedom of nature and culture simultaneously.”5
But please consider: we are sitting here today, in order to explore a question that describes nature, but which is meaningless for the enlightened person. The consequence of an error by Kant, that man was able to decide for himself, is that even our conference itself and our passionate will to understand and to know is ultimately reduced to competition over reproduction and care of our offspring. I doubt that anyone here seriously believes this.

2. Epistemologically unwanted

The contradiction that exists between the dominance of nature and Enlightenment/freedom is, however, epistemologically blocked during debate.
The Wikipedia article “Methodischer Kulturalismus” (“Methodical Culturalism”) gives a summary: The question of a reality independent of the subject” is rejected in current debate as metaphysical, because it “is not possible” for man to answer this question. Thus, allegedly we can either discuss a nature/culture boundary (which is meaningless for us because it dissolves in the biological world-view and does not fit with our enlightened perspective) or we can ask a question, which, according to Wikipedia, is “philosophy” and not natural science, as though philosophy appears to be something different to reality.
This is a positivistic absurdity, if one remembers that the non-answerability of a question is what all scientific hypotheses are based on. They are progressive because we have no answer! Because natural science is able to describe what is, and philosophy says what this means for us, a biologistic discrimination of philosophy is useful for simplification, but unproductive – and grotesque because we are operating with nature/culture as a pair of concepts that is not natural, but already philosophical interpretation and records aspects of reality, like nature and slavery, nature and mercy, among others.
As for every form of censure on thinking, there is also a good reason for the discrimination of philosophy. The mere concept and notion of the nature/culture boundary are metaphysically founded. We need only three logical steps: As culture is a human characteristic, the dichotomy of nature and culture is also the dichotomy of nature and man, the first principle of the Enlightenment! Secondly, in order to enable differentiation and boundary, culture must have something that cannot be nature.6 If, therefore, the dichotomy of nature and culture is also the dichotomy of nature and man, and culture must be at least partly something that cannot be nature – man, thirdly, must have something that is not nature, that must be extra-natural, which can be conceived as nothing other than supernatural.7a+b This tacit hypothesis of our conference theme recalls metaphysics as an alternative option to naturalism and is therefore without expectation, prejudice-free and productive.
Consequently the following paragraphs must concern the question of whether a possibly material monism creates the unity of the world, or whether the duality refers to the unity: which is represented in contrasting, antithetical pairs, which, like nature and culture, body and soul, mind and matter. They are so to speak fractal repetitions of the great Whole, whether the essence of these contrasts exists (“ex-sists”) in the persistence of duality, out of an immaterial principle. Freedom, Enlightenment and religion therefore stand and fall. Is man free or only an evolutionarily instructed reactive automaton? Is his face lit up by a spirit, or does it merely convey his hidden genotype to the world?7

3. Logic proves the unity of reality to be not monistic

Now, the notion of monism as sole cause cannot be investigated, because there is no dogmatically permissible place outside the monism, no place from which we can consider it. It is a different case with duality, which is formed of concepts whose relationship can be accessed by logic. As the basis of our thinking, concepts and logic are a common denominator underpinning all differences. They find themselves in a defined relationship to reality, which subjectively is always true, whatever the terms may mean for the individual. The concern of the following considerations, therefore, is the calculation itself, not the individual objects of the calculation.
Contrasting, antithetical pairs reflect the entirety of the world. They are inductively metaphysical and therefore interchangeable with other dualities. In order to find out how nature and culture interrelate, we can consequently turn a more abstract, formalised contrasting pair into the basis of a logical calculation and choose two maximally abstract categories that still reconstruct the inventory of the world: that which is “identical”, and that which is “different”.
It is an everyday experience that homologues that unite are denied unity, for in the unification they regress to being one, like the raindrop that falls into the sea – the first principle of the logic of forms, from which everything else is derived.8 Unity is possible only between heterologues. Their state of being different is not only not abolished by the unity. It reveals their real, unique character in the unity only, as in the unity of man or woman or as in the unity of body and soul. The antithetical nature of the different is, of course, naturally repellent to a unification. Therefore, the prerequisite of unity is also the uniformity of the heterologues: man and woman are according to their nature, their gender identity, irretrievably different, but are uniform in their essence as humans. Unlike the completely different, which is different by its nature and essence, like human and animal or fire and water, which are not predetermined to unity.
Uniformity, however, is also a logical problem. According to the first principle of the logic of forms nothing that is equal can form a unity. Also, performance of the unity cannot be a property of the heterologues as it would re-homogenise them in their function. A third element is necessary, which is the “entirely other” and which creates the unity. It necessarily pre-exists unity and is therefore a norm. Norm permits opposition and therefore freedom as well. Actually, unification is not an automatism, not a mechanical compulsion. Heterologues, like man and woman, can refuse unity. The unity of reality, which is experienced in the overcoming of opposites, is accordingly the natural origin of the freedom expressed by Immanuel Kant, over which every one of us, who is sitting here, can actually make a use of. That was conceded even by Hubert Markl who then, however, cancelled it again in biological fundamental principles.
As the logic of forms gives an account of nature, its statements apply to all antithetical pairs that presuppose the unity. Nature and culture are consequently, according to their appearance, contradicting and unmixed, but are according to their perceived essence uniform, therefore undivided and one. Now one could believe that this common essence is a confirmation, that nature is dominant (monistic). Logically, however, this is impossible, for if nature itself is part of the unity, it is not able, if we take the natural experiences in the logic of forms seriously, to effect this unity. Both heterologues can be discarded as the origin of the unity, for which the aforementioned third element is necessary. What, however, can we imagine this third element to be, which exists outside the unity of reality? Arithmetic provides clues to this.
The homogeneous is of course that which can be added and subtracted, it is therefore matter. Addition and subtraction symbolise increase and decrease. The sum of all natural numbers which can be obtained through addition is infinitely large. Equally large, namely infinite, is the sum of all natural numbers which can be obtained if one merely reverses the calculation, therefore through subtraction.
The antithesis to matter, the immaterial, therefore the spirit, is, for lack of physicality, known to be incapable of being added or subtracted. Its essence is dissemination, which in algebra is represented by multiplication. Multiplication’s reversal, division, shows something surprising: The sum of all natural numbers which can be obtained through multiplication and is infinite is exceeded by the results of division. If we reverse the calculation a second set of numbers arises, in addition to the set of natural numbers which is infinite. This set of broken non-periodical numbers,9 which is also infinite, shows therefore, set-theoretically speaking, something expansive, surplus, without an equivalent in the positive calculation. The broken numbers are described as non-rational (“irrational”) numbers for a good reason, not because they behave unreasonably, but because, as they take their place outside the relationships of whole, natural numbers, they transgress the relationships, are super-rational – the inroad of the irrational into reality. Anyone who takes this to be simple play of numbers should consider that the chemical elements, music and other reference systems are based on relationships in whole numbers.
The result thus far is that we do not yet know what the third element is that creates the unity, but we have come a step further. Reality, which is physically uniform, cannot itself be the monistic origin, as opposites persist in it. The notion of a biological or materialist monism, for example of a self-initiating evolution, is therefore not supported by the logic of natural forms.

4. The generative cause of dual unity

If this seems speculative to anyone, the following should be remembered. The terms and categories record reality, which we logically delimit from one another and which are reflected in arithmetic. They are precisely not speculative, unlike all new natural science hypotheses – which first have to be confirmed in experiments.
Intellectually one can doubt everything, the incorporation of mathematics into logic, the symmetry between reality and its comprehension in concepts, the link between language and the world etc. Doubt itself is metaphysical and boundless. It is opposed, however, by epistemic intuition, which obtains its rank from the fact that epistemology is grounded in the sensual perception. It is a spontaneous knowledge that something is at least improbable or that something is possible after all.10 Thus the unbiased observer, critically examining the elevation of evolution theory to a global formula, has barely no reasonable objection to raise against the theory itself as aspect explanation. It is obvious that the theory of evolution, even if its principles are partly hard to examine, is probable and true.
Epistemic intuition provides guidance from a position of superiority and non-intentionality. In the fortunate case analysis leads to a result which is deduced and not identical with the analysis itself – whereas pure perception is the result itself, without analytical preconditions, a question and an intellectual technique.
In contrast to biological analysis, the findings of which must be preceded by a question or hypothesis, the thing itself precedes perception and intellectual permeation. However, analytical calculation cannot itself do without mythical presuppositions (e.g. the existence of “the rationality” as the exercise of reason); conversely, even thinking in synthesis is meant to be logical. Even the two paths of knowledge are therefore co-ordinated to one another in antithesis, another duality which, without the unity of reality, cannot be imagined.11 Duality arising out of co-ordination is, after all, also the object of a natural science, of psychosomatics, which permits analytical conclusions to be drawn from the body/soul co-ordination without obliging the underlying assumption itself to be subject to analysis, to proof.12 The interplay of synthesis and analysis is obviously closer to the world’s state of intransparency than an analysis which, epistemologically speaking, cannot even justify itself.
However, for reasons of acceptance I limit myself here to analysis, which in arithmetic has identified the third element in question, the generative cause of unity, as being “the irrational”. The next apparent question is: Can the result of a calculation be something that is not already – at least functionally – contained in the calculation itself? Let us apply, therefore, the rules of the logic of forms to logic itself, to the tool without which no scientific and no philosophical understanding of reality is possible.
The opposite of logic is not illogic. The two are mutually exclusive and as a result are not predetermined to unity. The heterologue of logic is the paradox. An example from physics: The standard model of elementary particle physics is definitely true, as the universal theory of relativity is also definitely true (formal uniformity). The two cannot be brought into concord, they conflict with each other, and that is not illogical, but paradoxical, or one can say: super-logical. The functional difference between illogicality and super-logicality lies in the fact that the illogical can be determined as definitively impossible; the super-logical, paradoxes, on the other hand is (depending on states of knowledge) not logical, but is however possible. Paradoxes are therefore part of our world and only appear in their character in the unity with logic. Consequently the third element, which creates the unity of logic and paradox, can be neither logical nor paradoxical. What remains when we deduct everything from the world that is logical or paradoxical? The irrational.
Logic, the tool of our reasoning, points, when we apply it to itself, to something else and calls it a cause. Following the first rule of the logic of forms this cause cannot be logical or paradox. It manifests itself in arithmetic when the technique of dissemination is mechanically reversed. Reversal points towards the origin. At the same time the irrational appears, astonishingly, out of mere traction of the existing, that which relieves itself of our calculating logic, which is therefore greatly un-logical, that which transgresses relationships, that which religion reports in ancient pictures.13
Let us look back at what was said at the start: Evolution is not opposed by religion, but by the perception that reality is naturally dual. Heterologues are uniform and this rules out the self-inducement of duality because nature is characterised by the principle that something homologous cannot produce anything. Why the dualities, which testify to the contingent order of the world and are also epistemologically relevant, should revert to matter, is not discernible. On the contrary, they point to a third element and, ultimately, to something entirely different, something meta-physical.
The notion of a boundary between the heterologues within a unity appears not to be essential for epistemological understanding. Unity does not limit them, but supports the development of their essential character. Nature and culture, too, as a duality which presupposes the unity of the world, find themselves in a logical relationship. They are antithetical and, because even nature in duality is subject to human perception, uniform. This means that nature as an efficient cause, the dominance of nature, is logically not possible.
Indeed, logic itself, without which we are obliged to stop talking, is part of a duality and thus a model for understanding the world. It explains the generative cause of duality as the irrational, reflected in the freedom bestowed upon man. The irrational is the source that keeps the heterologues in hovering, steady co-ordination, the duality, that overcomes them as it strives towards unity. In the duality of mind and matter, the mind is granted its character of freedom and this enables us to take actions which biology and evolutionism are unable to explain; this even enables us unfortunately, as Kant said, to decide, when we want, against nature.


1. So says the Gießen-based biophilosopher Eckart Voland in his preceding lecture.

2 Hubert Markl: Natur und Kultur: Durch Evolution vereint!, in: Theorie, Formen und Konsequenzen eines Paradigmas in Natur, Technik und Kultur. Ed. Volker Gerhardt et al. Berlin 2011, pp.49-56

3 „Laziness and cowardice are the reasons why so great a portion of mankind, after nature has long since discharged them from external direction (naturaliter maiorennes), nevertheless remains under lifelong tutelage, and why it is so easy for others to set themselves up as their guardians. It is so easy not to be of age. Immanuel Kant: Beantwortung der Frage: Was ist Aufklärung?, in: Berlinische Monatsschrift 1783, Dez., p. 35 (Translator: Paul Halsall,

4 MEW 40,546

5 Cf., p. 54

6 The contrary is likewise obvious.

7a The state of life without the spiritual dimension is characterised by Thomas Mann in “Der Zauberberg” [„The Magic Mountain”]: “What then was life? It was warmth, the warmth generated by a form-preserving instability, a fever of matter, which accompanied the process of ceaseless decay and repair of albumen molecules that were too impossibly complicated, too impossibly ingenious in structure. It was the existence of the actually impossible-to-exist, of a half-sweet, half-painful balancing, in this restricted and feverish process of decay and renewal, upon the point of existence. It was not matter and it was not spirit, but something between the two, a phenomenon conveyed by matter, like the rainbow on the waterfall, and like the flame. Yet why not material – it was sentient to the point of desire and disgust, the shamelessness of matter become sensible of itself, the incontinent form of being. It was a secret and ardent stirring in the frozen chastity of the universal; it was a stolen and voluptuous impurity of sucking and secreting; an exhalation of carbonic acid gas and material impurities of mysterious origin and composition. It was a pullulation, an unfolding, a form-building (made possible by the overbalancing of its instability, yet controlled by the laws of growth inherent within it), of something brewed out of water, albumen, salt and fats, which was called flesh, and which became form, beauty, a lofty image, and yet all the time the essence of sensuality and desire. For this form and beauty were not spirit-borne; nor, like the form and beauty of sculpture, conveyed by a neutral and spirit-consumed substance, which could in all purity make beauty perceptible to the senses. Rather was it conveyed and shaped by the somehow awakened voluptuousness of matter, of the organic, dying-living substance itself, the reeking flesh.” (Translator H.-T. Lowe-Porter,

7b Where modern rational materialism, secularism and the substitution of ethos by the principles of evolution can lead was demonstrated during the Third Reich, Markus von Hänsel-Hohenhausen: Hitler und die Aufklärung. Der philosophische Ort des Dritten Reiches. Beitrag zur Theorie der modernen Despotien und zum Mythos der politischen Religion. Frankfurt a.M. 2013 [Hitler and the Enlightenment. The Third Reich in the History of Philosophy. A Contribution to the Theory of modern Despotism and to the Myth of the Nationalsocialism being a ‘political Religion’. Frankfurt a.M. 2013]

8 Cf. my book: Die Einheit der Wirklichkeit in logischer und mathematischer Formalisierung. [The Unity of Reality in its logical and mathematical Formalisation.] Frankfurt a.M. 2013

9 Numbers whose decimal places are not interrupted and not periodical; the so-called circular number is prominent. 3,14159...

10 The logical incorporation of mathematics is assumed to be a given on account of the high degree of congruency between mathematics and logic. We may also leave aside the big debate whether concepts lay hold of things in themselves or are only our way of seizing something eternally remaining unknown that we developed through evolution. Concepts are, in short, the only representation, and in this sense – for our perception – the objectively appropriate representation, of world-encompassing experience – and hence the common denominator of our discourse.

11 This observation is the object of my epistemological scrutiny: Ich denke, also glaube ich. Cogito ergo credo. Von Metaphysik und Glaubenswissen als Fundament und Gunst von Naturwissenschaft und westlicher Gesellschaft. Mit einem Vorwort von Joachim Kardinal Meisner. Bilingual edition: I think, therefore I believe. Cogito ergo credo. Metaphysics and religious Knowledge as a Fundament and beneficial Force within Natural Science and Western Society. With a Foreword by Joachim Kardinal Meisner. Frankfurt a.M., Munich, London, New York 2008, published as an American edition under the title: The True Countenance of Man. Science and Belief as Coordinate Magisteria (COMA). A Theory of Knowledge, 2012.

12 Logically regulated metaphysics is also the fundament of the Enlightenment, which proclaimed belief in “nature”, in “reason” and in the felicity of man as the basis of an all-analysing intellect. Even though the Enlightenment disavowed the myths, it cannot manage without myths.

13 At the same time the presence of the metaphysical, respectively of the absent, which is generated by two, is a phenomenon that can be observed in many locations. In linguistics, for example, the epistemological potency of language, which can be explained through language and thus refers to something other; in set theory the set that is to contain itself and demonstrates the problematic of self-inducement. The crossover of presence and representation as an alternative form of iteration also exists as an image theory concept, for example in the portrait “Las Meninas” by Velázquez. In music it is perhaps the hemiola, which surpasses itself to a third element without an increase of temporal substance; at the church service it is the bread, whose substance (significance) transforms.'