Nothing: the concept of absence in philosophy, science, and mathematics

The various aspects of the meaning of nothing have not always been clearly distinguished in philosophy. Therefore, the question of whether or not "nothing" can be thought - and if so, how - has been pursued in very different ways in the history of philosophy. This question can be dealt with in various philosophical disciplines; "nothing" can be treated as a topic of metaphysics and ontology (e.g. in Plato, in the commemoration of creatio ex nihilo, or in Hegel's metaphysics of the absolute), but "nothing" can also be described philosophically as an existential experience (e.g. in Martin Heidegger or Jean-Paul Sartre), or the traces of "nothing" can be analyzed as phenomena in the philosophy of language and logic, such as negation or falsity. Occasionally, nothingness itself is negated in the process; for example, the impossibility of nothingness in nature is a tenet of Aristotle's natural philosophy (horror vacui).

Presocratics

The question of nothingness has preoccupied Western philosophy since its very pre-Socratic beginning. The Greek philosopher Parmenides of Elea treats the subject in the only fragment of his that has survived, his doctrinal poem On Nature:

From these lines we can infer the instruction not to concern oneself with the non-being and instead to give all attention to the being alone. For it is impossible to speak about the non-being, since at the same moment as one says something about it, one presupposes its being again. Moreover, being and thinking are equivalent: accordingly, one cannot think about the nothing. In this way, a definition of the task of science emerges: worthwhile research can have anything as its subject, except nothingness. The saying of Parmenides of Elea is considered the first formulation of abstract metaphysical reflection in ancient Greece and serves as a starting point for Plato's dialogue Sophistes.

Plato

Plato relativizes Parmenides' position of absolute nothingness. In the dialogue Sophistes he defines the nothing as the not-being and this finally in a longer chain of argumentation as diversity. In the process, five highest categories/ideas are developed, which are irreducible and in which all other ideas participate. It is through participation in these five ideas that everything else first becomes what it is without being identical to the five ideas. The five ideas are being, rest and motion, identity and difference. Each of these ideas is identical with itself and participates in the other ideas. Through diversity the possibility of non-being is opened up. The idea of rest is identical with itself, but different from the other four ideas. It participates, for example, in the idea of being, but it is not the idea of being. The idea of difference, then, opens up the possibility of non-being.

Late Antiquity and Middle Ages

In early Christian philosophy, the problem arises in the discussion of divine creation: according to Augustine, it can only have occurred ex nihilo, out of nothing, for anything else would not be a creation but merely a transformation. Tertullian differentiates two ways of speaking a nihilo, 'from nothing', without a cause of its own, and ex nihilo: nothingness as substance; this, according to Tertullian, leads to gnosis. Nicolaus of Cusa understands nothingness as alteritas, the 'otherness', which is specifically created for a possible being.

nihil privativum

In the early modern period, different aspects of nothingness were distinguished. Under the concept of nihil privativum, the nothing is defined, for example, as a specific absence of something or as a lack. This is a logical opposition that assigns a lesser ontological status to the negated: Darkness is only the absence of light, evil only the absence of good, and so on. This idea, which originated in Platonism, also plays a role in theodicy.

Rationalism: Theorem of the reason

In rationalism, both Leibniz and Wolff have determined the principle already formulated by Cicero "Nothing happens without a cause" (lat. nihil sine causa fit, De divinatione 2,61) in the theorem of the sufficient cause as an authoritative metaphysical principle. Leibniz states that "[...] nothing happens without there being a cause [Ursache] or at least a determinant reason [raison déterminante], i.e. something that can serve to establish a priori why something exists rather than does not exist and why something exists just so rather than in a different way." Wolff discussed the logical meaning in relation to the concept of nothingness as follows: "Where something exists from which one can understand why it is, this has a sufficient reason (§ 29). Therefore, where there is none, there is nothing from which one can understand why something is, namely, why it can become real, and therefore it must arise from nothing. Therefore, whatever cannot come into being from nothing must have a sufficient reason why it is, than it must be possible in itself, and must have a cause that can bring it into being, if we are speaking of things that are not necessary. Now since it is impossible for anything to come into being from nothing, so also everything that is must have its sufficient reason why it is."

Kant

In the transcendental analytics of the Critique of Pure Reason, Immanuel Kant added at the end of the appendix a small consideration of the opposition of possibility and impossibility in relation to the categories. To each class of categories corresponds also their negation. According to this, "nothing" is to be distinguished, in accordance with the category titles quantity, quality, relation and modality, into thought thing, lack of something, pure conception or mere form, and unding (cf. adjacent table).

The ens rationis is thereby a fiction, a contradiction-free concept of an object that cannot be given in experience (cf. also noumenon). It stands in the 1st place, which in the other tables (of the forms of judgment, of the concepts of understanding) is assigned to quantity, perhaps because no quantity can correspond to it in contemplation. With the nihil privativum is meant a deprivation, an absence or lack of a quality that is in principle experienceable (e.g. darkness as lack of light), it stands on the place reserved for qualities. Kant explains empty perception without an object by the example of the forms of perception space and time; it is to be assumed that geometrical figures, empty forms etc. also fall under this concept. Here, as in 2., a certain quality is not denied, but something without substance is imagined. Since substance falls under the category title of relation, the ens imaginarium stands in this place. Lastly follows the unding or nihil negativum the imagining of an object under a contradictory term or with an impossible form (such as the Penrose triangle).

"The first is that the first is a thing, and the second is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing, and the third is a thing. But both are empty concepts. On the other hand, nihil privativum (n.2) and ens imaginarium (n.3) are empty data to concepts. If light has not been given to the senses, then darkness cannot be imagined, and if extended beings have not been perceived, space cannot be imagined. The negation, as well as the mere form of apprehension, are, without a real, no objects." (Immanuel Kant: AA 000003III, 233) = KrV B 328

Hegel

For Hegel, nothingness is the opposite concept to being. He begins his science of logic with the three determinations "being", "nothing", "becoming". Being, "pure being" is to be understood as the indeterminate immediate. Since pure being is said to be indeterminate, it can have no quality, no inner complexity of any kind, nor can there be any relations to other things or thoughts. The immediacy of pure being emphasizes once again that pure being is not subject to any external conditions, has no cause, but is simply itself. The thought of pure being thus turns out to be completely empty, and what is thought in this empty thought is actually nothing. The determinations of pure being and pure nothingness prove to be the same, and also the thought of pure nothingness is identical with the thought of pure being.

Core ideas of this quote are:

• For Hegel, pure being is "pure abstraction."
• From this property he lets follow that being is the "absolute-negative".
• If Being is the Absolute-Negative, it is Nothing.

Trendelenburg and Dilthey

Friedrich Adolf Trendelenburg, in direct opposition to Hegel, denied that a bridge between being and nothingness to becoming could be established in pure thought. In this relation, fundamental to Hegel's dialectic, Trendelenburg saw a hidden recourse to Anschauung, which Hegel negated or overlooked. "Pure being, equal to itself, is rest; nothingness - equal to itself - is rest. How does the moving becoming come out of the unity of two resting conceptions? Nowhere in the preliminary stages is the movement pre-formed, without which becoming would be only being. I was not the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one who knew that I was the only one. But when thought produces an other from that unity, it evidently adds this other and tacitly subdues the movement in order to bring being and non-being into the flow of becoming. [...] Out of being, a conceded abstraction, and nothingness, a likewise conceded abstraction, cannot suddenly arise becoming, this concrete, life-and-death-dominating, view." Trendelenburg's disciple Wilhelm Dilthey, in the same vein, critically stated with respect to Hegel's system, "But every metaphysics of this kind is directed from the outset by an inner contradiction in its foundation. That which is beyond our experience cannot even be made plausible by analogy, much less proved, if the means of justification and proof, logical connection, is deprived of ontological validity and scope."

Heidegger versus Carnap

According to Martin Heidegger's lecture What is Metaphysics? the "nothing" and the "being" belong together. They are not the same, but they condition each other and belong together. Only through the "nothing" does "being" reveal itself as a "strangeness" or as the "other". This "nothing" is clearly perceptible in the "mood" of fear, not in the fear of something definite, but in the deep "fear of", or "because of", which is hidden in us. Not quite indefinite, but also not graspable in words, precisely the fear of "nothing". In such a fear one is indifferent to everything, and equally indifferent. Whether table or chair, death or life, it has no relevance. A strange calmness pervades one, almost as in the mood of boredom, which is tangibly closest to being, and yet not quite. This small difference felt by us between the two moods, again not graspable in words, but palpable as something "missing," is "nothingness."

Prominently, Rudolf Carnap, as a representative of logical empiricism (Vienna Circle) and middle analytic philosophy, accused Martin Heidegger's existentialism of falsely using the term "The Nothing" as if it stood for a particular entity. Rudolf Carnap rebuked this point in Heidegger in his essay "Overcoming Metaphysics through Logical Analysis of Language." According to Carnap, the assumption that the concept "The Nothing" has a content is based on a confusion between the logical and grammatical structure of concepts and propositions. Analytic philosophy of language attempts to show that "nothing" can and must be understood simply as "not something," so that no such transformation is possible. Its analysis is thus meant primarily as a critique of metaphysics.

According to Carnap, all propositions about nothingness are based on linguistic confusion. Although the formation of the noun "the nothing" is syntactically correct, propositions containing the expression fall into the class of meaningless propositions, since they have no empirical content and cannot possibly be verified. Although verificationism is considered a failed project, Carnap's analysis of nothingness (which was originally directed primarily against Heidegger's Being and Time) has become a consensus in analytic philosophy.

Heidegger himself rejected these attacks: from his point of view, it was dogmatic to admit logic and language analysis as the only philosophical methods. His Existentialism of 1927 therefore attempts to relativize the role of logic and language within the whole of human existence. In his lecture What is Metaphysics, Heidegger held against logical empiricism that the modern sciences were based on logical principles without addressing nothingness. Logical empiricism, as a "philosophy of science," must therefore confine itself to a limited realm of knowledge of what exists that is accessible to a methodical development of the world (science). Heidegger admits that sciences can and must only imagine the nothing as a negation of a being, as a lack, which, however, would not do justice to the phenomenological character of the nothing as nothing.

Richard Hönigswald also reacted to Heidegger's handling of the term with a polemical critique: "Incomparable as it is, the "nothing" broods comforting anxiety by, as the obvious and precisely therefore surprising expression goes, "nichtet." "It is therefore more original than the not and the negation." - However, such insights, as one realizes on closer examination, elude all scruples. They lie, as it were, beyond its conditions and powers. For misgivings always mean questions; now, how far questions reach down into the uncanny depths of the "nothing" in the first place cannot, in principle, be determined."

Sartre: "Nothing" but freedom

In his work Being and Nothingness, Jean-Paul Sartre defines man as the form of being that brings nothingness into reality and thereby distinguishes itself from all other (unconscious) being. From the awareness that man has of the possibility of non-being, he derives the capacity of "negation". This refers to the ability to distance oneself from certain images of the future and the past. Through this capacity of negation, man has the freedom to design himself into the future and to detach himself from the past. This freedom is further reinforced because man can also negate the form of his own present ("I am what I will be") and thus is also not "dependent" on it or "fixed" by it. According to Sartre, nothingness is the freedom that is given to man and that cannot be rejected.

Sartre also points out in his work Being and Nothingness that nothingness cannot actually be grasped by concepts of being. According to Sartre, the transcendent concept of nothingness can only be approximately clarified due to the non-existence of a content, e.g. in the demarcation between one moment and the following one. If we tried to imagine a boundary here, we would not be able to do so, and this is precisely where we would find the "nothing".

Bloch: Philosophy of the not-yet-being

A differentiated philosophy of nothingness can also be found in Ernst Bloch. Under the category of not-yet-being, Bloch grasps the various forms of the human experience of lack as an expression of a fundamental nothingness of a present in which, however, tendencies towards a possible, full being are laid out.

Derrida: "Nothing" but silence

In his critique of Foucault's interpretation of the Descartian "cogito", Jacques Derrida (Cogito und die Geschichte des Wahnsinns. In: Die Schrift und die Differenz) also develops a definition of "nothing". "Nothing" is the insane indeterminacy beyond the "cogito experience" liberated from it, which as a firm basis gives certainty about our own existence, but not beyond it. Because of the nature of "nothing", it cannot be spoken about, since language is the expression of reason, which confronts "nothing" and keeps it in check. "Nothingness" thus reveals itself exclusively in silence.

The Buddhist term shunyata (Sanskrit, Jap. 空, kū) means emptiness or voidness. An equation of shunyata (Mahayana) and nothingness (nihilism) is usually avoided. The Japanese philosopher Keiji Nishitani is an exception: through precise knowledge of Western and Eastern philosophy, he succeeds in a parallel presentation of nihil and shunyata in existentialist language. In the translation of books describing exercises in Zen Buddhism, nothingness is also spoken of in this respect. In the ideal, this is the practice of non-existent attachment. The much-used term nirvana was equated with nothingness through mistranslation, but it means something like "blown away.

Hans Waldenfels finds a contradiction in his analysis of nothingness: