The numbers are mathematical. But the mathematical is not numerical. This means the mathematical is not reduceable to numbers. When we see things quantitatively, we tend to think that numbers correspond to things. Often, we confuse the forest for trees. The mathematical is the forest and the numbers are merely the trees. In our everyday world, the forest stands for the wilderness. We cut individual tress and not the forest. Although, we may clear the forest by cutting every tree that makes it yet the forest remains as absent. This is because forest is not just a collection of trees.
The mathematical is prior to the numbers. One can only count if one has some pre-understanding of addition. Martin Heidegger critiqued our merger of the mathematical with the metaphysical. We merge the mathematical with the metaphysical when we confuse the trees for the forest. This means we think of things as object against a numbered or spatial background. This turn toward spacial or uniform background but measurable began with Newton’s rejection of Aristotle’s motion and the embracing of Descartes pure rational subject. This made the mathematical reduceable to the numerical. This then led us to entify , thingify, reify, objectify everything in the world including God. This means we have absolutized numbers. This is its turn makes everything isolated from everything and renders it countable. We then begin to think that it is the trees that is the forest.
Heidegger returns to Greek notion of the mathematical as learnable and teachable and de-absolutizes the numbers. Heidegger says that the essence of the mathematical is not numerical. It is the mathematical that makes it possible for us to think of a feature of Being that makes entities learnable and teachable as regular and describable. Heidegger thus, tries to overcome our mathematical projection of nature. We seem to have come to numericize nature and forgot its mathematical dimension. Numericization of nature entified Being. This brings us to what Heidegger calls the forgetting of Being. Hence, for Heidegger, the mathematical is not reduceable to the numerical and the numerical is not the ontological.
It is the mathematical that is primary for Heidegger. It is this orientation to the mathematical that de-ontotheologizes his understanding of Being. Being that is a noun then becomes Being understood through the dynamism of a verb. The nominal static, entified Being is replaced by the dynamic becoming Being. The Being is therefore, becoming. Being becomes temporal and not atemporal. But the becoming of Being is still understood under some measurable spacial and uniform background. We are still in the absolute space of Newton. To move away from this entrapment, we have to move from the numerical to the mathematical. This will take us away from the static but measurable spatial background of Newton to our thought to dynamic intertwined spacetime , matter – energy of Einstein. We can trace this origin of this movement in Heidegger , but it truly blossoms in the work of Alain Badiou.
Badiou takes us closer to the mathematical when he rejects the tendency to atomize reality. Atomic thinking begins with the smallest unit of thinking. These units are numericized and are isolated fragments. A Cartesian pure conscious subject / self demands this atomization of reality. Badiou on the other hand, begins with the multiple that is based on a creative chaotic principle. This multiciplity is inaccessible to every process of counting or numericizing. Being is thought by Badiou as multiple and not as one. One can stand for an definite origin or beginning. Multiplicity is not closed like one. It is open . Hence, multiplicity brings us to the groundlessness as facticity of Being . This groundless facticity is mathematical.
The groundless mathematical is close to the real of the Jacques Lacan. Thus, in as much as the real is unknowable and unsayable,’ what we say is never real!’ . In the same way, the numerical is not mathematical. It is not reduceable to the mathematical. Badiou uses set theory to bring us closer to the mathematical. Set theory is a language of immanence. There is no outside or beyond it. There is nothing outside set theory. A set theory is about multiplicity, a set of the many things considered as one ( classical understanding)
We can think of an infinite set. It has larger than infinite set of subsets. Infinity according George Cantor comes in different sizes. But we have to note that an infinite set is not a set of all sets. If we analyze any set, it will have numerous subsets with the exception of an empty set. But, with light of the axiomatic set theory, we think that a set is multiple without one.(Axiomatic set theory) It means set is a multiple of nothing. Hence, we may say that the mathematical is the one that stands outside as well as inside the infinite set. It is that which makes everything countable or numerical.
A number in its basic form is a multiplicity of unities. As unities numbers are not pure multiplicities. In this sense, the numerical is also multiple but is a set of unities. But when it comes to infinite set, the multiple is pure without one. The multiple is not reduceable to one. Thus, set theory leads us to think the multiple in its irresuduceable purity. This also means mathematics makes it possible to think Being, that is multiple. This is why mathematics is ontology. If mathematics is ontology. It becomes a revelation of Being. Being is manifested as a multiple. Being, therefore, is not atomistic. It is dynamic complexity.
This also tells us ethics and morality are multiple as well as mathematical. What we consider as a moral value becomes a way of counting or measuring how morality is lived by us. But what we consider as moral value is itself not one but is multiple. It is an enssemble of values or axiologies. Even what we think of as truth is also multiple and what we count as false is opposite or subtraction of the multiple but still as multiple. Everything in some sense is mathematical. This statement is more proved by medicine today than any other thing. All our health parameters are numbers. Pythagoras has somehow staged a comeback ! Everything is mathematical. Therefore, with Johanes Kepler , we may say that God is the greatest Mathematician ( Geometer).
