A Pragmatic Start for a Beautiful Pair
February 17, 2012 § Leave a comment
The status of self-referential things is a very particular one.
They can be described only by referring to the concept of the “self.”
Of course, self-referential things are not without conditions, just as any other thing, too. It is, however, not possible to describe self-referential things completely just by means of those conditions, or dependencies. Logically, there is an explanatory gap regarding their inward-directed dependencies. The second peculiarity with self-referential things is that there are some families of configurations for which they become generative.
For strongly singular terms no possible justification exists. Nevertheless, they are there, we even use them, which means that the strong singularity does not imply isolation at all. The question then is about how we can/do achieve such an embedding, and which are the consequences of that.
Despite the fact that there is no entry point which could by apriori be taken as a justified or even salient one we still have to make a choice which one actually to take. We suppose that there is indeed such a choice. It is a particular one though. We do not assume that the first choice is actually directed to an already identified entity as this would mean that there already would have been a lot of other choices in advance. We would have to select methods and atoms to fix, i.e. select and choose the subject of a concrete choice, and so on.
The choice we propose to take is neither directed to an actual entity, nor is it itself a actual entity. We are talking about a virtual choice. Practically, we start with the assumption of choosability.
Actually, Zermelo performed the same move when trying to provide a sound basis for set theory  after the idealistic foundation developed by Frege and others had failed so dramatically, leading into the foundational crisis of formal sciences . Zermelo’s move was to introduce choosability as an axiom, called the axiom of choice.
For Zermelo’s set theory the starting point, or if you prefer, the anchor point, lies completely outside the realm of the concept that is headed for. The same holds for our conceptualization of formalization. This outside is the structure of pragmatic act of choice itself. This choice is a choice qua factum, it is not important that we choose from a set from identified entities.
The choice itself proposes by its mere performance that it is possible to think of relations and transformations; it is the unitary element of any further formalization. In Wittgenstein’s terms, it is part of the abstract life form. In accordance to Wittgenstein’s critique of Moore’s problems1, we can also say that it is not reasonable, or more precise: it is without any sense, to doubt on the act of choosing something, even if we did not think about anything particular. The mere executive aspect of any type of activity is sufficient for any a posteriori reasoning that a choice has been performed.
Notably, the axiom of choice implies the underlying assumption of intensive relatedness between yet undetermined entities. In doing so, this position represents a fundamental opposite to the attitude of Frege, Russell and any modernist in general, who always start with the assumption of the isolated particle. For these reasons we regard the axiom of choice as one of the most interesting items in mathematics!
The choice thus is a Deleuzean double-articulation , closely related to his concept of the transcendental status of difference; we also could say that the choice has a transcendental dualistic characteristics. On the one hand there is nothing to justify. It is mere movement, or more abstract, a pure mapping or transformation, just as a matter of fact. On the other hand, it provides us with the possibility of just being enabled to conceive mere movement as such a mapping transformation; it enables us to think the unit before any identification. Transformation comes first; Deleuze’s philosophy similarly puts the difference into the salient transcendental position. To put it still different, it is the choice, or the selection, that is inevitably linked to actualization. Actualization and choice/selection are co-extensive.
Just another Game
So, let us summarize briefly the achievements. First, we may hold that similarly to language, there is no justification for formalization. Second, as soon as we use language, we also use symbols. Symbols on the other hand take, as we have seen, a double-articulated position between language and form. We characterized formalization as a way to give a complicated thing a symbolic form that lives within a system of other forms. We can’t conceive of forms without symbols. Language hence always implies, to some degree, formalization. It is only a matter of intensity, or likewise, a matter of formalizing the formalization, to proceed from language to mathematics. Third, both language and formalization belong to particular class of terms, that we characterized as strongly singular terms. These terms may be well put together with an abstract version of Kant’s organon.
From those three points follows that concepts that are denoted by strongly singular terms, such as formalization, creativity, or “I”, have to be conceived, as we do with language, as particular types of games.
In short, all these games are being embedded in the life form of or as a particular (sub-)culture. As such, they are not themselves language games in the original sense as proposed by Wittgenstein.
These games are different from the language game, of course, mainly because the underlying mechanisms as well as embedding landscape of purposes is different. These differences become clearly visible if we try to map those games into the choreostemic space. There, they will appear as different choreostemic styles. Despite the differences, we guess that the main properties of the language game apply also to the formalization game. This concerns the setup, the performance of such games, their role, their evaluation etc.etc., despite the effective mechanisms might be slightly different; for instance, Brandom’s principle of the “making it explicit” that serves well in the case of language is almost for sure differently parameterized for the formalizatin or the creativity game. Of course, this guess has to be subject of more detailed investigations.
As there are different natural languages that all share the same basement of enabling or hosting the possibility of language games, we could infer—based on the shared membership to the family of strongly singular terms— that there are different forms of formalization. Any of course, everybody knows at least two of such different forms of formalization: music and mathematics. Yet, once found the glasses that allow us to see the multitude of games, we easily find others. Take for instance the notations in contemporary choreography, that have been developed throughout the 20ieth century. Or the various formalizations that human cultures impose onto themselves as traditions.
Taken together it is quite obvious that language games are not a singularity. There are other contexts like formalization, modeling or the “I-reflexivity” that exist for the same reason and are similarly structured, although their dynamics may be strikingly different. In order to characterize any possible such game we could abstract from the individual species by proceeding to the -ability. Cultures then could be described precisely as the languagability of their members.
Based on the concept of strongly singular terms we first proof that we have to conceive of formalization (and symbol based creativity) in a similar way as we do for language. Both are embedded into a life form (in the Wittgensteinian sense). Thus it makes sense to propose to transfer the structure of the “game” from the domain of natural language to other areas that are arranged around strongly singular terms, such as formalization or creativity in the symbolic domain. As a nice side effect this brought us to the proper generalization of the Wittgensteinian language games.
Yet, there is still more about creativity that we have to clarify before we can relate it to other “games” like formalization and to proof the “beauty” of this particular combination. For instance, we have to become clear about the differences of systemic creativity, which can be observed in quasi-material arrangements (m-creativity), e.g. as self-organization, and the creativity that is at home in the realm of the symbolic (s-creativity).
The next step is thus to investigate the issue of expressibility.
1. In an objection to Wittgenstein, Moore raised the skeptic question about the status of certain doubts: Can I doubt that this hand belongs to me? Wittgenstein denied the reasonability of such kind of questions.
-  Zermelo, Set theory
-  Hahn, Grundlagenkrise
-  Deleuze & Guattari, Milles Plateaus