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Laruelle, Deleuze, Badiou: Sheaf theory (Part I)

Two dozen arrows:

Following the call for a universalist mathematics, we have found that a sheaf theory (a term from Middle English meaning “two dozen arrows”) is needed.

I would like to take a break from my usual posts on German idealism to try to apply my understanding of what I’ve learned so far to contemporary debate. The following is a very sketchy overview of the various areas we will be heading, beginning with sheaves, moving on through to topos theory, to Grothendieck topology (category theory), to quantum set theory, and so forth.

This sketch is obviously absolutely incomplete, obviously subject to much error, and obviously highly Fragmented in kind. Yet, as we have revealed, even Fragments do have a positive efficacy of their own. My aim here is to creatively synthesize a lot of complex mathematics so as to provide a directory for others who are interested in this general project of universalist mathematics.

Using the resources I have, and my limited spiritual gift of discernment, let us begin our journey into the abyss…

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Schlegel, Novalis, Goethe: Continuous integration (Part III)

The birth of continuum:

And so, we find that these otherwise dis-continuous Fragments of differentiated information, the uncertainties of knowledge, the limits of our language, the void(s) of our subjectivites, the gaps in space-time, the appearance of a primal negativity of Life turn and turn into a positivity and concern for the continuous integration of Life on the level of our immanent experience.

The ‘aim’ of Object-Oriented Ontology, should there be one, is to avoid dealing with this linguistic negativity ever again. Instead, it is to try to think of a positivity of substance. The balancing of these two approaches, then, will give us our ideal. We must strive to continue, to map what we have learned into an onto-logics whereby we may keep functioning not despite but because of our de-organ-ization. We have seen before the dis-continuity brought about by the precision demanded by the linguistic turn.

We have looked and indeed to an extent we are still looking at ourselves in the mirror, only to reveal the violence of our being. We know that what lies within us is the most monstrous Crisis of them all, but we know we must carry on Nonetheless. The ‘aim’ of Object-Oriented Ontology, should there be one, is to see with-and-beyond these linguistic traps to the positivity of Being as multiplicity. To fixate our Sphinxous glance on the text is to lose sight of the physicality of the book itself, to lose sight of our health, our very act of perpetual reading. It is to lose sight of the poly-valence of the World.

Read Novalis, Logological Fragments II, page 69:

NovalisContinuum

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Schlegel, Novalis, Goethe: Fragmented Body (Part II)

Fragmented Body:

We have seen that Fragmentation plays a role, and a very decisive role at that. With the “church in the Wilderness”, we have also seen that we may bring together our Fragments to help ease the pain.

But, here it seems we are left with an aporia: The monstrous image of the fragmented body, what are we make of it? In early Lacan, we have the image of the corps morcelé, the body-in-pieces, which gives us an eternal anxiety (see here). Even the body is not complete by such a communion, and even still it remains Fragmented.

In Deborah A. Harter’s Bodies in Pieces: Fantastic Narrative and the Poetics of the Fragment we find a beautiful series of questions on page 3:

FragmentedBody

The problem of Fragmentation and the Fragmented Body is important to consider because  in the last instance it is intimately tied up with the promulgation of violence. The infamous surrealist images of mutilated women, the representations of abused and cut-up women in literature, film, art, and so forth should mark a crisis of post-modernity.

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Schlegel, Novalis, Goethe: Fragmentation (Part I)

Fragmentation:

From our Wilderness theology, we note that “The Wilderness is a place of Crisis”. I would like to extrapolate more on this thought.

This seems to imply, in the end, that our individual Wanderings are therefore Fragments of the Wilderness itself, taken as a Whole. We attend to Crisis, yes, but insofar as we are finite, we cannot attend to all of them. We missed many Fragments in the past, many in the present, and it is also certain that we will miss many in the Future. We may say that our testimony is an exposition of our personal experience in Wandering; it is an account of our Individuation.

Wandering is on one hand an activity, it is something we do in the Wilderness. It is an activity which acts upon the self. On the other hand, Wandering is a particular insofar as we may speak of this or that Wandering as if it were an encounter. So long as we are Wandering absolutely, there is Fragmentation which occurs. Insofar as we do not Wander, there are truths which we may arrive at momentarily. Yet, in absolute terms, since there is always Wandering so there is also always Fragmentation.

To get moving again, I would like to inquire into the nature of Fragmentation. The Fragment form has been employed by many thinkers of influence upon me, most notably Novalis, Nietzsche, and Wittgenstein. The Stanford Encyclopedia of Philosophy notes Novalis’ use of Fragments (see here) as follows:

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Schleiermacher, Novalis, Barth: Wilderness Theology (Part III)

[ROUGH DRAFT #1]

Dragons and the wilderness:

If you look for information on a man named “Samuel Vincent”, after searching for some while you’re likely to find this short, two-sentence summary (see here): “Pastor Samuel Vincent is a typical representative of French Protestantism from the South of France in the early 19th century. His writings and the theological reviews he helped to found contributed greatly to the development of theological thought in France.”

Fair enough: Sam Vincent was just an ordinary man.

Yet, it is only through his ordinariness that I was able to come to a better understanding of what I wish to call “Wilderness theology”. I like Sam because he, too, insists upon the separation between “the Bible and Revelation as such”. To set the mood, I’ll quote at some length:

The content of Protestantism is the Gospel, its form is freedom of examination » (Le fond du protestantisme, c’est l’Evangile ; sa forme, c’est la liberté d’examen). This often quoted sentence gives an inkling of the general tone of the book. In it, Vincent stresses the difference between religion, the living faith of believers, and ecclesiastical organisation. He recalls that the Church is not essential to salvation, it must merely be useful and efficient, which is only possible if it acknowledges each person’s full freedom of examination, especially in matters of faith.Vincent also stressed the distance between the Bible and Revelation as such, which is primarily a matter of conscience, even of individual conscience. For him the Reformation cannot be limited to what the reformers said or wrote : the latter could not immediately display all its potential.

For Vincent, spiritual freedom and freedom of examination go together. He was therefore one of the great instigators of the liberal trend in French-speaking Protestantism. His vision of man was rather optimistic (this was implied in his concept of freedom and he did not mention “original” sin) ; he claimed that freedom of examination be applied to the biblical texts and wanted them examined scientifically, in accordance with the historical methods of his time.

At the same time, Vincent cared for the growth of believers’ individual piety, while warning his fellow Protestants against ready-made concepts of faith. Faith requires permanent and individual efforts in such areas as thought and freedom.

If I were to, in advance, provide a verse which characterizes Wilderness Theology, I would have to give Malachi 1:3 (KJV) “And I hated Esau, and laid his mountains and his heritage waste for the dragons of the wilderness.” A dragon, here, is much like our understanding of the Sphinx. In the Wilderness, of all the Dragons one should meet, it is the self which frightens the most.

In any case, a connection or a bond nonetheless is made to our beloved Schleiermacher by way of Vincent, who advocated his theology. As we have found in our encounter of moving with and beyond Barth, it is indeed a “mediated Schleiermacher” that we need to return with a stronger, scarier kind of universalism.

Can we, with the help of Sam Vincent, think with and beyond Barth in developing a (non-)theological and (non-)hypothetical account of the Wilderness?

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Schleiermacher, Novalis, Barth: Revelatory anchoring (Part II)

An oscillating continuum:

Paul Tillich in Systematic Theology (1951) wrote that “[t]heology moves back and forth between two poles, the eternal truth of its foundations and the temporal situation in which the eternal truth must be received.” I think the best way to approach wilderness theology is through such systematic thought which leads us to understand its content through “revelatory anchoring”.

Herein the name “theology” marks a certain form, i.e. it must contain an oscillation, for such is the Spirit. Thus, I find myself in accord with Adam Kotsko’s continuum-proposal (see here) that sparked a great discussion in the comments section. Of particular interest to me was Tillich’s proposition:

“Philosophy formulates the questions implied in human existence, and theology formulates the answers implied in divine self-manifestation under the guidance of the questions implied in human existence. This is a circle which drives man to a point where question and answer are not separated…”

To recap, both philosophy and theology therefore belong to the realm of thought. As a result, and as we have found (see my post here), they both cannot be teachable in the way that mathematics might be.

The commenter continues by suggesting that “The primary difference is that though theology and philosophy both exist in the realm of thought (and thus exist in a continuum), theology begins with data that is not native or natural to human thought: revelation.” noting well that the historical event (Religion) always comes before-hand to condition theology, while Philosophy proper is markedly ahistorical and unconditional — an infinite task.

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Schleiermacher, Novalis, Barth: The Sphinx (Part I)

The Sphinx slouching towards Bethlehem to be born:

Upon our realization that immanent “life” is at once both a matter of life and death, we fall into a certain humbling “illness” which marks the ascetic ideal as we pass through it to bring out our “second nature”.

Thus far, we have determined, as found in Nietzsche and the Shadow of God by Didier Franck, Bettina Bergo, and Philippe Farah, “The Plurality of the Body”, page 127, the following:

NovalisNietzscheBody

At this stage, I believe it is appropriate to turn to a more theological debate here so as to best be able to capture these nuances. The two thinker I have appointed to pair up with Novalis are Schliermacher, who was a companion of Novalis, and his contemporary Karl Barth, who wrote at great lengths on both of these men.

We take our point of departure from Nietzsche’s Sphinx, in conjunction with a passage from Barth’s in his exegesis of Romans 7:14-25 under the heading, “The Reality of Religion” (pp 257-59), wherein he evokes Schlegel’s image of the Sphinx (Addresses) in tandem with a positioning of Schliermacher:

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