Task of the Philosopher. Thought of the Day 75.0

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Poincaré in Science and Method discusses how “reasonable” axioms (theories) are chosen. In a section which is intended to cool down the expectations put in the “logistic” project, he points out the problem as follows:

Even admitting that it has been established that all theorems can be deduced by purely analytical processes, by simple logical combinations of a finite number of axioms, and that these axioms are nothing but conventions, the philosopher would still retain the right to seek the origin of these conventions, and to ask why they were judged preferable to the contrary conventions.

[ …] A selection must be made out of all the constructions that can be combined with the materials furnished by logic. the true geometrician makes this decision judiciously, because he is guided by a sure instinct, or by some vague consciousness of I know not what profounder and more hidden geometry, which alone gives a value to the constructed edifice.

Hence, Poincaré sees the task of the philosophers to be the explanation of how conventions came to be. At the end of the quotation, Poincaré tries to give such an explanation, namely in referring to an “instinct” (in the sequel, he mentions briefly that one can obviously ask where such an instinct comes from, but he gives no answer to this question). The pragmatist position to be developed will lead to an essentially similar, but more complete and clear point of view.

According to Poincaré’s definition, the task of the philosopher starts where that of the mathematician ends: for a mathematician, a result is right if he or she has a proof, that means, if the result can be logically deduced from the axioms; that one has to adopt some axioms is seen as a necessary evil, and one perhaps puts some energy in the project to minimize the number of axioms (this might have been how set theory become thought of as a foundation of mathematics). A philosopher, however, wants to understand why exactly these axioms and no other were chosen. In particular, the philosopher is concerned with the question whether the chosen axioms actually grasp the intended model. This question is justified since formal definitions are not automatically sufficient to grasp the intention of a concept; at the same time, the question is methodologically very hard, since ultimately a concept is available in mathematical proof only by a formal explication. At any rate, it becomes clear that the task of the philosopher is related to a criterion problem.

Georg Kreisel thinks that we do indeed have the capacity to decide whether a given model was intended or not:

many formal independence proofs consist in the construction of models which we recognize to be different from the intended notion. It is a fact of experience that one can be honest about such matters! When we are shown a ‘non-standard’ model we can honestly say that it was not intended. [ . . . ] If it so happens that the intended notion is not formally definable this may be a useful thing to know about the notion, but it does not cast doubt on its objectivity.

Poincaré could not yet know (but he was experienced enough a mathematician to “feel”) that axiom systems quite often fail to grasp the intended model. It was seldom the work of professional philosophers and often the byproduct of the actual mathematical work to point out such discrepancies.

Following Kant, one defines the task of epistemology thus: to determine the conditions of the possibility of the cognition of objects. Now, what is meant by “cognition of objects”? It is meant that we have an insight into (the truth of) propositions about the objects (we can then speak about the propositions as facts); and epistemology asks what are the conditions for the possibility of such an insight. Hence, epistemology is not concerned with what objects are (ontology), but with what (and how) we can know about them (ways of access). This notwithstanding, both things are intimately related, especially, in the Peircean stream of pragmatist philosophy. The 19th century (in particular Helmholtz) stressed against Kant the importance of physiological conditions for this access to objects. Nevertheless, epistemology is concerned with logic and not with the brain. Pragmatism puts the accent on the means of cognition – to which also the brain belongs.

Kant in his epistemology stressed that the object depends on the subject, or, more precisely, that the cognition of an object depends on the means of cognition used by the subject. For him, the decisive means of cognition was reason; thus, his epistemology was to a large degree critique of reason. Other philosophers disagreed about this special role of reason but shared the view that the task of philosophy is to criticise the means of cognition. For all of them, philosophy has to point out about what we can speak “legitimately”. Such a critical approach is implicitly contained in Poincaré’s description of the task of the philosopher.

Reichenbach decomposes the task of epistemology into different parts: guiding, justification and limitation of cognition. While justification is usually considered as the most important of the three aspects, the “task of the philosopher” as specified above following Poincaré is not limited to it. Indeed, the question why just certain axioms and no others were chosen is obviously a question concerning the guiding principles of cognition: which criteria are at work? Mathematics presents itself at its various historical stages as the result of a series of decisions on questions of the kind “Which objects should we consider? Which definitions should we make? Which theorems should we try to prove?” etc. – for short: instances of the “criterion problem”. Epistemology, has all the task to evoke these criteria – used but not evoked by the researchers themselves. For after all, these criteria cannot be without effect on the conditions for the possibility of cognition of the objects which one has decided to consider. (In turn, the conditions for this possibility in general determine the range of objects from which one has to choose.) However, such an epistemology has not the task to resolve the criterion problem normatively (that means to prescribe for the scientist which choices he has to make).

Biogrammatic Vir(Ac)tuality. Note Quote.

In Foucault’s most famous example, the prison acts as the confluence of content (prisoners) and expression (law, penal code) (Gilles Deleuze, Sean Hand-Foucault). Informal Diagrams are proliferate. As abstract machines they contain the transversal vectors that cut across a panoply of features (such as institutions, classes, persons, economic formation, etc), mapping from point to relational point, the generalized features of power economies. The disciplinary diagram explored by Foucault, imposes “a particular conduct upon a particular human multiplicity”. The imposition of force upon force affects and effectuates the felt experience of a life, a living. Deleuze has called the abstract machine “pure matter/function” in which relations between forces are nonetheless very real.

[…] the diagram acts as a non-unifying immanent cause that is co-extensive with the whole social field: the abstract machine is like the cause of the concrete assemblages that execute its relations; and these relations between forces take place ‘not above’ but within the very tissue of the assemblages they produce.

The processual conjunction of content and expression; the cutting edge of deterritorialization:

The relations of power and resistance between theory and practice resonate – becoming-form; diagrammatics as praxis, integrates and differentiates the immanent cause and quasi-cause of the actualized occasions of research/creation. What do we mean by immanent cause? It is a cause which is realized, integrated and distinguished in its effect. Or rather, the immanent cause is realized, integrated and distinguished by its effect. In this way there is a correlation or mutual presupposition between cause and effect, between abstract machine and concrete assemblages

Memory is the real name of the relation to oneself, or the affect of self by self […] Time becomes a subject because it is the folding of the outside…forces every present into forgetting but preserves the whole of the past within memory: forgetting is the impossibiltiy of return and memory is the necessity of renewal.

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The figure on the left is Henri Bergson’s diagram of an infinitely contracted past that directly intersects with the body at point S – a mobile, sensorimotor present where memory is closest to action. Plane P represents the actual present; plane of contact with objects. The AB segments represent repetitive compressions of memory. As memory contracts it gets closer to action. In it’s more expanded forms it is closer to dreams. The figure on the right extrapolates from Bergson’s memory model to describe the Biogrammatic ontological vector of the Diagram as it moves from abstract (informal) machine in the most expanded form “A” through the cone “tissue” to the phase-shifting (formal), arriving at the Strata of the P plane to become artefact. The ontological vector passes through the stratified, through the interval of difference created in the phase shift (the same phase shift that separates and folds content and expression to move vertically, transversally, back through to the abstract diagram.)

A spatio-temporal-material contracting-expanding of the abstract machine is the processual thinking-feeling-articulating of the diagram becoming-cartographic; synaesthetic conceptual mapping. A play of forces, a series of relays, affecting a tendency toward an inflection of the informal diagram becoming-form. The inflected diagram/biogram folds and unfolds perception, appearances; rides in the gap of becoming between content and expression; intuitively transduces the actualizing (thinking, drawing, marking, erasing) of matter-movement, of expressivity-movement. “To follow the flow of matter… is intuition in action.” A processual stage that prehends the process of the virtual actualizing;

the creative construction of a new reality. The biogrammatic stage of the diagrammatic is paradoxically double in that it is both the actualizing of the abstract machine (contraction) and the recursive counter-actualization of the formal diagram (détournement); virtual and actual.

It is the event-dimension of potential – that is the effective dimension of the interrelating of elements, of their belonging to each other. That belonging is a dynamic corporeal “abstraction” – the “drawing off” (transductive conversion) of the corporeal into its dynamism (yielding the event) […] In direct channeling. That is, in a directional channeling: ontological vector. The transductive conversion is an ontological vector that in-gathers a heterogeneity of substantial elements along with the already-constituted abstractions of language (“meaning”) and delivers them together to change. (Brian Massumi Parables for the Virtual Movement, Affect, Sensation)

Skin is the space of the body the BwO that is interior and exterior. Interstitial matter of the space of the body.

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The material markings and traces of a diagrammatic process, a ‘capturing’ becoming-form. A diagrammatic capturing involves a transductive process between a biogrammatic form of content and a form of expression. The formal diagram is thus an individuating phase-shift as Simondon would have it, always out-of-phase with itself. A becoming-form that inhabits the gap, the difference, between the wave phase of the biogrammatic that synaesthetically draws off the intermix of substance and language in the event-dimension and the drawing of wave phase in which partial capture is formalized. The phase shift difference never acquires a vectorial intention. A pre-decisive, pre-emptive drawing of phase-shifting with a “drawing off” the biogram.

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If effects realize something this is because the relations between forces or power relations, are merely virtual, potential, unstable vanishing and molecular, and define only possibilities of interaction so long as they do not enter a macroscopic whole capable of giving form to their fluid manner and diffuse function. But realization is equally an integration, a collection of progressive integrations that are initially local and then become or tend to become global, aligning, homogenizing and summarizing relations between forces: here law is the integration of illegalisms.

 

Speech. Thought of the Day 17.0

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Speech, is a gesture, an indication, or a pointing toward, a certain intended signification. Speech, if it is understood, brings a certain something before us, but what is the status of that something? Firstly, given that language is equivocal, the signified necessarily goes beyond any attempt to signify it. As such, language never affords total expression, but rather, is merely the linguistic embodiment of an attempt to signify. It is therefore the case that these significations have the status of “Ideas,” which target, or aim at total expression but are constantly outstripped by the “things themselves” which they signify. The signified is never present before the act of expression; rather, it is this act of expression which realizes it as an intention. It is, furthermore, appropriate to say that we have, or possess, a language as the sum total of available significations. Language is intrinsically historical, in the sense that any synchronic moment possesses all previous synchronic moments within it. Any particular present carries with it all presents occurring prior to it. The distinction between the synchronic and the diachronic, therefore, cannot be maintained in a language as it is lived. It is the case, therefore, that any particular signification becomes available as a kind of ‘sedimentation’ within the ‘tradition’ of a language. The significative intention, therefore, must draw from available meanings but is also limited by the ‘world’ as the limit of possible meanings. The speaking subject, therefore, through the power of expression, is able to draw from available meaning and in turn, through them, constitute a new meaning. Understanding the meaning, therefore, is a process of taking up the signification of others, or having them “dwell within me,” such that a new ‘style’ of thought has been awakened. What has, thereby, been ‘acquired’ will remain available, without the need to reactivate the original process of constitution. A new ‘sedimentation’ has been constituted, which does not erase, or eliminate, the ‘sedimentations’ previously available. Rather the new ‘acquisition’ is incorporated into the cultural tradition that is language and is added as a new possibility for an expressive intention. The speech of others comes to “dwell” within me in a movement of transcendence, beyond the merely available meanings of the language, and is understood the moment I am able to take it within myself and express it anew. It seems to be the case, therefore, that what is available to me is not solely my ‘own,’ but ‘ours’ in the sense that what is available to me is available to everyone and only becomes mine specifically when, through my mute intention, I take it up into myself and express it anew. The ‘tradition,’ or language, is that which gives us the means of realizing our significative, or mute, intentions, however, at the same time it is constituted as the result of our expressivity.