# Dialectics: Mathematico-Philosophical Sequential Quantification. Drunken Risibility.

Figure: Graphical representation of the quantification of dialectics.

A sequence S of P philosophers along a given period of time would incorporate the P most prominent and visible philosophers in that interval. The use of such a criterion to build the time-sequence for the philosophers implies in not necessarily uniform time-intervals between each pair of subsequent entries.

The set of C measurements used to characterize the philosophers define a C−dimensional feature space which will be henceforth referred to as the philosophical space. The characteristic vector v⃗i of each philosopher i defines a respective philosophical state in the philosophical space. Given a set of P philosophers, the average state at time i, i ≤ P, is defined as

a⃗i = 1/i ∑k=1i v⃗k

The opposite state of a given philosophical state v⃗i is defined as:

r⃗i = v⃗i +2(a⃗i −v⃗i) = 2a⃗i − v⃗i

The opposition vector of philosophical state v⃗i is given by D⃗i = r⃗i − v⃗i. The opposition amplitude of that same state is defined as ||D⃗i||.

An emphasis move taking place from the philosophical state v⃗i is any displacement from v⃗i along the direction −r⃗i. A contrary move from the philosophical state v⃗i is any displacement from v⃗i along the direction r⃗i.

Given a time-sequence S of P philosophers, the philosophical move implied by two successive philosophers i and j corresponds to the M⃗i,j vector extending from v⃗to v⃗j , i.e.

M⃗i,j = v⃗j – v⃗i

In principle, an innovative or differentiated philosophical move would be such that it departs substantially from the current philosophical state v⃗i. Decomposing innovation moves into two main subtypes: opposition and skewness.

The opposition index Wi,j of a given philosophical move M⃗i,j is defined as

Wi,j = 〈M⃗i,j, D⃗i〉/  ||D⃗i||2

This index quantifies the intensity of opposition of that respective philosophical move, in the sense of having a large projection along the vector D⃗i. It should also be noticed that the repetition of opposition moves lead to little innovation, as it would imply in an oscillation around the average state. The skewness index si,j of that same philosophical move is the distance between v⃗j and the line L defined by the vector D⃗i, and therefore quantifies how much the new philosophical state departs from the respective opposition move. Actually, a sequence of moves with zero skewness would represent more trivial oscillations within the opposition line Li.

We also suggest an index to quantify the dialectics between a triple of successive philosophers i, j and k. More specifically, the philosophical state v⃗i is understood as the thesis, the state j is taken as the antithesis, with the synthesis being associated to the state v⃗k. The hypothesis that k is the consequence, among other forces, of a dialectics between the views v⃗i and v⃗j can be expressed by the fact that the philosophical state v⃗k be located near the middle line MLi,j defined by the thesis and antithesis (i.e. the points which are at an equal distance to both v⃗i and v⃗j) relatively to the opposition amplitude ||D⃗i||.

Therefore, the counter-dialectic index is defined as

ρi→k = di→k /||M⃗i,j||

where di→k is the distance between the philosophical state v⃗k and the middle-line MLi,j between v⃗i and v⃗j. Note that 0 ≤ di→k ≤ 1. The choice of counter-dialectics instead of dialectics is justified to maintain compatibility with the use of a distance from point to line as adopted for the definition of skewness….

# Deleuzian Grounds. Thought of the Day 42.0

With difference or intensity instead of identity as the ultimate philosophical one could  arrive at the crux of Deleuze’s use of the Principle of Sufficient Reason in Difference and Repetition. At the beginning of the first chapter, he defines the quadruple yoke of conceptual representation identity, analogy, opposition, resemblance in correspondence with the four principle aspects of the Principle of Sufficient Reason: the form of the undetermined concept, the relation between ultimate determinable concepts, the relation between determinations within concepts, and the determined object of the concept itself. In other words, sufficient reason according to Deleuze is the very medium of representation, the element in which identity is conceptually determined. In itself, however, this medium or element remains different or unformed (albeit not formless): Difference is the state in which one can speak of determination as such, i.e. determination in its occurrent quality of a difference being made, or rather making itself in the sense of a unilateral distinction. It is with the event of difference that what appears to be a breakdown of representational reason is also a breakthrough of the rumbling ground as differential element of determination (or individuation). Deleuze illustrates this with an example borrowed from Nietzsche:

Instead of something distinguished from something else, imagine something which distinguishes itself and yet that from which it distinguishes itself, does not distinguish itself from it. Lightning, for example, distinguishes itself from the black sky but must also trail behind it . It is as if the ground rose to the surface without ceasing to be the ground.

Between the abyss of the indeterminate and the superficiality of the determined, there thus appears an intermediate element, a field potential or intensive depth, which perhaps in a way exceeds sufficient reason itself. This is a depth which Deleuze finds prefigured in Schelling’s and Schopenhauer’s differend conceptualization of the ground (Grund) as both ground (fond) and grounding (fondement). The ground attains an autonomous power that exceeds classical sufficient reason by including the grounding moment of sufficient reason for itself. Because this self-grounding ground remains groundless (sans-fond) in itself, however, Hegel famously ridiculed Schelling’s ground as the indeterminate night in which all cows are black. He opposed it to the surface of determined identities that are only negatively correlated to each other. By contrast, Deleuze interprets the self-grounding ground through Nietzsche’s eternal return of the same. Whereas the passive syntheses of habit (connective series) and memory (conjunctions of connective series) are the processes by which representational reason grounds itself in time, the eternal return (disjunctive synthesis of series) ungrounds (effonde) this ground by introducing the necessity of future becomings, i.e. of difference as ongoing differentiation. Far from being a denial of the Principle of Sufficient Reason, this threefold process of self-(un)grounding constitutes the positive, relational system that brings difference out of the night of the Identical, and with finer, more varied and more terrifying flashes of lightning than those of contradiction: progressivity.

The breakthrough of the ground in the process of ungrounding itself in sheer distinction-production of the multiple against the indistinguishable is what Deleuze calls violence or cruelty, as it determines being or nature in a necessary system of asymmetric relations of intensity by the acausal action of chance, like an ontological game in which the throw of the dice is the only rule or principle. But it is also the vigil, the insomnia of thought, since it is here that reason or thought achieves its highest power of determination. It becomes a pure creativity or virtuality in which no well-founded identity (God, World, Self) remains: [T]hought is that moment in which determination makes itself one, by virtue of maintaining a unilateral and precise relation to the indeterminate. Since it produces differential events without subjective or objective remainder, however, Deleuze argues that thought belongs to the pure and empty form of time, a time that is no longer subordinate to (cosmological, psychological, eternal) movement in space. Time qua form of transcendental synthesis is the ultimate ground of everything that is, reasons and acts. It is the formal element of multiple becoming, no longer in the sense of finite a priori conditioning, but in the sense of a transfinite a posteriori synthesizer: an empt interiority in ongoing formation and materialization. As Deleuze and Guattari define synthesizer in A Thousand Plateaus: The synthesizer, with its operation of consistency, has taken the place of the ground in a priori synthetic judgment: its synthesis is of the molecular and the cosmic, material and force, not form and matter, Grund and territory.

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# Disapproval resolution to test Government in Rajya Sabha.Why or Why Not the Justification?

My reflections are based on the views expressed by the Economic Times yesterday, which a friend of mine was kind enough to share.

From the news, the blurb for which is as under:

The government is up against an unexpected hurdle in the Rajya Sabha on the bill for scrapping Rs 500 and Rs 1000 notes. While the ordinance promulgated for extinguishing the notes was replaced by the Specified Bank Notes Bill in the Lok Sabha on Tuesday, the Opposition is set to exploit a procedural opening to derail the government’s efforts in the Rajya Sabha…..But the twist in the tale came at the Rajya Sabha Business Advisory Committee meeting on Tuesday, where Congress MP T Subbarami Reddy sought time to move a resolution “seeking disapproval” of the ordinance itself. The BAC has accepted this after his party backed him along with other Opposition members. This is likely to be taken up together with government’s bill slated for Thursday….

Take:

Legally yes, this is a possibility. Practically no, for the costs incurred would be humungous. Passing bills or rather introducing them as money bills is a commonwealth practice, unlike how these are treated in the US, where revenue bills are equally influenced by representatives as well as the senate to a point of governmental shutdown due to non-passage of budgetary legislations. The whole of the commonwealth is lacking on this equality accorded to the upper house, whereas the only couple of checks to safeguard how the Raja Sabha isn’t relegated in legislative duties as far introducing a money bill is considered is firstly in the definition of money bill, which has 7 provisions, of which “only” any of those provisions would meet the criteria of a money bill; and secondly the speaker of the lower house needs to show extreme discretion in consultation with secretaries of both the houses before declaring the bill as money bill. The latter provision installs political neutrality in the speaker of the lower house, which incidentally fails in this scenario, but could also have passed if the secretaries were listened to. Although, the last part in the previous statement is a mere speculation to say the least.

Apart from this parliamentary procedure, regaining legal tender for the old denominations is a costly affair, for exchange nodes would have evaporated by then barring the zonal offices of the RBI, which as it is would continue acting to accept these old denominations until 31st March. For such a legal tender to become valid for a month would turn banking system inside-out throwing restocking at branches out of gear. Though BAC has accepted this resolution, opposition numbers in the upper house are already heading towards a changing equation with the current opposition still maintaining an edge, but with the 5-states poll, BJP might head for a improvement in numbers rollover. Congress-backed resolution would undoubtedly face flak from the ruling dispensation in the upper house in the form of disruptions and once it is recess time, this resolution going through would find a harder patch to clear. All I could say is expect a tremendous amount of lobbying by the BJP to nullify oppositional gains, if any.