Brassier, Grant: A Brief Return to Nature

There are staunch enemies of philosophies of nature, chief among them being mysticism, romanticism and the countless number of anthropic and theological thoughts creeping out the noetic morass of first causes. The theories of quantum mechanics can circumvent the notions of primary cause or primary mover, as following the works of Michio Kaku, the atoms to begin with could without the aid of any external agency start to bounce. Along such lines of thought Schelling, in his early period, focuses on forces and powers. One cannot feel a little stunned when Schelling describes the creation of the universe as a series of explosions in the First Outline.  As several critiques and tributes of/to Schelling show, it is his empirical inaccuracies (due to the time period mostly) and his later articulation of freedom which dominates and over writes the very possibility of nature philosophy. The central issue for nature philosophy becomes the tension between eliminativism and materialism (in the Žižekian/Badiouian/Lacanian sense) – between to what degree nature should be grounded without relying on a concept or structure which neither undermines the discoveries of contemporary science nor supports an anthropic view. But to return to nature philosophy – it seems that the process of realist eliminativism runs into the issue of emergence at some point and, with that conflict, the problem of freedom is reinserted into thought.

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For Brassier, ‘Speculative’ is typically a philosophy that begins by drawing attention to the identification between thinking and being, or, mind and reality thereby repudiating empirical naturalism and Kantian critical philosophy. Brassier thinks that Meillassoux and Grant both lend legitimacy to this paradigm even if only for lending it a singular materialist twist. The latter two thinkers retain a flavor of the appearance-reality distinction albeit in different philosophical contexts. The philosophical context for Grant is primarily based on the distinction between natura naturata and natura naturans, while the one for Meillassoux is based on the distinction between the phenomenal and mathematical properties. Although, Grant’s philosophy flirts with materialism and when he says that ‘nature thinks’, it is not to be taken as an equivocation of thinking and being, but must be considered as a complication of idealism or as idealism being the realism about the idea. In this case, the opposition between materialism and realism is all about the former being concerned with the interior and the latter with the outer/exterior. The problem remains with the ‘Subject’- that which thinks the out there and the in here.

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Philosophy of Quantum Entanglement and Topology

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Many-body entanglement is essential for the existence of topological order in condensed matter systems and understanding many-body entanglement provides a promising approach to understand in general what topological orders exist. It also leads to tensor network descriptions of many-body wave functions potentializing the classification of phases of quantum matter. The generic many-body entanglement is reduced to specifically 2-body systems for choice of entanglement. Consider the equation,

S(A) ≡ −tr(ρA log2A)) —– (1)

where, ρA ≡ trBAB ⟩⟨ΨAB | is the density matrix for part A, and where we assumed that the whole system is in a pure state AB.

Specializing AB⟩ to a ground state in a local Hamiltonian in D dimensions spatially, the central observation being that the entanglement between of a region A of size LD and the (much larger) rest B of the lattice is then often proportional to the size |σ(A)| of the boundary σ(A) of region A,

S(A) ≈ |σ(A)| ≈ LD−1  —– (2)

where, the correction -1 is due to the topological order of the topic code, thus signifying adherence to Boundary Law observed in the ground state of gapped local Hamiltonian in arbitrary dimension D, as well as in some gapless systems in D > 1 dimensions. Instead, in gapless systems in D = 1 dimensions, as well as in certain gapless systems in D > 1 dimensions (namely systems with a Fermi surface of dimension D − 1), ground state entanglement displays a logarithmic correction to the boundary law,

S(A) ≈ |σ(A)| log2 (|σ(A)|) ≈ LD−1 log2(L) —– (3)

At an intuitive level, the boundary law of (2) is understood as resulting from entanglement that involves degrees of freedom located near the boundary between regions A and B. Also intuitively, the logarithmic correction of (3) is argued to have its origin in contributions to entanglement from degrees of freedom that are further away from the boundary between A and B. Given the entanglement between A and B, introducing an entanglement contour sA that assigns a real number sA(i) ≥ 0 to each lattice site i contained in region A such that the sum of sA(i) over all the sites i ∈ A is equal to the entanglement entropy S (A),

S(A) = Σi∈A sA(i) —– (4) 

and that aims to quantifying how much the degrees of freedom in site i participate in/contribute to the entanglement between A and B. And as Chen and Vidal put it, the entanglement contour sA(i) is not equivalent to the von Neumann entropy S(i) ≡ −tr ρ(i) log2 ρ(i) of the reduced density matrix ρ(i) at site i. Notice that, indeed, the von Neumann en- tropy of individual sites in region A is not additive in the presence of correlations between the sites, and therefore generically

S(A) ≠ Σi∈A S(i)

whereas the entanglement contour sA(i) is required to fulfil (4). Relatedly, when site i is only entangled with neighboring sites contained within region A, and it is thus uncorrelated with region B, the entanglement contour sA(i) will be required to vanish, whereas the one-site von Neumann entropy S(i) still takes a non-zero value due to the presence of local entanglement within region A.

As an aside, in the traditional approach to quantum mechanics, a physical system is described in a Hilbert space: Observables correspond to self-adjoint operators and statistical operators are associated with the states. In fact, a statistical operator describes a mixture of pure states. Pure states are the really physical states and they are given by rank one statistical operators, or equivalently by rays of the Hilbert space. Von Neumann associated an entropy quantity to a statistical operator and his argument was a gedanken experiment on the ground of phenomenological thermodynamics. Let us consider a gas of N(≫ 1) molecules in a rectangular box K. Suppose that the gas behaves like a quantum system and is described by a statistical operator D, which is a mixture λ|φ1⟩⟨φ1| + (1 − λ)|φ1⟩⟨φ2|, |φi⟩ ≡ φ is a state vector (i = 1, 2). We may take λN molecules in the pure state φ1 and (1−λ)N molecules in the pure state φ2. On the basis of phenomenological thermodynamics, we assume that if φ1 and φ2 are orthogonal, then there is a wall that is completely permeable for the φ1-molecules and isolating for the φ2-molecules. We add an equally large empty rectangular box K′ to the left of the box K and we replace the common wall with two new walls. Wall (a), the one to the left is impenetrable, whereas the one to the right, wall (b), lets through the φ1-molecules but keeps back the φ2-molecules. We add a third wall (c) opposite to (b) which is semipermeable, transparent for the φ2-molecules and impenetrable for the φ1-ones. Then we push slowly (a) and (c) to the left, maintaining their distance. During this process the φ1-molecules are pressed through (b) into K′ and the φ2-molecules diffuse through wall (c) and remain in K. No work is done against the gas pressure, no heat is developed. Replacing the walls (b) and (c) with a rigid absolutely impenetrable wall and removing (a) we restore the boxes K and K′ and succeed in the separation of the φ1-molecules from the φ2-ones without any work being done, without any temperature change and without evolution of heat. The entropy of the original D-gas ( with density N/V ) must be the sum of the entropies of the φ1- and φ2-gases ( with densities λ N/V and (1 − λ)N/V , respectively). If we compress the gases in K and K′ to the volumes λV and (1 − λ)V , respectively, keeping the temperature T constant by means of a heat reservoir, the entropy change amounts to κλN log λ and κ(1 − λ)N log(1 − λ), respectively. Indeed, we have to add heat in the amount of λiNκT logλi (< 0) when the φi-gas is compressed, and dividing by the temperature T we get the change of entropy. Finally, mixing the φ1- and φ2-gases of identical density we obtain a D-gas of N molecules in a volume V at the original temperature. If S0(ψ,N) denotes the entropy of a ψ-gas of N molecules (in a volume V and at the given temperature), we conclude that

S0(φ1,λN)+S0(φ2,(1−λ)N) = S0(D, N) + κλN log λ + κ(1 − λ)N log(1 − λ) —– (5)

must hold, where κ is Boltzmann’s constant. Assuming that S0(ψ,N) is proportional to N and dividing by N we have

λS(φ1) + (1 − λ)S(φ2) = S(D) + κλ log λ + κ(1 − λ) log(1 − λ) —– (6)

where S is certain thermodynamical entropy quantity ( relative to the fixed temperature and molecule density ). We arrived at the mixing property of entropy, but we should not forget about the initial assumption: φ1 and φ2 are supposed to be orthogonal. Instead of a two-component mixture, von Neumann operated by an infinite mixture, which does not make a big difference, and he concluded that

S (Σiλi|φi⟩⟨φi|) = ΣiλiS(|φi⟩⟨φi|) − κ Σiλi log λi —– (7)

Von Neumann’s argument does not require that the statistical operator D is a mixture of pure states. What we really needed is the property D = λD1 + (1 − λ)D2 in such a way that the possible mixed states D1 and D2 are disjoint. D1 and D2 are disjoint in the thermodynamical sense, when there is a wall which is completely permeable for the molecules of a D1gas and isolating for the molecules of a D2-gas. In other words, if the mixed states D1 and D2 are disjoint, then this should be demonstrated by a certain filter. Mathematically, the disjointness of D1 and D2 is expressed in the orthogonality of the eigenvectors corresponding to nonzero eigenvalues of the two density matrices. The essential point is in the remark that (6) must hold also in a more general situation when possibly the states do not correspond to density matrices, but orthogonality of the states makes sense:

λS(D1) + (1 − λ)S(D2) = S(D) + κλ log λ + κ(1 − λ) log(1 − λ) —– (8)

(7) reduces the determination of the (thermodynamical) entropy of a mixed state to that of pure states. The so-called Schatten decomposition Σi λi|φi⟩⟨φi| of a statistical operator is not unique even if ⟨φi , φj ⟩ = 0 is assumed for i ≠ j . When λi is an eigenvalue with multiplicity, then the corresponding eigenvectors can be chosen in many ways. If we expect the entropy S(D) to be independent of the Schatten decomposition, then we are led to the conclusion that S(|φ⟩⟨φ|) must be independent of the state vector |φ⟩. This argument assumes that there are no superselection sectors, that is, any vector of the Hilbert space can be a state vector. On the other hand, von Neumann wanted to avoid degeneracy of the spectrum of a statistical operator. Von Neumann’s proof of the property that S(|φ⟩⟨φ|) is independent of the state vector |φ⟩ was different. He did not want to refer to a unitary time development sending one state vector to another, because that argument requires great freedom in choosing the energy operator H. Namely, for any |φ1⟩ and |φ2⟩ we would need an energy operator H such that

eitH|φ1⟩ = |φ2⟩

This process would be reversible. Anyways, that was quite a digression.

Entanglement between A and B is naturally described by the coefficients {pα} appearing in the Schmidt decomposition of the state |ΨAB⟩,

AB⟩ = Σα √pαAα ⟩ ⊗ |ΨBα ⟩ —– (9)

These coefficients {pα} correspond to the eigenvalues of the reduced density matrix ρA, whose spectral decomposition reads

ρA = ΣαpAα⟩⟨ΨAα—– (10)

defining a probability distribution, pα ≥ 0, Σα pα = 1, in terms of which the von Neumann entropy S(A) is

S(A) = − Σαpα log2(pα—– (11)

On the other hand, the Hilbert space VA of region A factorizes as the tensor product

VA = ⊗ i∈A V(i) —– (12)

where V(i) describes the local Hilbert space of site i. The reduced density matrix ρA in (10) and the factorization of (12) define two inequivalent structures within the vector space VA of region A. The entanglement contours A is a function from the set of sites i∈A to the real numbers,

sA : A → ℜ —– (13)

that attempts to relate these two structures, by distributing the von-Neumann entropy S(A) of (11) among the sites i ∈ A. According to Chen and Vidal, there are five conditions/requirements on entanglement contours that need satiation.

a. Positivity: sA(i) ≥ 0

b. Normalization: Σi∈AsA(i) = S(A) 

These constraints amount to defining a probability distribution pi ≡ sA(i)/S(A) over the sites i ∈ A, with pi ≥ 0 and i Σipi = 1, such that sA(i) = piS(A), however, do not requiring sA to inform us about the spatial structure of entanglement in A, but only relating to the density matrix ρA through its total von Neumann entropy S(A).

c. Symmetry: if T is a symmetry of ρA, that is AT = ρA, and T exchanges site i with site j, then sA(i) = sA(j).

This condition ensures that the entanglement contour is the same on two sites i and j of region A that, as far as entanglement is concerned, play an equivalent role in region A. It uses the (possible) presence of a spatial symmetry, such as invariance under space reflection, or under discrete translations/rotations, to define an equivalence relation in the set of sites of region A, and requires that the entanglement contour be constant within each resulting equivalence class. Notice, however, that this condition does not tell us whether the entanglement contour should be large or small on a given site (or equivalence class of site). In particular, the three conditions above are satisfied by a canonical choice sA(i) = S (A)/|A|, that is a flat entanglement contour over the |A| sites contained in region A, which once more does not tell us anything about the spatial structure of the von Neumann entropy in ρA.

The remaining conditions refer to subregions within region A, instead of referring to single sites. It is therefore convenient to (trivially) extend the definition of entanglement contour to a set X of sites in region A, X ⊆ A, with vector space

VX = ⊗i∈X V(i) —– (14)

as the sum of the contour over the sites in X,

sA(X) ≡  Σi∈XsA(i) —– (15)

It follows from this extension that for any two disjoint subsets X1, X2 ⊆ A, with X1 ∩ X2 = ∅, the contour is additive,

sA(X1 ∪ X2) = sA(X1) + sA(X2—– (16)

In particular, condition 2 can be now recast as sA(A) =S(A). Similarly, if X, X ⊆ A, are such that all the sites of X1 are also contained in X2, X1X2 ,then the contour must be larger on X2 than on X1 (monotonicity of sA(X)),

sA(X1) ≤ sA(X2) if X1 ⊆ X2 —– (17)

d. Invariance under local unitary transformations: if the state |Ψ′AB is obtained from the state AB by means of a unitary transformation UX that acts on a subset X ⊆ A of sites of region A, that is |Ψ′AB⟩ ≡ UXAB, then the entanglement contour sA(X) must be the same for state AB and for state |Ψ′AB.

That is, the contribution of region X to the entanglement between A and B is not affected by a redefinition of the sites or change of basis within region X. Notice that it follows that  Ucan also not change sA(X’), where X’ ≡ A − X is the complement of X in A.

To motivate our last condition, let us consider a state AB that factorizes as the product

AB⟩ = |ΨXXB⟩ ⊗ |ΨX’X’B—– (18)

where X ⊆ A and XB ⊆ B are subsets of sites in regions A and B, respectively, and X’ ⊆ A and X’B ⊆ B are their complements within A and B, so that

VA = VX ⊗ VX’, —– (19)

VB = VXB ⊗ VX’B —– (20)

in this case the reduced density matrix ρA factorizes as ρA = ρX ⊗ ρX’ and the entanglement entropy is additive,

S(A) = S(X) + S(X’) —– (21)

Since the entanglement entropy S(X) of subregion X is well-defined, let the entanglement profile over X be equal to it,

sA(X) = S(X) —– (22)

The last condition refers to a more general situation where, instead of obeying (18), the state AB factorizes as the product

AB⟩ = |ΨΩAΩB⟩ ⊗ |ΨΩ’AΩ’B, —– (23)

with respect to some decomposition of VA and VB as

tensor products of factor spaces,

VA = VΩA ⊗ VΩ’A, —– (24)

VB = VΩB ⊗ VΩ’B —– (25)

Let S(ΩA) denote the entanglement entropy supported on the first factor space VΩA of  VA, that is

S(ΩA) = −tr(ρΩA log2ΩA)) —– (26)

ρΩA ≡ trΩB |Ψ ΩA ΩB⟩⟨Ψ ΩA ΩB| —– (27)

and let X ⊆ A be a subset of sites whose vector space VX is completely contained in VΩA , meaning that VΩA can be further decomposed as

VΩA  ≈ VX VX’ —– (28)

e. Upper bound: if a subregion X ⊆ A is contained in a factor space ΩA (24 and 28) then the entanglement contour of subregion X cannot be larger than the entanglement entropy S(ΩA) (26)

sA(X) S(ΩA) —– (29)

This condition says that whenever we can ascribe a concrete value S(ΩA) of the entanglement entropy to a factor space ΩA within region A (that is, whenever the state AB factorizes as in (24) then the entanglement contour has to be consistent with this fact, meaning that the contour S(X) in any subregion X contained in the factor space ΩA is upper bounded by S(ΩA).

Let us consider a particular case of condition e. When a region X ∈ A is not at all correlated with B, that is ρXBX ⊗ ρB,then it can be seen that X is contained in some factor space ΩA such that the state |Ψ ΩA ΩB itself further factorizes as |Ψ ΩA⟩ ⊗ |ΨΩB, so that (23) becomes

AB⟩ = |Ψ ΩA⟩ ⊗ |ΨΩB ⊗ |ΨΩ’AΩ’B ⟩, —– (30)

and S(ΩA) = 0. Condition e then requires that sA(X) = 0, that is

ρXBX ⊗ ρB sA(X) = 0, —– (31)

reflecting the fact that a region X ⊆ A that is not correlated with B does not contribute at all to the entanglement between A and B. Finally, the upper bound in e can be alternatively announced as a lower bound. Let Y ⊆ A be a subset of sites whose vector space VY completely contains VΩA in (24), meaning that VY can be further decomposed as

VY VΩA ⊗ VΩ’A —– (32)

e’. Lower bound: The entanglement contour of subregion Y is at least equal to the entanglement entropy S(ΩA) in (26),

sA(Y) ≥ S(ΩA) —– (33)

Conditions a-e (e’) are not expected to completely determine the entanglement contour. In other words, there probably are inequivalent functions sA : A → ℜ that conform to all the conditions above. So, where do we get philosophical from here? It is through the entanglement contour through selected states that a time evolution ensuing a global or a local quantum quench characterizing entanglement between regions rather than within regions, revealing a a detailed real-space structure of the entanglement of a region A and its dynamics, well beyond what is accessible from the entanglement entropy alone. But, that isn’t all. Questions of how to quantify entanglement and non-locality, and the need to clarify the relationship between them are important not only conceptually, but also practically, insofar as entanglement and non-locality seem to be different resources for the performance of quantum information processing tasks. Whether in a given quantum information protocol (cryptography, teleportation, and algorithm . . .) it is better to look for the largest amount of entanglement or the largest amount of non-locality becomes decisive. The ever-evolving field of quantum information theory is devoted to using the principles and laws of quantum mechanics to aid in the acquisition, transmission, and processing of information. In particular, it seeks to harness the peculiarly quantum phenomena of entanglement, superposition, and non-locality to perform all sorts of novel tasks, such as enabling computations that operate exponentially faster or more efficiently than their classical counterparts (via quantum computers) and providing unconditionally secure cryptographic systems for the transfer of secret messages over public channels (via quantum key distribution). By contrast, classical information theory is concerned with the storage and transfer of information in classical systems. It uses the “bit” as the fundamental unit of information, where the system capable of representing a bit can take on one of two values (typically 0 or 1). Classical information theory is based largely on the concept of information formalized by Claude Shannon in the late 1940s. Quantum information theory, which was later developed in analogy with classical information theory, is concerned with the storage and processing of information in quantum systems, such as the photon, electron, quantum dot, or atom. Instead of using the bit, however, it defines the fundamental unit of quantum information as the “qubit.” What makes the qubit different from a classical bit is that the smallest system capable of storing a qubit, the two-level quantum system, not only can take on the two distinct values |0 and |1 , but can also be in a state of superposition of these two states: |ψ = α0 |0 + α1 |1.

Quantum information theory has opened up a whole new range of philosophical and foundational questions in quantum cryptography or quantum key distribution, which involves using the principles of quantum mechanics to ensure secure communication. Some quantum cryptographic protocols make use of entanglement to establish correlations between systems that would be lost upon eavesdropping. Moreover, a quantum principle known as the no-cloning theorem prohibits making identical copies of an unknown quantum state. In the context of a C∗-algebraic formulation,  quantum theory can be characterized in terms of three information-theoretic constraints: (1) no superluminal signaling via measurement, (2) no cloning (for pure states) or no broadcasting (mixed states), and (3) no unconditionally secure bit commitment.

Entanglement does not refute the principle of locality. A sketch of the sort of experiment commonly said to refute locality runs as follows. Suppose that you have two electrons with entangled spin. For each electron you can measure the spin along the X, Y or Z direction. If you measure X on both electrons, then you get opposite values, likewise for measuring Y or Z on both electrons. If you measure X on one electron and Y or Z on the other, then you have a 50% probability of a match. And if you measure Y on one and Z on the other, the probability of a match is 50%. The crucial issue is that whether you find a correlation when you do the comparison depends on whether you measure the same quantity on each electron. Bell’s theorem just explains that the extent of this correlation is greater than a local theory would allow if the measured quantities were represented by stochastic variables (i.e. – numbers picked out of a hat). This fact is often misrepresented as implying that quantum mechanics is non-local. But in quantum mechanics, systems are not characterised by stochastic variables, but, rather, by Hermitian operators. There is an entirely local explanation of how the correlations arise in terms of properties of systems represented by such operators. But, another answer to such violations of the principle of locality could also be “Yes, unless you get really obsessive about it.” It has been formally proven that one can have determinacy in a model of quantum dynamics, or one can have locality, but cannot have both. If one gives up the determinacy of the theory in various ways, one can imagine all kinds of ‘planned flukes’ like the notion that the experiments that demonstrate entanglement leak information and pre-determine the environment to make the coordinated behavior seem real. Since this kind of information shaping through distributed uncertainty remains a possibility, folks can cling to locality until someone actually manages something like what those authors are attempting, or we find it impossible. If one gives up locality instead, entanglement does not present a problem, the theory of relativity does. Because the notion of a frame of reference is local. Experiments on quantum tunneling that violate the constraints of the speed of light have been explained with the idea that probabilistic partial information can ‘lead’ real information faster than light by pushing at the vacuum underneath via the ‘Casimir Effect’. If both of these make sense, then the information carried by the entanglement when it is broken would be limited as the particles get farther apart — entanglements would have to spontaneously break down over time or distance of separation so that the probabilities line up. This bodes ill for our ability to find entangled particles from the Big Bang, which seems to be the only prospect in progress to debunk the excessively locality-focussed.

But, much of the work remains undone and this is to be continued…..

 

Brassier and Rehabilitating Philosophies of Nature

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Brassier takes the continental tradition to task for unchallengingly accepting the liquidation of epistemology and in the process launching a counter-scientific ontology and metaphysics of nature, where the latter is treated not just as an antidote to scientific reductionism, but at the same time taken as a corrective to the ‘positivistic’ naturalization of the analysis of mind, with the emergence of cognitive science as the most obvious consequence. Brassier is seen to be championing for science in relation to neurology and ‘Correlationism’ that somehow justifies the scientific way of thinking, but the question that remains unformulated is the difference he shares with Meillassoux’s formalism and his notion of philosophical access to it. It seems that Brassier is seduced by the existence of the world and tends to ignore the importance of image by avoiding realities of image[s].  These still are images, because of the ways in which our nervous system works. Thus science may pose a threat to a certain kinds of commonsense and certain types of folk metaphysics, but at the same time, it could replace the ones threatened with a set of others. In a way, a complete theoretical/epistemological suspension is untenable. This is also a claim of ‘Correlationism’ as all our access to the world is mediated through the day-to-day phenomenological world of lived experiences or what Heidegger referred to as the world of ‘everydayness’. But, this is not doing justice to his thought, as he explicitly maintains in his Alien Theory that in order to attain an adequate conceptual grasp of the unitary nature of physical reality, it is necessary to achieve a complete theoretical suspension of the image of the world derived from perceptual intuition. In other words, physical theory has to effect a rigorously mathematical circumvention of those imaginative limitations inherent in the physiologically rooted cognitive apparatus with which an aleatory evolutionary history has saddled us. Thus, the chief obstacle standing in the way of a proper scientific understanding of the physical world would seem to be that of our species’ inbuilt tendency to process information via epistemic mechanisms which invariably involve an operation of subtraction from the imperceptible physical whole. The case of neurology is, a bit more difficult. One of the things that the neuroscientist will wish to explain is the neurological base of this phenomenological lived experience. If we begin from the premise that one form of science seeks to discover the causal mechanisms or agencies that underlie phenomena or effects, then the phenomenon in question for the neurologist will be this lived experience or image of the world. As a result, this image of the world cannot be dispensed with without neurology becoming unintelligible. However, even here we find stark departures from our image of the world. For example, I experience myself as a centralized agency making decisions and choices based on a transparency to myself. Yet neurology reveals that in fact “I” am a non-linear network of neurons without transparency, unity, or center. Likewise, these scientists reveal that the reasons we give for doing things are often wildly at odds with the mechanisms behind these things. Here, one gets a feeling that ‘correlationists’ would not give any credence to such thoughts for they are at odds with the structure of the ordinary lived experience. As Husserl rightly points out in his Ideas I:

“The existence of Nature cannot be the condition for the existence of consciousness since Nature itself turns out to be a correlate of consciousness: Nature is only as being constituted in regular concatenations of consciousness.”

When asked about this particular project rehabilitating philosophies of nature, Brassier outlined it as:

  1. These counter-scientific conceptions of nature represent a neo-Aristotelian resurgence in contemporary continental philosophy;
  2. That the model of representation whose critique underwrites the liquidation of epistemology is a willful caricature; and
  3. That a naturalized but non-adaptationist account of representation provides the basis for a conception of epistemology capable of prosecuting scientific realism and countermanding the regressive tenor of these neo-Aristotelian philosophies of nature.

Schelling, Iain Hamilton Grant and Differential Nature(s) 1.0

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Schelling has often been at the receiving end for his idiosyncrasies or the frequent jumps that he undertook providing a lack of synthetic conflation and therefore missing on a philosophical system. He has most importantly been confined to near total oblivion in the English-speaking fraternity of philosophers and has had to face rebarbative charges against him. Although, there are some sympathetic voices emanating from the continental tradition in trying to revive his importance, like Slavoj Zizek, who has extensively fused the German with Lacanian psychoanalysis, citing Marx’s critique of speculative idealism as derived from Schellingian formulations of post-Hegelian universe of finitude-contingency-temporality. Zizek even goes a step ahead by crediting Schelling over Heidegger as the progenitor of ‘Artificial Earth’. But, it is Grant’s ‘Philosophies of Nature After Schelling’, which takes up the issue of graduating Schelling to escape the accoutrements of Kantian and Fichtean narrow transcendentalism.

Schelling gave a new twist to understanding nature by going past the Kantian nature as subject to necessary laws, as for Kant, nature enjoyed a formal sense. Kant overlooks the phenomenological deficit by arguing for subject’s access to forms of intuition and categories to bear upon what it perceives. Schelling discovers the problematic by raising the issue of subject’s spontaneity to judge in terms of categories. This dynamism of ‘becoming’ is what incites Grant to look into the materialist vitalism in Schelling’s understanding of nature. Grant frees Schelling from the grips of narrow minded inertness and mechanicality in nature that Kant and Fichte had presented nature with. This idea is the Deleuzean influence on Grant. Kant himself pondered over this dilemma, but somehow couldn’t come to terms with subject taking a leap from its determinism in crafting episteme. For, if nature was formal in its adherence to necessary laws, then splitting this boundedness to nature from subject’s autonomous or self-determining cognitivity would arrest the leap from determinism. In a way, Kant falls into the pit that he tries to negotiate, but comes out in conceding to nature the generation of self-determining organisms that possibilizes disinterested aesthetic pleasure in his third critique.  It didn’t take Schelling any Herculean effort to underline the central problems with this position of Kant, but it has taken a path of deliberate neglect of Schelling’s discovery of nature as more subject than object in modern readings of the philosopher.

Grant affirms the cardinality of Schelling’s naturephilosophie as the core, rather than just a phase as against Heidegger’s proclamation of Schelling’s discovery of nature as a fleeting episode, despite Heidegger paying fullest respects to Schelling for his profoundest grasp of spirit because of his commencing from the philosophy of nature. In a remarkable tour de force, Grant takes the accusation of Eschenmayer’s against Schelling head on and helps resurface the identity between nature and history. This identity is derived from Schelling’s insistence on freedom arising from nature, as the latter’s final and most potentiating act, the idea that constantly irritated Eschenmayer. Nature is history also helped Schelling cut the umbilical cord between evolution and teleology, in that he could fix his impressions on Carl Friedrich Kielmeyer’s signaling of a new epoch in natural history, thus getting over with transcendental philosophy’s obsession with fixed forms. That the inertness of nature was already on the way of getting dislodged, was proved by Kielmeyer’s influence on the earliest programme of the German comparative Biology, by which Schelling had himself been mightily influenced. As Kielmeyer had noted in his writings,

“I myself would like to derive all variation in the material of inert nature from a striving for heterogenesis, analogous to that in the organism, in the soul of nature.”

Schelling and Kielmeyer were fellow travelers in the sense that both recognized the fundamental delusion of the Kantian possibility of using a piori principles in deducing external nature. Grant makes a very affirmative intervention in here, when he elevates Deleuzean admonition to the fact that only contemporary French philosophy offers a scathing attack on the modern philosophy since its inception by Descartes holding the verdict of ‘nature not existing for itself’. This whole notion of becoming over being is wrought about by seemingly imperceptibly small and infinitely many changes. Or as Schelling maintains:

“Nature admittedly makes no leap; but it seems to me that this principle is much misunderstood if we try to bring into a single class of things which nature has not only separated, but has itself opposed to one another. That principle says no more than this, that nothing which comes to be in nature comes to be by a leap; all becoming occurs in a continuous sequence.”

This continuous sequential becoming is what has made Schelling to look at forces more potently rather than at phenomena as the measure of the differentials between the things that are separated by nature, but only as factors pertaining to becoming. This is a direct supplement to Kielmeyerian account of natural history, converting the principles underlying transcendental philosophy from the phenomenal and the somatic nature to making the somatic into the phenomenal products of a priori dynamics,  without making the phenomenal somatic coextensive with nature as such.  Products as such, for Schelling were discontinuities in nature and therefore not in the real sense speculative, as this was based on the principle of an Idea of nature as against nature and as ‘materiality is not yet corporeality’.

 

Phaneroscopy/Phanerology de-agentify

Yes, it is a limitation to break the world/universe, or what have you into the binaries. A resolution of the same ain’t possible, until one either exercises an asymptotic progression/regression machine on it, and thus relegating the whole into an aporetic point of philosophical frustration that goes by the name of dialectics, or, one somehow experiences an event of binaries morphing into one another. Such a collapse of the one into the other gravitates the defining points of differences into identities, and this goes by the name of Laruellean “decisionism-in-the-last-instance”. So, dialectics with the second method goes on a honeymoon where minds of the left spend countless nights trying to get it back to the realistic domain (pun intended!!!).

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I’d be sorry to be getting into territories that speak the language of failed poets/prose writers, for otherwise, I’d not be able to justify how bad a writer I really am!!! The lightened poetry of non-sense and/of Being: Even if such a poetry did exist (for me, at least it never did), then it was probably the romantic ideal of the by-gone philosophical ages, and we seem to have come a long way out of it, but still cling on to the symptoms of such an era. Pity!! It is not conjoining the obscure with the nothingness, or the Other World. It is rather the tunnelling of the lyrical aspect with the nothingness, a Schellingian approach to when he says that without confrontation, there is nothing of the creation possible. Dialectical, yes, in a way, but also the underside of it, which is considered a pariah, an outcast, an avoided and avoidable theory of creativity, or what I understand as Leper Creativity. Yes, losing identity could be viewed as relative here. But as I said, “could be”, and I refuse to truck with it imposed-consciously. And hereby, I also answer a subsequent point: “it” is uncharacteristic of holding true to the pillars of what constitutes it. Far-fetchedly, “it” is like what Wittgenstein would say: rise up the rung of the ladder and then discard it. But, a difference is to be spotted here. For Wittgenstein, the climber discards the ladder, whereas in this the present context, with each rising up on the rung of the ladder, a sort of dehumanization takes place in terms of awe/sublime/incapacitation. In other words, a sense of belonging to the “it” is bred in the “we” (agents/agencies) undoubtedly, but is lost sight of due to the intense flows of the “it” in time. A sort of exponential hypertrophy of the “it” due to “we”, or loosely saying emergentism in which node/nodes of “we” are simply sucked in. So, “we” build up the “it”, and lose it identity-wise in the process.

On similar lines, the knowledge of surplus is bluntly replaced by the awareness of it, an excess that is wasted more than it is used, and a kind of “solar anus” in the Bataillean sense, truly. Philosophical aesthetics falling in the hands of terrorizing hermeneutics: yes, I concur on this. This is one of the reasons, why I have started advocating phaneroscopy/phanerology over phenomenology, and it comes close to your recent studies on the quantum physics. But, then do we have a choice? We are yet to be defeated by the exploding solar anus, even though we are well on our way to a crushing defeat. Analogically, when someone says that “a world without capitalism is possible”, I tell of such Occupy/World Social Forum pundits that it is, but in a way that is stripped of agencies, and not otherwise. Sorry for the hubris here on my part, but my way of looking into these aspects could either mean that I am going a bit too far in my analysis, or getting really cracked brain now. On the point of polarity between order and disorder becomes unidentifiable when I say of lemniscate obscuring the horizon. Why do I say this? For me, order is nothing but an echo of a disordered anarchy that still reverberates. With this, I quash ethics, and I have no qualms in doing so, for a whole new set of rules need to be rewritten/rethought in this very darkness, which incidentally is on the avoidable radar still, but is making a stealthy invasion upon us, and before time will annihilate us, and de-anthropocentrize. Can’t help feeling sorry for Kant now for sure.

“It” is the cosmic “capitalism”.

Is Philosophy Revenant?

This piece is in no way trying to endorse the polemical happenings in philosophy on the continent and across the channel and the Atlantic in the English speaking countries. The tradition of analytic philosophy and continental philosophy are indeed compossible and also in a way in a state of cold war. But one thing that is running like a common thread in the minds of many of the philosophers is the proclamation of the ‘End of Philosophy’. I want to shy from giving recognition to the eschatology that philosophy is facing and hence try to show that the death of philosophy is in no way in sight as it would mean the tragic abandonment of reflection and meaning, which keeps me in doubt if at all we would want to suffer such a loss. Indeed we do face a spate of intellectual terrorism and often badly defined and badly done philosophy, but then our valiant attempt, to echo Oliver Wendell Holmes, ‘to churn void and make cheese’ isn’t here to stay.

We have heard that physics is nearing its end. Physicists are trying to set up a system of equations which are together called the Grand Unified Theories (GUT) that would enable to answer all the possible phenomena in the Universe. Although this claim has been made for a long time, the end as such is in no way in sight. Similarly starting with the initial years of the last century, philosophical problems or systems are either being given the confident death knell or they have been branching off to explore new fields. This in a nutshell definitely lends legitimacy to what Ernst Gellner said in his Words and Things: “a cleric who loses his faith abandons his calling, but a philosopher who loses his redefines his subject.” But on the other hand there have been constant questions asked about the purposefulness nature of doing philosophy in the first place. The only philosophy one might engage in after all that has happened would no longer make any pretense of being in control of the absolute. Indeed, it would have to forbid itself to think the absolute, lest it betray the thought. And yet it must not allow anything to be taken away from the emphatic concept of the truth. This contradiction which was closely followed in the earlier days of the Frankfurt School critical theory tradition defined the precise element of the purpose of doing philosophy.

It is definitely not the case of growing contempt towards philosophy, but a sense of decadence in doing it. This despondency in no way should be linked with the building up of contempt. Bertrand Russell in his ‘Unpopular Essays’ thinks that if contempt for philosophy is developed to the point, at which it becomes systematic, then it becomes a philosophy.

My intention in this talk is to side with what EM Forster once said: “Death destroys a man; the idea of death saves him.” In this particular saying, I wish to substitute man with philosophy. It is precisely this thought or the idea that philosophy is dead, that the entire studies in philosophy are continuing in the process of ongoing history.

One must remember the fact that when the Greeks spoke of the end of philosophy, they had telos in mind as the end and not like today’s usage wherein the end depicts the cessation or the terminal end of doing philosophy. Philosophy from the days it began had one companion always following it and that was sophistry. That clearly does not mean that we need to read the history of philosophy along with a history of anti-philosophy.

Before going any further, I would like to quote from Kierkegaard’s Fear and Trembling:

“Heraclitus the obscure said, ‘One cannot pass twice through the same stream’. Heraclitus the obscure had a disciple who did not stop with that, he went further and added, One cannot do it even once’. Poor Heraclitus, to have such a disciple! By this amendment the thesis of Heraclitus was so improved that it became an Eleatic thesis which denies movement, and yet the disciple decided only to be a disciple of Heraclitus… and to go further-not back to the position Heraclitus had abandoned.” 

In the universities where new courses in psychology, anthropology, applicative sciences and business sciences are being set up rapidly, philosophy departments are seeing a major decrease in enrollment. Even funds at the disposal of philosophy studies are getting reduced. This could very well mean that philosophy is at an end. This phenomenon is precisely what Heidegger calls the growing impact of specialists in the sense of being more scientific and less democratic control on the various aspects of associate life. This particular train of thought could very well be linked with Plato’s philosopher kings not getting manifested. Heidegger here expresses concern with the emergence of power vested in an uncontrolled manner that he condemns as being very deceitful and dangerous with the ever-increasing inevitability of ‘striking at the heart of the state’. This power according to Heidegger is democratic in format. Many contemporary philosophers are trying to label this scenario in a psychiatric metaphoric manner by terming it as schizophrenic.

The end could be thought of in two manners: the first being Philosophy coming full circle, and hence an aporia is reached and to do philosophy, one starts from where one originally began. This notion is Hegelian. The other is the doctrine of ‘Quietism’, which indicates the clarification of language such that the philosophical problems are not solved but dissolved, the Wittgensteinian notion. He says in the Philosophical Investigations that we are seeking complete clarity in that philosophy is given peace and hence is no more tormented by the questions that bring itself into it (PI, #133). If this is achieved, it is possible to will a stoppage to doing philosophy. But that is not all. There is Deleuze with his proclamation of the end of the verticality of ideas and replaced by the horizontality of ideas, the rhizomatic. I’ll be concentrating on Deleuze’s treatment at the hands of Badiou.

On the continent, it was Nietzsche, who is responsible for killing God. He never achieved any success in consummating philosophy, in setting it any impossible task, but then showed the futility in the very act of doing philosophy. His non-acceptance of traditional pillars of the ideas of classical age indeed persuaded the non-analytical philosophers to accept thinking as the systematic distortion of reality and Heidegger further cemented his notions. If the philosophers on the continent subscribe to this stand, it is indeed trying to correlate with the Hegelian notion of ‘coming full circle’ and thus getting stuck in nostalgia. Heidegger’s notion of ‘metaphysics’ is precisely the idea that being is order,  objectively given for once and all. If being is decidedly given once and for all, history is arrested and finds itself in a closed circuit thus ruling out any possibility of openness.  Heidegger cites in his lecture on the end of philosophy, the overturning of metaphysics at the hands of Marx. Metaphysics is still a talk of some philosophers either as a continuation of the classical thought or by analytical tradition in which it is taken to connote rigidified ‘regional ontologies’ deprived of the historicity that one traces in the Kantian and Husserlian transcendental as the condition for the possibility of any philosophy or science. Heideggerian notion of metaphysics in contemporary philosophy is largely rejected.

As I promised earlier, my focus is on the philosophical thought of Deleuze. To take his treatment at the hand of French philosopher, Badiou is my primary interest here. His contribution could lead us into a created framework wherein we could be led out of the labyrinth of this badly defined continental philosophy. This might not be any space of hope as it could also play itself on the flip side. There are occasions where his doxa that are traces or rather traits of the Heideggerian or Deleuzian doxa are compelling him to fall prey to; thus cutting off a truer confrontation with the radicality of his work that he starts off with.

Badiou talks of the reinvention of the categories of truth and subject against Nietzschean critique, eventuality, politics vis-a-vis ontology born again and the treatment of European nihilism and capitalism. He takes the cases of Heidegger and Deleuze in explicating these issues. In his treatment of Heidegger in the Manifesto and of Deleuze in the Clamor for Being, he has caricatured Heidegger’s opinion supporting crypto-teleology of the ‘end of philosophy’, while opening up the thought of Deleuze for a conceptual confrontation. Badiou’s system echoes Deleuze’s philosophical injunctions in that he never believed metaphysics to die a natural death but insisted it’s stifling at the hands of sophistry, philosophical thought as immanently multiple and without taking any recourse to nostalgia as far as explaining phenomenon like Nihilism.

For philosophy to be revenant, Badiou advocates a concept called ‘Platonism of the multiple’. According to Badiou, the first responsible cause of the death is borrowed from Lacan’s concept of Suture. That philosophy sutures (binds) itself with the non-philosophical conditions i.e. the destiny and the praxis of philosophy is sutured with these conditions. His four conditions are politics, science, art and love. For instance, political suture: Marxism, that is philosophy binding itself to a particular political programme. It is extremely essential if philosophy has to travel historically, these sutures are to be retained. The problem of the end of philosophy arises in the case of ‘double suture’ when a belief in the complicity of the ‘metaphysics of subjectivity’ and technological determined totalitarianism is maintained. Such complicitous natures urge philosophy to abandon its consistency and thus compel a cadence of a kind. This is in a nutshell is the jettisoning of independent procedures philosophy is used to take to.

Badiou demands that philosophy thinks of the discontinuity in the productions of evental subjects as holes in the fabric of knowledge thus undermining living philosophical traditions and reinventing Subject and Truth. Both these reinvented categories are thought of as ‘event’ emerging out of the void (inconsistency) of any situation. His fidelity to the event as rare, the subject as finite fragment of the post-event objectless truth and truth as the event of the void of the situation has adverse ramifications. In his study on Deleuze, the only way of reinventing these categories is through the reinvention of meontology that is the equating of Being with Multiple-Composition of the world through set theory. This is his Platonism of the Multiple. Badiou not only denies the phenomenological subject, but also the continuity of Being thus rejecting the notion of philosophical temporality. To that even Deleuze was anti-phenomenological in his approach, as he would take the experience to its utmost consequences and then de-suturing the subject/object distinction to make it impersonal.

Badiou took the approach to the Set Theory only to discern his denial of the concept of experience and primacy of language. If truth has to be given a rebirth as objectless, the problem of indiscernible must be dealt with. He takes the help of the set-theoretical approach to de-suture being and language. He defines truth as the singular and extra-linguistic production of the multiplicity within one of the four conditions viz, politics, science, art and love of philosophy. If truth is looked at like a supplement rather than any recourse to the transcendence, then there is this inconsistency of the void in the form of an indiscernible (not nameable, but capable of conceptualization), and then are we not dealing with the truth of the situations as such rather than the truth of this situation? What singularity can we attach to this inconsistency? Are truths only to be differentiated on the basis of decisive intervention of meaning? Badiou’s taking to meontology fails in its defence of the singularity of the event. So it seems clear here that the very destination of Deleuze’s thought is the One, and that the profusion of cases does not attest to their irreducible singularity and that alleged philosophy of the event is already there.

As for the treatment meted by Badiou on the topicality of Eternal Return, the opposition is Nietzsche contra Mallarme and is regarded on the basis of chance and accountable to the topology of the fold. Badiou opposes any conceptual probabilism that would allow Events to be tendentially captured by the entropy of the Same. Univocity must approve of divergence. However, Badiou is not too articulating in his distinction between the actual and the virtual with regard to the Bergson’s duration. In Deleuze’s treatment of entropy (D&R), the thought is for both the efficacy of the statistical reduction of events to identity and the inability of this position to account for its own genesis and for genesis itself, a sort of a double bind. What is questionable though is the very transformation of entropy to simulacrum. The philosophical ‘plane of immanence’ and the scientific ‘plane of reference’ are in a sort of unproblematic opposition and this antagonism precisely is the continuity for the philosophical endeavour.

Both Badiou and Deleuze share an utter disdain for ‘End of Philosophy’ and Badiou especially feels a deep scorn for spreading the ‘Empire of Opinion’ as in one conference, he said that ‘The Freedom of Opinion is the Enemy of Philosophy’.

Gerald Bruns mentions in his end of philosophy essays that philosophy is to be located at the level of the singular and irreplaceable rather than at the level of the universal and the necessary. He talks about this openness precisely in the sense of alterity in that this openness finds a way of substitutability of the sovereignty of the subject. Bruns believes that philosophy can recapture ‘an intimacy with the world’ of the kind Levinas talked about of the relation of proximity. This means that our relation with the world is not just confined to purely a theoretical one, but that of practical relation with those situated within an ongoing history. Now with the primacy placed on the practical, ethics can be given a privileged position in establishing a dialogue between philosophy and literature. This thesis aims at subverting the inherited conception of philosophy as the foundation of knowledge by elevating the singular over the universal and event over the law.

I do agree to a complete detour being taken on the continent in the very practice of doing philosophy and that was the reason why I had commented on Badiou being the protector. Postmodernism sounded the death knell for the classical way of thinking of philosophy in terms of grand narratives. Micro or localized narratives are the more sensibly thought of in answering the changing world scenario. Even by the time, post-modernism could actually sink in by dethroning the ideas related to modernism, talks of ‘Performatism’ started to surface. This concept signifies the sign, subject to come together in ways for creating the aesthetic experience of transcendency…locating it in a place where meaning is constructed. Performatism is looked at as ‘New Faith’. Together these new epochal ideas have come to be known as ‘New Sincerity’ and are the talk in the west of a loose connection between cultural studies and philosophy post 9/11.

Thus is to concur that philosophy as revenant is indeed what we are witnessing today as the break from the ideas of the classical ages gone by is getting more and more subscriptions. All is not lost, if we pay heed to deconstruction techniques in the sense that the end is deferred and yet to come. We need to get the old methodology back from its marginalized occupied space to the center. This may just be a lot of demand but then it is the most viable way to encounter this apocalypse.

If philosophy is to be realized, it has to be eliminated – Marx…..