Ideological Morphology. Thought of the Day 105.1


When applied to generic fascism, the combined concepts of ideal type and ideological morphology have profound implications for both the traditional liberal and Marxist definitions of fascism. For one thing it means that fascism is no longer defined in terms of style, for e.g. spectacular politics, uniformed paramilitary forces, the pervasive use of symbols like fasces and Swastika, or organizational structure, but in terms of ideology. Moreover, the ideology is not seen as essentially nihilistic or negative (anti-liberalism, anti-Marxism, resistance to transcendence etc.), or as the mystification and aestheticization of capitalist power. Instead, it is constructed in the positive, but not apologetic or revisionist terms of the fascists’ own diagnosis of society’s structural crisis and the remedies they propose to solve it, paying particular attention to the need to separate out the ineliminable, definitional conceptions from time- or place- specific adjacent or peripheral ones. However, for decades the state of fascist studies would have made Michael Freeden’s analysis well-nigh impossible to apply to generic fascism, because precisely what was lacking was any conventional wisdom embedded in common-sense usage of the term about what constituted the ineliminable cluster of concepts at its non-essentialist core. Despite a handful of attempts to establish its definitional constituents that combined deep comparative historiographical knowledge of the subject with a high degree of conceptual sophistication, there was a conspicuous lack of scholarly consensus over what constituted the fascist minimum. Whether there was such an entity as generic fascism even was a question to think through. Or whether Nazism’s eugenic racism and the euthanasia campaign it led to, combined with a policy of physically eliminating racial enemies that led to the systematic persecution and mass murder, was simply unique, and too exceptional to be located within the generic category was another question to think through. Both these positions suggest a naivety about the epistemological and ontological status of generic concepts most regrettable among professional intellectuals, since every generic entity is a utopian heuristic construct, not a real thing and every historically singularity is by definition unique no matter how many generic terms can be applied to it. Other common positions that implied considerable naivety were the ones that dismissed fascism’s ideology as too irrational or nihilistic to be part of the fascist minimum, or generalized about its generic traits by blending fascism and nazism.


Morphed Ideologies. Thought of the Day 105.0


edited political spectrum

The sense of living in a post-fascist world is not shared by Marxists, of course, who ever since the first appearance of Mussolini’s virulently anti-communist squadrismo have instinctively assumed fascism to be be endemic to capitalism. No matter how much it may appear to be an autonomous force, it is for them inextricably bound up with the defensive reaction of bourgeoisie elites or big business to the attempts by revolutionary socialists to bring about the fundamental changes needed to assure social justice through a radical redistribution of wealth and power. According to which school or current of Marxism is carrying out the analysis, the precise sector or agency within capitalism that is the protagonist or backer of fascism’s elaborate pseudo-revolutionary pre-emptive strike, its degree of independence from the bourgeoisie elements who benefit from it, and the amount of genuine support it can win within the working class varies appreciably. But for all concerned, fascism is a copious taxonomic pot into which is thrown without too much intellectual agonizing over definitional or taxonomic niceties. For them, Brecht’s warning at the end of Arturo Ui has lost none of its topicality: “The womb that produced him is still fertile”.

The fact that two such conflicting perspectives can exist on the same subject can be explained as a consequence of the particular nature of all generic concepts within the human sciences. To go further into this phenomenon means entering a field of studies where philosophy of the social sciences has again proliferated conflicting positions, this time concerning the complex and largely subliminal processes involved in conceptualization and modeling in the pursuit of definite, if not definitive, knowledge. According to Max Weber, terms such as capitalism and socialism are ideal types, heuristic devices created by an act of idealizing abstraction. This cognitive process, which in good social scientific practice is carried out as consciously and scrupulously as possible, extracts a small group of salient features perceived as common to a particular generic phenomenon and assembles them into a definitional minimum which is at bottom a utopia.

The result of idealizing abstraction is a conceptually pure, artificially tidy model which does not correspond exactly to any concrete manifestation of the generic phenomenon being investigated, since in reality these are always inextricably mixed up with features, attributes, and surface details which are not considered definitional or as unique to that example of it. The dominant paradigm of the social sciences at any one time, the hegemonic political values and academic tradition prevailing in a particular geography, the political and moral values of the individual researcher all contribute to determining what common features are regarded as salient or definitional. There is no objective reality or objective definition of any aspect of it, and no simple correspondence between a word and what it means, the signifier and the signified, since it is axiomatic to Weber’s world-view that the human mind attaches significance to an essentially absurd universe and thus literally creates value and meaning, even when attempting to understand the world objectively. The basic question to be asked about any definition of fascism therefore, is not whether it is true, but whether it is heuristically useful: what can be seen or understood about concrete human phenomenon when it is applied that could not otherwise be seen, and what is obscured by it.

In his theory of ideological morphology, the British political scientist Michael Freeden has elaborated a nominalist and hence anti-essentialist approach to the definition of generic ideological terms that is deeply compatible with Weberian heuristics. He distinguishes between the ineliminable attributes or properties with which conventional usage endows them and those adjacent and peripheral to them which vary according to specific national, cultural or historical context. To cite the example he gives, liberalism can be argued to contain axiomatically, and hence at its definitional core, the idea of individual, rationally defensible liberty. however, the precise relationship of such liberty to laissez-faire capitalism, nationalism, the sanctuary, or the right of the state to override individual human rights in the defense of collective liberty or the welfare of the majority is infinitely negotiable and contestable. So are the ideal political institutions and policies that a state should adopt in order to guarantee liberty, which explains why democratic politics can never be fully consensual across a range of issues without there being something seriously wrong. It is the fact that each ideology is a cluster of concepts comprising ineliminable with eliminable ones that accounts for the way ideologies are able to evolve over time while still remaining recognizably the same and why so many variants of the same ideology can arise in different societies and historical contexts. It also explains why every concrete permutation of an ideology is simultaneously unique and the manifestation of the generic “ism”, which may assume radical morphological transformations in its outward appearance without losing its definitional ideological core.


Conjuncted: Indiscernibles – Philosophical Constructibility. Thought of the Day 48.1

Simulated Reality

Conjuncted here.

“Thought is nothing other than the desire to finish with the exorbitant excess of the state” (Being and Event). Since Cantor’s theorem implies that this excess cannot be removed or reduced to the situation itself, the only way left is to take control of it. A basic, paradigmatic strategy for achieving this goal is to subject the excess to the power of language. Its essence has been expressed by Leibniz in the form of the principle of indiscernibles: there cannot exist two things whose difference cannot be marked by a describable property. In this manner, language assumes the role of a “law of being”, postulating identity, where it cannot find a difference. Meanwhile – according to Badiou – the generic truth is indiscernible: there is no property expressible in the language of set theory that characterizes elements of the generic set. Truth is beyond the power of knowledge, only the subject can support a procedure of fidelity by deciding what belongs to a truth. This key thesis is established using purely formal means, so it should be regarded as one of the peak moments of the mathematical method employed by Badiou.

Badiou composes the indiscernible out of as many as three different mathematical notions. First of all, he decides that it corresponds to the concept of the inconstructible. Later, however, he writes that “a set δ is discernible (…) if there exists (…) an explicit formula λ(x) (…) such that ‘belong to δ’ and ‘have the property expressed by λ(x)’ coincide”. Finally, at the outset of the argument designed to demonstrate the indiscernibility of truth he brings in yet another definition: “let us suppose the contrary: the discernibility of G. A formula thus exists λ(x, a1,…, an) with parameters a1…, an belonging to M[G] such that for an inhabitant of M[G] it defines the multiple G”. In short, discernibility is understood as:

  1. constructibility
  2. definability by a formula F(y) with one free variable and no parameters. In this approach, a set a is definable if there exists a formula F(y) such that b is an element of a if F(b) holds.
  3. definability by a formula F (y, z1 . . . , zn) with parameters. This time, a set a is definable if there exists a formula F(y, z1,…, zn) and sets a1,…, an such that after substituting z1 = a1,…, zn = an, an element b belongs to a iff F(b, a1,…, an) holds.

Even though in “Being and Event” Badiou does not explain the reasons for this variation, it clearly follows from his other writings (Alain Badiou Conditions) that he is convinced that these notions are equivalent. It should be emphasized then that this is not true: a set may be discernible in one sense, but indiscernible in another. First of all, the last definition has been included probably by mistake because it is trivial. Every set in M[G] is discernible in this sense because for every set a the formula F(y, x) defined as y belongs to x defines a after substituting x = a. Accepting this version of indiscernibility would lead to the conclusion that truth is always discernible, while Badiou claims that it is not so.

Is it not possible to choose the second option and identify discernibility with definability by a formula with no parameters? After all, this notion is most similar to the original idea of Leibniz intuitively, the formula F(y) expresses a property characterizing elements of the set defined by it. Unfortunately, this solution does not warrant indiscernibility of the generic set either. As a matter of fact, assuming that in ontology, that is, in set theory, discernibility corresponds to constructibility, Badiou is right that the generic set is necessarily indiscernible. However, constructibility is a highly technical notion, and its philosophical interpretation seems very problematic. Let us take a closer look at it.

The class of constructible sets – usually denoted by the letter L – forms a hierarchy indexed or numbered by ordinal numbers. The lowest level L0 is simply the empty set. Assuming that some level – let us denote it by Lα – has already been

constructed, the next level Lα+1 is constructed by choosing all subsets of L that can be defined by a formula (possibly with parameters) bounded to the lower level Lα.

Bounding a formula to Lα means that its parameters must belong to Lα and that its quantifiers are restricted to elements of Lα. For instance, the formula ‘there exists z such that z is in y’ simply says that y is not empty. After bounding it to Lα this formula takes the form ‘there exists z in Lα such that z is in y’, so it says that y is not empty, and some element from Lα witnesses it. Accordingly, the set defined by it consists of precisely those sets in Lα that contain an element from Lα.

After constructing an infinite sequence of levels, the level directly above them all is simply the set of all elements constructed so far. For example, the first infinite level Lω consists of all elements constructed on levels L0, L1, L2,….

As a result of applying this inductive definition, on each level of the hierarchy all the formulas are used, so that two distinct sets may be defined by the same formula. On the other hand, only bounded formulas take part in the construction. The definition of constructibility offers too little and too much at the same time. This technical notion resembles the Leibnizian discernibility only in so far as it refers to formulas. In set theory there are more notions of this type though.

To realize difficulties involved in attempts to philosophically interpret constructibility, one may consider a slight, purely technical, extension of it. Let us also accept sets that can be defined by a formula F (y, z1, . . . , zn) with constructible parameters, that is, parameters coming from L. Such a step does not lead further away from the common understanding of Leibniz’s principle than constructibility itself: if parameters coming from lower levels of the hierarchy are admissible when constructing a new set, why not admit others as well, especially since this condition has no philosophical justification?

Actually, one can accept parameters coming from an even more restricted class, e.g., the class of ordinal numbers. Then we will obtain the notion of definability from ordinal numbers. This minor modification of the concept of constructibility – a relaxation of the requirement that the procedure of construction has to be restricted to lower levels of the hierarchy – results in drastic consequences.

Evental Sites. Thought of the Day 48.0


According to Badiou, the undecidable truth is located beyond the boundaries of authoritative claims of knowledge. At the same time, undecidability indicates that truth has a post-evental character: “the heart of the truth is that the event in which it originates is undecidable” (Being and Event). Badiou explains that, in terms of forcing, undecidability means that the conditions belonging to the generic set force sentences that are not consequences of axioms of set theory. If in the domains of specific languages (of politics, science, art or love) the effects of event are not visible, the content of “Being and Event” is an empty exercise in abstraction.

Badiou distances himself from\ a narrow interpretation of the function played by axioms. He rather regards them as collections of basic convictions that organize situations, the conceptual or ideological framework of a historical situation. An event, named by an intervention, is at the theoretical site indexed by a proposition A, a new apparatus, demonstrative or axiomatic, such that A is henceforth clearly admissible as a proposition of the situation. Accordingly, the undecidability of a truth would consist in transcending the theoretical framework of a historical situation or even breaking with it in the sense that the faithful subject accepts beliefs that are impossible to reconcile with the old mode of thinking.

However, if one consequently identifies the effect of event with the structure of the generic extension, they need to conclude that these historical situations are by no means the effects of event. This is because a crucial property of every generic extension is that axioms of set theory remain valid within it. It is the very core of the method of forcing. Without this assumption, Cohen’s original construction would have no raison d’être because it would not establish the undecidability of the cardinality of infinite power sets. Every generic extension satisfies axioms of set theory. In reference to historical situations, it must be conceded that a procedure of fidelity may modify a situation by forcing undecidable sentences, nonetheless it never overrules its organizing principles.

Another notion which cannot be located within the generic theory of truth without extreme consequences is evental site. An evental site – an element “on the edge of the void” – opens up a situation to the possibility of an event. Ontologically, it is defined as “a multiple such that none of its elements are presented in the situation”. In other words, it is a set such that neither itself nor any of its subsets are elements of the state of the situation. As the double meaning of this word indicates, the state in the context of historical situations takes the shape of the State. A paradigmatic example of a historical evental site is the proletariat – entirely dispossessed, and absent from the political stage.

The existence of an evental site in a situation is a necessary requirement for an event to occur. Badiou is very strict about this point: “we shall posit once and for all that there are no natural events, nor are there neutral events” – and it should be clarified that situations are divided into natural, neutral, and those that contain an evental site. The very matheme of event – its formal definition is of no importance here is based on the evental site. The event raises the evental site to the surface, making it represented on the level of the state of the situation. Moreover, a novelty that has the structure of the generic set but it does not emerge from the void of an evental site, leads to a simulacrum of truth, which is one of the figures of Evil.

However, if one takes the mathematical framework of Badiou’s concept of event seriously, it turns out that there is no place for the evental site there – it is forbidden by the assumption of transitivity of the ground model M. This ingredient plays a fundamental role in forcing, and its removal would ruin the whole construction of the generic extension. As is known, transitivity means that if a set belongs to M, all its elements also belong to M. However, an evental site is a set none of whose elements belongs to M. Therefore, contrary to Badious intentions, there cannot exist evental sites in the ground model. Using Badiou’s terminology, one can say that forcing may only be the theory of the simulacrum of truth.