7
Filozofski vestnik | Volume XLII | Number 1 | 2021 | 7–23 | doi: 10.3986/fv .42.1.01
* National Institute of Biology, Ljubljana, Slovenia
Matjaž Ličer*
Temporality in Badiou’s Ontology and  
Greater Logic
Alain Badiou has often remarked that the single most central question of his 
philosophy is the following: How does a novelty inscribe itself into a specific 
situation? What are the strategies for delineating, within a given situation, with-
in a given world, the new from the old? What are the necessary and sufficient 
conditions for the possibility of a novelty in a world? These questions hold a 
very specific meaning within Badiou’s system of thought and in reference to his 
terminology. One can partly localize this meaning by an overview of Badiou’s 
conceptualization of ontology as mathematics – should one choose to accept 
it
1
 – in Being and Event
2
 and partly by his construction of the Greater Logic (the 
logic of the transcendental) in Logics of Worlds.
3
 This, however, does not seem to 
suffice. Within Badiou’s work there exists an underlying theme of temporality, 
which seems relevant to the topic of novelty, change, and historicity, but is, as 
far as we can tell, never dealt with in detail.
It is difficult to conceive a thought of change without a certain immersion in 
time, into the before and after. An event, this paradoxical and momentary lapse 
of reason (in all the nuances of the word), splits the world into before and af-
ter, not into here and there. Event is, to use the language of Being and Event, a 
historical rather than, for lack of a better word, a spatial term. We are therefore 
tempted to ask: Why is historicity rather clearly exposed in Being and Event, but 
temporality is not? There are two possible answers to this question: either there 
is no need for the concept of temporality within Badiou’s work or, alternatively, 
historicity, temporality, and the Greater Logic are indeed intertwined and we 
might benefit from finding a concept of temporality that sheds more light on 
Badiou’s thought of change. In this text, we opt for the latter. We will attempt to 
1
 Roland Bolz, “Mathematics is Ontology? A Critique of Badiou’s Ontological Framing of Set 
Theory”, Filozofski vestnik, 41 (2/2020), pp. 119–142. 
2
 Alain Badiou, Being and Event, trans. O. Feltham, Continuum, New York, 2005.
3
 Alain Badiou, Logics of Worlds: Being and Event, 2, trans. A. Toscano, Continuum, New 
York, 2009. 

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matjaž ličer
present a specific concept of temporality that seems immanent to – or at least 
compliant with – Badiou’s thought of change. 
In order to do this, however, we must take a detour and sketch a brief overview 
of what we understand to be the key features of change and novelty in Being and 
Event and Logics of Worlds. Let us begin with a situation. A situation is defined, 
in the broadest sense of the term, as a consistent multiple, as a structured multi-
ple, namely a multiple for which there exists a specific and specifiable criterion 
of counting its elements as one. A specific situation is always structured by the 
count-as-one according to a specific predicate of the situation language. Any 
situation can be constructed as a multiple of elements (which are themselves 
multiples) that can be subsumed to a specific predicate or a specific set of pred-
icates. All other multiples, not counted-as-one by the situation’s criterion of the 
count, are said to be subtracted from this particular situation. This subtractive 
multiplicity, this inconsistent multiplicity (of multiples) not counted-as-one by 
the situation, is where all potential novelties reside. Any potential novelty exists 
within a situation, but is not counted-as-one by the situation’s regime of the 
count (sans-papiers in a political state are an example). Subsets, free from all 
specific predicates of the situation’s regime of the count, are denoted (following 
Paul Cohen) as generic subsets. In Being and Event, this existence-without-rec-
ognition is presented in the situation with the proper name, the name of the 
void: Ø. This generic inconsistent multiple, marked by the symbol Ø, is a subset 
of every situation but it is not an element of every situation. This tension be-
tween inclusion and belonging provides an ontological base for the appearance 
of a novelty and leads to the following question: What are the conditions of the 
possibility of the inscription of the existent-within-the-situation in the language 
of the situation that does not count this existing entity as one of its elements? 
Obviously, one cannot fulfil these conditions within the existing language of the 
situation, within the existing regime of the count – otherwise the entity would 
already have been counted as one within the situation. 
The possibility of a novelty can therefore only stem from an extension of the 
situation to its generic base. In other words, any possibility of a novelty depends 
on the possibility of the extension of the regime of the count to multiples sub-
tracted from the current regime of the count. Novelty depends on the possibil-
ity of forcing the recognition of certain generic subsets of the situation as its 
elements. This, however, cannot be done without changing the regime of the 

9
temporality in badiou’s ontology and greater logic
count. If the situation’s regime of the count cannot change, then what is count-
ed as one within the situation also cannot change. In such (constructible) situa-
tions there can be no novelty. Or to put it differently: any situation defined by an 
immutable regime of the count is incapable of novelty. 
Situations with an immutable regime of the count can be very simply illustrat-
ed: these are the multiples with no tension between inclusion and belonging. 
Whatever belongs to such a situation is always already included in it. (Note that 
this property cannot be reversed since it can be shown that each multiple has 
at least one subset that does not belong to it as an element.) In Being and Event 
such situations are called natural (i.e. not historical). An example of a natural 
situation is a human cell: everything included in this specific biological multi-
ple also belongs to a human cell as one of its elements. A cell’s nucleus is, for 
example, a subset and an element of the cell. Furthermore, the cell’s nucleus is 
in itself a natural situation: everything included in the nucleus also belongs to it 
as one of its elements. The same holds for the DNA in the nucleus – and for the 
phosphates and sugars in the DNA backbone, etc. This property of ‘naturalness’ 
therefore transfers from a subset to its subsets – for this reason such sets are 
called transitive or normal sets. Normal sets are, to quote Badiou, “the schema 
of the maximum equilibrium of presented-being”.
4
This remark is as interesting as it is unclear. It is by no means obvious what is 
meant here by “equilibrium”. In order to proceed, we need to establish some 
sort of grasp of what an equilibrium might be. As we will see, introducing a strict 
concept of equilibrium will bring us one step closer to the concept of temporal-
ity at work in Being and Event. First notice that the above quote signifies a shift 
from a mathematically and logically dense vocabulary into physics. Equilibrium 
is primarily a dynamical, physical term. Furthermore, “maximum equilibrium” 
seems to be a pleonasm – anything less than “maximum” equilibrium is by defi-
nition not an equilibrium at all. This pleonasm does, however, give some further 
substantiation, perhaps inadvertently, to what will become our description of 
temporality within Badiou’s work.
Let us begin our illustration – and not much more – of this specific notion of 
time with an observation that the laws of physics are time-reversible, which 
4
 Badiou, Being and Event, p. 130.

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matjaž ličer
means that the equations describing these laws retain their mathematical form 
if we reverse the sign of the time variable. This does, however, not mean that all 
physical processes are easily reversable. As an illustration, imagine recording 
a planet circling a star for a few orbital cycles. We can now play this recording 
either forward or backward in time. The time-reversibility of planetary mechan-
ics is illustrated by the fact that we cannot, in general, distinguish whether the 
recording of a planet circling a star was played forward or backward in time. 
Another similar sketch: imagine recording a collision of two billiard balls, one 
bouncing off the other. Like before, one cannot determine from the recording 
alone whether the collision was played forward or backward in time. The laws 
of mechanics are invariant to time-reversal, they are symmetrical under the 
operation of changing the direction of time. So how can the arrow of time be 
determined in classical systems? If fundamental laws of the world are time-re-
versible, why do we, macroscopic beings, perceive the flow of time at all? Why is 
the past so fundamentally different from the future? Why do we see traces of the 
former but not of the latter? How does the irreversibility related to the arrow of 
time arise from the essentially reversible laws of classical physics?
To illustrate how these two demands are not inconsistent requires slightly 
stricter definitions of reversibility and irreversibility. Imagine a droplet of ink 
dropped in a bowl of water. As the droplet enters the water, the molecules of 
water randomly collide with the molecules of ink. Mixing between the ink and 
water occurs. The density of the ink molecules drops and ink molecules spread 
over a larger and larger area in a process known as diffusion. If, however, we 
were to record this process, there could be no doubt whether the recording is 
being played forward or backward in time. If the ink area shrinks, the recording 
is being played backwards in time. If the ink area spreads, the recording is being 
played forward in time. Time flows forward as the ink spreads. Time flows back -
ward if the ink shrinks (i.e. it does not). 
From this dictum alone it is clear that, in the classical realm, the direction of time 
becomes reasonably well-defined only in “large-enough” macroscopic systems 
that contain enough particles to allow for some sort of measure of order and dis-
order. How large is “large enough”? An infinite system would be ideal but a bowl 
of water and a droplet of ink suffice. At the other extreme, one ink molecule and 
one water molecule are clearly not enough. In other words, the arrow of time is a 
statistical property of a system and not a property of its basic constituents. Time 

11
temporality in badiou’s ontology and greater logic
flows in the direction in which the disorder of an isolated system increases. In 
an isolated system of an ink droplet in a bowl of water, the most ordered state 
of the system is the initial state where all of the ink molecules are still confined 
within the droplet and no mixing has yet occurred. As the diffusion mixes mol-
ecules of ink and water, the disorder in the system increases. If the system is 
left to itself, ink molecules will gradually spread over the entire volume of the 
bowl, reaching a state of maximum possible disorder. This, essentially, is the 
second law of thermodynamics, also known as the law of entropy. Its status is 
a bit different from other physical laws because it is, by its nature, a statistical 
law. Entropy is not a fundamental but rather a statistical quantity that measures 
the amount of disorder in a system. More precisely, the entropy of a particular 
state of the system can be computed from the number of ways in which we can 
rearrange the interchangeable constituents (ink molecules, on one hand, and 
water molecules, on the other) of the system and still get essentially this same 
system state. The law of entropy states that the entropy (the level of disorder) of 
an isolated system cannot decrease over time. Indeed, the entropy of the initial 
state (a self-contained droplet of ink in a bowl of water) of any isolated system 
will always be (equal to or) lower than the entropy of the final state (the fully 
mixed bowl of ink and water molecules). This follows from the fact that we can 
construct the initial state in fewer ways than the final state.
In thermodynamics, the state of a system with maximum possible entropy (max-
imum disorder) is defined as a state of equilibrium.
5
 In other words: a state of 
equilibrium is defined as the state that can be realized in the largest number 
of different ways. This is a statistical definition: if left to itself, any isolated sys-
tem will, through random fluctuations and basic probability, end up in the most 
probable state, i.e. the state that can be realized in the maximum number of 
ways – in a state of equilibrium. Once an isolated system reaches its equilibrium 
state, it will be extremely unlikely that it will ever depart far from equilibrium, 
simply because random fluctuations in the system will push it back towards the 
most probable state, which can be realized in the largest number of ways (and 
therefore exhibits maximum entropy) – a state of equilibrium.
5 This definition is only viable at high enough temperatures, but this need not concern us 
here. 

12
matjaž ličer
Note that there is no physical law which prevents the system from leaving equi-
librium. There is no law which makes it apodictically impossible for all the mol-
ecules of ink to reverse their velocities and migrate back through the bowl of 
water and condense themselves in the initial droplet. This reversal of diffusion 
is not impossible, it is merely highly improbable – one would have to wait sever-
al ages of the universe for this process to occur randomly. On the other hand, a 
fully mixed state of equilibrium is so probable (i.e. it can be achieved in a large 
number of ways / has high entropy / exhibits maximum disorder) that the sys-
tem may end up in equilibrium quite rapidly.
The point of this digression was twofold: first, to show that a state of equilibri-
um, casually mentioned by Badiou, can be defined in relation to order and dis-
order; and second, to show that the arrow of time can also be defined in relation 
to changes in order and disorder. There is a connection between temporality and 
order. Note that even though this illustration of temporality stems from classical 
physics, it is profoundly un-Newtonian in nature. Time, related to a change in 
order, is quite different from “true and mathematical time,” which in Newton’s 
own words (from the famous Scholium to the Definitions in Philosophiae Natura-
lis Principia Mathematica) “flows equably without regard to anything external.”
So, what happens with the arrow of time when an isolated system reaches equi-
librium? In short: since equilibrium implies maximum disorder, no change in 
the order within the system is any longer possible (i.e. probable). In other words: 
the state of equilibrium is stable. Consequently, the arrow of time can no longer 
be defined in equilibrium. Equilibrium is timeless. If undisturbed, any system 
already in equilibrium will persist in equilibrium. A recording of a droplet of ink 
in a bowl of water allows for a sense of temporality only as long as the disorder 
in the system increases, i.e. as long as the ink spreads. Once the ink is fully 
mixed with the water, playing this recording forwards or backwards no longer 
makes any difference – there can be no meaningful introduction of the arrow of 
time in such a system. 
Let us now return to the above-mentioned normal (transitive) sets, to “the sche-
ma of the maximum equilibrium of presented-being.” One can now read this 
statement as the statement that natural sets are essentially timeless. They are 
timeless in the sense that they do not allow for a change in order, they are sta-
ble. Badiou’s wording is completely consistent with our line of argument: “The 

13
temporality in badiou’s ontology and greater logic
ontological criterion for natural multiples is their stability, their homogeneity; 
that is, as we shall see, their immanent order.”
6
 This connectedness of “maxi-
mum equilibrium” and order in natural sets can be reformulated as the follow-
ing statement (which seems to be true, as far as we can tell): physical laws do 
not change over time. (One is almost tempted to evoke here the Leibniz criterion 
of the best possible world being the one with the simplest laws which allow for 
maximum complexity, i.e. maximum entropy – and hence stability.)
Another important consequence of the stability of natural sets, specifically of 
their structure, according to which every element is also a subset, directly im-
plies that an event is not possible in natural situations. In order for an event 
to be possible in a situation, the situation must allow for the inclusion of a set 
whose elements do not belong to the situation. Such a situation is by definition 
not a transitive (normal) set. Badiou denotes such situations as historical, and 
only historical sets, with their distinction between inclusion and belonging, are 
those that allow for the generic extensions necessary for the occurrence of a 
novelty, of an event. Once one agrees to temporality as a measure of the change 
in a situation’s order, the connection between historicity and temporality be-
comes quite clear: historicity is the potentiality of temporality.
Following Badiou, a novelty can only occur in a historical situation if an event, 
being an element of an evental site, becomes an element of the situation through 
an undecidable axiomatic decision of the faithful subject. This leads us to an 
interplay of temporality and fidelity. This interplay is not entirely unexpected: 
if one understands temporality in terms of a change in the situation’s order and 
if, similarly, subjective action primarily appears as a disruption of this order – 
then temporality and subjective fidelity must be somehow related. A relation 
between time and fidelity is indeed mentioned (and not much more) by Badiou 
in the following, somewhat infamous passage: 
The real difficulty is to be found in the following: the consequences of an event, 
being submitted to structure, cannot be discerned as such. I have underlined this 
undecidability according to which the event is only possible if special procedures 
conserve the evental nature of its consequences. This is why its sole foundation 
6 Badiou, Being and Event, p. 130. Emphasis added by M. L.

14
matjaž ličer
lies in a discipline of time, which controls from beginning to end the consequenc-
es of the introduction into circulation of the paradoxical multiple, and which at 
any moment knows how to discern its connection to chance. I will call this organ-
ised control of time fidelity.
7
The above lines perhaps become a bit more comprehensible if they are read 
under the assumption of the relationship between the flow of time and rising 
disorder. It is not the situation that unfolds in time – it is rather time itself that 
gets co-determined by the structural changes in the situational order: if the 
situational order does not change, the situation, even if it is itself historical, is 
effectively timeless. Structural changes in the situational order appear as the 
consequences of an event, this paradoxical presented multiple that lacks rep-
resentation. The very practise of controlling the consequences of an event, and 
of preserving the evental nature of these consequences, is also the practise of 
the disruption of the situational order, of its regime of the count. Of its presenta-
tion and representation – and thus its temporality. 
This operation of fidelity is twofold. First, it consists of claiming axiomatically 
(and undecidably) that the disorder of the situation has increased, and second, 
it demands that this increase in disorder, manifested as the appearance of the 
generic extension of the situation, must be recognized by the situation’s regime 
of the count. The fidelity of the subject to an event is a wager that history has al-
ready unfolded within the situation; something undecidable has been decided 
(an event did happen) and this decision will now have to be formalized retroac-
tively by a change in the situational order, by a change in what will have been 
admitted, anew, to the representation within the situation. In other words, the 
operation of the subject (the forcing) is to sustain the situation’s subtraction 
as belonging to a situation, to sustain the subtraction as it will have been pre-
sented and represented within the situation itself. This ‘will-have-been’ future 
anterior structure of the work of the subject, this intervention of subjective ur-
gency into objective impossibility, is what Badiou identifies as the fundamental 
law of the subject. The work of the subject is therefore closely coupled with any 
possible emergence of temporality within a given situation.
7 Badiou, Being and Event, p. 211. Emphasis in original.

15
temporality in badiou’s ontology and greater logic
One of the key tasks of Logics of Worlds is precisely to establish in more depth 
how this post-evental work of the faithful subject plays out in a particular sit-
uation or a world. Note that on the level of ontology nothing particular can be 
attributed to any situation. Being and Event does not deal with particular situ-
ations. It rather attempts to derive, from a specific minimal set of assumptions, 
an ontological base for the appearance of truths in any situation. A world, on 
the other hand, is a situation equipped with a transcendental, which must be 
understood as a general logical form of the objectivity of appearing
8
 or, more 
specifically, as a hierarchical scale of the intensities of the appearance of the 
multiples of a particular world. The task of deriving conditions of the appear-
ance of truths in a world is therefore focused not so much on the event itself, but 
rather on how evental consequences appear, through the work of the subject, as 
a material novelty in a particular world. Badiou’s shift from the ontology of pure 
multiples in Being and Event to their localization in a particular world in Logics 
of Worlds is demanded by the fact that being itself is only thinkable insofar as 
it belongs to a world, i.e. a specific world
9
, a world with a specific hierarchy of 
intensities of appearance, a world with a specific transcendental. Whereas a 
situation is a pure multiple of multiples, a world, through its transcendental, 
allows for a relational network of appearances. One of the driving questions 
behind Logics of Worlds is, to quote Badiou directly, a simple one
10
: “Why and 
how are there worlds rather than chaos?”
As remarked above, a transcendental is a specific set. More precisely: it is a set 
of intensities of appearances (hereinafter marked with the letters a,b,c,...p,q,...) 
in a situation. There are, of course, certain requirements that have to be met in 
order for a transcendental to have any specificity at all. These requirements are 
the formal properties required for a transcendental to be a specific set. We list 
them formally below, but in their essence they are quite literally mundane and 
elementary:
• A transcendental must be a partially ordered set, i.e. it needs to be reflexive 
(for any intensity of appearance a, a ≤ a), anti-symmetric (if a ≤ b and b ≤ a 
then a=b), and transitive (if a ≤ b and a ≤ c then a ≤ c). The property of tran-
8 Badiou, Logics of Worlds, p. 233.
9 Ibid., p. 113.
10
 Ibid., p. 101.

16
matjaž ličer
sitivity, for instance, can literally be read simply as: if tea appears warmer 
than coffee, and coffee appears warmer than juice, then tea appears warmer 
than juice. Similar examples can be found for all other properties on this list.
• A transcendental must allow for the existence of a minimum intensity of 
appearance (of all appearances, one appears with the least intensity). The 
minimum intensity of appearance µ signifies inexistence, or, in the language 
of Being and Event, inclusion in (as a subset) but not belonging to a situation 
(as an element). This demand is a logical translation of an empty set being 
a subset of every set. Sans-papiers belong to the French situation, but par-
ticular people without papers do not form a subset of the situation of France, 
they do not appear formally in the citizen register or as tax payers. They do 
not formally exist.
• A transcendental must allow for a conjunction  (appearances can overlap 
(intersect) into a new appearance) and for an envelope (appearances can 
combine into a union of appearances, amounting to a new appearance) of 
intensities of appearance.
• A transcendental must be a distributive set (an overlap of appearance p with 
an envelope of other appearances E(q) is an envelope of overlaps of appear-
ance p with each member q of E).
Any set with this minimum set of properties is called a Heyting algebra. If a 
transcendental is to be a specific set, it must be a Heyting algebra. These prop-
erties of a transcendental are the ones which allow for a specific hierarchy, a 
specific network of intensities of appearances, and are thus guarantors of a spe-
cific world.
A shift from ontology to logics further requires the extension of the theory of the 
subject from the domain of being to the domain of appearance. The subject, as 
introduced in Being and Event, is, strictly speaking, a local state of some specific 
(local) generic procedure. The latter amounts to a finite series of evaluations 
that some multiples, tied to a specific event, belong to – and should be repre-
sented in – a specific situation. What has no place here, should have a place 
here. In other words: the subject is introduced strictly as a localized entity, but 
the theory of the subject in Being and Event does not seem to be able to respond 
to its own demands. It is far from clear how and through what mechanisms the 
localization of the subject of Being and Event can take place. Frank Ruda points 
out that Being and Event elaborates somewhat on the subjective process, “but it 

17
temporality in badiou’s ontology and greater logic
does not give us all the conceptual tools needed to think subjectivisation prop-
er.”
11
 Ruda rather describes Badiou’s approach as “genericism” to emphasize the 
dominant role of ontology over logical localization. Consequently, an attempt 
was made in Logics of Worlds to develop formal theories of change
12
 and sub-
jective bodies.
13
 These passages might to some extent address Sam Gillespie’s 
objections in his discussion of Being and Event, i.e. that “Badiou’s mathemati-
cal formalism, which is perfectly capable of weaving complex multiplicities and 
rules out of nothing, is simply an empty game of manipulating symbols. The 
problem is not just that of giving the operation of presentation the same onto-
logical validity as sets; rather, what is needed is an analysis of why being must 
depend upon presentation as its material support, and what sort of framework 
may be necessary for such a dependency.”
14
 The importance of the translation 
of the theory of subject into the domain of logic was fundamental enough that 
Logics of Worlds opens precisely with a new definition of the subject: a singular 
subject is a material, corporeal “bearer of the dialectical overcoming of simple 
materialism.”
15
 In Logics of Worlds, the work of the subject therefore acquires a 
new signifier, materialist dialectic, which keeps affirming the following axiom: 
“There are only bodies and languages, except that there are truths.”
16
 In other 
words: the subject is an exception to the logic of the world. It is not difficult to 
locate dialectical trademarks already in what has been said above. 
Firstly, we note the thought of contradiction within a single framework of uni-
fying opposites (and also the consequences of an event through the subjective 
operation of fidelity). The thought of contradiction is imperative since an event 
is defined as a paradoxical entity that belongs to itself as an element. Secondly, 
the transformation of quantity into quality, which occurs through the work of 
the subject when a subjective body persists in fidelity to the event until a change 
in the regime of the count is established. 
11
 Frank Ruda, “To the End: Exposing the Absolute”, Filozofski vestnik, 41 (2/2020), pp. 311–
340.
12
 Badiou, Logics of Worlds, p. 357.
13
 Ibid., p. 451.
14
 Sam Gillespie, The Mathematics of Novelty: Badiou’s Minimalist Metaphysics, Melbourne, 
re.press, 2008. 
15
 Badiou, Logics of Worlds, p. 45.
16
 Ibid., p. 4.

18
matjaž ličer
And thirdly, the negation of negation. Whenever the transcendental representa-
tion of a world is restructured, whenever a change in the regime of the count 
is achieved, a specific negation within this world has been itself negated. It is, 
however, not at all unambiguous what the negation of a specific appearance 
might be. As pointed out by Badiou,
17
 one can define negation in relation to 
three fundamental principles of thought: i) the principle of identity, p = p; ii) the 
principle of the excluded middle or tertium non datur, p U p; and iii) the princi-
ple of non-contradiction, (p  p). An operation of negation that obeys the last 
two principles is a classical negation. Negation can, however, violate the princi-
ple of the excluded middle and obey the principle of non-contradiction – such 
a negation is part of the so-called intuitionistic logic (developed by Brower and 
Heyting). Finally, negation can also violate both the principle of the excluded 
middle and the principle of non-contradiction – such a negation is a paracon-
sistent negation. Since the logic of appearing allows for a continuous spectrum 
of transcendental degrees of appearance p, the same must hold for the negation 
of p. In other words: while the ontology is itself classical, the logic of appear-
ance violates the principle of the excluded middle and is therefore intuitionistic.
The crucial point regarding the possibility of any dialectic is, however, that, 
within intuitionistic logic, the negation of negation does not, in general, lead 
back to the beginning but rather signifies a transgression of the original situa-
tion. This shift from the key principle of classical logic, 
 p = p, 
to the new principle, 
 p ≥ p,
turns out to be a differentiating property of the intuitionistic logic of the tran-
scendental, the Greater Logic. In order to see that this shift is immanent to Ba-
diou’s logic of appearing, we need to describe in more detail the concept of the 
negation on the level of appearance – or, as Badiou calls it, a reverse. What is, 
in other words, a reverse p of a specific appearance p? Let’s jump straight to 
the definition
18
 and state it in non-technical terms first: the reverse of a specific 
appearance is defined as a union of all appearances that have nothing in com-
17
 Alain Badiou, “The Three Negations”, Cardozo Law Review, 29 (5/2007), pp. 1877–1883.
18
 Badiou, Logics of Worlds, p. 168.

19
temporality in badiou’s ontology and greater logic
mon
19
 with the appearance undergoing reversal. Or, in the terminology of the 
logic of the transcendental: the reverse p of the specific appearance is an enve-
lope of all (transcendental degrees of) appearances that have minimal conjunc-
tion with the (transcendental degree of) appearance undergoing reversal. Since 
each member of the envelope p has minimal conjunction (i.e. has nothing in 
common) with p, the conjunction of p with the envelope also has a minimal 
degree of appearance: p  p = µ.
Now remember that the envelope of p is defined as a union of conjunctions of p 
with the members of any subset of appearances of the same world.
20
 Therefore, 
the transcendental degree of appearance of the envelope is always equal to or 
larger than p: E(p) ≥ p. The envelope E(p) of p equals p if and only if each mem-
ber q of the subset has nothing in common with p, or p  q = µ. Otherwise E(p) > 
p. Let us now return to the negation of negation, or the reverse of reverse,  p. 
The reverse of the reverse of p is a (double) envelope: an outer envelope over a 
subset of appearances q such that q  p = µ, where q stems from an inner enve-
lope of p over a subset of appearances r such that r  p = µ. Now, according to the 
definition of the reverse, p  p = µ. Therefore, p itself is also among the appear-
ances q over which the outer envelope operates. Therefore the outer envelope, 
or the reverse of reverse,  p, is greater than or equal to p:
 p ≥ p.
Thus, the logic of appearance, through its violation of tertium non datur, allows 
for the dialectical transgression through negation.
What about the materialistic part of materialist dialectic? The core of Badiou’s 
demonstration of this aspect of the work of the subject resides in his proof of the 
second constitutive thesis of materialism.
21
 This thesis implies, to use his words, 
that the ontological closure of the world implies its logical completeness. The on-
tological closure of the world is the starting point of the proof, and consists of 
the following statement: if x and y are, in the ontological sense of the word, 
multiples, then their union and intersection are also multiples. From this, the 
19
 Ibid., p. 107.
20
 Ibid., p. 163.
21
 Ibid., p. 345.

20
matjaž ličer
following consequence can be derived
22
 within the logic of the transcendental: 
if x and y appear in a world (with, say, intensities of appearance p and q), then 
all ordered pairs of their respective elements also appear in the world. In other 
words: if x and y appear in a world (with, say, intensities of appearance p and 
q), then their union and all their subsets also appear in this world. Whatever 
appears in a world is therefore, as proven by Lemma 1, ontologically ground-
ed within the world. This sweeps away any possibility of transcendence and 
hence implies materialism. (It needs to be noted that this route from ontological 
closure to logical completeness is only possible if one accepts that ontology is 
mathematics and that a transcendental has the structure of a Heyting algebra.) 
So, whatever appears has an ontological ground, but the reverse is not true: 
being does not necessarily appear.
The logical aspect of the proof
23
 requires the establishment of relations between 
the objects of a particular world. An object of a world is a multiple, appearing in 
that world, along with an envelope of conjunctions between this multiple and 
all other multiples appearing in that world. This envelope essentially measures 
how similar this multiple appears to all other appearing multiples of that par-
ticular world. Vaguely speaking: an object is a multiple, localized in a particular 
world through a set of similarities between itself and other multiples, appearing 
in that same world.
24
 The logical completeness of a world is synonymous with 
the fact that given the relations between the already-appearing objects of that 
world, the relations between these objects and any newly appearing object are 
already completely determined by an existing network of relationships. 
The second constitutive thesis of materialism, which establishes a connection 
between ontology and the logic of appearance, consequently indicates that an 
interruption of representation at the ontological level interrupts the consistency 
of relations on the level of appearance. A true change occurs as a transforma-
tion of the transcendental hierarchy on the level of appearance. The relation 
between temporality and order that we tried to establish at the level of ontology 
must therefore translate somehow also to the level of appearance. This transla-
tion takes the form of the negation of negation we referred to above: the nega-
22
 Ibid., p. 345.
23
 Ibid., pp. 345–352.
24
 Ibid., p. 245.

21
temporality in badiou’s ontology and greater logic
tion of a specific inexistent minimal appearance is itself negated to yield a new 
appearance in the world through a shift of the transcendental order – which 
gives rise to a temporality within the world:
The intensities of objects and relations are measured according to a singular tem-
poral transcendental, which objectivates in their appearing multiplicities such 
as ‘the firm stance of the group of anarchists from one end to the other’, or ‘the 
organizing role of the rail workers’ union’, or ‘the growing isolation of the Kurd-
ish communists’ and so on. In other words, the object absorbs, as elements of 
the multiplicity that it is, the modifications which include it within the time of 
the world, through which it only ‘changes’ to the extent that this ‘change’ is its 
appearing-in-the-world.
25
If time is to exist in a world, it exists only insomuch as the transcendental of 
the world experiences a disruption of its order by an event, by an appearance of 
inexistent objects that need to be integrated, through changes in the transcen-
dental hierarchy, into a new transcendental of the world, thus leading to a new 
order, a new present: 
The event cannot be the undivided encroachment of the past on the future or the 
eternally past being of the future. On the contrary, it is a separating evanescence, 
an atemporal instant which disjoins the previous state of an object (the site) from 
its subsequent state. We could also say that the event extracts from one time the 
possibility of another time. This other time, whose materiality envelops the con-
sequences of the event, deserves the name of new present. The event is neither 
past nor future. It presents us with the present.
26
An event presents us with the present, with what is presented but not repre-
sented, with what exists but does not appear. An event disjoins the previous 
state of an object from its subsequent state. It splits the world into the before 
and after, each with its own transcendental ordering. It is then up to the faithful 
subject to decide the undecidable dilemma: Did an event take place or not? Did 
the possibility of another time open up or not? Did the order of the world change 
25
 Ibid., p. 359.
26
 Ibid., p. 384.

22
matjaž ličer
or not? Now we can follow Badiou
27
 by asking: What is the outcome, for the in-
existent, of this negation of negation? What is the intensity of the appearance 
of the inexistent in the post-evental world? There are only three possibilities: 
the post-evental intensity of appearance can be either maximal, intermediate, 
or minimal. 
In the first possibility, the world experienced what Badiou calls a true event. 
There is no doubt that the transcendental of the world has changed and a spe-
cific temporality has emerged. In the second possibility, the post evental inten-
sity of the inexistent is intermediate: “something happens, but without radical 
effects, and in the general respect of the hierarchy of degrees of appearing in the 
world”.
28
 In this case, we cannot speak of any reordering of the transcendental 
in any fundamental sense. The change itself was not a true event, but rather 
what Badiou denotes as a weak singularity. This post-evental world remains 
timeless. The same holds for the last possibility, where the inexistent remains 
inexistent. Such a change is referred to as a false event, or a simulacrum of an 
event, and the post-evental world is exactly the same. 
Which of these three scenarios manifests itself depends ultimately on a purely 
subjective decision, a purely subjective choice. The assertion of the existence 
of this choice opens up a new path that leads far beyond this paper – here we 
can only briefly sketch one possible approach. The existence of this choice is 
guaranteed by the early axiomatic decision to use the axiomatic system of the 
Zermelo-Fraenkel set theory, supplemented by the axiom of choice.
29
 The axiom 
of choice guarantees, informally speaking, that for any set of nonempty sets, 
it is possible to choose one element from each set. (This seems trivial for finite 
sets, but is not obvious for infinite sets.) The existence of choice is, however, 
guaranteed by the axiom of choice also for infinite sets. Note that the axiom 
says nothing about how the choice should be performed, it merely guarantees 
that there is a choice. Of course, one might object that the validity of the axiom 
of choice by definition holds over any set of nonempty sets (i.e. having at least 
one element, hence being constructible via the operation of the count) and is 
27
 Badiou, “The Three Negations”, pp. 1877–1883.
28
 Ibid., p. 1882.
29
 See also: Oliver Feltham, “One or Many Ontologies? Badiou’s Arguments for His Thesis 
‘Mathematics is Ontology’”, Filozofski vestnik, 41 (2/2020), pp. 37–55.

23
temporality in badiou’s ontology and greater logic
thus inapplicable in the case of an event, which presents precisely subtracted, 
non-constructible, empty sets, for elements of which the faithful subject choos-
es to assert existence or not. The short answer to this objection lies in the fact 
that this choice is made from the position of the subject and from the subjective 
position the generic extension is not void, it is constructible.
The possibility of choice is perhaps one of the clearest demarcation lines be-
tween natural and historical situations. Choice is only given in historical situ-
ations that are capable of reinventing their own time. Out of this reordering of 
the world there emerges a new temporality, sustained by subjective fidelity – 
outside of a subjective body, there is no right or wrong answer to this choice and 
thus no temporality. Outside of a subjective body, there is not even any necessity 
for an answer to the question of whether the world can change or not – not an-
swering this question is already an answer. But there is always a choice.
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