0. I thought it more than nearly time for me to return to the text itself of Badiou’s Being and Event. So return to it I will and to more particularly to the opening paragraph of the first chapter proper of the book, “Meditation One. The One and the Multiple: the a priori conditions of any possible ontology.” I for one have found the paragraph to be quite challenging and I will, accordingly, with it in two posts. Today’s post will consider the first two sets of sentence(s) of the paragraph.

1. The first sentence(s) of the first paragraph read(s) as follows:

Since its Parmenidean organization, ontology has built the portico of its ruined temple out of the following experience: what presents itself is essentially multiple; what presents itself is essentially one.

With their use of italicized words, the use of the singular subject and verb with the predicate, “multiple,” and above all the opposition between the two predicates, “multiple” and “one,” the two near-sentences following the colon are at least initially arresting. Then, moreover, in the immediately following sentence(s), we find Badiou thinking that, with the “reciprocity of the one and being,” the bearing of which on the sentence(s) just given I will explore in the next post, we are faced with an “impasse.”

The reciprocity of the one and being is certainly the inaugural axiom of philosophy—Leibniz’s formulation is excellent: ‘What is not a being is not a being’—yet it is also an impasse; an impasse in which the revolving doors of Plato’s Parmenides introduces us to the singular joy of never seeing the moment of conclusion arrive.

It is the purpose of the present post to, first, spell out the reason why I think the two near-sentences following the colon in the text quoted at the outset are, though at least initially arresting, only initially arresting and present us with no impasse: the two propositions and their conjunction are all quite true. The post’s second aim is that of pointing out that the thesis of which “Leibniz’s formulation is excellent” and the thesis of the reciprocity of the one and being are two very different theses, as different as the true and the false; and that moreover, after a review of the two theses, we do not yet find ourselves presented with an impasse.

2. As a good, if not Aristotelian, at least neo-Aristotelian, I take it to be true that, in accordance with the “first” principle of non-contradiction, no being can both be and not be, in one and the same respect or way. It follows that no reality which presents itself can both be one and not be one, in one and the same respect or way. And, because whatever is one cannot be many or multiple, in one and the same respect or way, it follows further that no reality which presents itself can both be one and be many or multiple, in one and the same respect or way. But that is in one and the same respect or way. The foregoing does not at all entail that there is a metaphysical or ontological impossibility preventing a reality presenting itself from being both one and multiple, as long as it is one and multiple in two distinct respects or ways.

I’ll go a bit further here and affirm that it is actually the case that all things whatsoever which present themselves in immediate experience are both “essentially multiple” and “essentially one”; this is the case both for any whole which presents itself in immediate experience and for any part which presents itself in immediate experience. So affirming, then, that such is actually the case and then recalling that whatever is actual is possible, I will also affirm that it is thus possible, and so not impossible, for all things whatsoever which present themselves in immediate experience to be both essentially multiple and essentially one, albeit in two distinct respects or ways. There is then, thus far, no impasse.

2. Moving on to the second sentence(s) of the first paragraph, we should note that there are at least two quite distinct sets of propositions which the phrase “[t]he reciprocity of the one and being” (in the French original,* “la réciprocité de l’un et de l’être”) can be pointing to. One of the two expresses a Parmenidean view that there is at least one but only one “one” and there is at least one but only one “being” and further identifies the one one with the one being; spelled out, it might well read as follows:

There is at least one but only one one and there is at least one but only one being

and

the one is the being and the being is the one.

The other of the two propositions expresses the Leibnizean view, and that as well of Aristotelianism and neo-Aristotelianism, that there are many ones, or units, and many beings and further identifies every one, or unit, with a being and every being with a one, or unit, thus:

There are many ones, or units, and there are many beings

and

all units are beings and all beings are units.

(You will have recognized in the last conjunct, that all beings are units, a statement of the thesis standing behind the scholastic doctrine that “unity” is a “transcendental property” of being.)

The difference between the two conjunctions is the difference between the thesis of absolute monism and that of absolute pluralism. The thesis expressed by the one conjunction is simply not the thesis expressed by the other. It seems, then, if one adheres to the thesis expressed by Leibniz’s formulation, that if there is an impasse, it is by no means yet evident; to put it more nearly as Badiou might put it, the impasse is not yet present or has not yet presented itself to us.

3. In, then, neither the first of the first two sets of sentence(s) of the chapter’s first paragraph nor the second presents us with the impasse Badiou worried about.