0. In my previous post, “Reading Alain Badiou’s “Being and Event”: An Introduction (Or Perhaps Not),” I began the task of cautiously determining, as best I could, just what the theses constituting the philosophy of Alain Badiou might be, a task which the further task of comparing and contrasting these theses with those of the neo-Aristotelian perspective motivating this blog and that of determining their truth presuppose. In the present post I take one small step further in that determination, extracting what I can from the following passage from Being and Event (p. 3):

The initial thesis of my enterprise—on the basis of which this entanglement of periodizations [of our epoch] is organized by extracting the sense of each—is the following: the science of being qua being has existed since the Greeks—such is the sense and status of mathematics. However, it is only today that we have the means to know this. It follows from this thesis that philosophy is not centered on ontology—which exists as a separate and exact discipline—rather it circulates between this ontology (thus, mathematics), the modern theories of the subject and its own history.

1. Before getting to the main point of this post, let me briefly note some things which I think I at least somewhat understand and some things which I do not fully understand in the first five-eighths of the passage. I do understand the affirmation that “the science of being qua being has existed since the Greeks.” I think I also have something of an understanding, albeit a decidedly incomplete one, of his relating “the sense and status of mathematics” to the fact of the science of being qua being’s having existed since the Greeks, for, as is evident in a passage in his “Author’s Preface” to Being and Event which I quoted in “Reading Alain Badiou’s “Being and Event”: An Introduction (Or Perhaps Not),” he affirms (p. xiii) that:

[O]ntology, the science of being qua being, is nothing other than mathematics itself.

I do not yet, however, understand why it is, in his view, that “it is only today that we have the means to know” that “the science of being qua being has existed since the Greeks,” for thus far in the few pages of Badiou I have read, I have not seen any argument which would justify that affirmation, So, as I continue my reading of Badiou, I will have to remain alert to the possibility that the needed argument might appear.

Nor do I yet understand how “[i]t follows from this thesis that philosophy is not centered on ontology.” It is not just that I am not sure of just what the thesis is from which it is said to follow that “philosophy is not centered on ontology.” For, on the one hand, from the one premise alone, the thesis that “the science of being qua being has existed since the Greeks,” it does not at all follow that “philosophy is not centered on ontology.” And, on the other, from the one premise alone, the thesis that “it is only today that we have the means to know” that “the science of being qua being has existed since the Greeks,” it does not at all follow that “philosophy is not centered on ontology.” Nor, on a third hand, does the thesis at hand follow from the two premises together. In all three cases, one or more additional premises are needed if the thesis that “philosophy is not centered on ontology” is to follow as the conclusion of a valid argument. So, as I continue my reading of Badiou, I will have to remain alert to the possibility that the needed premise, or premises, and argument might appear.

2. a. Now for this post’s the main point, the presentation of which begins from the observation that Badiou’s assertion, that:

[P]hilosophy is not centered on ontology—which exists as a separate and exact discipline….

is a complex assertion, presupposing the truth of the following conjunction:

Ontology is a separate discipline from philosophy and ontology is an exact discipline.

From this, in accordance with the inferential step of known in the logician’s jargon as simplification, it follows that:

Ontology is a separate discipline from philosophy.

2. b. Let us now assume that, for any existent x and any existent y, if x is separate from y, then x and y are not identical. If we further assume that philosophy and ontology are existents of some sort, then it follows that if philosophy is separate from ontology, then philosophy and ontology are not identical. Assuming, then, with Badiou, that it is the case that philosophy is separate from ontology, we have the following argument, in Modus Ponens:

If philosophy is separate from ontology, then philosophy and ontology are not identical.

Philosophy is separate from ontology.

Therefore, philosophy and ontology are not identical.

Now we already know, as was brought out in the previous post, that for Badiou “ontology is nothing other than mathematics,” i.e., that

Ontology is mathematics.

This is also evident in Badiou’s glossing, in the passage on which this post is focused, “ontology (thus, mathematics).”

Given, however, that “philosophy and ontology are not identical,” or:

Philosophy is not ontology.

we have the following syllogism:

Ontology is mathematics.

Philosophy is not ontology.

Therefore, philosophy is not mathematics.

3. I said it was a small step and I indicated that I am proceeding cautiously. But the thesis that philosophy is not mathematics is no more insignificant than the thesis that ontology is mathematics. They will have their implications.

4. Bringing you along with me, willingly or not, I assumed above that, for any existent x and any existent y, if x is separate from y, then x and y are not identical. I also assumed that if philosophy and ontology are existents of some sort, then it follows that if philosophy is separate from ontology, then philosophy and ontology are not identical. I did not assume that for any existent x and any existent y, if x and y are not identical, then x is separate from y. Nor did I assume that if philosophy and ontology are not identical, then philosophy and ontology are separate. The separation of one thing from another is not at all the same thing at all as the one thing not being the other. As noticed above, however, Badiou is committed to the thesis that:

Ontology is a separate discipline from philosophy.

In my next post, I will engage in some initial explorations of what that thesis involves.