“The remarkable conceptual connection affirmed here [by the axiom of foundation] is that of the Other and foundation. This new Idea of the multiple stipulates that a non-void set is founded inasmuch as a multiple always belongs to it which is Other than it. Being Other than it, such a multiple guarantees the set’s immanent foundation, since “underneath” this foundational multiple, there is nothing which belongs to the initial set…

The hypothesis I advance is the following: within ontology,the axiom of choice formalizes the predicates of intervention. It is a question of thinking interventionin its being… Ontology declares…

“Hope is more contagious than any virus…”

(Originally written June 2020)

What is it usually like being an Emergency Room (ER) doctor when not on the frontlines of a pandemic? Responses will differ across the board, but I have always seen us ER docs as the stalwart guardians of the hospital entryway; the gatekeepers and stewards of the medical edifice. For most people in this country, we are the first doctors that they will be required to see in their time of concern or need. For many of these people, we are the first doctors to care for and diagnose…

It is hard for me to believe that the last post in my [Badiou and Science] series was a year and a half ago, and that there have only been two posts in the last two years.

Unfortunately, life gets in the way of grand passion projects such as this. As many of you know, my day/night job is working as a relatively new Emergency Room doctor, and to say that the current climate has been busy for me would be an understatement. …

“A great theory, which had to show itself capable of providing a universal language for all branches of mathematics, was born… It became possible to rigorously specify the notion of property, to formalize it by reducing it — for example — to the notion of a predicate in a first-order logical calculus, or to a formula with a free variable in a language with fixed constants… axiomatization is not an artifice of exposition, but an intrinsic necessity… Axiomatization is required such that the multiple, left to the implicitness of its counting rule, be deliveredwithout concept…” — Alain Badiou,Being…

“[The middle class], taken as a whole, is porous to racism, to xenophobia, to hatred of the destitute…we have a typically Western dialectical relation between an extreme arrogant self-satisfaction and a constant fear. Whence the definition of the art of democratic government these days: it is the art of making sure that this fear which animates their ideological and electoral base, the middle class, is not directed against them — the governments — but against this or that representative of the destitute masses… foreign workers, their children, refugees, the inhabitants of dark cities, fanatical Muslims. Here is the scapegoat sent…

“But [there are] also so many other [numbers than our traditional numbers], which finitude and the wretchedness of our inherited practice of Number keeps from us. How negligible are numbers amongst Numbers! The being of Number exceeds in every direction that which we know how to negotiate. Our strength, however, is that we possess a way of thinking of this excess of being over thought.” — Alain Badiou,Number and Numbers, pg. 157

If we are to take away anything from Badiou’s interpretation of the surreal numbers, it is that which is punctuated in this opening quotation: *we posses a…*

“And this is the problem: is it possible to identifyaNumber as opposed to sets of Numbers?… Does the numberless throng of Numbers necessarily lead us into ‘those indefinite regions of the swell where all reality is dissolved’? This is where trans-numeric inconsistency summons us to think thecut. Is it possible, in a fabric so dense that nothing any longer numbers it, to cut at aspecific point? Can one determine, by cutting, asingularNumber?” — Alain Badiou,Number and Numbers, pg. 140

Number (with a capital “N”) is how Badiou designates the “infinite swarm” of numbers…

“…along with reals and ordinals, [the surreals] contain an infinitely infinite throng of numbers whose existence no one has conceived of before, and which retroactively make our historical numbers seem like a minuscule deduction from all those abundant varieties of numerical being…” — Alain Badiou,Number and Numbers, pg. 107–108

As we are beginning to see, there is a significant difference between the numbers we typically encounter empirically in the world and those that our thought can grasp. …

“The impasse of ontology — the quantitative un-measure of the set of parts of a set — tormented Cantor… the multiple p(ωₒ) is the ontological schema of the geometric or spatial continuum. Demonstrating the continuum hypothesis, or (when doubt had him in its grips) refuting it, was Cantor’s terminal obsession: a case in which the individual is prey, at a point which he believes to be local or even technical, to a challenge of thought whose sense, still legible today, is exorbitant. For what wove and spun the dereliction of Cantor the inventor was nothing less than an errancy of…

“… the existence of zero, or the empty set, and the existence of an infinite set can in no way be deduced from “purely logical” presuppositions. They are axiomatic decisions, taken under the constraints of the historical injunction of being… The two axioms of the void and of the infinite structure the entire thinking of number… The fact that this is a matter of axioms and not of theorems means that the existence of zero and of the infinite is prescribed to thought by being…” -Alain Badiou,Number and Numbers, pg. 56–57

To review, we have already introduced some of…

Medical Doctor and Philosophy Enthusiast. Laying in wait for the Event and the Revolution…