Skip to main content

PS on indexicalism (and the logic of supplement)

Following the previous post, and considering the project I sketched in October, maybe indexicalism (see here for a broad idea of what it is) is less a (paradoxico-)metaphysics or a cosmology of incompleteness than a Logic in the sense of Hegel's Logik, formal but thoroughly inhaltliche. It is perhaps another Logic of being and its exterior, of borders and its determinations etc. It is a different Logic of negation and concrescence. Maybe it should be developed as in equally paraconsistent way but where a thorough rejection of the principle of explosion (that from contradiction anything can be derived) comes from the work of the Other, of the Outside - through supplement.

I have been developing a logic of supplement with a group of people; our starting point is to study, in the way of universal (or abstract) logic, thoroughly non-monotonic formal systems, we call them antimonotonic. In this system, every argument is non-monotonic. As a consequence, no addition can be made to any valid argument - and nothing can be removed from it. These systems are in a sense minimal but not to confuse with the minimal (intuitionistic) logic proposed by Johansson, we call them clean logics. It is easy to see that to clean a logic is a form of paraconsistetization, as developed by my colleague and co-author Alexandre Costa-Leite, Edelcio de Souza and Diego Dias (here is their 2016 paper). This is because if we add a contradiction to the premisses of any valid argument, it derives nothing - instead of deriving anything. Clean logics are paraconsistent in the strong sense that nothing makes the system explode.

Comments

Popular posts from this blog

Hunky, Gunky and Junky - all Funky Metaphysics

Been reading Bohn's recent papers on the possibility of junky worlds (and therefore of hunky worlds as hunky worlds are those that are gunky and junky - quite funky, as I said in the other post). He cites Whitehead (process philosophy tends to go hunky) but also Leibniz in his company - he wouldn't take up gunk as he believed in monads but would accept junky worlds (where everything that exists is a part of something). Bohn quotes Leibniz in On Nature Itself «For, although there are atoms of substance, namely monads, which lack parts, there are no atoms of bulk, that is, atoms of the least possible extension, nor are there any ultimate elements, since a continuum cannot be composed out of points. In just the same way, there is nothing greatest in bulk nor infinite in extension, even if there is always something bigger than anything else, though there is a being greatest in the intensity of its perfection, that is, a being infinite in power.» And New Essays: ... for there is nev...

The underground of concepts: my talk at the Marxism and the Pittsburgh School Conference

In few minutes I'll be presenting this talk in the Marxism and the Pittsburgh School conference in the UCL. I can still change the text but this is how it looks like now. The underground of concepts: McDowell on the productivity of Anschauungen Hilan Bensusan 1. Jean-François Lyotard diagnosed the idea that concepts do the productive work of thinking as a deception. It is not through a dynamics of concepts that conclusions are reached and it is not with the decisive intervention of them that conflicts between alternatives resolved. Lyotard compares the pretense that concepts think with the mystification that capital works. He argues that “what works is not the concept, […] the concept is [like] capital which pretends to work, but which [only] determines the conditions of labour, delimits the outsides and insides, the authorized and the prohibited” (Lyotard, Libidinal Economy, p. 13). This diagnosis, frequently lost in the middle of an ampler argumentation around t...

Talk on ultrametaphysics

 This is the text of my seminar on ultrametaphysics on Friday here in Albuquerque. An attempt at a history of ultrametaphysics in five chapters Hilan Bensusan I begin with some of the words in the title. First, ‘ultrametaphysics’, then ‘history’ and ‘chapters’. ‘Ultrametaphysics’, which I discovered that in my mouth could sound like ‘ autre metaphysics’, intends to address what comes after metaphysics assuming that metaphysics is an endeavor – or an epoch, or a project, or an activity – that reaches an end, perhaps because it is consolidated, perhaps because it has reached its own limits, perhaps because it is accomplished, perhaps because it is misconceived. In this sense, other names could apply, first of all, ‘meta-metaphysics’ – that alludes to metaphysics coming after physics, the books of Aristotle that came after Physics , or the task that follows the attention to φύσις, or still what can be reached only if the nature of things is considered. ‘Me...