metalogic/metaethics 2

i trace the grounds and consequences of a wager that metalogic is ethics.

lemma on non-hierarchical relationships

If you put yourself in a position to provide feedback, do not seek to escape feedback on the feedback. Far from being a waste of time, argumentative, a drag on efficiency, or a change of subject from what one was originally speaking about, reciprocity is a vector of steep dialectical ascent, i.e., one of the more straightforward ways in which the Good shows itself to be co-referenced in every intentional object, just as necessarily, and just as originally, as the True.

completeness and collapse

Hypothesis: A two-stage unintended collapse occurs when thought tries to place itself positively on the side of completeness: 1. Deductive completeness collapses to expressive completeness (universality). 2. The semantic dimension even of expressive completeness collapses, leaving us with a pure combinatorics of syntax.  Completeness, even when apparently affirmed as paradoxical, is on the side of the signifier, not even of the signified, certainly not of the Real that would incomplete their correlation.

Stakes: It looks as if projected totalities of sense get around to defending themselves by affirming their paradoxicality sooner or later, as a rule, but this wouldn’t immunize them against reductio if the suggested collapse can be shown to take place.

Note the intentionality-expelling vector dual to being ‘drawn in’ at the diagonal.

ways in which one might “have” a concept without knowing of what it is

  1. having an intension or sense without knowing (any/all) of its extension or referent
  2. having a question without knowing its answer
  3. having a sign without knowing its interpretation

metalogic and Lacan’s thesis

“There is no metalanguage” is not only not an observation that counts against putting metalogic (metamathematics) at the core of philosophical method; it even implies that philosophy must be metalogical. “There is no metalanguage” means that philosophy, always-already reflexive, does not and cannot wait for the device of the arithmetization of syntax in order to become metalogical, and conversely, that it cannot use the inapplicability of the metalanguage/object-language distinction to keep metalogical problems at arm’s length.

an opening remark on AM

I would have considered much of what I think about Davidson’s 1970 “Mental Events” too obvious to say to anyone who had read the article, except that a few months ago I learned a couple of facts that made me seriously rethink what I consider to be too obvious. Apparently

  1. It has not been widely noted or appreciated that anomalous monism depends on a diagonal argument, and
  2. Everyone thinks that anomalous monism has been summarily refuted (on its own, or under the general heading of “non-reductive physicalism”).

I suspect that these facts are not unrelated.

three things to notice about Sartre’s essay on materialism

  1. He thinks that he has a clear path through the labyrinth of reduction and emergence.
  2. He is mistaken.
  3. The effective target of his disjunctions is not, as he thinks, the mathematicity of dialectic, but, to the contrary, the postulate of organic unity in it, which belongs neither to mathematics nor to ethics (or one could say, less perspicuously, neither to science nor to history). In other words, just because it is possible to have a rigorous idea of an emergence which occurs because of and not despite total reduction, we do not thereby fall into the vulgar dialectical reconciliation of internal and external relations, of nature and history, etc. Why? Because what is authorized thereby is, as appropriate to a form of local emergence, a thought of disjunction, and not of global synthesis. It’s just that the disjunction, to be rigorous, has to be thought from both sides – from the side of the in-itself, from which there is no difference between the in-itself and the for-itself, and from the side of the for-itself, from which there is.

divergences between operationalism and metalogical dualism

AB: There is no one, only the count-as-one.

Reply: There is no one, only ones.

AB: This [operational interpretation of the count-as-one] is the most general definition of a structure.

Reply: Indeed, but because it is the most general, it is not the best. To give the most general definition of unity is, since the one is not, to vitiate structures, of which the unity of each is heterogeneous to the others, to the zero-point of simple consistency.  It is from the point of view of the All, that is, or of a total language that unity is operational (which is to say, nominal).

AB: The Idea of the Good is the most majestic form of the Great Temptation to deny that ontology is a situation, specifically one which reverses the vector of every other situation, by giving an axiomatic (implicit) definition of the pure multiple.

Reply: The Idea of the Good, or diagonalization, is the witness not of the incoherence (inconsistency) of ontology, but of its incompleteness, which however is also to say, of its inconsistency if imagined as completeso that any strictly axiomatic presentation is not merely implicit but necessarily falls infinitely short in its deductive consequences of ontology – or even, for that matter, of arithmetic – and this condition (the infinite excess even of ordinary arithmetic over its axiomatic presentation) must be dealt with at the outset.