u/lucasvollet

In the 19th century, mathematicians debated the foundations of their craft: too much of the work looked arbitrary, and multiple theories seemed to have no priority over one another — as with the non-Euclidean geometries. Kant's old response — that one unique form of space and time would suffice to unify deductive inference across mathematics — turned against itself: it triggered more doubt rather than less. If we depend on a prior framework, synthesized through intuition, to ground mathematics, what would make one such organization more grounded than another?
Into that scene steps Frege, with an answer: arithmetic propositions can be seen as purely analytic, and — more importantly — that their analyticity does not undercut their conceptual fruitfulness. Analyticity, for Frege, is a mark of the conceptual features a proposition brings to light and that are surfaced under study, not something achieved by mere manipulation of signs.
My next series argues two things. First, that the only way this thesis survives today is as a pragmatic claim about how to select the most prudent paths of inference in order to unify them into a coherent whole. Second, that this fails in scientific fields where such unification isn't even desired — history or sociology, for instance, where incommensurable conceptual frameworks are part of how understanding itself conflicts and develops.
I developed this arguments in multiple ways since 2017 (in several published articles, this being the main one from 2021: https://periodicos.sbu.unicamp.br/ojs/index.php/kant/article/view/8672336) with arguments designed to restore confidence in synthetic a priori judgments (specially inferences), as they are richer than analytic ones to track intensional distinctions that have more depth than merely Carnapian Intensions (individuated by the patterns of evidence they fit). There is nothing particularly original orrevolutionary in this reading, but if anyone is interested in it, I invite you to see my video-series developing the whole argument:

https://www.youtube.com/watch?v=NPAQAYlQ58A&t=17s

When we ask whether a LLmodel has "genuinely" grasped that “numbers can't be hot”, we are implicitly holding it to a standard of category-recognition that we assume is simply what conceptual competence is, full stop, for any mind whatsoever. I argue in the article bellow (Published by Topicos-Mexico/Q3 Scimago, last year) that standard of what counts as a category error, what counts as a well-formed question, what counts as the "right" categorial structure for numbers to have, all of this is not free-floating logical necessity. By arguing that modern natural language semantics are not born in neutrality, I try to show that the standards we take to be simply "what rationality is" - the transcendental categories, the forms of judgment, the synthetic unity of apperception - are not ahistorical bedrock. It is, on my account, transcendentally asserted - subrepticiously introduced in as if it were a condition of thought as such, when it is actually a hidden commitment of one semantic research program among possible others.

In the paper, I walk through a broadly Fregean/Russellian picture of reference, refined through exactly the Davidsonian and Lewisian machinery, in which sentences must have determinate truth-conditions relative to a prior, fixed typing of their referents (that picture seems to fix what a machine would need to understand: numbers as abstracta, temperature as a physical predicate, and a settled fact about which predicates apply to which sorts). I argue that none of these settle the matter. Ask me the whole article. Search my youtube channel for more.

https://preview.redd.it/2qaq9h5m5leh1.png?width=495&format=png&auto=webp&s=12bbf166ea446e3e5a14889743ebf8bfe08fe3a7

Drawing primarily on Rudolf Carnap’s intensional semantics, Ruth Barcan Marcus’s critique of extensional reduction, and broader traditions in compositional and structuralist theories of meaning, my new Video-Series (Link in my page) proposes that cognition cannot be adequately modeled through behavioral or extensional correspondence alone. Two systems may generate equivalent outputs while differing radically in the inferential pathways, conceptual dependencies, and normative constraints that sustain those outputs.

The argument develops through an analysis of translation, bilingual cognition, Carnapian intensional isomorphism, and the historical convergence between compositional semantics and structuralist theories of difference. These traditions are interpreted as parallel attempts to constrain interpretive anarchy by regulating the admissible space of meaning. The paper further argues that contemporary machine learning systems intensify this philosophical problem: the production of human-like outputs does not by itself establish equivalence in cognitive organization or semantic structure.

Against both eliminativist behaviorism and romantic appeals to inaccessible interiority, the essay defends a middle position in which intentional structure is treated as theoretically reconstructable without being reducible to surface correlations. The project reinterprets Carnap’s semantic program not as a merely formal exercise, but as an early attempt to articulate the conditions under which inferential differentiation becomes scientifically tractable.

But the work leaves this open:

If meaning gravitates unavoidably toward its strongest attractors, it remains unclear why the intensional/extensional distinction should matter at all, why a system producing the right attractors by thermodynamic rather than semantic means would fail the musculature test. This tension is the work's most productive unresolved problem.

Find the link in my page. Thanks.

The Kantian argument would be a version of his answer to Hume: associationists like pure classical empiricists overstate how much we can connect and associate; there must be some constraints in the realm of the possible that trace back to how our mind organize experience. So the same would go here: dead internet thesis overstates what nonsense can actually do. Even nonsense does not arise in a vacuum — it emerges within a field already structured by meaning, and that structure eventually asserts itself: a superstition exposed by a better connection, an older theory reframed by a stronger one. The Kantian point here is not trivial: higher synthesis is not optional. Once representations are connected, the pressure toward more coherent organization is built into the architecture of representation itself. You cannot permanently stabilize a weaker structure when a stronger one is available. The flat earther machine fails not because we correct it from outside, but because the internal logic of constraint will not hold still at that level.

But here is where I think the theory gets something right, even if for the wrong reasons.

Most of our lives do not unfold in the paradigmatic spaces where constraints are strong — where mathematical relations have displaced naive associations, where differential structure is stable and overrepresented. Most of our lives happen in the regions where constraints are weaker, distinctions blur, and multiple incompatible connections can coexist without forcing a resolution. Politics. Social organization. Identity. Value. These are not domains where higher synthesis is automatically compelled.

And in those regions, the danger is not chaos. It is something more insidious: coherent, functional, self-sustaining nonsense — systems that successfully simulate sense across deep contradictions, not by resolving them, but by stabilizing at exactly the level of coherence needed to keep the deeper inconsistency permanently below the threshold of higher synthesis.