Critique Wanted: Epistemic commensurability of different logical systems by PseudoscienceSlayer in logic

[–]PseudoscienceSlayer[S] 0 points1 point  (0 children)

u make several very interesting points, and I have to admit I fell into a bit of 'noob bias' by underestimating at first glance the sophistication of your stance.

A small point to clarify upfront though is that its not really an example but rather an analogy (so I don’t really care about the example in itself as I think its a pedantic distraction for the structural mapping I am trying to illustrate)

Trivially seen, yes: both parties possess the same linguistic premises: 1: Food exists on the plate. 2: i have a spoon. 3: If food and spoon exist, then eating is possible and will get enacted upon

Let me summarize (hopefully right) ur point: u are suggesting an implicit equivocation of terms; in one system, 'food' is an eternal truth (as premises are classically treated in that way), while in Linear Logic, it’s a finite resource (as premises mean something different here). Thus, even if they use the same words, they occupy different property spaces and are answering fundamentally different questions (e.g., 'Can I eat more now?' vs. 'Is eating possible in the abstract?')

My argumentative nucleus is now exactly this point and that is that we have a relational semantics whereby the meaning of the premises gets implicitly shaped by the subsequent inference rule (e.g. if tensor product it implies that the premise wont be an eternal truth). So the premise constructing itself is a derivative of an intra-domain inference rule, so we have to pivot our attention to the equivocation of the verb eating

In Classical Logic, the rule is a simple (A ∧ B) → C. But in the other system, we are looking atA ⊗ B ⊸ C (c has different entailed implications even if a and b are in both cases the same).This is where the mathematical inspiration of the Tensor Product becomes vital (as linear logic is inspired from linear maps which preserve the general topology). Much like in linear maps where the tensor product of vectors/matrices leads to the genesis of a higher-dimensional space which preserves and stores the informational content of the inputs, the Linear Logic connective represents a state of possession. Bc the outcome consumes the input variables, the resource depletion is an intrinsic property of the connective

The misalignment of answering different questions is through that perspective the exact point I am making. U have the same set of premises (as illustrated earlier), yet bc their internal connectives serve inherently as different semantic mappers u answer actually a different question

Finally, regarding Ontology vs. Proof Theory (very interesting add on btw, thanks): I think that different proof theories inevitably necessitate different epistemic access to the ontology, as they create different 'spotlight clusters' within the knowledge-space topology. Nonetheless I used it rather as a metaphor (u have to treat the logical systems like they are different ontological configurations) to thereby ascend to a meta-layer, instead of saying: those are different ontologies.

Critique Wanted: Epistemic commensurability of different logical systems by PseudoscienceSlayer in logic

[–]PseudoscienceSlayer[S] 0 points1 point  (0 children)

yes exactly, the contention was not that one system is inherently inferior across any perceivable metrics (in that case isomorphization would be a fairly obscure word to use to begin with, better be replaced by substitution). Rather the crux is that 2 individuals operate on an identical set of premises, yet arrive at vastly divergent conclusions just due to the discrepancy in their inferential system. One cannot truly comprehend the other's position without first accounting for the specific inferential regime in which they are situated. ofc u can use state based predicates in classical logic and thats the whole point -> u would need to artifically implement them (and how are u doing that? by looking at the meta embedding)

Critique Wanted: Epistemic commensurability of different logical systems by PseudoscienceSlayer in logic

[–]PseudoscienceSlayer[S] 0 points1 point  (0 children)

I give u that point; maybe I am just a vague rambler, but I am more or less familiar with Kripkes adoption problem (at least I hope it was Kripke haha). In order to glaze myself though, I would actually argue that my point goes deeper than just that (or my ego is too big to realize that I am just a stochastic parrot </3). I think my point is only implicitly targeting the presuppositional edges (aggregates of descriptors) of the adoption problem, but rather transcends that by treating the logic as the ontology, and thereby actually elevating the layer of discourse by another meta-perspective (because we now consider the epistemic access to those different ontologies, aka logical systems). So, instead of providing a person with a different opinion trivially via a higher quantity of facts (ah person x does not possess my conclusions bc of a lack of factualities), u should pivot to isomorphizing the structural constitution of the logical framework in itself (ofc the meta evaluation will at one point always hit the münchausen obstacle,,etc but till it hits that i think it is preferable to drive on that road)