Linear logic is the shit. I've been reading up a lot on linear logic and certain things I have a hunch it closely corresponds to and I'm convinced it's the form

Linear logic is the shit. I've been reading up a lot on linear logic and certain things I have a hunch it closely corresponds to and I'm convinced it's the formalism for 21st century. Basically, it's like classical logic but with two players. From player 1's point of view, player 2's AND has different semantics than his own AND. It's the logic of state developing over time. In classical logic a statement can only be true since negative eternity and it will be true until eternity. On the other hand, linear logic deals with statements like "I have a dollar" which can be spent on an ice cream. Therefore, at some point, "I have a dollar" was false, then it became true, and then it became false again. It's also the logic that captures the difference between a reference and a value which is weirdly important. Unix's "everything is a file" should actually be recast as "everything is a reference". The Rust borrow checker is based on a subset of linear logic and it's the secret sauce of said compiler. It can reason statically about dynamic systems. I'll make some claims that I can support with papers if need to be so ask if you want proof. Currently, probability is based on measure theory however linear logic can also be used (Vovk bases probability on game theory which is essentially linear logic). Generative adversarial networks (which are based on minimax) are based on linear logic as minimax is very linear logical. I would go as far as to say that mathematics, in addition to axiom of choice also needs an axiom of adversarial choice. Axiom of choice assumes that you can always pick the best possible option, however you need to be able to account for your worst possible options as well. All mathematical optimization falls outside of classical logic. The funniest thing is that this idea, the duality of things is very old. Dialectics is very firmly rooted in Western philosophy (Aristotle, Kant, Hegel, you know the usual suspects) however no one ever extended it to a formal logic. Karl Marx (I hate Marx but realize that his ideas might have influenced people so knowing why he was wrong is worth something) also talked about a similar idea (https://en.wikipedia.org/wiki/Dialectical_materialism https://en.wikipedia.org/wiki/Dialectical_materialism). In particular Engel's summary is work exploring https://en.wikipedia.org/wiki/Dialectical_materialism#Engels's_dialectics https://en.wikipedia.org/wiki/Dialectical_materialism#Engels... They are essentially talking about linear logic, however the third rule is very much wrong, negation of negation is not a part of a logic of two opposites. It can also be used as the foundation of probability instead of the more traditional measure theory. I can talk about this for hours.