The logic I "find" in the world is an approximation I make; — Srap Tasmaner
I think it helps to see we are pursuing a model of causality when we talk about the logic, structure, rationality or intelligibility of nature. Otherwise you are getting too hung up on the human mathematical practice and it’s semiotic peculiarities. You get caught out by the fact that semiosis is itself a symbolic and mechanical way of regulating the material world, and the material world then has its own organic logic - that of a self-organising dissipative structure.
So we have to be able to step back and see the whole of a modelling relation in which the model and the world have their own causalities, their own logics. And what would then universalise them as aspects of the one “logical” cosmos is the further step of understanding how the mechanical and the organic are the two poles of a meta-dichotomy. They can mutually exist as “other” to each other.
So the usual monistic and foundationalist instinct is to reduce our models of cosmic logic or cosmic cause to a single central truth. But semiosis and systems science explain why this quest proves so hard. It is because causality/logic is irreducibly complex in the triadic way that systems thinking describes.
The approach to the goal of a unity of opposites has to begin with the grant that anything might be the case. The “ground” of being is a pure material potential/pure logical vagueness. An everythingness of unstructured fluctuation.
We can know this is the most reasonable starting point or initial conditions as we can wind back from the developed state of the Universe today. We can see that the Universe is the most fundamental expression of an organic causality in that it is the grand self-organising dissipative structure that constrains all else due to the laws of thermodynamics and symmetry breaking.
And we can also see that one of the possibilities that exists in this general dissipative state of order is life and mind - the evolution of an informational causality, a localised symbolic and mechanical regulation that cuts across the Universe’s global dissipative project.
Modelling can control entropy flows for its own purposes as it has codes to create memories that stand outside the world of ordinary self-organising dynamics. It can manufacture networks of switches - like enzymes, neurons, utterances, logic gates - that switch material flows off and on with dichotomous certainty.
So we can say nature just self organises under the logic/causality of dissipative structure. But that itself is a statement we are then making about “the real world” from the cosy mechanistic confines of our modelling relation with that world.
And therein lies the problem. Or at least the knot of complexity which makes people’s heads explode with its self-referential Goedelian incompleteness. We can only seem to map the territory. We realise we are applying a mechanical perspective to what it itself now claimed as being the “other” of the organic. This doesn’t compute. The regress appears infinite. We are spat back out of our metaphysics into dualistic confusion.
Yet this need not be the case. If we can understand the world vs model relation in terms of an actual natural dichotomy - one that unites the organic and mechanical as complementary and reciprocal aspects of being - then we can formulate a triadic vantage point that sees both sides to the one more complex whole.
That is why I champion biosemiosis. It goes beyond pragmatism to speak to the scientific “how” of how negentropic organisms exist by mechanically ratcheting the entropic gradients of a dissipating cosmos.
In a nutshell, the material world has physical dimension. It costs time, space and energy to cause things to happen. And the way to then stand outside this world so as to model and regulate it is to thus lack the constraints of being dimensioned. To systematically reduce that dimensional involvement between model and world until it becomes the zero cost presence of an information bit or Euclidean 0D point.
The sly trick of life and mind, with their memories and informational order, is that they don’t actually have to dematerialise themselves to be literally dimensionless ghosts or whatever. As processes, they just have to be able to encode the world using a symbolic machinery that involves a small and constant entropic cost per unit of information captured and stored.
The brain burns nearly a quarter of our calories. But we can afford that because we use our brains to feed our mouths. And while feeding our mouths has been top of mind for most of history, the brain is a flexible enough bit of hardware that it could also learn to run verbal and mathematical systems of semiosis on top of its evolved genetic and neural ones. Homo sapiens could ascend the ladder of world models to ever greater dimensionless abstraction and so aspire to regulate the material dimensional world from some ever less materially constrained - and hence more purely informational - place.
So again, our big metaphysical question here is what is the fundamental model of the causality/logic of the Universe? And this quest is already irreducibly complex because we are mechanical systems modelling an organic world in the mechanical way that looks to contradict everything about that world.
This seems an irresolvable problem. But it is also the larger semiotic inevitability. Organic order - the evolution of a Universe structure by the logic of dissipation - had to create the possibility of its own mechanical regulation to the degree it became crisply dimensional and thus gave causal reality to whatever could then conceal its dimensionality - ie: the further realm of 0D symbols. Or at least semiotic systems which could afford information storage as a very small and constant cost.
A word is a puff of air. But we can make it stand for anything in terms of some unit of socially meaningful information. An enzyme is a chain of amino acids, but the body can toss one into the biochemical fray and regulate the direction of any metabolic reaction. A neuron is an abrupt act of depolarisation, but it can stack up levels and levels of Bayesian predictive routines. A number can be encoded in the 1s and 0s of a logic gate, but the resulting mathematical structure encoded in a pattern of electrically-powered switching can function as a useful model in any way a human cares to imagine.
The brute materiality of the Cosmos is the ground of its own antithesis in terms of bringing to life - being the cause - of the mechanical symbol processing that transcends the Comos’s strictly dimensional existence.
Yet look closely enough - understand semiosis as physical process with a small but constant cost per unit - and you can reunite the model with its world. We see that life and mind are part of the Cosmic fabric as all they really do is aid its dissipation by applying Bayesian modelling to the creation of paths that locally accelerate the global diktat of the Second Law.
We speak of causality when we talk of material structure. We speak of logic when we talk about informational structure. And both those things are different, yet also fundamentally connected. In formal terms, we would get closest to the metaphysical truth by being able frame them as two halves of the one larger dichotomy. And to do that, we have to dig away at the third thing of the way the two halves indeed connect. The story of the switches and ratchets which are the Janus interface bridging the epistemic machines with their ontologised environments.
Or if we switch from this synchronic perspective to the “other” of the developmental/evolutionary diachronic perspective, then we have to dig away at the third thing of the way the two halves could co-arise from some shared initial state or a vagueness … which is neither dimensional, nor dimensionless, but now “other” to dimensionality in general. In other words, the Apeiron - the everythingness that is neither yet a something, nor yet distinguishable from a nothing, but “exists” as a logical ground for any resulting structured material being.
This is certainly a twisty saga. But it is the systems metaphysics Anaximander first articulated, Peirce formalised, and which science is cashing out in twin pronged fashion as it comes to model the Universe as a self-organising dissipative structure and life/mind as itself the machinery of models that can further ratchet this generalised cosmic flow.