In fact, some kind of intuition of logical principles might be innate. Maybe even animals. — boundless
Yep. Animals can induce or form associations. They can tell the difference between one, two three and many. But deduction, like the counting, or learning grammatical structure, is something no other animal but humans can turn into a fluid skill. So we can make something of that. The mindset behind logical and physical accounts of the world has some neuroantomical basis. We evolved this basic habit of thought that is recursive. We find it easy to think in a nested hierarchical fashion. A calculus of distinctions.
We likely evolved this first over a million years of tool making/using, and then this was further solidified by the development of articulate speech. We needed to think in terms of sequences of construction. Hold a rock and chip it into a desired form. Face the world and turn it into a “who did what to whom” narration.
So there is a pragmatic ground to how we might think reality is optimally decoded. A grammatical instinct. A semiotic system of rules and words, relations and relata, syntax and semantics. A habit of mind that proved itself by its sturdy usefulness over a million years. Even though it was not about the world but about our being able to impose ourself in a mechanical fashion - action sequences leading to desired results - on our world.
Thus there is a ground. But it is neither something of the world or even of our minds. It is a propositional attitude that arose from a semiotic modelling relation with the world. It is neither a pure realism or a pure idealism. It is something that cognitively worked. A tool using hominid could structure its world with a hierarchical order. A grammatical sapiens could impose a further level of still more consciously-distancing narrative structure,
We see then the ancient world where causality continued to have a human-centric narrativism, The animistic and magical thinking where the landscape is alive with spirits and powers. Even at the time of the Hesiod, the Greeks were equally comfortable with causal explanations that “the gods did it” as some more naturalistic account of why a storm blew up or sickness took a child.
Then we get to Anaximander and the first systematic naturalism. We have dialectical reasoning that develops into a variety of causal accounts such as hylomorphism and atomism. We have geometry and arithmetic becoming formalised by the constraints - the closure - of proofs.
What was a logic and causality of narration becomes a logic and causality founded in number rather than words. And this in turn becomes dialectically divided as science and maths. The grammar of physical nature and the grammar of pure ideas.
So yes, logic and causality seem to speak from different spheres today. And we are as comfortable with that as those of the Hesiod era were comfortable mixing the registers of mythical and animistic accounts with more physical and naturalistic accounts.
It seems to work that there is structured speech about the real physics of the world and the true or valid arguments of the mind.
And yet dig down. It all starts and ends in the pragmatism of the semiotic modelling relation we have with the world. What works - and thus what we believe in - is our ability to impose an imagined structuring order on our lived reality.
The foundation of logical and causal thinking is this uneasy thing that is neither properly a realism or an idealism. It is instead a system for constructing dialectical structure - nested hierarchies or recursive pattern - that can fashion the world into ways that conform with our desires.
We use models of logic/causality to constrain nature mechanically. It started with tool-making, then society-making, then civilisation and technology making.
And we are left uneasy - some even claim a foundational crisis - as it is all kind of both weirdly intuitive yet also neither clearly of the world or of the mind.
But, on the other hand, even understanding the concept of 'usefulness' relies on understanding logic. What do you think? — boundless
Self-referentiality is not an issue for a self-organising system. Circularity creates problems. Hierarchies fix them. The disjunction of the dyad becomes the conjunction of the triad.
Let's say that, indeed, logical principles are a 'reflection' of an intelligible structure of the world. How could one 'prove' this view? — boundless
I am taking the Peircean approach here. Truth is what a rational process of inquiry arrives at in the limit.
We hazard a guess, take the risk of assuming a belief, and then discover the pragmatic consequences of doing that. We systematically doubt what we have assumed until we reach a point that further doubt has become useless. Moot. A difference that no longer could make a difference in practice.
Proof seems a really big thing. But it is only important to the deductive phase of Peirce’s three stages in the development of a state of reasonable belief.
We start with the abductive guess. An idea about an explanation. Then we apply a process of deduction that is rigorous in terms of being closed for entailment. We break down our intuition into a set of specific logical expectations. This formal encoding of a proposition - if A, then B, or however we might phrase it - proposes a consequence we can then measure in terms of what actually follows. We can inductively confirm the proposition to the degree that it isn’t being contradicted.
But in order to accept a view or another, it might be needed to be shown that such a view is better than others (or a skeptical approach on the issue). — boundless
If the semiotic modelling relation has been working for life and mind since its biological beginning, and a semiosis founded in number is merely the latest instantiation of this natural story, then that would be a pretty grounded tale I would have thought.
One that is neither stranded in realism or idealism but founded in a lived relation that humans have with their world.