That's why I think, Boehme, while extremely mystical and esoteric, hits on an essential feature of reality. Definition requires difference. — Count Timothy von Icarus
I need to get back to Boehme and Schelling.
:up:
I'm not sure what the fundemental dichotomies would be. ... Order - chaos seems like it may be essential one. — Count Timothy von Icarus
They all seem fundamental. What about Aristotle's hylomorphism of form and matter?
But I personally settled on an ur-dichotomy of dichotomies.
:grin:
That is everything can be encompassed by the vague~crisp developmental contrast offered by Peirce, and the local~global dichotomy of hierarchy theory, that also speaks to triadic structure, but as that which is the fully developed.
So one dichotomy represents the process that is dynamical becoming - the vague start in a Firstness that culminates in a completely definite finality of Thirdness.
The other dichotomy represents the completed structure that is a Thirdness - the being that emerges as the dynamically stable limit of all that developmental becoming.
So you have two axes that are arranged orthogonally, and thus themselves compose a holistic dichotomy of being and becoming. The possibility of becoming divided into the local and global of a Thirdness - a stabilising hierarchical structure - is matched with the fact of arriving at that state of fundamental division.
If this Peircean logical story works, then it should be easy enough to map all other metaphysical-strength dichotomies to its ontic structure.
So chaos~order would fit to the local~global axis of being as the systems story of global constraints shaping local degrees of freedom in hierarchy theory.
And it would fit the vague~crisp axis of becoming as being also the view that it takes time for the global constraints (or the sameness of a global coherence) to evolve, and thus time for the local freedoms (or local differences) to be given some final restrictive shape.
A problem though is that "chaos" tends to be an ill-defined word itself. In probability theory, it speaks not just to a certain randomness - or lack of order - but to a more specific class of disorderliness.
Unsurprisingly, there is a further dichotomy at work - which is why chaos~disorder would be considered a non-fundamental dichotomy. A chaotic regime is randomness that is fractal, scalefree, open, and without a mean. It is ruled by powerlaw statistics. The other kind of disorder is the more familiar realm of Gaussian or Bell Curve randomness, that has a single scale, which is thus closed by a boundary, and does have a definite mean or equilibrium average state.
This is a technical point. And one could say that the new maths of deterministic chaos still isn't describing what we really mean by "true chaos" as it is still a state of disorder bounded by a pattern - the pattern that is a powerlaw or log/log differential equation. A "true chaos" indeed may seem more like a "true vagueness" in the popular conception, as it would be fluctuations completely without bounds. And powerlaw regimes are definitely bounded in a fashion that completely predicts the statistical patterns that must thus arise.
But anyway. My argument is that once you get the trick that is a metaphysical dichotomy, you can trace dialectics back to its own source. Which is what Peircean pansemiotic logic is about.
Haven't heard this. Why is this so? — Count Timothy von Icarus
Background independence is needed because a quantum version of general relativity would presume that the spacetime metric would itself fluctuate with gravitational self-interaction. So spacetime must be made part of the emergent mix in the next level of a unifying theory.
The Cosmos - as both a container and the contents - would have to arise as a developmental dichotomy. And so the very thing of "a point of view" - as a story of the invariances of fundamental symmetries - would have to emerge and become a stable feature.
So I am cashing out the notion of "points of view" as speaking to the need to ground descriptions of worlds in terms of their generalised invariances
Relativity is all about how local differences don't make global differences - and in fact instead reveal the global sameness.
QFT is all about how the same can apply through gauge symmetry to locales. What global invariance cannot "see", is then what makes the local degrees of freedom, or variance. And this is why particles are shaped by their own local permutation symmetries - the SU(3)xSU(2)xU(1) deal of the Standard Model.
Again, dichotomies rule. The Big Bang starts at the Planck scale where GR and QFT don't yet experience any local~global distinction in scale. The energetic fluctuation is just as "curved" as the curved container that is meant to make it distinctive as "a fluctuation". So in fact there is no point of view to be had when there is no distinction between the local QFT differences and the global GR metric sameness.
But as the Big Bang starts to expand~cool from that point, then you have the emergence of invariance on two opposed scales - the QFT local scale symmetries that frame the fluctuations, and the GR global scale symmetries that track the shape of their container.
How does it deal with the apparent experimental confirmation of contextuality (i.e. the same thing observed can occur at different times for different observers). — Count Timothy von Icarus
Do you mean non-locality? Well time - understood as the measure of rest mass locality - has to be emergent as well.
A world composed just of radiation is timeless in the sense that there is action at less than c. It is only when particles gain mass that going less than c, and thus experiencing locality as the possibility of being different, becomes a thing.
A photon experiences no time on its journey. So it already lives in the non-local world. But mass breaks that symmetry to introduce a new variety of physical difference. Another point of view arises where there is the radiation bath of the CMB that "sees" time only as a generalised drop in temperature, and then all the bits of material crud that has gained local mass, along with a fractured collection of different gauge interactions, to become fermions living in a local "proper time" view of reality.
So local~nonlocal would be a further dichotomy or symmetry breaking that follows on to give greater emergent richness and complexity to time as a "dimension".
A photon only sees time as a structure of thermal decoherence. For some reason, it winds up red-shifted when its wavefunction collapses.
An electron lives in a more exciting world where it could be deflected by another particle at any moment. It gets to exchange momentum through a whole history of localised events.