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@kutschkem: Representation is fine and well, as we could talk of the univers resembling some form of a computation, but once we transpose from representation to ontology, therein starts trouble. There's just some step were you have to sacrify the definition of Matter if you want to believe the univers is truly both physical and computational. Or at least so I sense, I was in fact interested with a counter argument. (2/2)
@kutschkem: I think I didn't make myself clear, I am concerned with a physical computational univers, so my comment relates to a very general definition of computation. Regarding the scope of your argument, which I find reasonnable by the commun definition of the words "information" and "computation", you're accepting information to be represented with a state of matter (a bit is stored in some capacity or whatever). (1/2)
@kutschkem: I think the link relates to a definition where information is taken as "matter in motion", change of matter and its arrangement; in a way, it may imply that we are (or contain) a fixed state(s) from which variation of matter can be measured (hence establishing the comparative point upon which re-arrangement of matter produces what's commonly known as information). Under such a view, all there is is matter, information is a convenience word. My take is rather: suppose there's only matter, suppose also we're not in some monism, how do "bits" of matter interact ?
@Conifold: interesting take, mathematics can seek depth in the steps of a reasoning because it starts by simplifying/abstracting-away, philosophy attempt to embrace the complexity of reality and is hence forced to extend rather than dig, it's as if it were some analogy to the uncertainty principle (in quantum physics): a bound amount of "thinking-energy" which is either dispensed in depth or in extent.
It's then more of a termonological task to qualify such "anchors" as "more certain beliefs" or "axioms" as long as you understand how the reasoning operates: make a fixed combination of propositions and see how (combined with your tools of deduction) the resulting corpus of demonstrated/argumented propositions holds (well or not).
There might just be something of a good intuition in the way you've perceived philosophy, there exists - for every philosopher - some functional axioms, these would not maybe be technically equivalent to what axioms represent in the axiomatic-logical understanding, but they act as anchors for the reasoning, at least in some temporary capacity, until the consequent construction/result shows shortcomings or distinct mistakes.
it's an interesting take (+1) no doubt, I just wanted to make sure I understood. Kant did not deny existence of reality, he simply put it out of pure-reason's reach. Hegel seems to have introduced the idea of a subject converging toward reality (as a totality). The vedic systems usually establish an immediate link between the subject and reality, first by containement (in mereological terms) and second by isomorphism (atman is brahman). As to Schrödinger, I have no idea, but was he not in the line of Copinhaguen interpretation, hence maybe refuting reality as an aim of science ?
Sorry for the mismatch between the transcendent and transcendental (thinking in french). So I take it the natural in kantian philosophy is in the phenomena's scoop (as "parsed" by a human). For some reason I thought his definition of the transcendent (and Godly by extention) is just an abstractive way of saying (that which is out of our cognitive reach), but it might just turn out he really meant God as a supra-natural span of being/reality. Could that be a fair interpretation of his thoughts ?
Thanks for the recommandation. As to Kant pinning any notion of certainty on empirical truth, that's only partially true, the transcendental aspect of his philosophy almost avoids any talk of certainty as pure reason would attempt it.
If I may, how does ZFC encore infinitely many axioms ? Otherwise, Godel's generative mechanism for undecidable propositions does in fact suggest you can have "axioms" at will.