...you're discussing branches of philosophy (ontology, epistemology and methodology), in the context of extra dimensions...
approximately so. :wink:
_on ontology:
Ontology is the study of existence and being, right? So talking about 4D in an ontological context means discussing whether or not 4D "exists".
well, first part right, but conclusion wrong, in the shadow of bimodal logic.
thinking ontologically about any entity (generic 4-spaced in this case) means not determining whether it is or not (able to exist) although it doesn't exclude these considerations.
ontological distinctions concern not only whether or not, but also how, when/where, who and why of the matter. so 'talking about 4D in an ontological context means discussing' mainly
how something is, in what ways it's ecSisting/functioning/operating, under what conditions. not only if or not.
etymologically(=truly,actually),
ontology means the '
study of the logic of Being of beings(things,entities,events...)', not simply the study of being.
also, computer/information sciences, especially semantic web building today, has taken and appropriated 'ontology' concept into ots own domain, usually meaning a list of possible entities/processes within a given system.
_similarily,
epistemology is the study of the logic of knowing. how we acquire knowledge, how we learn, how we think the thinking. epistemological knowledge is the knowledge of the 'understanding/knowing' processes, a meta-understanding. it is the study of background structuring processes functioning (oranismically) behind the apparent (surface) understanding.
for an exemple of epistemological hierarchy(after K Palmer), aha:
(unbound totality)
data
fact
theory
paradigm
episteme
ontology
this is an epistemological hierarchy with (undefined) and...
.data at one end of the knowing process, being chosen out of undefined totality by bounding sense-media. these percepts are taken as...
.facts, because the state of perceptual media is usually taken as objectively given, static and unchangeable. a socially constructed reality. on the facts (as consensual givens)...
.theories(=seeings, perspectives) are elaborated. however, these are implicitly driven by previling...
.paradigms in their disciplinary/social contexts. paradigms (from para+doxa(Dogma,opinion in contrast to Ratio)) are assumptions behind theories, based on, or have to do with our schemas., i.e. inner coherence of our thought; paradigm shift - when assumptions behind theories change. however, paradigms rest on...
.epistemes - fundamental categories of our thought. in philosophy known as philosophical category theory such as that of Aristotle or Kant. deeper still, 'allowing' the Being of all these, are the...
.ontologies. this is the ontological level of our understanding of the world, underlying even the categorical level. however, the level of ontology has become fragmented in our times and civilisation. Being itself is considered a paradox, and as all the 'normal' people are considering Aristotle's identity dictum as fundamental and the only possible, this has become the deepest Taboo of today: the omnipresence of paradox.
_methodology is the study of (the logic) of methods, as you say.
so for exemple, me knowing/using the 4valued (~4dimensional) logic of Nagarjuna or Boole and it's relation to socially stabilised 'normal' aristotelian logic, i explained (implicitly, back up in this post) how bimodal logic limits the possible outcomes of any inquiry into fundamentally dual results which are most often than not inadequate to wholeness.
so being methodological means keeping track not only of What one is doing, but parallely being aware of How one is doing it, and understanding and acting on/out of that.
When I talk about higher dimensional spaces, they are defined to be purely abstract and mathematical. If yours are not, then we're not talking about the same thing.
well, again. this is a prime exemple of dual logic: either/or.
but you can go on talking about purely abstract and mathematical and i can go on with my research, and there doesn't have not to be any disagreement: if you are aware of the vast context of your mathematical specification, and I of the contexts of my (transdisciplinary) knowledge, we can BOTH see that the sea in which our disciplinary understandings float is the same. that is the deeper ground on which we can meet in meaningful insights, without despecting the other's approach, but mutually supporting each other's strenghts, and pointing out the weaknesses.
for the isomorphic issue, just play with the languague, or get etymological. that word is used outside of mathematical contexts. for exemple translate it as 'certain(iso) kind of smilarity of morphe(shape)'. you can use it then out of the mathDomain boundaries. (biology for exemple...)
As for life-flows and experiential continuums, I have no idea what you're talking about. I very much doubt these things would be isomorphic to multidimensional spaces, any more than a torus is isomorphic to "happiness".
actually, you might be closer with the torus/happiness exemple than you think. (oh no ! he cannot be serious on that, can he ?

) anyway, by experiential continuum i mean the incessant flow of the happening of the experience. in tibetan vajrayana, there is this conception of "rgyud" - the continuum, the 'thread' of ecSistence, the very fact that there rather IS something than nothing present. this means that all we encounter (science & multidimensional spaces included), we encounter in an incessant flow or continuum of experience.
actually, i wanna discuss consciousness in the light of multidimensional contexts. i claim that the structure of experiencing (of whether subjectivity, or objectivity, or of a measurement of an objective scientific experiment) is structured by the structure of the internal experiential space-time geometries.
in other words, that any percept is interdependent (mutually arising) with consciousness, and that it is the
structure of the consciousness (which is undoubtedly multidimensional, otherwise no multidimensional thought could be distinguished or contained in the history of our time-binfing activity as humans)
that determines the structuring of experience(of appearances).
therefore, it is not what appears to us that appears, but it is how it appears that truly appears. what appears and how it appears are not same. what appears is different from how it appears, and we conformally mistake the latter for the former. we cannot understand fully what/how/where we think, without understanding what techniques/methods and media(consciousness in any case) we use for our understanding.
so to cut this straight: anyone into any hyperspatial theories AND speculations on the multidimensional nature of consciousness ? ( which is just another word for Being with emphasis on its aspect of presence. (from the indo-european languague-traditions. you know, there was no word for
existence in european tradition and no word for
Being in arabic languague world. before the greek knowledge was temporally exiled into Arab hands, transcribed by the Arabs, and then re-discovered after middle-ages and re-translated back from Arabic. so the Arabs got Being and europeans EcSistence in exchange. we know greeks mainly from the translations from the Arabic transcriptions. there was no such distinction as Being/existence prior to this cultural interaction))