Timeline for Is there a name for "inaccessible" concepts
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10 events
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| Mar 27, 2022 at 19:32 | comment | added | CriglCragl | @Uro: Then you hold a Mathematical Platonust view, a common & popular stance in modern philosophy: plato.stanford.edu/entries/platonism-mathematics I would call that math-mysticism, the shadow of Pythagoras: philosophy.stackexchange.com/questions/69573/… It basically contradicts the whole basis of progress in science, turn to evidence. | |
| Mar 27, 2022 at 19:17 | comment | added | Uro | As for the reality of it, I don't know. Not coming from a philosophical background, even though I have opinions I am sure I miss subtleties in the meaning of the word "real" and might misuse some words, but I think we disagree on that. I view mathematics as something that would "exist" (in some abstract sense but exist nonetheless) even if there were no worlds to "witness" it. Not as some specific theory with this and that set of axioms, but as a self-consistent and self-defining logical "thing" that, on some level, contains truths about itself and other things that are within its reach. | |
| Mar 27, 2022 at 19:10 | comment | added | Uro | I see for your first point, then if we count these types of interactions, we could be able to interact with some of them, but the interaction is ultimately very limited. For instance, we can understand conceptually hypercomputation, we can come up with theorems related to it and prove them, we can even determinate the result for very specific automata, but ultimately those results are very constrained, and a universe that does not support hypercomputation will never be able to extract everything there is to extract from them. | |
| Mar 27, 2022 at 18:30 | comment | added | CriglCragl | @Uro: As per dimensions example, interacting with a mental model counts. Rapidly cumulative things like en.wikipedia.org/wiki/… can still be interacted with conceptually. The distinction I make, is that I don't think unrealisable mathematics can meaningfully be called real, if abstractions or tokens of them can't interact with our world. They're literally metaphysical & not subject to any possible evidence. This is rooted in my view of mathematics, that it derives fundamentally from the world, not a platonic realm | |
| Mar 27, 2022 at 16:05 | comment | added | Uro | We can't interact with them, since they are abstract mathematical objects. I think what I call "strongly inaccessible" is related to what you describe in your last comment, but goes beyond that since it lifts the restriction of having to work with with the "stuff" that actually is in our universe and refers to things that are mathematically thinkable but that couldn't be thought no matter what arrangement of any amount of matter given our laws of physics. | |
| Mar 27, 2022 at 15:38 | comment | added | CriglCragl | I guess the true limit, would relate to the limits of assembling all the matter in our universe into a computation, using the then remaining entropy. But as discussed here, I don't think even that is a limit: 'What will humanity do IF and when technological progression ends?' philosophy.stackexchange.com/questions/89770/… | |
| Mar 27, 2022 at 15:34 | comment | added | CriglCragl | @Uro: Can we interact with those beings, & their universes? If not, ever, by any means, they are not part of our reality. If we can, we can come to share their understanding. But "If something about the mind of a knower means that is impossible, such as them being more advanced technologically than humans but uninterested in communicating, likely full communication may never be established." 'From the post Can knowledge exist that humans are incapable of understanding?' Linked above. This however, means not accessible, but not fundamentally inaccessible | |
| Mar 27, 2022 at 13:38 | comment | added | Uro | So even if there are limits on what can be conceptualised in our universe, I do believe there could be things beyond that limit, and even if such concepts had no meaning in ours, what matters to me is whether or not there is a theoretical mathematical model in which there can be arguably sentient beings which can make sense of it. In fact, them having no meaning in ours might probably even be a necessary condition to be unthinkable in our universe. | |
| Mar 27, 2022 at 13:34 | comment | added | Uro | Among all possible mathematical models that can be said to model something akin to a universe, I can not believe there isn't even a single one in which not only there exist things that can be described as sentient and in which, due to having laws of physics that enable much more complex behaviors (say, hypercomputation) for that universe's equivalent of matter, sentient beings are able to produce unique thoughts that couldn't be thought in our own no matter what. Whether or not such universes actually physically exist and are real does not matter to me: they mathematically could. | |
| Mar 27, 2022 at 12:22 | history | answered | CriglCragl | CC BY-SA 4.0 |