Dear En,
I will try to answer to your question if there is a way to imagine the form (or format) of how structures (forms) [[in a Platonistic sense]] can exist without people?
First it should be clarified that the question "how XYZ can exist without people?" concerns not only Platonistic items but all kind of existence comprising its material aspects. Here we touch an old philosophical problem which has never found a satisfactory solution. Consider a video system filming material reality. This system reproduces reality "in its own way," including 3D 竊' 2S mapping and thereby reconfigurations of proportions, and generally some deformation of colors.
As humans, we are outside of the circuit linking the system to reality, and vice versa. In other terms, we can check the degree of adequacy between reality and its mapping by the system. And more especially, w can know whether the system is effectively video REPRESENTING parts of reality, or for example a hologram synthesizer CREATING it.
But regarding the links between human cognition and reality this cognition is supposed to represent, the situation is essentially different. Here, we cannot get out of the circuit, since we are unavoidably integrated to it. Of course, if someone assure us that trees are red or blue for her or him, we can reply to her or him that for a very significant majority of humans trees are green. However, we cannot know anything about elements of reality "pe se", ie reality such it exists beyond its conditioning by cognition. Perhaps our cognition deforms colors just like video systems can do it, and only cognition modalities globally shared by a significant majority of humans give us the illusion of "objectively green" trees and of a sky "objectively varying from blue to gray". Perhaps reality is created by our cognition, and only the (highly hypothetical) "fact" (??) that a significant majority of humans share very similar cognition modalities permits us to say (or to hope?) that we share a "same" reality. Here, a big problem occurs: since all philosophical and/or scientific approaches of the link between human cognition and reality are intrinsically conditioned by human cognition, there is a genuine CIRCULARITY, and, by definition, any tentative to break out of circularity is metaphysical. So a lot of philosophical/metaphysical theories are competing about this issue; some among them seem rather zany, others are more plausible. But in absolute terms they are all equivalent in this sense that they are neither provable, nor refutable. The thesis claiming that the material reality such as we perceive it could also exist WITHOUT PEOPLE is NOT the most convincing; by contrast it encounters terrible lacks of consistency.
Briefly speaking , not only the idea of a Platonistic reality is highly problematic. No conception of reality escape to irresolvable epistemological problems. Material reality is "familiar", but sole familiarity does not mean knowledge.
Facing material reality, all we can do is to seek the simplest way to approach it. I mean the simplest way in the philosophical sense of the term, which is not ever simple in the common sense.
Consider a macroscopic physicist, in order to avoid supplementary problems concerning quantum epistemological considerations about "reality" taking sometime very exotic forms. This macro-physicist, before beginning her or his purely physical investigations should theoretically interrogate her/himself if the phenomenon to investigate "really exist", because - always theoretically - it would be futile to investigate a phenomenon which perhaps "does not exist." But since all consideration about the "existence of material reality" are metaphysical and thus without definitive solution, and since on the other hand these metaphorical controversies do not add anything to a purely physical investigation, the physicist mentioned above can operate AS IF the existence of the material reality would be "obvious", and although this is NOT the case, the macro-physicist's (tacit) choice to neglect all metaphysics is a legitimate way to avoid complications being absolutely useless in her/his domain.
That is what I mean roughly speaking by "simplicity" in the philosophical sense of the term.
Now I wonder why people working about foundations of mathematics and/or links between mathematics and physics would not adopt an equivalent attitude regarding Platonism IF this represents the simplest way to approach these issues. I insist on this IF. For the moment, the issue if Platonism represents the simplest way to approach mathematical foundations and links between mathematics and physics. But it is a manner to say that there is no reason to develop any apriorism against Platonism because of the immaterial reality it presupposes. The material world the physicist mentioned above consider tacitly as existing could also not exist. It is not materiality which could elucidate the question why the material world exist instead of not existing. Why then deny a priori
the existence of an immaterial word existing - exactly like the material world - because it is existing, in the event that mathematics as object of DISCOVERY would the simplest way to approach FOM and related issues?
Of course to know if it is so, me must return to your other question: How can we accede to an immaterial world au cas oﾃｹ il existerait?
Here I think we must avoid that what some people reproach to Paul Benacerraf. According to Benacerraf, Platonism is weakened by the "fact" (?) that for an immaterial Platonistic world of objectively existing mathematics, there is nothing equivalent to human empirical cognition. But this point is neither specially astonishing, nor an anti-Platonistic argument. Since a Platonistic world is not a material one, its investigation modalities are not necessarily equivalent to empirical cognition.
According to my own standpoint - it is not the only one; our little Platonistic family is not family quarrel free, as this contest confirms it - the best way to decide between Platonism and its challenging approaches consists on comparison under epistemological criteria such as simplicity in the logical sense of this term, complexity of primary and secondary hypotheses, internal consistency, consistency on the level of consequences and so on.
Here is an example how proceed in this way, and more precisely an example to consider in its historical context. As you know, Saccheri, arround 1730, tried to prove Euclid's parallel postulate by reductio ad absurdum. He thought that replacing the parallel postulate by one of its both negations would entail a lot of inconsistencies. But these inconsistencies did not occur, could not occur. Despite himself, unwittingly, Saccheri was doing non-euclidean geometry, and this almost a century before it was discovered by Bolyai, Lobachevsky and others.
The case of Saccheri is interesting; it evokes a bit that of Columbus. The latter, hyperfocussing on his project to discover a new route to India, did not realize until the end of his life that he had discovered a new continent. At least, this is our common contemporary vision. But anyway, Saccheri corresponds to this scenario. Hyperfocussing on his project to "prove" Euclid's parallel postulate by reductio ad absurdum, desperate by the unavoidable failure of this project, Saccheri could or would not realize that he had discovered the possibility of non-euclidean geometry and even non-euclidean geometry as such. But it is commonly agreed that Sacceri was doing non-euclidean geometry without being conscious of it. For my part I think, for we can do something unwittingly, this "something" must exist objectively. Hence the case of Saccheri represents an argument "advocating" Platonism, but "advocating" of course does not represent a proof. As on the other hand ALL this is metaphysics, and the question of proof does not even arise. But we can compare Platonism to its competing approaches under the criteria mentioned above.
Saying that the Platonistic mathematical world exist just like the material world which exist on its side instead of not existing, well, it is perhaps a heavy hypothesis, but not heavier than the hypothesis concerning the existence of the material world.
Let us now compare the Platonistic hypothesis to yours.
If I understand well, you are postulating that our brains belonging to the material universe are subsequently subjected to the laws governing this latter. Symmetrically our brains can accede to the laws of the material universe. This is another case, but personally I think to hold in terms of overall consistency, it requires a lot of secondary hypotheses. First, our brains certainly belong to the material universe in this sense that they are in space-time. But do they also belong to the material universe in a physical sense emphasizing specificity of physical laws? The opinions are divided about this point. First me must mention here the so-called "anthropic principle" in its weak and strong versions. For the weak version, I think there is no problem. Simplifying, we can formulate it as "Since there is an evolution beginning with inert matter and being achieved by human brain", the properties of the material universe must be compatible with this evolution. No problem, but un universe "allowing" the emergence of the human brain is only a necessary, but certainly not a sufficient condition for the effective apparition of our brains. So some people formulated the "strong anthropic principle", somewhat like ""Since there is an evolution beginning with inert matter and being achieved by human brain", the properties of the material universe must IMPLY this evolution". Well, if I said "somewhat like ...", that is because the exact formulation of the "strong anthropic principle" is controversial even among its supporters. And other people deny its validity. So this "principle" is not a principle but just a very complex and controversial hypothesis. On the other hand, each approach making links of cerebral structures and our knowledge concerning physical laws should entirely master the issue touched by the "strong anthropic principle", and this it not possible since neither this latter, neither its challenging approaches can be proved or refuted.
A each one to see if the Platonistic hypothesis is not, epistemologically speaking, much simpler.
Well, this discussion keeps open and must be continued. I will also do my best to answer to your further questions formulated in other posts.
With kind regards
A bientﾃｴt, j'espﾃｨre
Peter
