Dear Carl Sebastian Andersson,
You pose very important questions to which fundamental science today has no answer. Basic science is undergoing a crisis of understanding, crisis of interpretation and representation, "loss of certainty" (Morris Kline, "Mathematics: The Loss of Certainty,") and "trouble with physics" (Lee Smolin, "Trouble with Physics"). By the way, the second book of Professor Morris Kline in Russian is called "Mathematics. Search for Truth "(in English В«Mathematics and the Search for KnowledgeВ»). Notice the difference in names ...
Carlo Rovelli wrote a good article in 2018: Physics Needs Philosophy / Philosophy Needs Physics The same can be said with respect to Mathematics: "Mathematics Needs Philosophy / Philosophy Needs Mathematics." The problem of the "foundations of mathematics" (justification of mathematics) is more than a hundred years old. I call this problem the problem of the ontological basification of mathematics, which means knowledge in general.
Mathematician L. Faddeev in an interview The equation of the evil spirit for the journal В«ExpertВ» (2007) claimed, "that just as physics solved all the theoretical problems of chemistry, thereby "closing" chemistry, so mathematics will create a "unified theory of everything" and "close" physics."... How can mathematics "close physics" if the problem of justification of mathematics (ontological basification) is not solved. For some reason, mathematicians are currently facing the age-old problem of the justification of mathematics, "language of Nature", "swept under the rug." Just look at the "Millennium Problems" of the Clay Mathematics Institute. The "Millennium Problems" are being solved, but the unsolved problem в„-1 for cognition as a whole remains - the problem of justification of mathematics (ontological basification).
В Quantum theory and General relativity are phenomenological (parametric, operationalistic) theories without an ontological basification. Quantum theory will not give an answer to the nature of consciousness. It is necessary to "dig" into the ontology to the most remote meaning-distinguishable depths. But new breakthrough ontological ideas are also needed. Ontology should go towards mathematics and physics, and mathematics and physics should go towards ontology. Here, dialectics in the spirit of Plato, Cusa and Whitehead will be a good helper.
I began the search for truth thirty years ago through "digging" with the philosophy of consciousness, with the introduction of the concept-attractor "Vector of consciousness" ... The try to draw a "curve of consciousness" for three million years from the first tool (chopper) to the modern point. As the doctor of physical and mathematical sciences Alexander Zenkin (1937-2006) said in SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS : "the truth should be drawn ... ". I completely agree with this conclusion.
To overcome the crisis of understanding in the philosophical basis of fundamental science, one must first understand, as Carlo Rovelli notes: "What is space?", and only then answer the question - "What is time?" To understand is to "grasp structure" (G. Gutner "Ontology of mathematical discourse"). What structure? The ontological structure of the primordial process, common to the existence of Nature and thought - the eternal holistic process of generation of meanings and structures (material-idal). Here it is good to recall the philosophical testament of Paul Florensky: "We repeat: worldunderstanding is spaceunderstanding".
Please look at my щтещдщпшсфд ideas and give, if possible, your critical comments.
With kind regards,
Vladimir