Due to Kant, some contemporaries attempted to understand the psychology and motivation of "Mathematics". Iinvariably they returned to the classical but incorrect understanding of mathematics as Euclidean geometry. Using newly granted freedoms to criticise and innovate philosophers like Jahnke, Vollkert following Fichte started to look at the nature of space and mathematical signs.
Unfortunately, the concepts of space were derived from theological traditions and the very tools to discuss or think about it were derived from theosophy. One finds a naive Eikon of purity covering many complex ideas, as well as new terminology to describe spiritual or ghostly relationships as Strukturs. Philosophers struggled to realise deeply repressed concerns about the epistemology of their current knowledge, how they actually came to know, describe or understand any given thing. Indeed where did the givenness of a thing come from? Spirits, ghosts, ancestors and Gott figure heavily in this struggle to create a demythologised language to describe the issues.
A lot of Humes ideas are accepted by Kant. But Hulme was a congruent agnostic or even atheist.Kant was not of that persuasion and could not officially be in Prussian society if he wished to be licensed to teach.
Much of what Kant is forced to write is not honest, even if it is his opinion. He had to struggle to connect the various elements of his experience into a coherent form , and this oftentimes was not logically or experientially possible! Thus he has to innovate with transcendent distinctions which restore spirituality in some form to his otherwise unremitting soulless mechanical conclusions.
Hulme was quite content to accept things as thet were, much like Parmenides, but Kant was under pressure to defend the faith.
The ideas therefore around this time are revolutionary in that they struggle to break the grip of centuries of religious propaganda, but for the most part fail to make anything truely clear. By creating a climate of confusion, however, radical thinkers could chink there way through the blanket conformity and set the philosophers mind free to follow conclusions where they led.
Today, I would recommend watching the trilogy called The Matrix to understand the complex notions that underpin ones experience of reality. Much of the underlying notions for this film while interesting reading represent only the struggle to free themselves from dominant religious and theological paradigms, mythologies of an earlier technological society.
I do not agree with the rewriting of historical documents to reflect current understanding. But I do think redaction of texts is important to remove obfuscation and foggy terminology and beliefs, or rather to re present the subject area in current terms. Really, in doing this one constructs a new topic inspired by the old, and maybe not as wide ranging as the old because that wideness of range in fact revealed fatal flaws in the conception of the older topic.
What I have done is look at the foundations of "mathematics" and found that it has no foundation beyond a name change? The name change from Astrology to Mathematics cut it off from the rhetorical roots of the subject and the philosophy of its main developers. The result also reduced the philosophical introductory treatise/ text book, the Stoikeioon, to a mere engineering/mechanical drawing text, but this is what enabled it to survive for millennia in the popular imagination of the intellectuals..
Why do I study it today? It forms part of a fundamental western philosophy that combines east and western knowledge in a meditative praxis from which one can freely invent a congruent description of human interaction with space. Space or Shunya is never " pure" or virginal. Space is always pregnant with possibility.
The pursuit of the abstract is the pursuit of the spititual in another guise, but we can never extricate ourselves from life's most basic instincts or subjective processes inherent in our sensual selves. Thus tautology is fundamental to new departures from concrete experiences. Tautology is our gateway to effective analogies and ontological gravitas.
Taking the Kantian rhetoric that mathematics regards the general in the particular, while philosophy regards the particular in the general as the poetic wordplay that it is helps one to understand the tautological nature of Kantian philosophy. These plays on words work as poetry, but force ideas into a taut logical relationship which may or may not be factual. Mnemonically they are fantastic tools, but as descriptions of ones experience they are founded on an incipient circularity, or a cyclic structuring which makes the ideas beholden to each other.
Now the success of these tautologies may in fact invite a notion of cyclicity or circularity in nature or natural philosophy, but the existence of the Spiral form reveals that their is a "third" way, or rather the assumption of circularity would be inexact in multiple situations.
The reality we experience is almost but not quite perfectly circular in process. Thus we do not, as Herakletos observed ever step into the same river twice or even ever again! However for certain objects this is not apparent over millennia of cycles because the variation is so slow, but for others we hardly know of their existence because they vary so rapidly. The symbols of the snake and the ring , the snake biting its own tail potently represent that narrow experiential space in which we apparently exist, and which at any moment could be swept aside by spatial processes so powerful as to beggar comprehension.
What we " know" today is founded on metrons that we use to measure extensively and intensively. And because we do not interpret metrons generally it does not matter so much that they are often tautological, what does matter is that they are applied as metrons, not as de facto conceptions of reality.
For example the expansion of mercury as a metron of Temperature is an intensive metron. It measure internal magnitudes in a wide range of objects. One conceives that inside the object magnitudes are behaving in such a manner as to expand or contract mercury. Mercury does not tell us how this magnitude behaviour operates, but it provides data to falsify or verify a guess or hypothesis.
Newton would not accept the explanation of the kinetic theory until and unless an observable model could be shown to account for mercury rising. We do accept it because years of testing the hypothesis have mounted up the evidence. In a similar way we accept the Huygens wave theory of light over Newton's corpuscular one, despite the mechanical evidence being non existent at the then microscopic scales.
Thus we have 2 examples of how the circularity inherent in religious beliefs about existential matters have been adopted into the foundations of physics as principles of conservation: conservation of mass, conservation of energy, and yet we have no direct empirical observation of fundamentals of such theories until recently. Microscopy has advanced to provide us with images of gold atoms, but the images are computer generated images based on data sets collected on a theoretical basis other than direct light impingement!
What this means is that we see the world through the conceptual paradigms we accept. We create our images of the world and impose them on reality as discrete objects. It is only when reality bites back that we realise we have not quite got it right. We live approximately and pragmatically in an approximation of reality. Our only conception that makes sense of this is what has come to be known as fractal.
The name is new but the concept is quite ancient: spheres within spheres ad infinitum? Only they are not " spheres" but toroidal vorticular structures that are dynamically approximated as spheres by our conceptual framework or paradigms.
So an object can be an object or a symbol/ icon. The state it exists in is solely down to my ontological perception. Thus all existence is down to one's ontological perception, all depends on what one accepts.
When I consider Kant and Schelling, Leibniz and Descartes school, the argument was because they wanted to argue, because they did not want a third way. They had an adversarial system and by god they were going to be adversaries. Yet as I have pointed out the descriptions are cyclical not opposite. This type of debate occupied far too much time and promoted wrong headedness. It even divided the scientific community sending them spiralling off down the wrong track.
All have suffered the consequences of such pithy debates on a wrong premise
At least in commentary the wrangling over the concepts is patently a mis-apprehension of the same process! For the word construe and construction are related directly, making it a tautology to attempt to make a sharp distinction between the two things that are in any case cyclically construed! If both distinctions are construed, then that is tantamount to saying they construct their difference and thus both are constructive! Their difference is not in thir process but their product! However if the product of one is a behavioural one, then the product of the same process must also be a behavioural one. So if one iqs not careful to specify the unique product one has to conclude the process and behaviour are the same or similar.
Now if I specify the product in terms of notation, thn I can maintain a clear distinction, but I distort the processes so disruptively as to make the distinction meaningless and impractical. Today we teach people that mathematics is producing strings of abstract symbols, while philosophy is producing streams of scholarly papers on interesting topics!
For this reason mathematics alienates itself and brings about its own demise! The only hope for mathematics is computer science, and it's only hope is a wider interaction with the common rhetoric of life. Fortunately so many everyday things can now be encoded in software it makes that goal seem easier. But in fact software is becoming so standardised that no one is really interested in pushing the philosophical exploration much further, except an innovative few.
The hope is to regenerate an interest in hacking the software pile, in encouraging code warriors who can sift through and sort out the really interesting possibilities. To truely democratise what is fast becoming an elite tool and a mark of intellectual prowess. The encoding of process in space is magic made plain, but it is still very specialist or geeky to do. India has a state policy to make its intellectual capital that of software engineering. This will give its intelligentsia a huge advantage in a growing computerised world. Similarly, if all educational systems think right they can rescue software and mathematics from obscurity and make them part of everyday rhetoric, everyday philosophy.
A measure of success will be when the poorest drunkard in inebriation brawls over which software language best encodes his real experience of being down and out!