Kant and his philosophy of mathematics and corporeal nature

Discussions on the philosophical foundations, assumptions, and implications of science, including the natural sciences.

Kant and his philosophy of mathematics and corporeal nature

Postby volatileworld on June 22nd, 2014, 7:08 am 

Immanuel Kant in ''Critique of Pure Reason'' (1781) wanted to defend a priori knowledge of the world, that is mathematics, theoretical physics and metaphysics. If you are familiar with history of philosophy, Kant reacted to the famous debate between Rationalists (Leibniz, Descartes, Spinoza) and Empiricists (Locke and especially David Hume). Rationalists claimed that the source of knowledge is reason and innate ideas, while empiricists claimed that the source of knowledge is experience through the senses. Both are right from their perspective. Kant said that to speak about innate ideas in our mind which ground mathematics,physics and metaphysics (a priori knowledge) as rationalists did is lazy and unconvincing argument. David Hume has shown that everything comes from experience but Hume had problems with establishing mathematics on firm ground because maths speak of experience a priori. He could not explain how mathematics is possible! Kant tried to defend this a priori knowledge and so-called synthetic a priori judgments on which mathematics is based.

In order to defend synthetic a priori knowledge (such as mathematics and theoretical physics) Kant tried to argue about the necessary conditions which make our experience possible. He argued that our understanding gives laws to nature and we know nature only how it appears to us, but not how it is in itself. All phenomena appear in the forms of our sensible intuition. These pure forms are space and time. That is, it is our mind which imposes space and time and orders and organizes our experience in it. Mathematics constructs objects in pure intuition of space and time. This way mathematics is possible a priori and yet necessary applies to the objects of experience since all objects of experience appear in space and time. Kant called mathematics the master of nature. According to Kant, our knowledge is grounded in the so-called synthetic unity of apperception or original unity of consciousness. It prescribes laws and structure to the manifold of sensible intuition which we acquire through the senses. According to Kant, even the laws of physics are determined by our faculty of understanding. Kant speaks about the categories of the understanding of which he gives 12, 4 groups having 3 categories. Kant claimed there must be 4 fundamental interactions.

Kant had influenced such mathematicians as Henri Poincaré and David Hilbert. In philosophy of mathematics Kant belongs to intuitionist school. It is also interesting to study the logicist school, that is Frege, Russell. I claim that we will not understand ultimate reality unless we view everything as a system of mathematics, theoretical physics, philosophy of science and cognitive science. Cognitive science is of absolute importance in understanding ultimate reality because all our thoughts about the world originate in our brain. Philosophy of science and philosophy of mind cannot be left out if you want to understand the ultimate reality.
It seems that philosophy of corporeal nature was buried by modern science! The true purpose of proper metaphysics of corporeal nature is to assist mathematics and physics. They should go together. It does not matter that people did not know about the Higgs boson or the mathematical description of general relativity 200 years ago. What Kant knew is fundamentals - how our knowledge about the world in general is possible. If you know the roots of your knowledge, the epistemological basis of mathematics and physics, everything else is just details. To understand ultimate reality we must understand how we understand things in the first place! That is, we must have the picture of our cognitive faculties in general. This yields the big picture of the Universe how it appears to us.
That's why I took Kant who asked and provided answers in his work to the questions: ''how is mathematics possible?''. ''How is physics possible?''. ''How is metaphysics as science possible?''.

How to deal with the fact that the Universe is infinitely divisible mathematically and in thought but it is not made of infinitely many parts? We know that smallest meaningful lenght is Planck lenght. Therefore it does not make sense that mathematics and our thoughts can divide space infinitely! Also Kant provides a good explanation why it is so. Kant claims that space and time is not a property of things as they are in themselves but rather projections of our mind. We see not things-in-themselves but appearances of them! That is, we see not strings, quantum loops, Leibniz's monads or whatever fundamental entity but how they appear in our consciousness (phenomena). All phenomena appear in forms of space and time, that is pure forms of our sensible intuition. Space and time is not a property of fundamental entities (things-in-themselves) but rather our mode of seeing (''intuiting'') them. Thus appearances can be divided infinitely mathematically and in thought and yet it does not mean that they are made of infinitely many parts. Because things-in-themselves/strings/monads are not actually divisible, the appearances of them in space and time are divisible.

I argue that the ultimate reality is the grid of cells (grid of monads) which is mathematical structure of space and time from which our experience (phenomena in consciousness) emerges. I have used Kant's construction of corporeal nature together with philosophy of Fichte, Hegel and Leibniz to model our cognitive faculty of understanding as the grid of cells.

Summary of the project:
Kant’s transcendental philosophy argues about the necessary conditions to make our experience and a priori knowledge of the objects of experience (mathematics, theoretical physics, metaphysics) possible. Those conditions together with philosophy of Fichte, Hegel and Leibniz are used to model our cognitive framework (and the Universe as it appears to us) as quantum computer. The cognitive faculty of understanding is defined as the grid of cells where logical forms of thought relate cells together. The grid is transcendental unity of self-consciousness (synthetic unity of apperception) and is quantum entangled structure of space-time. Unit cellis the purest expression of reason (or consciousness). Reason is outside computation but it performs computations in this transcendentally ideal space (2D holographic grid of 6D cells) where cells perform quantization and our thoughts are formed by synthesis of cells. Time is present in every cell as the rate of it and represents an act of spontaneity ‘’I think”. The grid is the framework of natural language, mathematics and is unitary system of fundamental forcesof physics. Language reflects the world. All phenomena are described by mathematics. Unit cell is unit sensor and the grid is sensorium. Fundamental forces and our sense perception are related. The cells are in superposition of states from possible worlds. The grid is synthesized by the productive imagination under the categories of the understanding. In this process our apperception causes cells to take definite states from the superposition of states and conscious experience of empirically real objects in 3D space emerges. Curvature of empirically real space depends on the rate of cell (rate of time parameter). Self-conscious subjects are merely anautonomous parts of the Universal Quantum Computer (Universal Consciousness). Hegelian dialectic is the program which Universal Consciousness (Reason) runs by thinking itself. This program starts the Universe. Unit cell has two opposite values which alternate (expressing the dialectic nature of reason). The complexity in the world arises as patterns (schemata) of mutual limitations and determinations of cells producing greatest possible variety. The Universe is physical-moral system: both mathematics, fundamental forces of physics, metaphysics (theoretical reason) which construct the world and morality (practical reason) which describes how we ought to act in the world originate from the same source - Hegel’s ”the Idea” (Reason).
Many aspects of the model are discussed such as the origin of space and time, our a priori knowledge (logic, mathematics, physics, limits of computability), how the world is described by mathematics, unity of the fundamental forces, gravity in relation to information processing,
the arrow of time, the nature of quantum phenomena, universal grammar of natural languages, reconcilation of physicalism and idealism, the possibility of free will in deterministic Universe, our action in relation to perception, theology and our place in the Universe in general. Since the grid is invariant structure within which all our knowledge and experience is produced, it is considered as the basis for Theory of Everything. With it we achieve what Hegel called ”Absolute Knowledge” – the times of full self-consciousness, rational freedom and humanity in harmony with the Universe.

My project can be accessed here:
just google:
Our Cognitive Framework as Quantum Computer: Leibniz’s Theory of Monads under Kant’s Epistemology and Hegelian Dialectic

What do you think? I think that Kant and post-Kantian German Idealism (such as Fichte, Hegel) can assist modern physics and mathematics in understanding the ultimate reality. Any more ideas about German Idealism in the context of modern science?
volatileworld
 


Re: Kant and his philosophy of mathematics and corporeal nat

Postby owleye on June 22nd, 2014, 9:20 am 

Somewhere there is a leap of ontological speculation in what I'm reading that turns its transcendental ideality / empirical reality into transcendental reality. I agree that Kant's noumena from the Critique would lead one in that Leibnizean direction, but in my view, Kant was influenced by the criticism he later received on this concept in which he later recognized it as a standpoint, at least as I see it anyway.

And besides, Kant maintains a distinction between epistemology and ontology. As such, at least in my view, with the advances in science of the 19th century, most notably that of Darwin, had he lived into that era, Kant would have realized that the a priori consideration he took toward knowledge can be founded upon our genetic endowment, and though not directly empirical, has a basis in what science is capable of elucidating. Indeed, further advances in science and philosophy (notably Frege) as well as mathematics have only served to indicate that empiricism has a stronger place in the scheme of things than was admitted by Kant's outlook. This is not to say that Kant's solution to the problems he faced, re: empiricism and rationalism, are unworthy. Indeed, quite the opposite. Indeed, empiricism itself is probably not what brought about the pillars of physics of the 20th century. However, I don't believe any of this warrants taking the Leibnizean "things-in-themselves" as the direction one should revert to in one's ontology.
owleye
 


Re: Kant and his philosophy of mathematics and corporeal nat

Postby BadgerJelly on June 24th, 2014, 10:47 am 

Did Kant ever actually use the term "epistemology"?
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