
Lux(λ) |光灵|GEB|Sep 30, 2025 13:09
Why did the universal formal mainstream language shift from geometry to mathematical logic and then to computational science.
From the era of Euclidean geometry to the era of Kant, even the formal proof language commonly used in philosophy is geometry. Example: Descartes/Spinoza and others used geometry to prove their philosophical theories.
Why use geometry as a metaphysical logical proof language?
That is nothing but geometry, which is a shortcut for us humans to naturally understand objects. Natural numbers are also naturally presented from objects, and geometry is also the structure naturally presented by objects.
Why does geometry need to shift to mathematical logic?
Because geometry can no longer prove many fields, such as the fact that the diagonal of a square with a side length of 1 is an irrational number. Unreasonable numbers do not appear natural, and Descartes roughly equated geometric proofs with mathematical logic using a Cartesian coordinate system. Mathematical logic better expresses the world of irrational numbers than geometry. At this time, a large number of scientists/philosophers entered the field of mathematical logic, using it as the universal formal language of metaphysics. After the emergence of set logic theories such as Cantor and Frege, mathematical logic proofs became universal in the metaphysical world.
But why did mathematical logic jump back to computer science?
The same principle: that is, the ability to formalize mathematical logic is limited, and it cannot explain or prove things that evolve dynamically.
For example, in the proof of the incompleteness theorem, G ö del proved incompleteness using mathematical logic, while Turing proved incompleteness in mathematical formal systems using the theory of mechanical Turing machines.
But at this point, the dynamic mechanical proof of the computer is equivalent to the static mathematical logic proof.
And computer science is better able to describe/prove the dynamic evolution than mathematical logic.
Typical theory: Nash transformed the Turing ordinal logic system using non cooperative games. Typical use case: Bitcoin.
These two use cases cannot be directly judged and proven using mathematical logic, as static mathematical logic always requires an external 'G ö del' to judge. But computer science can be expressed dynamically through point-to-point distributed communication.
Mathematical logic is still limited to proving a certain thing.
And computational science has reached the point where it can prove evolutionary proof expressions that describe the relationships between multiple individuals.
Coincidentally, Nobel laureates in various fields are increasingly relying on computational science.
The use of metaphysical language itself is the boundary of things that can be described in the era, and the development of human culture relies on increasingly precise and complete metaphysical language. This may be the evolution of metaphysical language from geometry to mathematical logic, and now to the language of computational science.
The language of mathematical logic can better describe and prove the field of irrational numbers than geometry.
Computational science provides a better description and proof of the evolutionary logic of dynamic relationships than mathematical logic.
Share To
Timeline
HotFlash
APP
X
Telegram
CopyLink