Lexicon of Arguments

 

Thiel I 27
Mathematics/Kant/Thiel: Kant was not an expert mathematician. Approach to a novel philosophy of mathematics: doctrine of the "schema": is a procedure, to give a concept its image. The rule character of this method is that the "imagination" refers to the operativism, "Synthetic function" refers to constructivism.
Thiel I 28
In the "Critique of Pure Reason", Kant calls the "construction of concepts" an "intuitive use of reason" and later he calls it a "mathematical".
Thiel I 38
Mathematics/Kant/Thiel: Kant asks whether philosophy (in particular metaphysics) by appropriating the mathematical method could result in similar statements. His answer: clearly not.
Kant: Metaphysics is a knowledge of reason from concepts.
>Metaphysics/Kant, >Knowledge/Kant.
Mathematics is knowledge of reason from the construction of concepts.
Kant: Undoubtedly, our knowledge is expanded by mathematical knowledge; it is not empty, not merely analytical, it must be "synthetic."
Pure opinion: this encompasses empirical opinions, which is not sensation, but the form of the connection to perception and thus the order form of what is "given" to us.
Thiel I 39
There can be no empirical opinions which have not been inserted into the necessary forms of sensibility.
E.g. (grains) We can imagine gray and not gray elephants, but not spatial and non-spatial ones. Then spatiality and temporality have "reality" or objective validity.
Kant: Reality obeys the same laws as the subject of mathematics. "All views are extensive quantities." Hence also the objects of mathematics.
>Space, >Space/Kant.
Thiel I 47
Mathematics/Kant/Thiel: today, we are not much more advanced than Kant in terms of the problem of application, although his system shows its limitations.