The cookie settings on this website are adjusted to allow all cookies so that you have the very best experience. If you continue without changing your cookie settings, we'll assume that you are happy to receive all cookies on our website. However, if you would like to, you can change your settings at any time using the Change cookie settings link in the Special menu. 

Mathesis Universalis, Computability and Proof : 412

Mathesis Universalis, Computability and Proof : 412
Stefania Centrone, Sara Negri, Deniz Sarikaya, Peter M. Schuster
ISBN Number
List Price:
Our price:
  • Details
  • Send to friend
  • Customers also bought
  • Customer feedback
Save 13%
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes "the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined"; in another fragment he takes the mathesis to be "the science of all things that are conceivable." Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between "arbitrary objects" ("objets quelconques").

It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the "reasons" ("Grunde") of others, and the latter are "consequences" ("Folgen") of the former.

The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory.

The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
This field is required
A valid email is required
A valid email is required
This field is required

Product rating

Sign in to rate

Customer Reviews

There have been no reviews for this product.