Synthese library mathesis universalis computability and proof
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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” (“Gründe”) 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. A rigorous 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 ofthe relationship between mathematical rigor and demands for simplification.- 1 Bekijk alle specificaties
Taal: en
Bindwijze: Hardcover
Oorspronkelijke releasedatum: 06 november 2019
Aantal pagina's: 374
Illustraties: Nee
Hoofdredacteur: Stefania Centrone
Tweede Redacteur: Sara Negri
Co Redacteur: Peter M. Schuster
Hoofduitgeverij: Springer Nature Switzerland AG
Editie: 1
Extra groot lettertype: Nee
Product breedte: 155 mm
Product lengte: 235 mm
Studieboek: Ja
Verpakking breedte: 155 mm
Verpakking hoogte: 22 mm
Verpakking lengte: 235 mm
Verpakkingsgewicht: 740 g
EAN: 9783030204464