{"product_id":"9783030204495","title":"Synthese Library","description":"\u003ch1\u003eSynthese Library\u003c\/h1\u003e \u003ch2\u003eCentrone, Stefania; Negri, Sara; Sarikaya, Deniz; Schuster, Peter M.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn a fragment entitled \u003ci\u003eElementa Nova Matheseos Universalis \u003c\/i\u003e(1683?) Leibniz writes “the \u003ci\u003emathesis \u003c\/i\u003e[…]\u003ci\u003e \u003c\/i\u003eshall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the \u003ci\u003emathesis \u003c\/i\u003eto be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the \u003ci\u003emathesis \u003c\/i\u003eand conceives the \u003ci\u003emathesis \u003c\/i\u003eas 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 \u003ci\u003emathesis \u003c\/i\u003einvestigates possible relations between “arbitrary objects” (“\u003ci\u003eobjets quelconques\u003c\/i\u003e”). It is an abstract theory of combinations and relations among objects whatsoever.\u003c\/p\u003e\u003cp\u003eIn 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled \u003ci\u003eContributions to a Better-Grounded Presentation of Mathematics. \u003c\/i\u003eThere is, according to him, a \u003ci\u003ecertain objective connection \u003c\/i\u003eamong the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“\u003ci\u003eGründe\u003c\/i\u003e”) 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\u003ci\u003erigorous proof\u003c\/i\u003e 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.\u003c\/p\u003e\u003cp\u003eThe contributors of \u003cb\u003eMathesis Universalis, Computability and Proof\u003c\/b\u003e,  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, intuitionisticlogic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification. \u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2020-11-06\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030204495\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-20447-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 374\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45416696217740,"sku":"9783030204495","price":116.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030204495.jpg?v=1775704227","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030204495","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}