{"product_id":"6384709266","title":"Ingvar Johansson | PLATO'S NEGLECTED PROBLEM AND THE PROPERTY VIEW OF NUMBERS : Back to Euclid with some differences","description":"\u003ch2 style=\"display: none;\"\u003eInformation om Plato's neglected problem and the property view of numbers av Ingvar Johansson\u003c\/h2\u003e\u003cp\u003eI \u003cstrong\u003ePlato's neglected problem and the property view of numbers\u003c\/strong\u003e utforskar du Platons syn på tal och dess relevans idag. Boken riktar sig till dig som är intresserad av matematikens filosofi och vill förstå talens natur på djupet. Genom att återkoppla till Euclides och introducera en ny syn på tal, erbjuder författaren insikter som kan förändra ditt sätt att se på matematik. Du kommer att få en ny förståelse för sambandet mellan abstrakta begrepp och verkliga tillämpningar.\u003c\/p\u003e\u003cdiv class=\"product__accordion accordion quick-add-hidden\" style=\"background-color: #edeae3;\"\u003e\u003cdetails id=\"Details-collapsible_tab_1\"\u003e\u003csummary role=\"button\" aria-expanded=\"false\" aria-controls=\"ProductAccordion-collapsible_tab_1\" class=\"accordion__summary\"\u003e\u003cdiv class=\"summary__title flex\" style=\"padding: 0 2rem 0 2rem;\"\u003e\u003ch3 class=\"accordion__title inline-richtext\" style=\"line-height: 2.5rem;\"\u003eFörlagets information\u003c\/h3\u003e\u003c\/div\u003e\n\u003csvg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-caret\" viewbox=\"0 0 10 6\"\u003e\u003cpath fill-rule=\"evenodd\" clip-rule=\"evenodd\" d=\"M9.354.646a.5.5 0 00-.708 0L5 4.293 1.354.646a.5.5 0 00-.708.708l4 4a.5.5 0 00.708 0l4-4a.5.5 0 000-.708z\" fill=\"currentColor\"\u003e\u003c\/path\u003e\u003c\/svg\u003e\u003c\/summary\u003e\u003cdiv class=\"accordion__content rte\" id=\"ProductAccordion-collapsible_tab_1\" style=\"padding: 0 2rem 0 2rem;\"\u003e\n\u003cp\u003e\u003c\/p\u003e\n\u003cp\u003eIt is seldom noted in the philosophy of mathematics that Plato divides his world of forms or ideas into two different realms. In the higher realm, each pure number exists only as a unique entity, but in the lower realm it exists as a multiplicity. Such a bifurcation of numbers is not usually made in modern philosophy of mathematics, but this book argues that it needs to be made. Otherwise, the philosophical analysis of numbers cannot explain how, for instance, an addition such as 3 + 3 = 6 can refer to two distinct numbers 3.  \u003c\/p\u003e\n\u003cp\u003eOne way to account for this bifurcation is by means of the usually neglected property view of numbers. This book defends a version of this view, according to which the natural numbers are properties of collections, and the real numbers are properties of proportion-relations. It is also argued that the property view of numbers harmonizes well with the findings of modern empirical research on numerical cognition.  \u003c\/p\u003e\n\u003cp\u003eCentral to the book is Euclid´s notion of ratio, which is put forward in his Elements – here it is called proportion-relation . It is claimed that we need to revive Euclid´s distinction between numbers and magnitudes, as a distinction between two number lines, one for the original natural numbers and one for the real numbers. Strictly speaking, the original natural numbers cannot be regarded as a subclass of the real numbers. The line for the real numbers contains, however, numbers that are counterparts of the original natural numbers. \u003c\/p\u003e\n\u003cp\u003eIngvar Johansson is emeritus professor of theoretical philosophy at Umeå University, Sweden. Most of his writings are centered around questions in the philosophy of science and ontology.\u003c\/p\u003e\n\u003c\/div\u003e\u003c\/details\u003e\u003c\/div\u003e\u003cdiv class=\"product__accordion accordion quick-add-hidden\" style=\"background-color: #edeae3;\"\u003e\u003cdetails id=\"Details-collapsible_tab_1\"\u003e\u003csummary role=\"button\" aria-expanded=\"false\" aria-controls=\"ProductAccordion-collapsible_tab_1\" class=\"accordion__summary\"\u003e\u003cdiv class=\"summary__title flex\" style=\"padding: 0 2rem 0 2rem;\"\u003e\u003ch3 class=\"accordion__title inline-richtext\" style=\"line-height: 2.5rem;\"\u003eData om boken\u003c\/h3\u003e\u003c\/div\u003e\n\u003csvg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-caret\" viewbox=\"0 0 10 6\"\u003e\u003cpath fill-rule=\"evenodd\" clip-rule=\"evenodd\" d=\"M9.354.646a.5.5 0 00-.708 0L5 4.293 1.354.646a.5.5 0 00-.708.708l4 4a.5.5 0 00.708 0l4-4a.5.5 0 000-.708z\" fill=\"currentColor\"\u003e\u003c\/path\u003e\u003c\/svg\u003e\u003c\/summary\u003e\u003cdiv class=\"accordion__content rte\" id=\"ProductAccordion-collapsible_tab_1\" style=\"padding: 0 2rem 0 2rem;\"\u003e\n\u003cbr\u003e\u003cdiv style=\"padding: 0 20px 0 20px; border: thin solid #000000;\"\u003e\u003cp style=\"font-size: smaller;\"\u003e\u003cb\u003eBindning:\u003c\/b\u003e Häftat band.\u003cb\u003eÅr:\u003c\/b\u003e Utg. 2026. \u003cb\u003eOmfång:\u003c\/b\u003e 153 s. \u003cb\u003eISBN:\u003c\/b\u003e 9789172351479. \u003cb\u003eSpråk:\u003c\/b\u003e Engelska\u003c\/p\u003e\u003c\/div\u003e\n\u003cbr\u003e\u003cdiv style=\"padding: 0 20px 0 20px; border: thin solid #000000;\"\u003e\u003cp style=\"font-size: smaller;\"\u003e\u003cb\u003eFörfattare:\u003c\/b\u003e \u003ca href=\"\/search?q=title:Johansson+Ingvar\"\u003eJohansson, Ingvar\u003c\/a\u003e \u003cbr\u003e\u003cb\u003eTitel:\u003c\/b\u003e \u003ca href=\"\/search?q=title:Plato's+neglected+problem+and+the+property+view+of+numbers\"\u003ePlato's neglected problem and the property view of numbers\u003c\/a\u003e \u003cbr\u003e\u003cb\u003eUndertitel:\u003c\/b\u003e \u003ca href=\"\/search?q=title:Back+to+Euclid+with+some+differences\"\u003eBack to Euclid with some differences\u003c\/a\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eFörlag:\u003c\/b\u003e \u003ca href=\"\/search?q=vendor:Boket+Thales\"\u003eBokförlaget Thales\u003c\/a\u003e \u003cbr\u003e\u003cb\u003eSerie:\u003c\/b\u003e \u003ca href=\"\/search?q=Library+of+Theoria\"\u003eLibrary of Theoria\u003c\/a\u003e \u003cbr\u003e\u003cb\u003eGenre:\u003c\/b\u003e \u003ca href=\"\/search?q=Filosofi+och+id%C3%A9historia\"\u003eFilosofi och idéhistoria\u003c\/a\u003e \u003cbr\u003e\u003cb\u003eArtikelnr:\u003c\/b\u003e 6384709266\u003c\/p\u003e\u003c\/div\u003e\n\u003c\/div\u003e\u003c\/details\u003e\u003c\/div\u003e\u003chr\u003e\u003cp\u003e\u003cstrong\u003e\u003cem\u003ePlato's neglected problem and the property view of numbers\u003c\/em\u003e\u003c\/strong\u003e av \u003cstrong\u003eIngvar Johansson\u003c\/strong\u003e hittar du under genren \u003cstrong\u003eMatematik: allmänt\u003c\/strong\u003e inom \u003cstrong\u003eFilosofi\u003c\/strong\u003e i kategorin \u003cstrong\u003eNatur, vetenskap \u0026amp; teknik\u003c\/strong\u003e. Hitta fler liknande böcker:\u003cbr\u003e\u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='https:\/\/bok.hstrom.se\/collections\/natur-vetenskap-hvd'\"\u003eNatur, vetenskap \u0026amp; teknik\u003c\/button\u003e \u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='\/search?q=tag:Natur,%2Bvetenskap%2B%2Bteknik%2BFilosofi'\"\u003eFilosofi\u003c\/button\u003e \u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='\/search?q=tag:Natur,%2Bvetenskap%2B%2Bteknik%2BFilosofi%2BMatematik:%2Ballmänt'\"\u003eMatematik: allmänt\u003c\/button\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eHitta fler liknande böcker med dessa ämnesord:\u003c\/b\u003e\u003cbr\u003e\u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='\/search?q=tag:matematisk%2Bfilosofi'\"\u003ematematisk filosofi\u003c\/button\u003e \u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='\/search?q=tag:Platons%2Bidéer'\"\u003ePlatons idéer\u003c\/button\u003e \u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='\/search?q=tag:naturliga%2Btal'\"\u003enaturliga tal\u003c\/button\u003e \u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='\/search?q=tag:reella%2Btal'\"\u003ereella tal\u003c\/button\u003e \u003cbutton class=\"product-form__submit button button--secondary\" onclick=\"window.location.href='\/search?q=tag:proportion-relation'\"\u003eproportion-relation\u003c\/button\u003e \u003cbutton class=\"product-form__submit button button--full-width \" onclick=\"window.location.href='\/search?q=title:Johansson%2BIngvar%2BPlato's%2Bneglected%2Bproblem%2Band%2Bthe%2Bproperty%2Bview%2Bof%2Bnumbers'\"\u003eSök fler exemplar av denna bok\u003c\/button\u003e\u003cbutton class=\"product-form__submit button button--full-width \" onclick=\"window.location.href='\/search?q=title:Ingvar%2BJohansson'\"\u003eFler böcker av Ingvar Johansson\u003c\/button\u003e\u003c\/p\u003e","brand":"Bokförlaget Thales","offers":[{"title":"Ny bok \/ Häftat band","offer_id":53317697634571,"sku":"6384709266","price":198.0,"currency_code":"SEK","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0651\/8856\/1163\/files\/6384709266.jpg?v=1787447409","url":"https:\/\/bok.hstrom.se\/products\/6384709266","provider":"bok.hstrom.se | Antikvariat \u0026 Bokhandel","version":"1.0","type":"link"}