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<nav class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Glavni meni" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Glavni meni</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu 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href="/wiki/Glavna_stran" title="Obiščite glavno stran [z]" accesskey="z"><span>Glavna stran</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Pomo%C4%8D:Uvod"><span>Naučite se urejati</span></a></li><li id="n-Izbrani-članki" class="mw-list-item"><a href="/wiki/Wikipedija:Izbrani_%C4%8Dlanki"><span>Izbrani članki</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Posebno:Naklju%C4%8Dno" title="Naložite naključno stran [x]" accesskey="x"><span>Naključna stran</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Posebno:ZadnjeSpremembe" title="Seznam zadnjih sprememb Wikipedije [r]" accesskey="r"><span>Zadnje spremembe</span></a></li> </ul> </div> </div> <div id="p-obcestvo" class="vector-menu mw-portlet mw-portlet-obcestvo" > <div class="vector-menu-heading"> Skupnost </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Pomo%C4%8D:Vsebina" title="Kraj, kjer lahko prejmete pomoč"><span>Pomoč</span></a></li><li id="n-Pod-lipo" class="mw-list-item"><a href="/wiki/Wikipedija:Pod_lipo"><span>Pod lipo</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedija:Portal_skupnosti" title="O projektu, kaj lahko storite, kje lahko kaj najdete"><span>Portal skupnosti</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedija:Stik_z_nami"><span>Stik z nami</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Glavna_stran" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedija" src="/static/images/mobile/copyright/wikipedia-wordmark-sl.svg" style="width: 7.4375em; height: 1.375em;"> <img class="mw-logo-tagline" alt="prosta enciklopedija" 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class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Iskanje v Wikipediji" aria-label="Iskanje v Wikipediji" autocapitalize="sentences" title="Preiščite viki [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Posebno:Iskanje"> </div> <button class="cdx-button cdx-search-input__end-button">Išči</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Osebna orodja"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Videz"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Videz" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Videz</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sl.wikipedia.org&uselang=sl" class=""><span>Denarni prispevki</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Posebno:Registracija&returnto=Protislovje" title="Predlagamo vam, da si ustvarite račun in se prijavite, vendar to ni obvezno." class=""><span>Ustvari račun</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Posebno:Prijava&returnto=Protislovje" title="Prijava je zaželena, vendar ni obvezna [o]" accesskey="o" class=""><span>Prijava</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Več možnosti" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Osebna orodja" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Osebna orodja</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Uporabniški meni" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sl.wikipedia.org&uselang=sl"><span>Denarni prispevki</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebno:Registracija&returnto=Protislovje" title="Predlagamo vam, da si ustvarite račun in se prijavite, vendar to ni obvezno."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Ustvari račun</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebno:Prijava&returnto=Protislovje" title="Prijava je zaželena, vendar ni obvezna [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Prijava</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Strani za neprijavljene urejevalce <a href="/wiki/Pomo%C4%8D:Uvod" aria-label="Več o urejanju"><span>več o tem</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Posebno:MojiPrispevki" title="Seznam urejanj s tega IP-naslova [y]" accesskey="y"><span>Prispevki</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Posebno:MojPogovor" title="Pogovor o urejanjih s tega IP-naslova [n]" accesskey="n"><span>Pogovorna stran</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Vsebina" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Vsebina</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Uvod</div> </a> </li> <li id="toc-Zgodovina" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zgodovina"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Zgodovina</span> </div> </a> <ul id="toc-Zgodovina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-V_formalni_logiki" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#V_formalni_logiki"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>V formalni logiki</span> </div> </a> <button aria-controls="toc-V_formalni_logiki-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vklopi podrazdelek V formalni logiki</span> </button> <ul id="toc-V_formalni_logiki-sublist" class="vector-toc-list"> <li id="toc-Dokaz_s_protislovjem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dokaz_s_protislovjem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Dokaz s protislovjem</span> </div> </a> <ul id="toc-Dokaz_s_protislovjem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simbolična_reprezentacija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simbolična_reprezentacija"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Simbolična reprezentacija</span> </div> </a> <ul id="toc-Simbolična_reprezentacija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pojem_protislovja_v_aksiomatičnem_sistemu_in_dokaz_njegove_neprotislovnosti" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pojem_protislovja_v_aksiomatičnem_sistemu_in_dokaz_njegove_neprotislovnosti"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Pojem protislovja v aksiomatičnem sistemu in dokaz njegove neprotislovnosti</span> </div> </a> <ul id="toc-Pojem_protislovja_v_aksiomatičnem_sistemu_in_dokaz_njegove_neprotislovnosti-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Filozofija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Filozofija"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Filozofija</span> </div> </a> <button aria-controls="toc-Filozofija-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vklopi podrazdelek Filozofija</span> </button> <ul id="toc-Filozofija-sublist" class="vector-toc-list"> <li id="toc-Pragmatična_protislovja" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pragmatična_protislovja"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Pragmatična protislovja</span> </div> </a> <ul id="toc-Pragmatična_protislovja-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dialektični_materializem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dialektični_materializem"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Dialektični materializem</span> </div> </a> <ul id="toc-Dialektični_materializem-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Zunaj_formalne_logike" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zunaj_formalne_logike"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Zunaj formalne logike</span> </div> </a> <ul id="toc-Zunaj_formalne_logike-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Glej_tudi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Glej_tudi"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Glej tudi</span> </div> </a> <ul id="toc-Glej_tudi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sklici" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sklici"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Sklici</span> </div> </a> <ul id="toc-Sklici-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Viri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Viri"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Viri</span> </div> </a> <ul id="toc-Viri-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Vsebina" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Vklopi kazalo vsebine" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vklopi kazalo vsebine</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Protislovje</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="P9jdi na članek v drugem jeziku. Na voljo v 38 jezikih." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-38" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">38 jezikov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%86%D8%A7%D9%82%D8%B6_(%D9%85%D9%86%D8%B7%D9%82)" title="تناقض (منطق) – arabščina" lang="ar" hreflang="ar" data-title="تناقض (منطق)" data-language-autonym="العربية" data-language-local-name="arabščina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D0%BE%D1%80%D0%B5%D1%87%D0%B8%D0%B5_(%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0)" title="Противоречие (логика) – bolgarščina" lang="bg" hreflang="bg" data-title="Противоречие (логика)" data-language-autonym="Български" data-language-local-name="bolgarščina" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%D8%A7%D8%AA%DB%95%D8%A8%D8%A7%DB%8C%DB%8C" title="ناتەبایی – osrednja kurdščina" lang="ckb" hreflang="ckb" data-title="ناتەبایی" data-language-autonym="کوردی" data-language-local-name="osrednja kurdščina" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kontradikce" title="Kontradikce – češčina" lang="cs" hreflang="cs" data-title="Kontradikce" data-language-autonym="Čeština" data-language-local-name="češčina" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kontradiktion" title="Kontradiktion – danščina" lang="da" hreflang="da" data-title="Kontradiktion" data-language-autonym="Dansk" data-language-local-name="danščina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kontradiktion" title="Kontradiktion – nemščina" lang="de" hreflang="de" data-title="Kontradiktion" data-language-autonym="Deutsch" data-language-local-name="nemščina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Contradiction" title="Contradiction – angleščina" lang="en" hreflang="en" data-title="Contradiction" data-language-autonym="English" data-language-local-name="angleščina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kontra%C5%ADdiro_(filozofio)" title="Kontraŭdiro (filozofio) – esperanto" lang="eo" hreflang="eo" data-title="Kontraŭdiro (filozofio)" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Contradicci%C3%B3n" title="Contradicción – španščina" lang="es" hreflang="es" data-title="Contradicción" data-language-autonym="Español" data-language-local-name="španščina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D9%86%D8%A7%D9%82%D8%B6" title="تناقض – perzijščina" lang="fa" hreflang="fa" data-title="تناقض" data-language-autonym="فارسی" data-language-local-name="perzijščina" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Contradiction" title="Contradiction – francoščina" lang="fr" hreflang="fr" data-title="Contradiction" data-language-autonym="Français" data-language-local-name="francoščina" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Contradici%C3%B3n" title="Contradición – galicijščina" lang="gl" hreflang="gl" data-title="Contradición" data-language-autonym="Galego" data-language-local-name="galicijščina" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%AA%D7%99%D7%A8%D7%94_(%D7%9C%D7%95%D7%92%D7%99%D7%A7%D7%94)" title="סתירה (לוגיקה) – hebrejščina" lang="he" hreflang="he" data-title="סתירה (לוגיקה)" data-language-autonym="עברית" data-language-local-name="hebrejščina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%98%E0%A4%BE%E0%A4%A4_(%E0%A4%85%E0%A4%A8%E0%A5%8D%E0%A4%A4%E0%A4%B0%E0%A5%8D%E0%A4%B5%E0%A4%BF%E0%A4%B0%E0%A5%8B%E0%A4%A7)" title="व्याघात (अन्तर्विरोध) – hindijščina" lang="hi" hreflang="hi" data-title="व्याघात (अन्तर्विरोध)" data-language-autonym="हिन्दी" data-language-local-name="hindijščina" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kontradiksi" title="Kontradiksi – indonezijščina" lang="id" hreflang="id" data-title="Kontradiksi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijščina" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/M%C3%B3ts%C3%B6gn" title="Mótsögn – islandščina" lang="is" hreflang="is" data-title="Mótsögn" data-language-autonym="Íslenska" data-language-local-name="islandščina" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Contraddizione" title="Contraddizione – italijanščina" lang="it" hreflang="it" data-title="Contraddizione" data-language-autonym="Italiano" data-language-local-name="italijanščina" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%9F%9B%E7%9B%BE" title="矛盾 – japonščina" lang="ja" hreflang="ja" data-title="矛盾" data-language-autonym="日本語" data-language-local-name="japonščina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D0%B0%D1%80%D0%B0%D0%BC%D0%B0-%D2%9B%D0%B0%D0%B9%D1%88%D1%8B%D0%BB%D1%8B%D2%9B" title="Қарама-қайшылық – kazaščina" lang="kk" hreflang="kk" data-title="Қарама-қайшылық" data-language-autonym="Қазақша" data-language-local-name="kazaščina" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AA%A8%EC%88%9C" title="모순 – korejščina" lang="ko" hreflang="ko" data-title="모순" data-language-autonym="한국어" data-language-local-name="korejščina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D1%80%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Противречност – makedonščina" lang="mk" hreflang="mk" data-title="Противречност" data-language-autonym="Македонски" data-language-local-name="makedonščina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kontradiksi" title="Kontradiksi – malajščina" lang="ms" hreflang="ms" data-title="Kontradiksi" data-language-autonym="Bahasa Melayu" data-language-local-name="malajščina" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Contradictie" title="Contradictie – nizozemščina" lang="nl" hreflang="nl" data-title="Contradictie" data-language-autonym="Nederlands" data-language-local-name="nizozemščina" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Selvmotsigelse" title="Selvmotsigelse – knjižna norveščina" lang="nb" hreflang="nb" data-title="Selvmotsigelse" data-language-autonym="Norsk bokmål" data-language-local-name="knjižna norveščina" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sprzeczno%C5%9B%C4%87_(kwadrat_logiczny)" title="Sprzeczność (kwadrat logiczny) – poljščina" lang="pl" hreflang="pl" data-title="Sprzeczność (kwadrat logiczny)" data-language-autonym="Polski" data-language-local-name="poljščina" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Contradi%C3%A7%C3%A3o" title="Contradição – portugalščina" lang="pt" hreflang="pt" data-title="Contradição" data-language-autonym="Português" data-language-local-name="portugalščina" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D0%BE%D1%80%D0%B5%D1%87%D0%B8%D0%B5" title="Противоречие – ruščina" lang="ru" hreflang="ru" data-title="Противоречие" data-language-autonym="Русский" data-language-local-name="ruščina" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Contradiction" title="Contradiction – Simple English" lang="en-simple" hreflang="en-simple" data-title="Contradiction" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kontradikcia" title="Kontradikcia – slovaščina" lang="sk" hreflang="sk" data-title="Kontradikcia" data-language-autonym="Slovenčina" data-language-local-name="slovaščina" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D1%80%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Противречност – srbščina" lang="sr" hreflang="sr" data-title="Противречност" data-language-autonym="Српски / srpski" data-language-local-name="srbščina" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Mots%C3%A4gelse" title="Motsägelse – švedščina" lang="sv" hreflang="sv" data-title="Motsägelse" data-language-autonym="Svenska" data-language-local-name="švedščina" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kontradiksiyon" title="Kontradiksiyon – tagalogščina" lang="tl" hreflang="tl" data-title="Kontradiksiyon" data-language-autonym="Tagalog" data-language-local-name="tagalogščina" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%87eli%C5%9Fki" title="Çelişki – turščina" lang="tr" hreflang="tr" data-title="Çelişki" data-language-autonym="Türkçe" data-language-local-name="turščina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D0%B5%D1%87%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Суперечність – ukrajinščina" lang="uk" hreflang="uk" data-title="Суперечність" data-language-autonym="Українська" data-language-local-name="ukrajinščina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%D8%B6%D8%A7%D8%B1%D8%A8_(%D9%85%D9%86%D8%B7%D9%82)" title="تضارب (منطق) – urdujščina" lang="ur" hreflang="ur" data-title="تضارب (منطق)" data-language-autonym="اردو" data-language-local-name="urdujščina" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%C3%A2u_thu%E1%BA%ABn" title="Mâu thuẫn – vietnamščina" lang="vi" hreflang="vi" data-title="Mâu thuẫn" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamščina" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%9F%9B%E7%9B%BE" title="矛盾 – kitajščina" lang="zh" hreflang="zh" data-title="矛盾" data-language-autonym="中文" data-language-local-name="kitajščina" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%9F%9B%E7%9B%BE" title="矛盾 – kantonščina" lang="yue" hreflang="yue" data-title="矛盾" data-language-autonym="粵語" data-language-local-name="kantonščina" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q363948#sitelinks-wikipedia" title="Uredi medjezikovne povezave" class="wbc-editpage">Uredi povezave</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Protislovje" title="Ogled vsebinske strani [c]" accesskey="c"><span>Stran</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Pogovor:Protislovje&action=edit&redlink=1" rel="discussion" class="new" title="Pogovor o vsebinski strani (stran ne obstaja) [t]" accesskey="t"><span>Pogovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Spremeni različico jezika" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">slovenščina</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Pogledi"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Protislovje"><span>Preberi</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Protislovje&veaction=edit" title="Uredite to stran [v]" accesskey="v"><span>Uredi stran</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Protislovje&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Protislovje&action=history" title="Prejšnje redakcije te strani [h]" accesskey="h"><span>Zgodovina</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Orodja strani"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Orodja" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Orodja</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Orodja</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Več možnosti" > <div class="vector-menu-heading"> Dejanja </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Protislovje"><span>Preberi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Protislovje&veaction=edit" title="Uredite to stran [v]" accesskey="v"><span>Uredi stran</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Protislovje&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Protislovje&action=history"><span>Zgodovina</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Splošno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:KajSePovezujeSem/Protislovje" title="Seznam vseh strani, ki se povezujejo sem [j]" accesskey="j"><span>Kaj se povezuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:RecentChangesLinked/Protislovje" rel="nofollow" title="Zadnje spremembe na straneh, s katerimi se povezuje ta stran [k]" accesskey="k"><span>Povezane spremembe</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:PosebneStrani" title="Seznam vseh posebnih strani [q]" accesskey="q"><span>Posebne strani</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Protislovje&oldid=5992228" title="Trajna povezava na to redakcijo strani"><span>Trajna povezava</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Protislovje&action=info" title="Več informacij o tej strani"><span>Podatki o strani</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Navedi&page=Protislovje&id=5992228&wpFormIdentifier=titleform" title="Informacije o tem, kako navajati to stran"><span>Navedba članka</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:UrlShortener&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FProtislovje"><span>Pridobi skrajšani URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrCode&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FProtislovje"><span>Prenesi kodo QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tiskanje/izvoz </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Posebno:Book&bookcmd=book_creator&referer=Protislovje"><span>Ustvari e-knjigo</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Protislovje&action=show-download-screen"><span>Prenesi kot PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Protislovje&printable=yes" title="Različica te strani za tisk [p]" accesskey="p"><span>Različica za tisk</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> V drugih projektih </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Logical_contradiction" hreflang="en"><span>Wikimedijina zbirka</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://sl.wikiquote.org/wiki/Protislovje" hreflang="sl"><span>Wikinavedek</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q363948" title="Povezava na ustrezni predmet v podatkovni shrambi [g]" accesskey="g"><span>Predmet v Wikipodatkih</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Orodja strani"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Videz"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Videz</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Iz Wikipedije, proste enciklopedije</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sl" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Square_of_opposition,_set_diagrams.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Square_of_opposition%2C_set_diagrams.svg/250px-Square_of_opposition%2C_set_diagrams.svg.png" decoding="async" width="250" height="324" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Square_of_opposition%2C_set_diagrams.svg/375px-Square_of_opposition%2C_set_diagrams.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Square_of_opposition%2C_set_diagrams.svg/500px-Square_of_opposition%2C_set_diagrams.svg.png 2x" data-file-width="479" data-file-height="620" /></a><figcaption>Diagram kaže protislovne relacijske zveze med <a href="/w/index.php?title=Kategori%C4%8Dna_trditev&action=edit&redlink=1" class="new" title="Kategorična trditev (stran ne obstaja)">kategoričnimi trditvami</a> v <a href="/w/index.php?title=Logi%C4%8Dni_kvadrat&action=edit&redlink=1" class="new" title="Logični kvadrat (stran ne obstaja)">logičnem kvadratu</a> <a href="/w/index.php?title=Tradicionalna_logika&action=edit&redlink=1" class="new" title="Tradicionalna logika (stran ne obstaja)">Aristotelove logike</a>.</figcaption></figure> <p><b>Protislóvje</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> (s tujko <b>kontradíkcija</b><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:607</sup> in tudi <b>antinomíja</b>,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:55</sup> starinsko <i>protiréčje</i><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>) je v <a href="/w/index.php?title=Klasi%C4%8Dna_logika&action=edit&redlink=1" class="new" title="Klasična logika (stran ne obstaja)">klasični logiki</a> pojav ali stanje sestavljeno iz <a href="/wiki/Logika" title="Logika">logične</a> nezdružljivosti med dvema ali več <a href="/w/index.php?title=Trditev&action=edit&redlink=1" class="new" title="Trditev (stran ne obstaja)">trditvami</a> (<a href="/w/index.php?title=Propozicija&action=edit&redlink=1" class="new" title="Propozicija (stran ne obstaja)">propozicijami</a>). Pojavi se kadar dve trditvi vzeti skupaj vodita do dveh zaključkov (<a href="/wiki/Implikacija" title="Implikacija">implikacij</a>), ki tvorita logični, po navadi nasprotni inverziji drugega z drugim. <a href="/wiki/Aristotel" title="Aristotel">Aristotelov</a> <a href="/w/index.php?title=Zakon_o_neprotislovju&action=edit&redlink=1" class="new" title="Zakon o neprotislovju (stran ne obstaja)">zakon o neprotislovju</a> ilustrira splošno težnjo v uporabni logiki in pravi, da je »nemogoče reči o nečem, da je in da ni v enakem oziru in v enakem času.« </p><p>Razširjeno gledano zunaj klasične logike se lahko govori o protislovjih med <a href="/w/index.php?title=Akcija&action=edit&redlink=1" class="new" title="Akcija (stran ne obstaja)">akcijami</a>, kadar se predpostavi, da si njihovi vzroki med seboj nasprotujejo. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Zgodovina">Zgodovina</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=1" title="Uredi razdelek: Zgodovina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=1" title="Urejanje izvorne kode razdelka: Zgodovina"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>S tvorjenjem <a href="/wiki/Paradoks" title="Paradoks">paradoksa</a> je <a href="/wiki/Platon" title="Platon">Platonov</a> dialog <i><a href="/w/index.php?title=Evtidem&action=edit&redlink=1" class="new" title="Evtidem (stran ne obstaja)">Evtidem</a></i> prikazal potrebo po pojmu <i>protislovja</i>. V svojem dialogu je <a href="/w/index.php?title=Dionisodor_(sofist)&action=edit&redlink=1" class="new" title="Dionisodor (sofist) (stran ne obstaja)">Dionisodor</a> zanikal obstoj »protislovja,« <a href="/wiki/Sokrat" title="Sokrat">Sokrat</a> pa mu je nasprotoval: </p> <dl><dd>»Na svoje začudenje sem dejal: Kaj misliš Dionisodor? Velikokrat sem slišal in sem bil začuden, da sem slišal to tvojo tezo, ki jo vzdržujejo in rabijo <a href="/wiki/Protagora" title="Protagora">Protagorovi</a> učenci in mnogi pred njim. Zdi se mi dokaj presenetljiva in samomorilska kakor tudi uničujoča. Mislim, da sem verjetno o njeni resničnosti slišal od tebe. Izreka je, da ne obstaja nekaj kakor laž – človek mora reči kaj je resnično, drugače naj molči. Ali ni takšno tvoje mnenje?«</dd></dl> <p>Dionisodor se je res strinjal, da »ne obstaja nekaj kot je napačno mnenje ... ne obstaja nekaj kar je nevednost« in je od Sokrata zahteval naj ga ovrže. Sokrat se je odzval: »Kako naj te ovržem, če, kakor praviš, je treba reči, da je laž nemogoča?«<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="V_formalni_logiki">V formalni logiki</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=2" title="Uredi razdelek: V formalni logiki" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=2" title="Urejanje izvorne kode razdelka: V formalni logiki"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>Opomba: Simbol <a href="/w/index.php?title=%E2%8A%A5&action=edit&redlink=1" class="new" title="⊥ (stran ne obstaja)">⊥</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f282c7bc331cc3bfcf1c57f1452cc23c022f58de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \bot }"></span>, <i>falsum</i>) predstavlja poljubno protislovje z dualom simbolom <a href="/w/index.php?title=%E2%8A%A4&action=edit&redlink=1" class="new" title="⊤ (stran ne obstaja)">⊤</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \top }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊤</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \top }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf12e436fef2365e76fcb1034a51179d8328bb33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \top }"></span>, <i>verum</i>), ki predstavlja poljubno <a href="/w/index.php?title=Tavtologija&action=edit&redlink=1" class="new" title="Tavtologija (stran ne obstaja)">tavtologijo</a>. Protislovje se včasih označi kot »O<i>pq</i>«, tavtologija pa kot »V<i>pq</i>«. Desno zasukani simbol <a href="/w/index.php?title=%E2%8A%A2&action=edit&redlink=1" class="new" title="⊢ (stran ne obstaja)">⊢</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vdash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊢</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vdash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0c0d30cf8cb7dba179e317fcde9583d842e80f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle \vdash }"></span>) po navadi pomeni »sledi« ali »je dokazano«.</dd></dl> <p>V klasični logiki in še posebej v <a href="/wiki/Propozicijska_logika" title="Propozicijska logika">propozicijski logiki</a> in <a href="/w/index.php?title=Logika_prvega_reda&action=edit&redlink=1" class="new" title="Logika prvega reda (stran ne obstaja)">logiki prvega reda</a> je trditev <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> protislovje, <a href="/wiki/%C4%8Ce_in_samo_%C4%8De" class="mw-redirect" title="Če in samo če">če in samo če</a> je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi \vdash \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mo>⊢</mo> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi \vdash \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb2a11d466849d8b206a4a6c934264fe16835bb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.039ex; height:2.676ex;" alt="{\displaystyle \varphi \vdash \bot }"></span>. Ker za protislovnost <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> velja, da je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vdash \varphi \rightarrow \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊢</mo> <mi>φ</mi> <mo stretchy="false">→</mo> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vdash \varphi \rightarrow \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60875b3cd620fe51bd3d52cde99877beece9a333" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.713ex; height:2.676ex;" alt="{\displaystyle \vdash \varphi \rightarrow \psi }"></span> za vse <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> (ker je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bot \rightarrow \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊥</mi> <mo stretchy="false">→</mo> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bot \rightarrow \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45163f41b18eb09992b3a349ecc08f7c3727451b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.935ex; height:2.509ex;" alt="{\displaystyle \bot \rightarrow \psi }"></span>), se lahko dokaže katerakoli trditev iz množice <a href="/wiki/Aksiom" title="Aksiom">aksiomov</a>, ki vsebuje protislovja. To se imenuje »<a href="/w/index.php?title=Na%C4%8Delo_eksplozije&action=edit&redlink=1" class="new" title="Načelo eksplozije (stran ne obstaja)">načelo eksplozije</a>« ali »ex falso quodlibet« (»iz laži sledi vse«). </p><p>V <a href="/w/index.php?title=Polnost_(logika)&action=edit&redlink=1" class="new" title="Polnost (logika) (stran ne obstaja)">polni</a> logiki je <a href="/wiki/Formula" title="Formula">formula</a> protislovna, če in samo če je <a href="/w/index.php?title=Zadovoljivost&action=edit&redlink=1" class="new" title="Zadovoljivost (stran ne obstaja)">nezadovoljiva</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Dokaz_s_protislovjem">Dokaz s protislovjem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=3" title="Uredi razdelek: Dokaz s protislovjem" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=3" title="Urejanje izvorne kode razdelka: Dokaz s protislovjem"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članek: <a href="/wiki/Dokaz_s_protislovjem" title="Dokaz s protislovjem">dokaz s protislovjem</a>.</i></div></dd></dl> <p>Za trditev <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> velja, da je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vdash \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊢</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vdash \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a2839796eeedb8fa1b52ea144c0f42adc133021" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.586ex; height:2.676ex;" alt="{\displaystyle \vdash \varphi }"></span>, kar pomeni, da je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> tavtologija, oziroma, da je vedno resnična, če in samo če je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg \varphi \vdash \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi>φ</mi> <mo>⊢</mo> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg \varphi \vdash \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bcda508f1420c8819d5274380988ac290d2846c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.589ex; height:2.676ex;" alt="{\displaystyle \neg \varphi \vdash \bot }"></span>, ali, če je <a href="/wiki/Negacija" title="Negacija">negacija</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> protislovje. Zato <a href="/w/index.php?title=Formalni_dokaz&action=edit&redlink=1" class="new" title="Formalni dokaz (stran ne obstaja)">dokaz</a>, da je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg \varphi \vdash \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi>φ</mi> <mo>⊢</mo> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg \varphi \vdash \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bcda508f1420c8819d5274380988ac290d2846c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.589ex; height:2.676ex;" alt="{\displaystyle \neg \varphi \vdash \bot }"></span> tudi dokaže, da je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> resnična. Raba tega dejstva sestavlja tehniko dokaza s protislovjem, ki ga matematiki veliko rabijo. To velja le v logiki, ki kot aksiom rabi izključeni srednji <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\vee \neg A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∨</mo> <mi mathvariant="normal">¬</mi> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\vee \neg A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/323f5c2a8924ef707dcc24cee3bce1b148ec1367" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.619ex; height:2.176ex;" alt="{\displaystyle A\vee \neg A}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Simbolična_reprezentacija"><span id="Simboli.C4.8Dna_reprezentacija"></span>Simbolična reprezentacija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=4" title="Uredi razdelek: Simbolična reprezentacija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=4" title="Urejanje izvorne kode razdelka: Simbolična reprezentacija"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>V matematiki se simbol, ki predstavlja protislovje znotraj dokaza, razlikuje.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Nekateri simboli, ki se lahko rabijo za reprezentacijo protislovja, so: ↯, Opq, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow \Leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒⇐</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow \Leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0910f38ab10fa4e15bb398d89588f6a2147e6d0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.648ex; height:1.843ex;" alt="{\displaystyle \Rightarrow \Leftarrow }"></span>, ⊥, ↮ in ※. V vsakem <a href="/wiki/Simbolizem" title="Simbolizem">simbolizmu</a> se lahko protislovje zamenja za resničnostno vrednost »<a href="/w/index.php?title=Napa%C4%8Dno_(logika)&action=edit&redlink=1" class="new" title="Napačno (logika) (stran ne obstaja)">napačno</a>,« ki ga simbolizira na primer znak »<a href="/wiki/0" title="0">0</a>.« Velikokrat se vidi okrajšava <a href="/wiki/Q.E.D." title="Q.E.D.">Q.E.D.</a> ali kakšna različica takoj za simbolom protislovja – to se pojavi v dokazu s protislovjem, kjer se naznači, da je bila izvirna predpostavka napačna in, da mora biti njena negacija pravilna. </p> <div class="mw-heading mw-heading3"><h3 id="Pojem_protislovja_v_aksiomatičnem_sistemu_in_dokaz_njegove_neprotislovnosti"><span id="Pojem_protislovja_v_aksiomati.C4.8Dnem_sistemu_in_dokaz_njegove_neprotislovnosti"></span>Pojem protislovja v aksiomatičnem sistemu in dokaz njegove neprotislovnosti</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=5" title="Uredi razdelek: Pojem protislovja v aksiomatičnem sistemu in dokaz njegove neprotislovnosti" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=5" title="Urejanje izvorne kode razdelka: Pojem protislovja v aksiomatičnem sistemu in dokaz njegove neprotislovnosti"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Neprotislovnost&action=edit&redlink=1" class="new" title="Neprotislovnost (stran ne obstaja)">Dokaz o neprotislovnosti</a> zahteva (i) <a href="/w/index.php?title=Aksiomati%C4%8Dni_sistem&action=edit&redlink=1" class="new" title="Aksiomatični sistem (stran ne obstaja)">aksiomatični sistem</a> in (ii) prikaz, da se lahko formula <i>p</i> ter njena negacija <i>~p</i> izpeljeta v njem. Vendar po katerikoli metodi se izpeljuje, bodo dokazi o neprotislovnosti <i>izgledali</i> kot da zahtevajo primitivni pojem <i>protislovja</i> – še več, <i>izgleda</i>, da bo ta pojem moral biti istočasno »zunaj« formalnega sistema v definiciji tavtologije. </p><p>Ko je <a href="/w/index.php?title=Emil_Leon_Post&action=edit&redlink=1" class="new" title="Emil Leon Post (stran ne obstaja)">Emil Leon Post</a> v svojem delu iz leta 1921 <i>Introduction to a general theory of elementary propositions</i> razširil svoj dokaz neprotislovnosti propozicijske logike (to je logike) za tisto v delu <i><a href="/w/index.php?title=Principia_Mathematica&action=edit&redlink=1" class="new" title="Principia Mathematica (stran ne obstaja)">Principia Mathematica</a></i> (PM), je opazil, da v oziru na <i>posplošeno</i> množico <a href="/wiki/Postulat" class="mw-redirect" title="Postulat">postulatov</a> (aksiomov) ni mogel več samodejno priklicati pojma »protislovja« – takšnega pojma postulati ne bi vsebovali: </p> <dl><dd>»Glavna zahteva za množico postulatov je, da je neprotislovna. Ker običajni pojem neprotislovnosti vključuje tisto o protislovju, ki spet vključuje negacijo, in ker se ta funkcija ne pojavlja v splošnem kot primitivna v [<i>posplošeni</i> množici postulatov], je potrebna nova definicija.«<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Postova rešitev problema je opisana v prikazu <i>An Example of a Successful Absolute Proof of Consistency</i>, ki sta ga podala <a href="/w/index.php?title=Ernest_Nagel&action=edit&redlink=1" class="new" title="Ernest Nagel (stran ne obstaja)">Ernest Nagel</a> in <a href="/w/index.php?title=James_Roy_Newman&action=edit&redlink=1" class="new" title="James Roy Newman (stran ne obstaja)">James Roy Newman</a> in svojem delu <i><a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Gödel's</a> Proof</i> iz leta 1958. Tudi onadva sta opazovala problem glede na pojem »protislovja« s svojima običajnima »pravilnostnima vrednostima« »pravilnosti« in »napačnosti.« Opazila sta, da je: </p> <dl><dd>»značilnost tavtologije definirana s pojmoma pravilnosti in napačnosti. Ta dva pojma očitno vključujeta sklic na nekaj <i>zunaj</i> formulskega računa. Zato postopek, omenjen v besedilu, v resnici ponuja <i>interpretacijo</i> računa z zagotovitvijo modela za sistem. Zaradi tega avtorji niso storili tega kar so obljubili, namreč <b>definirati značilnost formul z izrazi čisto strukturnih gradnikov samih formul.</b>« [Res] ... dokazi o neprotislovnosti, ki temeljijo na modelih, in, ki dokazujejo iz pravilnosti aksiomov na njihovo neprotislovnost, le spremenijo problem.«<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Z danimi nekaterimi »primitivnimi formulami«, kot sta primitiva iz PM S<sub>1</sub> V S<sub>2</sub> [inkluzivni ALI], ~S (negacija), je treba definirati aksiome v izrazih teh primitivnih pojmov. Vseskozi Post prikazuje v PM in definira (kakor tudi Nagel in Newman, glej spodaj), da je značilnost <i>tavtologičnosti</i>, ki jo je treba še definirati, »podedovana«: če se začne z množico tavtoloških aksiomov (postulatov) in <a href="/w/index.php?title=Dedukcijski_sistem&action=edit&redlink=1" class="new" title="Dedukcijski sistem (stran ne obstaja)">dedukcijskim sistemom</a>, ki vsebuje <a href="/w/index.php?title=Substitucija_(logika)&action=edit&redlink=1" class="new" title="Substitucija (logika) (stran ne obstaja)">substitucijo</a> in <a href="/w/index.php?title=Modus_ponens&action=edit&redlink=1" class="new" title="Modus ponens (stran ne obstaja)">modus ponens</a>, bo <i>neprotislovni</i> sistem dal le tavtološke formule. </p><p>Kaj bo torej definicija <i>tavtologičnosti</i>? </p><p>Nagel in Newman sta tvorila dva <a href="/wiki/Nezdru%C5%BEljivi_dogodki" title="Nezdružljivi dogodki">medsebojno izključujoča</a> in izčrpljujoča se razreda K<sub>1</sub> in K<sub>2</sub> v katera pade (rezultat) aksiomov, kadar so njune spremenljivke, npr. S<sub>1</sub> in S<sub>2</sub>, prirejene iz teh razredov. To velja tudi za primitivne formule. Na primer: »Formula z obliko S<sub>1</sub> V S<sub>2</sub> je dana v razred K<sub>2</sub>, če sta obe S<sub>1</sub> and S<sub>2</sub> v K<sub>2</sub>, drugače ja dana v K<sub>1</sub>« in »Formula z obliko ~S je dana v K<sub>2</sub>, če je S v K<sub>1</sub>, drugače je dana v K<sub>1</sub>.«<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Nagel in Newman sta lahko sedaj definirala pojem <i>tavtologičnosti</i>: »formula je tavtologija, če in samo če pade v razred K<sub>1</sub> neglede v katerem od obeh razredov so postavljeni njeni elementi.«<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Sedaj je značilnost »biti tavtologičen« opisana brez sklica na model ali interpretacijo. </p> <dl><dd>Če je na primer dana formula, kot je ~S<sub>1</sub> V S<sub>2</sub> in prireditev K<sub>1</sub> v S<sub>1</sub> in K<sub>2</sub> v S<sub>2</sub>, se lahko ovrednoti in vstavi njen rezultat v enega od obeh razredov. Prireditev K<sub>1</sub> v S<sub>1</sub> postavi ~S<sub>1</sub> v K<sub>2</sub> – sedaj se lahko vidi, da ta prireditev povzroči, da formula pade v razred K<sub>2</sub>. Tako po definiciji ta formula ni tavtologija.</dd></dl> <p>Post je opazil, da če je sistem protisloven, lahko dedukcija v njem (to je zadnja formula v zaporedju formul izpeljana iz tavtologij) končno prinese sámo S. Ker lahko prireditev spremenljivke S izhaja iz razreda K<sub>1</sub> ali K<sub>2</sub>, dedukcija krši dedovalno značilnost tavtologije – izpeljava mora prinesti (ovrednotenje formule), ki bo padla v razred K<sub>1</sub>. Odtod je lahko Post izpeljal naslednjo definicijo protislovnosti <i>brez rabe pojma protislovja</i>: </p> <dl><dd>Deficija. <i>Sistem bo protisloven, če prinese trditev nespremenjene spremenljivke p [S je v Newmanovih in Nagelovih zgledih].</i></dd></dl> <p>Z drugimi besedami se lahko pojem »protislovja«razdeli kadar se konstruira dokaz neprotislovnosti – kar ga zamenja, je pojem »medsebojno izključujočih in izčrpljujočih se« razredov. Ni treba, da aksiomatični sistem, kar je še bolj zanimivo, nujno vsebuje pojem »protislovja.« </p> <div class="mw-heading mw-heading2"><h2 id="Filozofija">Filozofija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=6" title="Uredi razdelek: Filozofija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=6" title="Urejanje izvorne kode razdelka: Filozofija"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pristaši <a href="/wiki/Epistemologija" title="Epistemologija">epistemološke</a> teorije <a href="/w/index.php?title=Koherentizem&action=edit&redlink=1" class="new" title="Koherentizem (stran ne obstaja)">koherentizma</a> običajno trdijo, da je potreben pogoj za zagovor <a href="/w/index.php?title=Prepri%C4%8Danje&action=edit&redlink=1" class="new" title="Prepričanje (stran ne obstaja)">prepričanja</a> v tem, da mora biti prepričanje del logičnega neprotislovnega <a href="/wiki/Sistem" title="Sistem">sistema</a> prepričanj. Nekateri <a href="/w/index.php?title=Diateleizem&action=edit&redlink=1" class="new" title="Diateleizem (stran ne obstaja)">diateleisti</a>, kot tudi <a href="/w/index.php?title=Grahan_Priest&action=edit&redlink=1" class="new" title="Grahan Priest (stran ne obstaja)">Grahan Priest</a>, so razpravljali, da protislovje nujno ne zahteva neprotislovnosti.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pragmatična_protislovja"><span id="Pragmati.C4.8Dna_protislovja"></span>Pragmatična protislovja</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=7" title="Uredi razdelek: Pragmatična protislovja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=7" title="Urejanje izvorne kode razdelka: Pragmatična protislovja"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pragmatično protislovje se pojavi kadar vsak stavek argumenta nasprotuje trditvam, ki jih trdi. Neprotislovnost nastane v tem primeru, ker dejanje izraza namesto vsebine izrečenega izpodbija njegov zaključek.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Na primer verjetno <a href="/wiki/Friedrich_Wilhelm_Nietzsche" class="mw-redirect" title="Friedrich Wilhelm Nietzsche">Nietzschejeva</a> izjava, da nekdo ne sme ubogati drugih, ali <a href="/w/index.php?title=Mooreov_paradoks&action=edit&redlink=1" class="new" title="Mooreov paradoks (stran ne obstaja)">Mooreov paradoks</a>. Znotraj analitične tradicije jih vidijo kot <a href="/w/index.php?title=Samoizpodbijajo%C4%8Da_ideja&action=edit&redlink=1" class="new" title="Samoizpodbijajoča ideja (stran ne obstaja)">samoizpodbijajoče izjave</a> in <a href="/w/index.php?title=Izvr%C5%A1no_protislovje&action=edit&redlink=1" class="new" title="Izvršno protislovje (stran ne obstaja)">izvršna protislovja</a>. Druge tradicije jih obravnavajo bolj kot <a href="/wiki/Zen_budizem" title="Zen budizem">zenovske</a> <a href="/wiki/Koan" title="Koan">koane</a> v katerih avtorjevi nameni tvorijo protislovje s pomočjo tradicionalnega pomena, nato pa se sugerira nov pomen besede, ki ne nasprotuje izjavi. </p> <div class="mw-heading mw-heading3"><h3 id="Dialektični_materializem"><span id="Dialekti.C4.8Dni_materializem"></span>Dialektični materializem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=8" title="Uredi razdelek: Dialektični materializem" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=8" title="Urejanje izvorne kode razdelka: Dialektični materializem"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>V <a href="/wiki/Dialekti%C4%8Dni_materializem" title="Dialektični materializem">dialektičnem materializmu</a> se protislovja, kot so ipeljana iz <a href="/w/index.php?title=Hegeljanstvo&action=edit&redlink=1" class="new" title="Hegeljanstvo (stran ne obstaja)">hegeljanstva</a>, po navadi nanašajo na nasprotstvo, ki neločljivo obstaja znotraj enega področja, ene poenotene sile ali objekta. To protislovje v nasprotju z metafizičnim mišljenjem ni objektivno nemogoča stvar, ker te protislovje sile obstajajo v objektivni stvarnosti in se med seboj ne izničujejo, ampak dejansko definirajo obstoj druga druge. Po <a href="/wiki/Marksizem" title="Marksizem">marsistični</a> teoriji se lahko takšna protislovja najde na primer v dejstvu, da: </p> <dl><dd>(a) velikansko bogastvo in produktivne moči soobstajajo skupaj</dd> <dd>(b) obstaja skrajna revščina in beda</dd> <dd>(c) obstaja (a), ki je v nasprotju z obstojem (b).</dd></dl> <p>Hegeljanska in marksistična teorija določata, da bo <a href="/wiki/Dialektika" title="Dialektika">dialektična</a> narava zgodovine vodila do <a href="/w/index.php?title=Aufhebung&action=edit&redlink=1" class="new" title="Aufhebung (stran ne obstaja)">razveljavitve</a> ali <a href="/w/index.php?title=Teza,_antiteza,_sinteza&action=edit&redlink=1" class="new" title="Teza, antiteza, sinteza (stran ne obstaja)">sinteze</a> svojih protislovij. <a href="/wiki/Karl_Marx" title="Karl Marx">Marx</a> je zato predpostavil, da bo zgodovina logično naredila, da se bo <a href="/wiki/Kapitalizem" title="Kapitalizem">kapitalizem</a> razvil v <a href="/wiki/Socializem" title="Socializem">socialistično</a> družbo, kjer bodo <a href="/w/index.php?title=Proizvodna_sredstva&action=edit&redlink=1" class="new" title="Proizvodna sredstva (stran ne obstaja)">proizvodna sredstva</a> enako služila <a href="/wiki/Proletariat" title="Proletariat">izkoriščanemu in trpečemu</a> družbenemu razredu in tako bo razrešeno predhodno protislovje med (a) in (b).<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Mao_Cetung" title="Mao Cetung">Mao Cetungov</a> filozofski esej <i>O protislovju</i> (《矛盾论》) iz leta 1937 je podprl Marxove in <a href="/wiki/Vladimir_Ilji%C4%8D_Uljanov" class="mw-redirect" title="Vladimir Iljič Uljanov">Leninove</a> teze in predlagal, da je ves obstoj rezultat protislovja.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Zunaj_formalne_logike">Zunaj formalne logike</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=9" title="Uredi razdelek: Zunaj formalne logike" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=9" title="Urejanje izvorne kode razdelka: Zunaj formalne logike"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Graham%27s_Hierarchy_of_Disagreement-en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Graham%27s_Hierarchy_of_Disagreement-en.svg/250px-Graham%27s_Hierarchy_of_Disagreement-en.svg.png" decoding="async" width="250" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Graham%27s_Hierarchy_of_Disagreement-en.svg/375px-Graham%27s_Hierarchy_of_Disagreement-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Graham%27s_Hierarchy_of_Disagreement-en.svg/500px-Graham%27s_Hierarchy_of_Disagreement-en.svg.png 2x" data-file-width="707" data-file-height="530" /></a><figcaption>Protislovje na <a href="/w/index.php?title=Paul_Graham_(ra%C4%8Dunalni%C5%A1ki_programer)&action=edit&redlink=1" class="new" title="Paul Graham (računalniški programer) (stran ne obstaja)">Grahamovi</a> hierarhiji nesoglasij</figcaption></figure> <p><a href="/w/index.php?title=Pogovorni_jezik&action=edit&redlink=1" class="new" title="Pogovorni jezik (stran ne obstaja)">Pogovorna</a> raba lahko označuje akcije ali izjave, ki so si med seboj v naprotju, kadar so (ali so razumljene) kot posledica <a href="/w/index.php?title=Presupozicija&action=edit&redlink=1" class="new" title="Presupozicija (stran ne obstaja)">presupozicij</a>, ki so protislovne v logičnem smislu. </p> <div class="mw-heading mw-heading2"><h2 id="Glej_tudi">Glej tudi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=10" title="Uredi razdelek: Glej tudi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=10" title="Urejanje izvorne kode razdelka: Glej tudi"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Antinomija" class="mw-redirect" title="Antinomija">antinomija</a></li> <li><a href="/w/index.php?title=Argument_Clinic&action=edit&redlink=1" class="new" title="Argument Clinic (stran ne obstaja)">Argument Clinic</a>, skeč skupine <a href="/wiki/Monty_Python" title="Monty Python">Monty Python</a> v katerem dva diskutanta pri svojem prerekanju rabita le ponavljajoča se protislovja</li> <li><a href="/w/index.php?title=Nasprotnost&action=edit&redlink=1" class="new" title="Nasprotnost (stran ne obstaja)">nasprotnost</a></li> <li><a href="/wiki/Dvojno_merilo" title="Dvojno merilo">dvojno merilo</a></li> <li><a href="/w/index.php?title=Dvomiselnost&action=edit&redlink=1" class="new" title="Dvomiselnost (stran ne obstaja)">dvomiselnost</a></li> <li><a href="/wiki/Ironija" title="Ironija">ironija</a></li> <li><a href="/wiki/Oksimoron" title="Oksimoron">oksimoron</a></li> <li><a href="/w/index.php?title=Parakonsistentna_logika&action=edit&redlink=1" class="new" title="Parakonsistentna logika (stran ne obstaja)">parakonsistentna logika</a></li> <li><a href="/wiki/Paradoks" title="Paradoks">paradoks</a></li> <li><a href="/w/index.php?title=Tavtologija&action=edit&redlink=1" class="new" title="Tavtologija (stran ne obstaja)">tavtologija</a></li> <li><a href="/wiki/TRIZ" title="TRIZ">TRIZ</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Sklici">Sklici</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=11" title="Uredi razdelek: Sklici" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=11" title="Urejanje izvorne kode razdelka: Sklici"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="column-width: 25em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r5980307">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"»""«""›""‹"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.fran.si/iskanje?View=1&Query=protislovje">»protislovje«</a>. <i><a href="/wiki/Fran_(jezikovni_portal)" title="Fran (jezikovni portal)">portal Fran</a> 4.1</i>. 25. maj 2017<span class="reference-accessdate">. Pridobljeno 25. julija 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=neznano&rft.jtitle=portal+Fran+4.1&rft.atitle=protislovje&rft.date=2017-05-25&rft_id=http%3A%2F%2Fwww.fran.si%2Fiskanje%3FView%3D1%26Query%3Dprotislovje&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.fran.si/iskanje?View=1&Query=kontradikcija">»kontradikcija«</a>. <i>portal Fran 4.1</i>. 25. maj 2017<span class="reference-accessdate">. Pridobljeno 25. julija 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=neznano&rft.jtitle=portal+Fran+4.1&rft.atitle=kontradikcija&rft.date=2017-05-25&rft_id=http%3A%2F%2Fwww.fran.si%2Fiskanje%3FView%3D1%26Query%3Dkontradikcija&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFTavzes2002"> Tavzes (2002)</a>, str. 607.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.fran.si/iskanje?View=1&Query=antinomija">»antinomija«</a>. <i>portal Fran 4.1</i>. 25. maj 2017<span class="reference-accessdate">. Pridobljeno 25. julija 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=neznano&rft.jtitle=portal+Fran+4.1&rft.atitle=antinomija&rft.date=2017-05-25&rft_id=http%3A%2F%2Fwww.fran.si%2Fiskanje%3FView%3D1%26Query%3Dantinomija&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFTavzes2002"> Tavzes (2002)</a>, str. 55.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.fran.si/iskanje?View=1&Query=protire%C4%8Dje">»protirečje«</a>. <i>portal Fran 4.1</i>. 25. maj 2017<span class="reference-accessdate">. Pridobljeno 25. julija 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=neznano&rft.jtitle=portal+Fran+4.1&rft.atitle=protire%C4%8Dje&rft.date=2017-05-25&rft_id=http%3A%2F%2Fwww.fran.si%2Fiskanje%3FView%3D1%26Query%3Dprotire%25C4%258Dje&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">Dialog <i>Euthydemus</i> iz <i>The Dialogs of Plato v prevodu <a href="/w/index.php?title=Benjamin_Jowett&action=edit&redlink=1" class="new" title="Benjamin Jowett (stran ne obstaja)">Benjamina Jowetta</a></i> v: Knjiga 7 <i>Plato</i>: <a href="/w/index.php?title=Robert_Maynard_Hutchins&action=edit&redlink=1" class="new" title="Robert Maynard Hutchins (stran ne obstaja)">Robert Maynard Hutchins</a>, glavni urednik, 1952, <i><a href="/w/index.php?title=Great_Books_of_the_Western_World&action=edit&redlink=1" class="new" title="Great Books of the Western World (stran ne obstaja)">Great Books of the Western World</a></i>, <a href="/wiki/Enciklopedija_Britannica" title="Enciklopedija Britannica">Enciklopedija Britannica</a>, Inc., <a href="/wiki/Chicago" title="Chicago">Chicago</a>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFPakin2017"> Pakin (2017)</a>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFPost1921"> Post (1921)</a> v <a class="mw-selflink-fragment" href="#CITEREFvan_Heijenoort1967"> van Heijenoort (1967)</a>, str. 272.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text">krepko in ležeče dodano, <a class="mw-selflink-fragment" href="#CITEREFNagelNewman1958"> Nagel; Newman (1958)</a>, str. 109-110.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFNagelNewman1958"> Nagel; Newman (1958)</a>, str. 110-111.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFNagelNewman1958"> Nagel; Newman (1958)</a>, str. 111.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFPriest2006"> Priest (2006)</a>.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFStoljar2006"> Stoljar (2006)</a>, str. 87.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFSørensen2006"> Sørensen (2006)</a>.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFMao_Cetung1937"> Mao Cetung (1937)</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Viri">Viri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Protislovje&veaction=edit&section=12" title="Uredi razdelek: Viri" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Protislovje&action=edit&section=12" title="Urejanje izvorne kode razdelka: Viri"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r5453066">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-100{font-size:100%}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns dl,.mw-parser-output .refbegin-columns ol,.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li,.mw-parser-output .refbegin-columns dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="refbegin refbegin-columns references-column-count references-column-count-2" style="column-count: 2;"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFvan_Heijenoort1967" class="citation cs2">van Heijenoort, Jean (1967), <i>From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931</i>, Cambridge, MA: Harvard University Press, <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:ViriKnjig/0-674-32449-8" title="Posebno:ViriKnjig/0-674-32449-8"><bdi>0-674-32449-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=From+Frege+to+G%C3%B6del%3A+A+Source+Book+in+Mathematical+Logic+1879-1931&rft.place=Cambridge%2C+MA&rft.pub=Harvard+University+Press&rft.date=1967&rft.isbn=0-674-32449-8&rft.aulast=van+Heijenoort&rft.aufirst=Jean&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFMao_Cetung1937" class="citation cs2 cs1-prop-foreign-lang-source"><a href="/wiki/Mao_Cetung" title="Mao Cetung">Mao Cetung</a> (Avgust 1937), <a rel="nofollow" class="external text" href="https://www.marxists.org/reference/archive/mao/selected-works/volume-1/mswv1_17.htm"><i>Selected Works of Mao Tse-tung: ON CONTRADICTION</i></a> (v angleščini)</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=Selected+Works+of+Mao+Tse-tung%3A+ON+CONTRADICTION&rft.date=1937-08&rft.au=Mao+Cetung&rft_id=http%3A%2F%2Fwww.marxists.org%2Freference%2Farchive%2Fmao%2Fselected-works%2Fvolume-1%2Fmswv1_17.htm&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFNagelNewman1958" class="citation cs2"><a href="/w/index.php?title=Ernest_Nagel&action=edit&redlink=1" class="new" title="Ernest Nagel (stran ne obstaja)">Nagel, Ernest</a>; <a href="/w/index.php?title=James_Roy_Newman_1958&action=edit&redlink=1" class="new" title="James Roy Newman 1958 (stran ne obstaja)">Newman, James Roy</a> (1958), <i>Gödel's Proof</i>, New York University Press, Card Catalog Number: 58-5610</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=G%C3%B6del%27s+Proof&rft.pub=New+York+University+Press&rft.date=1958&rft.aulast=Nagel&rft.aufirst=Ernest&rft.au=Newman%2C+James+Roy&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFPakin2017" class="citation cs2 cs1-prop-foreign-lang-source">Pakin, Scott (19. januar 2017), <a rel="nofollow" class="external text" href="http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"><i>The Comprehensive LaTeX Symbol List</i></a> <span class="cs1-format">(PDF)</span> (v angleščini)<span class="reference-accessdate">, pridobljeno 26. julija 2017</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=The+Comprehensive+LaTeX+Symbol+List&rft.date=2017-01-19&rft.aulast=Pakin&rft.aufirst=Scott&rft_id=http%3A%2F%2Fwww.ctan.org%2Ftex-archive%2Finfo%2Fsymbols%2Fcomprehensive%2Fsymbols-a4.pdf&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFPriest2006" class="citation cs2"><a href="/w/index.php?title=Graham_Priest&action=edit&redlink=1" class="new" title="Graham Priest (stran ne obstaja)">Priest, Graham</a> (2006), <a rel="nofollow" class="external text" href="https://books.google.si/books?id=TMztJKtWWSAC"><i>In Contradiction: A Study of the Transconsistent</i></a> (2. izd.), Oxford University Press, <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:ViriKnjig/0-19-926330-2" title="Posebno:ViriKnjig/0-19-926330-2"><bdi>0-19-926330-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=In+Contradiction%3A+A+Study+of+the+Transconsistent&rft.edition=2.&rft.pub=Oxford+University+Press&rft.date=2006&rft.isbn=0-19-926330-2&rft.aulast=Priest&rft.aufirst=Graham&rft_id=https%3A%2F%2Fbooks.google.si%2Fbooks%3Fid%3DTMztJKtWWSAC&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFPost1921" class="citation cs2"><a href="/w/index.php?title=Emil_Leon_Post&action=edit&redlink=1" class="new" title="Emil Leon Post (stran ne obstaja)">Post, Emil Leon</a> (1921), <i>Introduction to a general theory of elementary propositions</i></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=Introduction+to+a+general+theory+of+elementary+propositions&rft.date=1921&rft.aulast=Post&rft.aufirst=Emil+Leon&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFSørensen2006" class="citation cs2 cs1-prop-foreign-lang-source">Sørensen, Michael Kuur (2006), <a rel="nofollow" class="external text" href="https://journals.aau.dk/index.php/ijis/article/download/181/121"><i>CAPITAL AND LABOUR: CAN THE CONFLICT BE SOLVED?</i></a> (v angleščini)<span class="reference-accessdate">, pridobljeno 28. maja 2017</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=CAPITAL+AND+LABOUR%3A+CAN+THE+CONFLICT+BE+SOLVED%3F&rft.date=2006&rft.aulast=S%C3%B8rensen&rft.aufirst=Michael+Kuur&rft_id=https%3A%2F%2Fjournals.aau.dk%2Findex.php%2Fijis%2Farticle%2Fdownload%2F181%2F121&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFStoljar2006" class="citation cs2">Stoljar, Daniel (2006), <i>Ignorance and Imagination</i>, Oxford University Press - U.S., <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:ViriKnjig/0-19-530658-9" title="Posebno:ViriKnjig/0-19-530658-9"><bdi>0-19-530658-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=Ignorance+and+Imagination&rft.pub=Oxford+University+Press+-+U.S.&rft.date=2006&rft.isbn=0-19-530658-9&rft.aulast=Stoljar&rft.aufirst=Daniel&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFTavzes2002" class="citation cs2"><a href="/w/index.php?title=Milo%C5%A1_Tavzes&action=edit&redlink=1" class="new" title="Miloš Tavzes (stran ne obstaja)">Tavzes, Miloš</a>, ur. (2002), <i>Veliki slovar tujk</i>, Ljubljana: Cankarjeva založba, <a href="/wiki/Vzajemni_bibliografski_sistem_COBISS" title="Vzajemni bibliografski sistem COBISS">COBISS</a> <a rel="nofollow" class="external text" href="https://plus.cobiss.net/cobiss/si/sl/bib/121003520">121003520</a>, <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:ViriKnjig/961-231-271-0" title="Posebno:ViriKnjig/961-231-271-0"><bdi>961-231-271-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=Veliki+slovar+tujk&rft.place=Ljubljana&rft.pub=Cankarjeva+zalo%C5%BEba&rft.date=2002&rft_id=https%3A%2F%2Fplus.cobiss.net%2Fcobiss%2Fsi%2Fsl%2Fbib%2F121003520%23full%23id-name%3DCOBISS&rft.isbn=961-231-271-0&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AProtislovje" class="Z3988"></span></li></ul> </div> <div role="navigation" class="navbox" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Wikipedija:Normativna_kontrola" title="Wikipedija:Normativna kontrola">Normativna kontrola: Narodne knjižnice</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q363948#identifiers" title="Uredite to na Wikipodatkih"><img alt="Uredite to na Wikipodatkih" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX531834">Španija</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11950282m">Francija</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11950282m">(data)</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4165171-6">Nemčija</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="http://uli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007557822005171">Izrael</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85031650">ZDA</a></span></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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