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<div class="field-block node-stanford-page-title block-layout-builder"> <div class="node stanford-page title string label-hidden"><h1>The Metaphysics Research Lab</h1> </div> </div> </div> </div> <div class="jumpstart-ui--two-column flex-container centered-container"> <div class="left-region flex-lg-3-of-12"> <div class="menu-block main block block-menu navigation menu--main"> <h2 aria-hidden="true" class="visually-hidden" id="menu-blockmain-menu">Main navigation</h2> <a href="#main-content" class="visually-hidden focusable su-skipnav su-skipnav--content">Skip to main content</a> <nav class="su-secondary-nav--light su-secondary-nav su-secondary-nav--static no-js" aria-label="secondary menu"> <div id="secondary-navigation" tabindex="-1" class="visually-hidden focusable">Secondary Navigation</div> <ul class="su-secondary-nav__menu su-secondary-nav__menu-lv1"><li class="su-secondary-nav__item"><a class="su-secondary-nav__link" href="/projects/center-explanation-consciousness"> Center for the Explanation of Consciousness </a></li><li class="su-secondary-nav__item"><a class="su-secondary-nav__link" href="/projects/computational-semantics-lab"> Computational Semantics Lab </a></li><li class="su-secondary-nav__item"><a class="su-secondary-nav__link" href="/projects/language-and-natural-reasoning"> Language and Natural Reasoning </a></li><li class="su-secondary-nav__item"><a class="su-secondary-nav__link" href="/projects/logical-dynamics-lab"> Logical Dynamics Lab </a></li><li class="su-secondary-nav__item"><a class="su-secondary-nav__link" href="/projects/pragmatic-enrichment-contextual-interface-lab"> Pragmatic Enrichment & Contextual Interface Lab </a></li><li class="su-secondary-nav__item"><a class="su-secondary-nav__link" href="/projects/psychosemantics-lab"> Psychosemantics Lab </a></li><li class="su-secondary-nav__item su-secondary-nav__item--active-trail su-secondary-nav__item--current"><a aria-current="true" class="su-secondary-nav__link" href="/projects/metaphysics-research-lab"> The Metaphysics Research Lab </a></li><li class="su-secondary-nav__item"><a class="su-secondary-nav__link" href="/projects/openproof-project"> The Openproof Project </a></li></ul></nav> </div> </div> <div class="flex-lg-9-of-12 main-region"> <div class="jumpstart-ui-skipnav-main-anchor block-jumpstart-ui"> <div id="main-content" tabindex="-1" class="visually-hidden focusable">Main content start</div> </div> <div class="field-block node-stanford-page-su-page-components block-layout-builder"> <div class="node stanford-page su-page-components entity-reference-revisions label-hidden"> <div class="paragraph-item ptype-stanford-layout"> <div class="ptype-stanford-layout paragraph paragraph--type--stanford-layout paragraph--view-mode--default"> <div class="layout layout--layout-paragraphs-one-column"> <div class="layout__region layout__region--main"> <div class="ptype-stanford-wysiwyg paragraph paragraph--type--stanford-wysiwyg paragraph--view-mode--default"> <div class="su-wysiwyg-text paragraph stanford-wysiwyg text-long label-hidden"><div class="align-right media-entity-wrapper image"> <div class="media image field-media-image label-hidden"> <img loading="lazy" src="/sites/g/files/sbiybj24086/files/styles/medium/public/media/image/metaphysics-lab_0.png?itok=W4s1SEF-" width="220" height="106" alt="Metaphyscis Research Lab"> </div> </div> <p>The Metaphysics Research Lab consists of a group of researchers located around the world collaborating with Edward N. Zalta on the axiomatic theory of abstract objects. This theory consists of principles that govern the abstract objects <em>presupposed</em> in the natural sciences, such as mathematical objects and relations, possible states, possible and future objects, etc. The two main principles of the theory are existence and identity conditions for abstract objects: ∃<em>x</em>(<em>A!x</em> & ∀<em>x</em>(<em>xF</em> ≡ φ)) and <em>A!x</em> & <em>A!y</em> → (∀<em>F</em>(<em>xF</em> ≡<em>yF</em>) → <em>x</em>=<em>y</em>).</p><p>Currently, Zalta and <a href="https://ai.stanford.edu/~nodelman/">Uri Nodelman</a> are working on a paper in which they define the technical notion of a ‘possibility’ (as used in the work of Humberstone, van Benthem, Holliday, and others) and derive the main principles that these researchers use to characterize these entities. The slides for a recent talk on this topic can be found <a href="https://mally.stanford.edu/presentations/2024-06-MCMP-Colloquium.pdf">here</a>.</p><p>Recently, Zalta collaborated with <a href="https://www.mcmp.philosophie.uni-muenchen.de/people/faculty/hannes_leitgeb/index.html">Hannes Leitgeb</a> and Nodelman on a paper that shows how object theory offers a logicist account of mathematics. This paper, “<a href="https://mally.stanford.edu/Papers/logicism.pdf">A Defense of Logicism</a>” is forthcoming in the <em>Bulletin of Symbolic Logic</em>. Zalta and Nodelman also recently collaborated on a paper that defines the primitive notions, and derives the axioms, of second-order Peano Arithmetic. This paper, “<a href="https://mally.stanford.edu/Papers/numbers-without-math.pdf">Number Theory and Infinity Without Mathematics</a>” is forthcoming at the <em>Journal of Philosophical Logic</em>. And Zalta's paper “<a href="https://mally.stanford.edu/Papers/routley-star.pdf">The Metaphysics of Routley Star</a>” is forthcoming at the <em>Australasian Journal of Logic</em>.</p><p>Other recent papers include:</p><ul><li>“<a href="https://onlinelibrary.wiley.com/doi/epdf/10.1111/nous.12451">Mathematical Pluralism</a>”, <em>Noûs</em> 2024 (published online open access)</li><li>“<a href="https://mally.stanford.edu/Papers/structuralism.pdf">Foundations for Mathematical Structuralism</a>” (with U. Nodelman) (<em>Mind</em>, 2014)</li><li>“<a href="https://mally.stanford.edu/Papers/computation.pdf">Steps Towards a Computational Metaphysics</a>” (with <a href="http://fitelson.org/">Branden Fitelson</a>) (<em>J. Philosophical Logic</em>, 2007)</li></ul><p>Links: </p><p><a href="https://mally.stanford.edu/">The Metaphysics Research Lab home page</a></p><h2>People</h2></div> </div> </div> </div> </div> </div> <div class="paragraph-item ptype-stanford-layout"> <div class="ptype-stanford-layout paragraph paragraph--type--stanford-layout paragraph--view-mode--default"> <div class="layout layout--layout-paragraphs-one-column"> <div class="layout__region layout__region--main"> <div class="ptype-stanford-lists paragraph paragraph--type--stanford-lists paragraph--view-mode--default"> <div class="visually-hidden su-margin-bottom paragraph stanford-lists su-list-headline string label-hidden"><h2>People</h2> </div> <div class="field field--name-su-list-view field--type-viewfield field--label-hidden"> <div class="field__item field__item-label-hidden"> <div class="views-element-container"><div class="stanford-people-grid view stanford-person grid-list-all js-view-dom-id-739fd461a6fd0d4041ffc39e8a2f1739e671be6d698799dd9e1db4f0c98f9592"> <div data-drupal-views-infinite-scroll-content-wrapper class="views-infinite-scroll-content-wrapper clearfix"><div> <ul class="su-list-unstyled grid-container-3"> <li> <div class="ds-entity--node ds-entity--stanford-person"> <div data-contextual-id="node:node=226:changed=1723755728&ds_bundle=stanford_person&ds_view_mode=stanford_h3_card_plain&langcode=en" data-contextual-token="7N_7pXbohP6WGXF4yw20P6O0wmSxK6loVQDbWkC_4KE" data-drupal-ajax-container=""></div><article class="su-card su-card--minimal"> <div class="node stanford-person su-person-photo entity-reference label-hidden"><div class="media-entity-wrapper image"> <div class="media image field-media-image label-hidden"> <picture> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_1192/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=QGzlFmEF 1x, /sites/g/files/sbiybj24086/files/styles/square_1900/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=fSI6XzCQ 2x" media="screen and (min-width: 992px)" type="image/webp" width="1192" height="1192"/> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_956/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=yu332RKg 1x, /sites/g/files/sbiybj24086/files/styles/square_1900/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=fSI6XzCQ 2x" media="screen and (min-width: 768px)" type="image/webp" width="956" height="956"/> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_956/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=yu332RKg 1x, /sites/g/files/sbiybj24086/files/styles/square_1192/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=QGzlFmEF 2x" media="screen and (min-width: 576px)" type="image/webp" width="956" height="956"/> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_478/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=BFmNVUYI 1x, /sites/g/files/sbiybj24086/files/styles/square_956/public/media/image/zalta-small_0.jpg.webp?h=641a6345&itok=yu332RKg 2x" media="(min-width: 0em)" type="image/webp" width="478" height="478"/> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_1192/public/media/image/zalta-small_0.jpg?h=641a6345&itok=QGzlFmEF 1x, /sites/g/files/sbiybj24086/files/styles/square_1900/public/media/image/zalta-small_0.jpg?h=641a6345&itok=fSI6XzCQ 2x" media="screen and (min-width: 992px)" type="image/jpeg" width="1192" height="1192"/> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_956/public/media/image/zalta-small_0.jpg?h=641a6345&itok=yu332RKg 1x, /sites/g/files/sbiybj24086/files/styles/square_1900/public/media/image/zalta-small_0.jpg?h=641a6345&itok=fSI6XzCQ 2x" media="screen and (min-width: 768px)" type="image/jpeg" width="956" height="956"/> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_956/public/media/image/zalta-small_0.jpg?h=641a6345&itok=yu332RKg 1x, /sites/g/files/sbiybj24086/files/styles/square_1192/public/media/image/zalta-small_0.jpg?h=641a6345&itok=QGzlFmEF 2x" media="screen and (min-width: 576px)" type="image/jpeg" width="956" height="956"/> <source srcset="/sites/g/files/sbiybj24086/files/styles/square_478/public/media/image/zalta-small_0.jpg?h=641a6345&itok=BFmNVUYI 1x, /sites/g/files/sbiybj24086/files/styles/square_956/public/media/image/zalta-small_0.jpg?h=641a6345&itok=yu332RKg 2x" media="(min-width: 0em)" type="image/jpeg" width="478" height="478"/> <img loading="lazy" src="/sites/g/files/sbiybj24086/files/styles/square_1900/public/media/image/zalta-small_0.jpg?h=641a6345&itok=fSI6XzCQ" width="1900" height="1900" alt="" /> </picture> </div> </div> </div> <div class="su-card__contents"> <div class="node stanford-person node-title ds label-hidden"><h3> <a href="/people/edward-n-zalta" hreflang="en">Edward N. 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