A Gödelian Perspective on Target-Directed Fitness in Cumulative-Selection Models

A Gödelian Perspective on Target-Directed Fitness in Cumulative-Selection Models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Gödelian Perspective on Target-Directed Fitness in Cumulative-Selection Models David Chernoguz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8398297/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Many widely used pedagogical models of cumulative selection — including Dawkins’ “weasel” program — define fitness as a monotonic function of distance to a fixed, externally specified target T that the evolving population never directly observes. We prove that any such target-dependent fitness function requires an external oracle supplying d(x, T ) at each generation, and that directed convergence is possible if and only if the algorithm is oracle-augmented. When the entire evolutionary process is idealized as a consistent formal system S powerful enough for arithmetic and T lies outside its axiomatic closure, Gödel’s first incompleteness theorem entails that statements of the form “bit i of x equals bit i of T ” are not uniformly decidable within S; consequently d(x, T ) cannot be computed internally. Experiments with n = 40 bit strings confirm the theoretical dichotomy: with the oracle, convergence is rapid and monotonic; without it, the dynamics reduce to an unbiased random walk. The Gödelian perspective is new; the underlying computational necessity of an oracle follows from the No Free Lunch theorems and has been noted by several authors. The analysis clarifies why target-dependent models, although vivid illustrations of cumulative improvement, cannot serve as non-teleological models of natural evolution, as they violate the causal locality of fitness defended in the propensity interpretation. Evolutionary Biology cumulative selection target-directed fitness oracle dependence Gödel incompleteness propensity interpretation of fitness causal locality evolutionary modelling Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8398297","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":562565928,"identity":"9c67ebd5-d86c-45fd-bb3f-5fdb19c91673","order_by":0,"name":"David Chernoguz","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYDCCA8wHGBgKLHjYG4jXwpbAwGAgwcNzgHgtPAYgLQzEa+E7fubjhx8GEjI87GefbvjBYCenS8iFkmdyN0v2gBzGk252s4ch2diMkHUGN3i3MfAAtdgzpLHd4GE4kLiNsBaeZ4x/QLbwP2O7+YdILWzMIFt4JNLYbhNli+SZNGNpGbCWZ2y3ZQyI8Avf8cMPP76psLHn4U9ju/mmwk6OoBZ0d5KmfBSMglEwCkYBDgAAatM7Au7P1KIAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0001-1747-3619","institution":"CalliFarma Therapeutics, Ltd.","correspondingAuthor":true,"prefix":"","firstName":"David","middleName":"","lastName":"Chernoguz","suffix":""}],"badges":[],"createdAt":"2025-12-18 18:49:05","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8398297/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8398297/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98727453,"identity":"faae83b6-25df-4575-ab27-97b63f3716fc","added_by":"auto","created_at":"2025-12-22 04:00:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":263754,"visible":true,"origin":"","legend":"","description":"","filename":"GodelianPerspectiveonTargetDirectedFitness5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8398297/v1_covered_da2d52b5-bd3b-4ea0-869e-0942e549d549.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Gödelian Perspective on Target-Directed Fitness in Cumulative-Selection Models\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"cumulative selection, target-directed fitness, oracle dependence, Gödel incompleteness, propensity interpretation of fitness, causal locality, evolutionary modelling","lastPublishedDoi":"10.21203/rs.3.rs-8398297/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8398297/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMany widely used pedagogical models of cumulative selection — including Dawkins’ “weasel” program — define fitness as a monotonic function of distance to a fixed, externally specified target T that the evolving population never directly observes. 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