Given a theory \u2013 e.g., in mathematics, theology, physics, sociology, political theory \u2013 what is it for the objects of that theory to be identical? Not all true theories give the same answer: it can depend on the objects of the theory.\u00a0The logic of identity, as current research stands, is largely confined to the standard framework of classical logic. Non-classical logics have proven to be important in philosophy, and they are promising for related disciplines. What we lack, as current research stands, are natural, simple, and widely applicable accounts of identity for the family of non-classical frameworks. This one-day Arch\u00e9 workshop will explore the prospects for non-classical logical approaches to identity and their possible applications.<\/p>\n
Venue:<\/strong> G03, Edgecliffe Schedule<\/strong><\/p>\n Titles and Abstracts<\/strong><\/p>\n Matteo Nizzardo \u2014 The Identity of Indiscernibles\u2019 Weakest Interesting Interpretation<\/strong><\/p>\n According to Strawson (1959) the principle of the Identity of Indiscernibles (PII) holds that no two individuals can share all their qualitative properties. This has been challenged by Rodriguez-Pereyra (2006), who suggests a weaker non-trivial interpretation of PII according to which no two individuals can share all their nontrivializing properties. I argue that Rodriguez-Pereyra’s reading of PII entails an infinite regress, which can be avoided only by committing to individuals that differ only numerically. I generalise the result to any interpretation of PII that is weaker than Strawson’s, and conclude that the weakest interesting version of PII is the one restricting the domain of quantification to qualitative properties only.<\/p>\n <\/p>\n JC Beall \u2014<\/strong> The leibnizian recipe, difference makers, and relative identity<\/strong><\/p>\n I think of identity relations as the product of the leibnizian recipe, which basically defines an identity relation R via a biconditional scheme:<\/p>\n aRb is true iff all relevant instances of PHI(a)<\u2014>PHI(b) are true.<\/p>\n aRb is false iff some relevant instance of PHI(a)<\u2014>PHI(b) is false.<\/p>\n Clearly, the entailment behavior of the identity relation R will turn not only on the entailment behavior of the biconditional in the scheme but also on the range of the schematic variable. Example: use classical-logic ingredients (ergo, classical material conditional) and R is an equivalence relation. Use subclassical ingredients (e.g., FDE) and, well, R certainly needn\u2019t be an equivalence relation (though, in the confines of some theories, can be an equivalence relation, depending on the language of the given theory and especially the range of PHI).<\/p>\n All of this is familiar; it\u2019s basically the standard recipe for identity relations. (And if you shop at the standard store for your ingredients, you\u2019ll get the standard identity relation sometimes called \u2018classical identity\u2019.) Let\u2019s assume \u2014 as I in fact believe \u2014 that this standard recipe is correct (though standard ingredients aren\u2019t necessary).<\/p>\n Against the backdrop of (by my lights) the somewhat perplexing debate over \u201crelative identity\u201d (e.g., Geach, Martin, van Inwagen, Rea), I show that relative identity relations simply drop out of the standard leibnizian recipe, at least if associated sets of \u201cdifference makers\u201d are made explicit.<\/p>\n Against some (so-called \u201cpure\u201d) relative-identity theorists, I think that we have not only a gazillion relative-identity relations (as all relative-identity theorists believe); we also have many (if not exactly a gazillion) non-relative identity relations \u2014 all easily traced back to the leibnizian recipe.<\/p>\n The result should be good news for so-called relative-identity theorists. The reason is that, to my knowledge, such theorists never actually explicitly define relative-identity relations; they just wave at features of \u201cis-the-same-PHI-as\u201d that\u2019s supposed to somehow define the relations. (But they don\u2019t, so far as I\u2019ve seen.) If I\u2019m right, relative-identity theorists are just leibnizian-recipe theorists with a few small twists.\u00a0\u00a0<\/strong><\/p>\n <\/p>\n Greg Restall \u2014 Exploring three-valued models for identity<\/strong> There is an very natural way to interpret the propositional connectives and quantifiers, relative to the algebra of three semantic values, {0, i<\/em>, 1} where 0 and 1 are understood as the traditional values of falsity and truth, and the third value is some intermediate value. The evaluation clauses do not, by themselves, determine the logic<\/em>, because for that<\/em>, you need to determine how models are used to provide a counterexample\u00a0to a sequent. If a counterexample is given by a model that assigns every premise the value 1 and assigns every conclusion a value other <\/em>than 1, the resulting logic is Kleene\u2019s strong three-valued logic, K3. If a counterexample is a model assigning every premise the value 1 or\u00a0i<\/em>\u00a0and every conclusion the value 0, the resulting logic is Priest\u2019s logic of paradox, LP. If a counterexample is a model assigning every premise the value 1 and every conclusion the value 0, you get the logic ST of Strict-Tolerant validity. ST is distinctive, in that it is<\/em>, in some sense, classical logic<\/em>\u2014<\/em>every classically valid sequent in this language is ST-valid\u2014but since it has strictly non-classical models, there are ST theories <\/em>which are not classical theories.<\/p>\n What does this mean for the logic of identity <\/em>in a three-valued context?<\/p>\n In this talk, I will explain how the classical <\/em>logic of identity, when interpreted in ST models, gives us a well-behaved class of three-valued models\u00a0for identity\u2014much larger than the traditional models for identity, used by afficianados of LP or K3\u2014which can be used to model the distinctive non-classical behaviour of identity statements, with a greater degree of freedom than we might have thought.<\/p>\n <\/p>\n Franz Berto \u2014 Counting the Particles: Permutations, Identity, and Indiscernibility\u00a0<\/strong><\/p>\n I\u2019d like to attack a certain view: the view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. In this talk, I introduce the Received View; I explain what I mean by \u201centity\u201d (synonymously, by \u201cobject\u201d and \u201cthing\u201d), and I argue that supporters of the Received View should agree with my characterization of the corresponding notion of entity (object, thing<\/em>). I also explain what I mean by \u201cidentity\u201d, and I show that supporters of the Received View agree with my characterization of that notion. Then, I argue that the concept of identity, so characterized, is one with the concept of oneness<\/em>. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. Finally, I say something on the problem of how reference to indiscernible objects with identity can be achieved.<\/p>","excerpt":"","slug":"metaphysics-seminar-6-2022-04-18","image":false,"all_day":false,"start_date":"2022-04-18 09:00:00","start_date_details":{"year":"2022","month":"04","day":"18","hour":"09","minutes":"00","seconds":"00"},"end_date":"2022-04-18 17:00:00","end_date_details":{"year":"2022","month":"04","day":"18","hour":"17","minutes":"00","seconds":"00"},"utc_start_date":"2022-04-18 08:00:00","utc_start_date_details":{"year":"2022","month":"04","day":"18","hour":"08","minutes":"00","seconds":"00"},"utc_end_date":"2022-04-18 16:00:00","utc_end_date_details":{"year":"2022","month":"04","day":"18","hour":"16","minutes":"00","seconds":"00"},"timezone":"Europe\/London","timezone_abbr":"BST","cost":"","cost_details":{"currency_symbol":"","currency_code":"","currency_position":"prefix","values":[]},"website":"","show_map":true,"show_map_link":true,"hide_from_listings":false,"sticky":false,"featured":false,"categories":[{"name":"Metaphysics and Logic group","slug":"metaphysics-and-logic-group","term_group":0,"term_taxonomy_id":47,"taxonomy":"tribe_events_cat","description":"","parent":0,"count":168,"filter":"raw","id":47,"urls":{"self":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/tribe\/events\/v1\/categories\/47","collection":"https:\/\/www.st-andrews.ac.uk\/arche\/wp-json\/tribe\/events\/v1\/categories"}}],"tags":[],"venue":{"id":2016,"author":"1","status":"publish","date":"2017-01-23 15:17:41","date_utc":"2017-01-23 15:17:41","modified":"2022-03-15 18:10:03","modified_utc":"2022-03-15 18:10:03","url":"https:\/\/www.st-andrews.ac.uk\/arche\/venue\/edgecliffe-g03\/","venue":"Edgecliffe G03","slug":"edgecliffe-g03","json_ld":{"@type":"Place","name":"Edgecliffe G03","description":"","url":"https:\/\/www.st-andrews.ac.uk\/arche\/venue\/edgecliffe-g03\/","address":{"@type":"PostalAddress"},"telephone":"","sameAs":""},"show_map":true,"show_map_link":true,"global_id":"www.st-andrews.ac.uk\/arche?id=2016","global_id_lineage":["www.st-andrews.ac.uk\/arche?id=2016"]},"organizer":[],"custom_fields":[],"json_ld":{"@context":"http:\/\/schema.org","@type":"Event","name":"Metaphysics Workshop: Logic of Identity","description":"<p>Given a theory \u2013 e.g., in mathematics, theology, physics, sociology, political theory \u2013 what is it for the objects of that theory to be identical?...<\/p>\\n","url":"https:\/\/www.st-andrews.ac.uk\/arche\/event\/metaphysics-seminar-6-2022-04-18\/","eventAttendanceMode":"https:\/\/schema.org\/OfflineEventAttendanceMode","eventStatus":"https:\/\/schema.org\/EventScheduled","startDate":"2022-04-18T09:00:00+01:00","endDate":"2022-04-18T17:00:00+01:00","location":{"@type":"Place","name":"Edgecliffe G03","description":"","url":"https:\/\/www.st-andrews.ac.uk\/arche\/venue\/edgecliffe-g03\/","address":{"@type":"PostalAddress"},"telephone":"","sameAs":""},"performer":"Organization"},"is_virtual":false,"virtual_url":null,"virtual_video_source":""}
\nTime:<\/strong> From 9am till 5pm on Monday April 18th, 2022 (BST)
\nFormat:<\/strong> In person
\nRegistration:<\/strong>\u00a0<\/strong> Please register your interest in attending by emailing our workshop organisers at mn85@st-andrews.ac.uk<\/p>\n\n
\nTitle: The Identity of Indiscernibles\u2019 Weakest Interesting Interpretation<\/li>\n
\nTitle: The leibnizian recipe, difference makers, and relative identity<\/li>\n
\nTitle: Exploring three-valued models for identity<\/li>\n
\nTitle: Counting the Particles: Permutations, Identity, and Indiscernibility<\/li>\n<\/ul>\n
\n<\/strong><\/p>\n