A Topos Foundation for Theories of Physics: I. Formal Languages for Physics Export

@article{citeulike:1221606, abstract = {This paper is the first in a series whose goal is to develop a fundamentallynew way of constructing theories of physics. The motivation comes from a desireto address certain deep issues that arise when contemplating quantum theoriesof space and time. Our basic contention is that constructing a theory ofphysics is equivalent to finding a representation in a topos of a certainformal language that is attached to the system. Classical physics arises whenthe topos is the category of sets. Other types of theory employ a differenttopos. In this paper we discuss two different types of language that can beattached to a system, S. The first is a propositional language, PL(S); thesecond is a higher-order, typed language L(S). Both languages provide deductivesystems with an intuitionistic logic. The reason for introducing PL(S) is that,as shown in paper II of the series, it is the easiest way of understanding, andexpanding on, the earlier work on topos theory and quantum physics. However,the main thrust of our programme utilises the more powerful language L(S) andits representation in an appropriate topos.}, archivePrefix = {arXiv}, author = {Doering, A. and Isham, C. J.}, citeulike-article-id = {1221606}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0703060}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0703060}, citeulike-linkout-2 = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2007quant.ph..3060D}, eprint = {quant-ph/0703060}, journal = {ArXiv Quantum Physics e-prints}, keywords = {algorithmic-information-theory, category-of-languages, category-of-systems, category-of-theories, category-theory, classicality, computability-logic, deep-inference, dev, effective-topos, executable, formal, formal-development, formal-language, formal-language-theory, formal-science, formal-system, formalization, higher-dimensional-category-theory, higher-dimensional-topos-theory, hyperdoctrine, iff, intuitionistic-logic, logics, managed-logic, metamodeling, metascience, modeling, nonclassicality, operational, parchments, physics, quantum-domain-theory, quantum-institutions, representation, rewriting-logic, theory-development, theory-selection, topos, topos-selection, topos-theory, unified-concept-theory}, month = {March}, posted-at = {2007-04-12 08:08:24}, priority = {2}, title = {A Topos Foundation for Theories of Physics: I. Formal Languages for Physics}, url = {http://arxiv.org/abs/quant-ph/0703060}, year = {2007} }

TY - JOUR ID - citeulike:1221606 L3 - citeulike-article-id:1221606 N2 - This paper is the first in a series whose goal is to develop a fundamentallynew way of constructing theories of physics. The motivation comes from a desireto address certain deep issues that arise when contemplating quantum theoriesof space and time. Our basic contention is that constructing a theory ofphysics is equivalent to finding a representation in a topos of a certainformal language that is attached to the system. Classical physics arises whenthe topos is the category of sets. Other types of theory employ a differenttopos. In this paper we discuss two different types of language that can beattached to a system, S. The first is a propositional language, PL(S); thesecond is a higher-order, typed language L(S). Both languages provide deductivesystems with an intuitionistic logic. The reason for introducing PL(S) is that,as shown in paper II of the series, it is the easiest way of understanding, andexpanding on, the earlier work on topos theory and quantum physics. However,the main thrust of our programme utilises the more powerful language L(S) andits representation in an appropriate topos. JF - ArXiv Quantum Physics e-prints TI - A Topos Foundation for Theories of Physics: I. Formal Languages for Physics KW - algorithmic-information-theory KW - category-of-languages KW - category-of-systems KW - category-of-theories KW - category-theory KW - classicality KW - computability-logic KW - deep-inference KW - dev KW - effective-topos KW - executable KW - formal KW - formal-development KW - formal-language KW - formal-language-theory KW - formal-science KW - formal-system KW - formalization KW - higher-dimensional-category-theory KW - higher-dimensional-topos-theory KW - hyperdoctrine KW - iff KW - intuitionistic-logic KW - logics KW - managed-logic KW - metamodeling KW - metascience KW - modeling KW - nonclassicality KW - operational KW - parchments KW - physics KW - quantum-domain-theory KW - quantum-institutions KW - representation KW - rewriting-logic KW - theory-development KW - theory-selection KW - topos KW - topos-selection KW - topos-theory KW - unified-concept-theory AU - Doering, A AU - Isham, CJ PY - 2007/March// UR - http://arxiv.org/abs/quant-ph/0703060 ER -