Erik Palmgren Formalization in typed theories versus untyped theories
نویسندگان
چکیده
Abstract: Structuralism, in a well-known form, says that entities are logically, psychologically, epistemologically, linguistically, or ontologically secondary to the relations they stand in. But what of the relations themselves? Are they secondary to the second-order relations they stand in? Does the same hold for second-order relations, and for relations of arbitrary high order? Someone who answers "yes" to this question I will call an ω-structuralist. I will make some brief comments on why one might want to be an ωstructuralist, but the main part of the talk will be devoted to how one can be one: ω-structuralism seems, prima facie, to fall victim to a number of vicious regresses. In order to address these, I will bring in some models and tools from homotopy theory, higher-order category theory, and non-wellfounded set theory. My aim is to show that ω-structuralism can be framed as a consistent and coherent thesis, as long as we keep a su ciently open mind about what kinds of formal structure to allow in our philosophical methodology. Erik Palmgren Formalization in typed theories versus untyped theories Rasmus K. Rendsvig Dynamics of Informational Cascades
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