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The Constitution of Abstract Objects
Author(s) -
Trajkovski Miroslava
Publication year - 2021
Publication title -
theoria
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 16
eISSN - 1755-2567
pISSN - 0040-5825
DOI - 10.1111/theo.12207
Subject(s) - referent , abstraction , term (time) , object (grammar) , epistemology , relation (database) , constitution , character (mathematics) , equivalence (formal languages) , mathematics , pure mathematics , computer science , philosophy , artificial intelligence , linguistics , law , physics , geometry , political science , quantum mechanics , database
An abstract singular term is a term that is built in a particular way which is given by the principle of abstraction. Given that F and G are variables, N is a term‐forming operator, and E is an equivalence relation, the principle of abstraction is usually stated as: (F)(G)(NF = NG iff E[F,G]). I distinguish between logical and phenomenological principles of abstraction in the sense that the left‐hand side is abstrahendum and the right‐hand side is abstrahens in the former; in the latter it is vice versa. Frege says that we “carve up the content in a way different from the original one [in the abstrahens], and this yields us a new concept [in the abstrahendum].” I shall follow an approach that differs from the Fregean. Instead of taking an object to be defined as the referent of a term constructed as a singular term, I will take it that an object is the referent of a constitutional act which I explain along Husserlian lines. I will argue that the logical principle of abstraction for numbers demands two steps of abstraction (not exactly Cantorian ones), and that the first one was hidden. When made explicit this step reveals its phenomenological character.