Categorical pairs and the indicative shift. (English) Zbl 1261.18002
The purpose of this paper is to introduce a category-theoretic pattern that complements the F. W. Lawvere fixed-point theorem [Repr. Theory Appl. Categ. 2006, No. 15, 1–13 (2006; Zbl 1089.18004); Category Theory Homology Theory Appl., Proc. Conf. Seattle Res. Center Battelle Mem. Inst. 1968, 2, 134–145 (1969; Zbl 0218.18002)]. The author produces a construction for indirect self-reference that applies directly both to situations in ordinary languages and to Gödel’s incompleteness theorem [K. Gödel, Monatsh. Math. Phys. 38, 173–198 (1931; Zbl 0002.00101; JFM 57.0054.02)]. The paper is in the lines of the author’s ones [Kybernetes 34, No. 1–2, 129–150 (2005; Zbl 1073.03003); Syst. Res. 13, No. 3, 293–310 (1996; Zbl 0860.03007); Ser. Knots Everything 6, 1–110 (1995; Zbl 1149.03301)].
Reviewer: Hirokazu Nishimura (Tsukuba)
MSC:
| 18A99 | General theory of categories and functors |
| 03A05 | Philosophical and critical aspects of logic and foundations |
Keywords:
category; categorical pair; \(2\)-category; indicative shift; self-reference; Lawvere’s fixed-point theorem; Gödel’s incompleteness theoremCitations:
Zbl 1089.18004; Zbl 0218.18002; Zbl 1056.92002; Zbl 1073.03003; Zbl 0860.03007; Zbl 1149.03301; JFM 57.0054.02; Zbl 0002.00101References:
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