A Logical Analysis of A Series and B Series

Yasuo Nakayama


Ever since McTaggart claimed that he had proven the unreality of time, nearly a
hundred years have passed. However, there are still controversial discussions about
whether A series implies a contradiction. One of the reasons for this confusion goes
back to some obscurity in the concepts of A and B series. In this paper, I will
clarify these two concepts by proposing two axiomatic theories, the theory of complex
B series and that of complex A series. Then, I will prove the consistency of both
theories. Furthermore, I will show that both theories are mutually translatable.


philosophy; 20th century philosophy; complex A-series; complex B-series; axiom system; theory of time; tense; logical analysis; reconstruction of the consistency; A-series; B-series

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