讲座预告 | Gregory Landini：Tractarian logicism 太阳集团城娱8722 2021-11-02 22:58

Speaker: Prof. Gregory Landini

Time: 11:00-12:30 am, Nov. 3rd, Beijing 

          (9:00-10:30 pm, Nov. 2nd, Iowa)

Zoom number: 881 627 22280

password: 488654

Chair: Prof. Zheng Wei Ping (Xiamen University)

Commentators: Prof. Zheng Wei Ping

Commentators: Dr. Bei Zhi En (Sun Yat-sen University)

Sponsors:

Chinese Society for Contemporary Foreign Philosophy (CSCFP)

Institution of Logic and Cognition & Department of Philosophy, Sun Yat-sen University

Prof. Landini has authored five books: Repairing Bertrand Russell’s 1913 Theory of Knowledge (Palgrave, 2021); Frege's Notations; what they are and how they mean (Palgrave/MacMillan 2012); Russell (Routledge, 2010), Wittgenstein’s Apprentice with Russell (Cambridge, 2007) and Russell's Hidden Substitutional Theory (Oxford, 1998). He has published many articles in the philosophy of logic and metaphysics. His teaching and research interests include modal logic, the foundations of mathematics, philosophy of mind, philosophy of language, and the history of analytic philosophy.

This presentation argues that Wittgenstein was a logicist, but held a uniquely Tractarian conception of logicism. Frege’s logicism held that arithmetic is a study conducted by the synthetic a priori science of the logic of functions which impredicatively assures the existence of functions. Numbers are logical objects (abstract particulars) correlated with functions. Whitehead-Russell logicism maintains that pure mathematics is a study conducted by the synthetic a priori science of logic which impredicatively assures the existence of relations in intension, and studies relational structures by studying relations independently of any contingencies of their exemplification. No branch of mathematics (not even geometry) involves abstract particulars (e.g., no numbers, geometric figures, classes/sets). Tractarian logicism rejects both, but is a hybrid maintaining that logic and mathematics are shown by the practice of calculating outcomes of recursive functions. In his view, Wittgenstein excludes abstract particulars, but rejects both the Russellian and Fregean sciences of logic in favor of recursive functions whose existence and operation are shown.