Uploaded October 2025 | Updated September 2026, 2 weeks ago
Title: The mathematical objection to artificial (machine) intelligence
Abstract: Alan Turing develops the idea of machine intelligence in a series of lectures and papers between 1947 and 1952. In some of them he addresses the mathematical objection (his term) whose gist is the claim that humans can assert some mathematical truths that exceed the abilities of computing machines. We first ask why Turing took so seriously the mathematical objection. After all, even if some humans surpass machines in their mathematical abilities, this by itself does not undermine the project of machine intelligence. Our answer is that the mathematical objection raises a dilemma with respect to Turing’s core claims about machine intelligence and forces him to relinquish at least one of them. We then clarify and discuss Turing’s reply to the mathematical objection, namely, that the machine that plays against the human in the Turing test is not a static machine but an enhanced machine.
(Joint work with Ben Gershon)
Title: The mathematical objection to artificial (machine) intelligence
Abstract: Alan Turing develops the idea of machine intelligence in a series of lectures and papers between 1947 and 1952. In some of them he addresses the mathematical objection (his term) whose gist is the claim that humans can assert some mathematical truths that exceed the abilities of computing machines. We first ask why Turing took so seriously the mathematical objection. After all, even if some humans surpass machines in their mathematical abilities, this by itself does not undermine the project of machine intelligence. Our answer is that the mathematical objection raises a dilemma with respect to Turing’s core claims about machine intelligence and forces him to relinquish at least one of them. We then clarify and discuss Turing’s reply to the mathematical objection, namely, that the machine that plays against the human in the Turing test is not a static machine but an enhanced machine.
(Joint work with Ben Gershon)
