In this paper I argue that Turing’s responses to the mathematical objection are straightforward, despite recent claims to the contrary. I then go on to show that by understanding the importance of learning machines for Turing as related not to the mathematical objection, but to Lady Lovelace’s objection, we can better understand Turing’s response to Lady Lovelace’s objection. Finally, I argue that by understanding Turing’s responses to these objections more clearly, we discover a hitherto unrecognized, substantive thesis in his philosophical thinking about the nature of mind.