Abstract

The central idea of Lakatos’ quasi-empiricism view of the philosophy of mathematics is that truth values are transmitted bottom-up, but only falsity can be transmitted from basic statements. As it is falsity but not truth that flows bottom-up, Lakatos emphasizes that observation and induction play no role in both conjecturing and proving phases in mathematics. In this paper, I argue that Lakatos’ view that one cannot obtain primitive conjectures by induction contradicts the history of mathematics, and therefore undermines his quasi-empiricism theory. I argue that his misconception of induction causes this view of Lakatos. Finally, I propose that Wittgenstein’s view that “mathematics does have a grammatical nature, but it is also rooted in empirical regularities” suggests the possibility to improve Lakatos’ view by maintaining his quasi-empiricism while accepting the role induction plays in the conjecturing phase.