Lakatos' Quasi-Empiricism Revisited.

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 bottomup, 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. [ABSTRACT FROM AUTHOR]