There are two main aims of this thesis: the first is to demonstrate that

there is an important version of empiricism - "methodological empiricism"

- which is a central part of the empiricist tradition but has been neglected in

current philosophy of science. The second aim is to develop methodological

empiricism in light of current science. The first aim is met by first articulating

what I take methodological empricism to mean, alongside articulating the

more dominant version of empiricism - "epistemic empiricism". I explicate

both via several characteristics for each, and then trace a history of both

positions from Ancient Western philosophy up until current times. Finally,

I give evidence of the neglect of methodological empiricism in current

philosophy of science. The second aim is met by, first, presenting four criteria

for a current version of methodological empiricism that are directly derived

from the characteristics of methodological empiricism through its history. I

then consider three topics within recent philosophy of science that prima facie

pose a challenge to methodological empiricism, all of which can be broadly

characterised as appearing to be non-empirical in some way - analogue

confirmation, philosophy of computer simulations, and non-empirical theory

confirmation. It is argued that, ultimately, analogue confirmation and

computer simulation are compatible with methodological empiricism, but

that non-empirical theory confirmation is not. I argue that this should gives

us good reason to reject non-empirical theory confirmation.