In a 1978 lecture in Tokyo, Foucault drew a comparison between his own philosophical methodology and that of ‘Anglo-Saxon analytic philosophy’, claiming the label ‘analytic philosophy of politics’ for his own approach. This may seem like a somewhat surprising comparison given the gulf between contemporary analytic and continental philosophy, but I argue that it is a very productive one which indeed might help us reconsider this gulf. I proceed through a comparison between Foucault and the speech act theory of J. L. Austin, one of the analytic philosophers Foucault had in mind in his Tokyo lecture. By focusing on the methodological commonalities between Foucault and Austin, this article identifies the core of a philosophical methodology that cuts across the analytic/continental divide in philosophy in general while constituting a powerful alternative to the methods applied by analytic political philosophers specifically. This approach, which I term ‘analytic critique’, is one that starts from a critical analysis of what happens in ordinary lived experience and theorizes ‘bottom-up’ in an avowedly politically engaged way – thereby challenging the conceptual and political aloofness of contemporary political philosophy in the liberal-Rawlsian tradition. Foucault’s appropriation of the label ‘analytic philosophy’, it is argued, ought to function as a call to more imaginative methodological-theoretical engagement across the traditional division between continental and analytic approaches.