The attribution of beliefs and other propositional attitudes is best understood as a form of measurement, however counter-intuitive this may seem. Measurement theory does not require that the thing measured should be a magnitude, or that the calibration of the measuring instrument should be numerical. It only requires a homomorphism between the represented domain and the representing domain. On this basis, maps measure parts of the world, usually geographical locations, and 'belief' statements measure other parts of the world, namely people's aptitudes. Having outlined an argument for this view, I deal with an obvious objection to it: that self-attribution of belief cannot be an exercise in measurement, because we are all aware, from introspection, that our beliefs have an intrinsically semantic form. Subsequently, I turn to the philosophical and methodological ramifications of the measurement theoretic view. I argue, first, that it undermines at least one version of constructivism and, second, that it provides an effective alternative to the residually Cartesian philosophy that underpins much qualitative research. Like other anti-Cartesian strategies, belief-attribution-as-measurement implies that the objective world is far more knowable than the subjective one, and that reality is ontologically prior to meaning. I regard this result as both plausible and welcome.