Bonjour suggests something similar in In Defense of Pure Reason, p.5:
Could an argument of any sort be entirely justified on empirical grounds? It seems clear on reflection that the answer to this question is "no." Any purely empirical ingredient can, after all, always be formulated as an additional empirical premise. When all such premises have been explicitly formulated, either the intended conclusion will be explicitly included among them or it will not. In the former case, no argument or inference is necessary, while in the latter case, the needed inference clearly goes beyond what can be derived entirely from experience. Thus we see that the repudiation of all a priori justification is apparently tantamount to the repudiation of argument or reasoning generally, thus amounting in effect to intellectual suicide.
What response can the radical empiricist make to this?