He actually says "I do not believe in the primacy of the scientific method as a source of knowledge", and later, that [in order to successfully advance a particular scientific field] we need to "admit the presence and value of non-scientific knowledge". The nature of this non-scientific knowledge is not entirely clear from the essay but seems to be some mixture of culture and common sense.
He throws out several such claims without addressing the problems that come along with accepting non-quantifiable or non-scientific knowledge into a traditionally scientific discipline. For example, if you make a hypothesis that is not quantifiable, how can you determine the degree to which your data supports it?