The study begins with the arguments used by Th. Cole and L. Schiappa for their well-known position regarding Plato’s influence upon the genesis of theory of rhetoric in ancient Greece. According to Cole and Schiappa, theory of rhetoric as a special discipline was made possible by the birth of metaphysical philosophy and its outlining of a basic theoretical frame in which theoretical rhetoric could be placed as a formal discipline pertaining to the extra-informative dimension of logos-as-style aside from the true, informative knowledge of things reflected in logos-as-philosophy. Subsequently the article discusses four treatises preserved in the Hippocratic collection: these are the De carnibus, De flatibus, De arte and De vetere medicina (mostly written in the form of a speech, and thus classified as rhetorical Hippocratic writings). We focus our attention on the reflexive procedures and terminology which the authors use to refer to the construction of the text itself. This reflexive feature, embracing both the form and the content of a text, is captured by the term hupothesis and the verb hupotithesthai. Surprisingly, the same term hupothesis denotes the all-knowing and all-pervading materialized cosmic mind. This cosmos-structuring principle, known from the late Ionic cosmology of Anaxagoras of Clazomenae, Archelaus of Athens and Diogenes of Apollonia, thus also functions as a text-structuring principle. This compositional function can be observed in the parallel texture of the treatises De carnibus and De flatibus, where the cosmological principle certifies its validity insofar as it is able to embody in a cosmological narrative all the partial topics characteristic for the broad encyclopaedic scope of Greek pre-metaphysical thought. On the other hand, only speech makes obvious the causal and other connections between partial things and structures. This method of making invisible things visible and observable by means of speech became an important part of the self-understanding of early Greek rhetoric. Similarly, the all-governing power of the cosmic mind served as a model for the universal power of speech, lauded by Gorgias. Thus, the late “Anaxagorean” phase of Greek cosmology was a clearly discursive practice, a reflected way of constructing a “physical” prose. Plato’s later attempt to reformulate rhetoric as a special formal discipline and to subordinate it to the new metaphysical philosophy largely neglects this discursive feature of late cosmology.