Following the relational and mythic mapping of early Greek cosmology, the Pythagorean and Platonic traditions introduced a decisive abstraction of cosmic order through mathematics and harmony. Possibility was no longer apprehended solely through observation or narrative; it became structured, intelligible, and amenable to formalisation. The cosmos itself was construed as an ordered field, a system in which potentialities resonated according to principles of proportion, symmetry, and relational consistency.
Pythagoras and his followers emphasised number as the generative principle of possibility. The ratios underlying musical intervals were not merely auditory phenomena; they were reflections of cosmic order. The very structure of potential — what could occur, align, or harmonise — was thought to be encoded in numerical relations. In this sense, mathematics became both the medium and the measure of construal, offering a universalised framework in which possibility could be articulated and anticipated.
Plato extended this approach in his cosmology and metaphysics, positing the cosmos as an intelligible whole governed by forms, harmonics, and geometric order. In the Timaeus, the cosmos is presented as a living, rational entity, where the “world-soul” organises matter according to harmonious proportions. Potentiality is therefore not arbitrary; it is embedded within relational structures that define what is possible, coherent, and aesthetically resonant. The cosmos becomes a field in which constraints and freedoms are simultaneously specified by the underlying mathematical-harmonic order.
This period marks a critical shift in construal: the cosmos is no longer merely relational in the mythic sense, nor solely observed for patterns; it is rationalised and formalised. Possibility is now understood as structural resonance, actualisable when elements align according to pre-existing mathematical relations. The horizon of potential expands in abstraction, yet remains deeply relational, reflecting the interplay between number, proportion, and cosmic intelligibility.
In sum, the Pythagorean and Platonic innovations inaugurate a cosmos in which mathematics mediates, constrains, and enables possibility. Potential is not unbounded: it is relationally structured, intelligible, and harmonically coherent. The musical cosmos establishes a paradigm in which human thought can apprehend, anticipate, and participate in the unfolding of cosmic potential — a pattern of construal that will echo through Aristotle, the medieval synthesis, and the mechanistic universes of early modern science.