Abstract
We study a contemporary need to complement analytic philosophy with pendular, synthetic approaches. We provide new definitions of the dyad analytics/synthetics and complete it with a natural third, horotics. Some historical trends to support a synthetic/horotic paradigm are studied: (i) Peirce’s ideas around his logic of continuity – non Cantorian continuum and existential graphs – emphasizing the importance of mathematical gestures, (ii) Gödel’s understanding of intuitionism as a synthetic counterpart of classical logic, along with a new horotic approach to his work, (iii) Contemporary mathematical achievements (1950-2000), difficult to understand from analytical philosophy perspectives. Finally, we indicate some main features that a systematical synthetic/horotic reasoning should enforce, in order to fulfill its historic sequence.
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