The Indemonstrables of Chrysippus of Soli in Marlo logical diagrams. Could propositional calculus be nothing but syllogisms?
Marcos Bautista López Aznar
Abstract.
It has traditionally been considered that, while Aristotelian syllogism was limited to justifying a logic of terms, the indemonstrables established by the Stoics and Chrysippus of Soli (280 – 206 BC) laid the foundation for the validity of the logic of sentences. However, and thanks to the quantification of the predicate postulated by Hamilton and Jevons among others, we do not apply different principles when representing propositional calculus or Aristotelian syllogisms in our diagrams. The differences we find depend on what diagram we use, but not on what kind of logic we represent. Peirce claimed that reasoning is subject to the general laws of nervous action. In this regard, when representing the indemonstrables in Marlo expectations networks, which try to emulate the parallel processing related to the excitatory and inhibitory synapses of our neurons, it seems sufficient to appeal to the fact that by eliminating certain combinations their alternatives become necessary. However, in Marlo diagram, serial processes related to reasoning using verbal propositions take center stage: we reach conclusions by linking the middle term of the premises in the same way that we do in the syllogism, and in this case, reasoning is also subject to the general laws of communication.
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