The Logic of Relatives

Pragmatic Information

“…Valid referring relations, SπO, and all TNRs are true in the ordinary sense of "truth" because they conform to the normal conventional applications of their signs, S; they are narratives in all cases because it is impossible to refer to any particular material entity whatsoever apart from some context of experience that involves events unfolding over time; and they are representations because the S in each case invariably stands for something other than itself. It has been argued that TNRs are crucial to the discovery of pragmatic information in sign systems in general [7][8][9]. Because our world is so pervaded by valid SπO representations from the highest cortical processes downward, their very familiarity makes the pragmatic mapping of a name onto a certain person seem much simpler than it is.…”

An Argument for Systems Grammar

“…The problem this distinction presents for Chomsky is that possible worlds (as distinct from the real world) only have whatever properties may come from being represented but lack the peculiar particularities that come with being real. With respect to the intermediates between being and merely being represented, the relatively few phenomena that bridge the gap pragmatically are invariably TNRs (per proofs already cited, especially, Peirce, 1897;Oller, 1996aOller, , 1996b. TNRs are the only signs that connect the material and mental realms through real actions that syntactically link pragmatic (material entities, relations, etc., manifested in dynamic contiguities unfolding over time) with semantic categories (mental or conceptual entities, classes, sets, etc., manifested in similarities).…”

“…Some, notably Barsalou (1999), went so far as to suggest that perceptual symbol theory (a strong variant of embodiment theory) could dispense with abstract symbols by putting perceptual elements (icons of some sort) in their place. While it has been shown by strict mathematical logic that abstract symbols must be grounded at first in perceptual icons (Oller, 1996a;Peirce, 1897;and as implicit in Tarski, 1936and as implicit in Tarski, /1956and as implicit in Tarski, , 1944and as implicit in Tarski, /1949 which are accessed through indexes as argued empirically by Ballard, Hayhoe, Pook, and Rao (1997) and by Harnad (1990), this does not mean that fully abstract symbols can be entirely replaced by icons.…”

The Post‐Modern Transcendental of Language in Science and Philosophy

“…Peirce's contribution consists, indeed, in the proposal of an 'algebra of relations', correcting in a semiotic/semantic way the early formalistic proposal of an 'algebra of logic' by Ernst Schröder, without any necessary reference to a knowing, conscious subject [6], and consistent with his ontology of a 'semiotic naturalism' [9]. Edmund Husserl also shared this same criticism against Schröder formalism, almost in the same years, but independently from Peirce's semiotics.…”

“…Practically, all the objects and the operations that are usefully formalized in set theory, and then in calculus and logic-including the 'exponentiation' operation for forming function spaces, and the consequent 'evaluation function' over function domains-can be usefully formalized also in CT, with a significant difference, however. Instead of considering objects and operations for what they 'are' as it is in set theory, in CT we are considering them for what they 'do' [37, p. 53], 6 Effectively, the notion of duality is well-known in logic, mathematics and physics that are plenty of dual notions. For example, in mathematics, a function and its inverse are dual, just as 'and' and 'or' in logic, according to the De Morgan laws, or a function and its Fourier transpose in physics.…”