This new volume on logic follows a recognizable format that
deals in turn with the topics of mathematical logic, moving from
concepts, via definitions and inferences, to theories and axioms.
However, this fresh work offers a key innovation in its 'pyramidal'
graph system for the logical formalization of all these items. The
author has developed this new methodology on the basis of original
research, traditional logical instruments such as Porphyrian trees,
and modern concepts of classification, in which pyramids are the
central organizing concept. The pyramidal schema enables both the
content of concepts and the relations between the concept positions
in the pyramid to be read off from the graph. Logical connectors
are analyzed in terms of the direction in which they connect within
the pyramid.
Additionally, the author shows that logical connectors are of
fundamentally different types: only one sort generates propositions
with truth values, while the other yields conceptual expressions or
complex concepts. On this basis, strong arguments are developed
against adopting the non-discriminating connector definitions
implicit in Wittgensteinian truth-value tables. Special
consideration is given to mathematical connectors so as to
illuminate the formation of concepts in the natural sciences. To
show what the pyramidal method can contribute to science, a pyramid
of the number concepts prevalent in mathematics is constructed. The
book also counters the logical dogma of 'false' contradictory
propositions and sheds new light on the logical characteristics of
probable propositions, as well as on syllogistic and other
inferences.
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