By Paul R. Halmos
From the Preface: "Algebraic common sense [addresses] the various difficulties of mathematical good judgment and the idea of polyadic Boolean algebras, with which this quantity is usually involved. It is meant to be a good manner of treating algebraic good judgment in a unified demeanour. the cloth is out there to a basic mathematical viewers; no large wisdom of algebra or good judgment is required ... apart from a mild Boolean origin, the quantity is basically self-contained."
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Extra info for Algebraic logic
Methods and methodologies: an introduction 11 altogether. Echoing suggestions from A. Freddoso and C. Normore,21 Karger argued that what Ockham intends by the modes of personal supposition is a theory of inference, not a theory of quantification. Karger’s analysis is based on a reconstruction of Ockham’s theory, and like any reconstruction needs to be evaluated for its correctness if our goal is to get it right about what Ockham was doing. Briefly, Karger contends, the theory lays out a system of rules for determining the validity of inferences for categorical sentences that cannot be made to conform to the standard categorical forms.
30 Finally, the strictness of the quantificational comparison was questioned for Ockham’s supposition theory as a whole: perhaps Ockham is not trying to construct a system of quantificational analysis in our sense, but rather an algorithmic hermeneutics, providing a mechanism by which to generate possible readings of propositions from among which interpreters can choose the one they think best fits. If nothing else is clear at this stage, it is most certain that the debate over Ockham’s theory of supposition and the modes of personal supposition will continue.
While some single aspect or feature of some doctrine from the past might be picked out and rationally reconstructed without much contextual baggage, historical reconstructions are heavily weighed down by philosophical context. , Ockham, or Ockham and the Ockhamists). It might engage in 20 margaret cameron the careful, often highly tedious, examination of long-unread manuscripts authored by unfamiliar or unknown logicians, setting into meticulous context the details of logical theorizing of the past, and bringing these moments in the history of logic to a contemporary audience (although not necessarily in contemporary terms).