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Functional Logic • Inquiry and Analogy • 13
Inquiry and Analogy • Higher Order Propositional Expressions Higher Order Propositions and Logical Operators (n = 2) By way of reviewing notation and preparing to extend it to higher order universes of...
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Functional Logic • Inquiry and Analogy • 14
Inquiry and Analogy • Umpire Operators The measures of type present a formidable array of propositions about propositions about 2‑dimensional universes of discourse. The early entries in their...
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Functional Logic • Inquiry and Analogy • 15
Inquiry and Analogy • Measure for Measure Let us define two families of measures, by means of the following equations: Table 14 shows the value of each on each of the 16 boolean functions In terms of...
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Functional Logic • Inquiry and Analogy • 16
Inquiry and Analogy • Extending the Existential Interpretation to Quantificational Logic One of the resources we have for this work is a formal calculus based on C.S. Peirce’s logical graphs. For now...
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Functional Logic • Inquiry and Analogy • 17
Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Our excursion into the expanding landscape of higher order propositions has come round to the point where we can...
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Functional Logic • Inquiry and Analogy • 18
Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Last time we took up a fourfold scheme of quantified propositional forms traditionally known as a “Square of...
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Functional Logic • Inquiry and Analogy • 19
Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Reflection is turning a topic over in various aspects and in various lights so that nothing significant about it...
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Functional Logic • Inquiry and Analogy • 20
Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Table 21 provides a thumbnail sketch of the relationships discussed in this section. Resources Logic Syllabus...
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Functional Logic • Inquiry and Analogy • 21
Inquiry and Analogy • Generalized Umpire Operators To get a better handle on the space of higher order propositions and continue developing our functional approach to quantification theory, we’ll need...
View ArticleSurvey of Precursors Of Category Theory • 4
A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to...
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