Inquiry and Analogy • Higher Order Propositional Expressions

Higher Order Propositions and Logical Operators (n = 1)

A higher order proposition is a proposition about propositions.  If the original order of propositions is a class of indicator functions then the next higher order of propositions consists of maps of type

For example, consider the case where   There are exactly four propositions one can make about the elements of   Each proposition has the concrete type and the abstract type   From that beginning there are exactly sixteen higher order propositions one can make about the initial set of four propositions.  Each higher order proposition has the abstract type

Table 11 lists the sixteen higher order propositions about propositions on one boolean variable, organized in the following fashion.

• Columns 1 and 2 taken together present a form of truth table for the four propositions   Column 1 displays the names of the propositions for = 1 to 4, while the entries in Column 2 show the value each proposition takes on the argument value listed in the corresponding column head.
• Column 3 displays one of the more usual expressions for the proposition in question.
• The last sixteen columns are headed by a series of conventional names for the higher order propositions, also known as the measures for = 0 to 15.  The entries in the body of the Table show the value each measure assigns to each proposition

Resources

• Logic Syllabus
• Boolean Function
• Boolean-Valued Function
• Logical Conjunction
• Minimal Negation Operator
• Introduction to Inquiry Driven Systems
• Functional Logic • Part 1 • Part 2 • Part 3
• Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History

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