In Alanzo Church's "A Formulation of the Simple Theory of Types" (The Journal of Symbolic Logic 5 no.2 (1940) 56--68, DOI:10.2307/2266170), he adopts the convention that terms of type $\iota$ are nonlogical constants (I presume $\iota$ is chosen because terms of this type are called "individuals"), and terms of type $\omicron$ are for truth values. More explicitly, Church states:

In the interpretation of the theory it is intended that the subscript shall indicate the type of the variable or constant, $\omicron$ being the type of propositions, $\iota$ the type of individuals, ... (56-57)

So it seems clear that $\iota$ specifically is chosen for "individuals".

I'm at a loss as to why $\omicron$ was chosen, and if there is a mnemonic meaning for it (just as "individual", shortened to "i", then converted to Greek gives us $\iota$).

Question: Is there a reason why $\omicron$ was chosen to denote the type of truth values?

  • $\begingroup$ IMO there is no "special" reason; most likely, the choice of $\iota$ (iota) and $\omicron$ (omicron) is due in analogy with the pair $1$ (one) and $0$ (zero), reserving the numerals for further use. $\endgroup$ Feb 26 at 14:13


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