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Peirce’s 1870 “Logic of Relatives” • Comment 11.9

PNG

Definitions 1

Definitions 1

Definitions 2

Definitions 2

Definitions 3

Definitions 3

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Dyadic Relation F

Dyadic Relation F
\text{Figure 39. Dyadic Relation}~ F

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Definitions 1

\begin{array}{lll}  P ~\text{is total at}~ X & \iff & P ~\text{is}~ (\ge 1)\text{-regular at}~ X.  \\[6pt]  P ~\text{is total at}~ Y & \iff & P ~\text{is}~ (\ge 1)\text{-regular at}~ Y.  \\[6pt]  P ~\text{is tubular at}~ X & \iff & P ~\text{is}~ (\le 1)\text{-regular at}~ X.  \\[6pt]  P ~\text{is tubular at}~ Y & \iff & P ~\text{is}~ (\le 1)\text{-regular at}~ Y.  \end{array}

Definitions 2

\begin{array}{lll}  P ~\text{is a pre-function}~ P : X \rightharpoonup Y & \iff & P ~\text{is tubular at}~ X.  \\[6pt]  P ~\text{is a pre-function}~ P : X \leftharpoonup Y & \iff & P ~\text{is tubular at}~ Y.  \end{array}

Definitions 3

\begin{array}{lll}  P ~\text{is a function}~ P : X \to Y & \iff & P ~\text{is}~ 1\text{-regular at}~ X.  \\[6pt]  P ~\text{is a function}~ P : X \leftarrow Y & \iff & P ~\text{is}~ 1\text{-regular at}~ Y.  \end{array}

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Figure 39

LOR 1870 Figure 39 (39)