 McCall emphasizes that the logic CC1 is only one among many possible systems satisfying the theses of Aristotle and Boethius. Although CC1 is a system of connexive logic, its algebraic semantics appears to be only a formal tool with little explanatory capacity. In CC1, the constant truth functions 1, 2, 3, and 4 can be defined as follows (McCall1966, p. 421): 1 := (p → p), 2 := ~(p ↔ ~p), 3 := (p ↔ ~p), 4 := ~(p→ p), for some sentence letter p. As Routley and Montgomery (1968, p. 95) point out, CC1 “can be given a semantics by associating the matrix value 1 with logical necessity, value 4 with logical impossibility, value 2 with contingent truth, and value 3 with contingent falsehood. However, many anomalies result; e.g. the conjunction of two contingent truths yields a necessary truth”. Moreover, McCall points out that CC1 has some properties that are difficult to justify if the name ‘connexive logic’ is meant to reflect the fact that in a valid implication A → B there exists some form of connection between the antecedent A and the succedent B. Axiom A4, for example, is bad in this respect. On the other hand, CC1 might be said to undergenerate, since (A ∧ A) → A and A → (A ∧ A) fail to be theorems of CC1. Routley and Montgomery (1968) showed that the addition of the latter formulas to only a certain subsystem of CC1 leads to inconsistency. For a defense of Angell’s PA1 against Routley and Montgomery’s critical observations see Bode 1979.