In this paper, we defend the main claims of our earlier paper “Mental Fictionalism as an Undermotivated Theory” (in The Monist) from Gábor Bács’s criticism, which appeared in his “Mental fictionalism and epiphenomenal qualia” (in Dialectica). In our earlier paper, we tried to show that mental fictionalism is an undermotivated theory, so there is no good reason to give up the realist approach to the folk psychological discourse. The core of Bács’s criticism consists in that our argumentation rests on an equivocation concerning the folk psychological concepts of conscious experiences. In our present argumentation, at first, we shortly recapitulate our earlier argumentation and Bács’s main objection to it. After that, we argue against the case of equivocation, claiming that it rests on a highly implausible and unsupported verificationist approach. Lastly, in answering another remark of Bács’s, we discuss the possibility of a realist mental fictionalism and conclude that it is an incoherent standpoint.
Let $\mathbb {B}_{k}$ be the general Boolean algebra and $T$ a linear operator on $M_{m,n}(\mathbb {B}_{k})$. If for any $A$ in $M_{m,n}(\mathbb {B}_{k})$ ($ M_{n}(\mathbb {B}_{k})$, respectively), $A$ is regular (invertible, respectively) if and only if $T(A)$ is regular (invertible, respectively), then $T$ is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over $\mathbb {B}_{k}$. Meanwhile, noting that a general Boolean algebra $\mathbb {B}_{k}$ is isomorphic to a finite direct product of binary Boolean algebras, we also give some characterizations of linear operators that strongly preserve regular (invertible, respectively) matrices over $\mathbb {B}_{k}$ from another point of view.