Browsing by Author "Payette, Gillman"

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    A study in the logic of institutions
    (2012-07-13) Payette, Gillman; Zach, Richard
    In my dissertation A Study in the Logic of Institutions I develop a logical system for reasoning about institutions and their consistency. Since my dissertation is a work in logic rather than one in socio-political philosophy, I don’t defend a particular theory of institutions. Instead, I did as Yogi Bera suggested and simply took the fork in the road. A well-developed account of institutions is given by John Searle in (1995); and (2010). His account bases all social reality on language, and I use his account to provide a logic for institutional norms. Briefly, social reality is constructed via language by making our intentions clear to one another. And we do this via speech acts. There is one particular type of speech act that is important to institutions: declarations. Declarations bring about new social objects and create social states of affairs. It is via declarations that social institutions are created. In so far as groups recognize an institution sustaining/making authority, that authority has the ability to generate new institutional rules via declarations. According to Vanderveken (1990, 1991); see also Searle and Vanderveken (1985), speech acts have a logic. That is, performing one speech act can satisfy the conditions of having performed another speech act. A priest declaring a baby baptized will also make it so that the priest has asserted that the baby is baptized, for instance. More importantly, certain declarations will result in the declarations of some of the logical consequences of the initial declarations. I characterize the set of speech acts that stand in that relationship and develop a logical system around that characterization. The formal framework incorporates action and permits representations of complex institution-dependent relations, e.g., rights and duties. I further develop this formalism to investigate the notion of normative consistency. I show how to represent at least a minimal conception of normative inconsistency within the formal framework, and characterize its properties. I conclude by comparing my work to that of others.
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    Counterfactual Logic: A Modern Overview
    (2024-01-26) Rios Flores, Mohamar; Bauer, Kristine; Zach, Richard; Cunningham, Clifton; Payette, Gillman
    Lewis (1973) described a family of logics for reasoning about counterfactual statements. These logics also contained additional connectives for reasoning about comparative possibility statements and modalities. Moreover, Lewis described a possible world semantics involving a ``sphere system'' that effectively lets you talk about some worlds being more ``similar'' to a given world than others. The resulting theory is very powerful and flexible in many ways similar to the theory of normal modal logics. Unfortunately, Lewis provided an extremely terse formal description of the theory with many important theorems, definitions, and details omitted or described vaguely. There are no other resources that present a complete formal description of this theory. Without this formal description one is unable to propose new logics in this family and prove soundness and completeness theorems for them. To remedy this, we present a reformulation of Lewis' theory using modern methods and notation. All definitions are described formally and all core results are proven in explicit detail. We include an informal overview of the different kinds of statements associated with each connective. The semantics is reformulated in terms of frames. The syntax includes additional rules and theorems to make it easier to use. Both the soundness and the strong soundness theorems are proven. The completeness theorem uses canonical models and the entire construction is shown explicitly. The first edition of Counterfactuals (Lewis, 1973) had an error exposed by Krabbe (1978) that led to the second edition (Lewis, 2001) having a more complex definition. So we present a reformulation of Krabbe's construction within our modernized setting.
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    Ramification, Structure and Ground
    (2023-07) Kiani, Amirhossein; Zach, Richard; Zach, Richard; Fantl, Jeremy; Liebesman, David; Payette, Gillman; Linsky, Bernard
    This dissertation sets out to explore a deep interconnection between highly structured relational entities, various notions of grounding and ramified typed systems. It is argued that together these three form a powerful alliance that contributes to a unified picture of reality within which a cluster of recent puzzles of ground and grain can be resolved.