Validity, Logic, and Models
Pepijn Vrijbergen
Abstract:
This thesis is an investigation into the nature of logic and validity. The motivating intuition is that we could understand why the intuitionist should come to their conclusions, even if we were Platonists ourselves. According to the standard account, an argument is valid only if it preserves truth in all Tarskian models due to logical form. Although information necessarily has logical structure, we argue, with Szabó [2012] and Brandom [1994], that the restriction of validity to “formal” arguments is hard to defend. Moreover, existing proposals to demarcate the logical constants by means of invariance are uncomfortably circular.
Furthermore, the Tarskian tradition focuses exclusively on particular set-theoretic structures. However, many reasoning problems require other models and therefore alternative logics, such as intuitionistic and relevance logic, modal logics, closed-world reasoning, and finite logics for computer science. Besides, Stenning and Van Lambalgen [2012] have shown that although people often don’t conform to the standards of classical logic, they turn out quite consistent if we model their reasoning using other systems.
The core of this thesis is that an argument is valid if it necessarily preserves truth on the model of interest. I will argue that models are indispensable for thought and that necessity can be explained by the stability of models. The most basic models (of the “ordinary world”) determine the construction of scientific and mathematical models and vice versa in a dialectical process. Logics are systems that capture patterns of valid arguments on types of models by focusing only on expressions that have a central role in logical structure. Normativity comes in at the level of constructing the right model and at the level of evaluating arguments on the model. The resulting position is a task-relative logical pluralism.