Philosophy of logic/ Philosophical logic
As widely recognized, one of the important problems surrounding Aristotelian (assertoric) syllogistic theory concerns the logical role that singular propositions might play in this theoretical framework. This presentation will initially focus on this problem.
We'll show first that Aristotle's work doesn't provide an unambiguous answer to the problem. Then, we'll consider post-Aristotelian solutions, which assimilate singular propositions to categorical propositions. Although these solutions partially hit the target, we'll see that they lack a full semantic grounding. This grounding is required to constitute philosophically adequate elucidations of the issue.
An attempt to fill the above semantic gap might be conducted along the lines of Nino Cocchiarella's interpretation of singular propositions. His theory constitutes a sortalist approach to proper names and would provide the semantic foundation lacking in the post-Aristotelian proposals. However, as we'll point out, a Cocchiarellan-inspired solution wouldn't conform to the Aristotelian truth conditions for singular propositions. Moreover, this solution and, in general, any attempt to interpret singular propositions as categorical might conflict with Aristotle's view of universals.
The above difficulty leads us to explore the alternative of extending Aristotle's syllogistic to singular propositions, instead of attempting to assimilate them to categorical propositions. For this purpose, we'll propose two formal sortal logics that will capture such a syllogistic theory as extended to singular propositions. One of the systems is an axiomatic system, and the other a natural deduction system. We'll show that Aristotelian intuitions ground both systems.
During the last years, the discussion about the normative role of logic in human reasoning has raised a vigorous philosophical debate. Although it has traditionally been held that logic is normative for reasoning, a deeper inquiry has led to questioning this connection and even refuting the thesis that logic is a normative discipline (Russell, 2020). This reconsideration has been possible in light of the current theoretical developments in the philosophy of logic and the psychology of reasoning. Beginning with Harman's Skeptical challenge (Harman, 1986), and analyzing responses in the line of bridge principles to justify the normative constraints of logic for reasoning (MacFarlane, 2004), I propose to look at the core concepts involved in this debate. This analytical inquiry will make it possible to smooth the way to sketch out an argument for the normative role of logic for reasoning. The stance I try to defend is close to social naturalism, insomuch as it is supported by a dialogical characterization of normativity and reasoning ((Dutilh-Novaes, 2021; Dogramaci, 2015; MacKenzie, 1989).
Metainferences have recently come into focus as a useful way of analyzing substructural properties of logical consequences. as a new way to characterize a logic, as a way to analyze the debate between global and local validity, and as a toolkit for understanding abstract features of consequence relations. In this talk, I am going to discuss what are the connections between valid inferences and their valid metainferences. I will explore the notions of external and internal logical consequences in the context of mixed Many-Valued Consequences. Then, I present some substructural paraconsistent features that are part of some non-transitive logics. There are some paraconsistent elements that connect Priest's Logic of Paradox (LP) and the Strict-Tolerant approach ST: giving up Cut in the latter has as a consequence the loss of other metainferences, closely connected with Modus Ponens and Explosion labeled as Meta-modus Ponens and Meta-explosion. This feature can be generalized elaborating a new notion of paraconsistency.
The main topic for this talk is Everett Nelson's connexive logic. First, we will go through a brief overview behind the philosophical motivations for this system, including the various views Nelson held with regards to the validity of some well- known logical principles. Then, we will go over a relational semantics for the axiomatic system. We will find that a relational semantics reveals a clear picture of the behavior of the compatibility relation between propositions without being loaded with technical details, as it sometimes happens with possible worlds semantics.