Humble Connexivity

Logic and Logical Philosophy 28 (2019)
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Abstract

In this paper, I review the motivation of connexive and strongly connexive logics, and I investigate the question why it is so hard to achieve those properties in a logic with a well motivated semantic theory. My answer is that strong connexivity, and even just weak connexivity, is too stringent a requirement. I introduce the notion of humble connexivity, which in essence is the idea to restrict the connexive requirements to possible antecedents. I show that this restriction can be well motivated, while it still leaves us with a set of requirements that are far from trivial. In fact, formalizing the idea of humble connexivity is not as straightforward as one might expect, and I offer three different proposals. I examine some well known logics to determine whether they are humbly connexive or not, and I end with a more wide-focused view on the logical landscape seen through the lens of humble connexivity.

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Citations of this work

The Evidential Conditional.Vincenzo Crupi & Andrea Iacona - 2022 - Erkenntnis 87 (6):2897-2921.
Strictness and connexivity.Andrea Iacona - 2021 - Inquiry: An Interdisciplinary Journal of Philosophy 64 (10):1024-1037.
Rewriting the History of Connexive Logic.Wolfgang Lenzen - 2022 - Journal of Philosophical Logic 51 (3):525-553.

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References found in this work

Connexive implication.Storrs Mccall - 1966 - Journal of Symbolic Logic 31 (3):415-433.
Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
Presuppositions and Antipresuppositions in Conditionals.Brian Leahy - 2011 - Proceedings of Semantics and Linguistic Theory:257-274.

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