Is validity a social construct?

Is validity a social construct? This question might seem preposterous or even absurd to some, but I feel like being a bit provocative this morning. In this post, I aim to examine whether the standards of logical coherence we adhere to might actually be shaped by social constructs.

Let's start with some context. The logic we refer to as "classical" in the twentieth century is somewhat of a misnomer. It's hardly the logic of the ancients. For instance, Aristotle, while not having a conditional, believed in existential import—that is, the idea that any true generalisation must have at least one true instance. The Stoics had a concept akin to the material conditional, but their logical arsenal was limited beyond that.

During the medieval period, logicians devised numerous unique and intriguing logics in an attempt to blend pagan philosophy with Christianity. The Enlightenment era primarily involved the revival of old texts and fragments. However, the logic of the twentieth century is distinct from these historical precedents. It was when mathematicians took the helm that a significant shift occurred, marked by a newfound obsession with consistency. That consistency was deemed the measure of logical coherence is not my point of contention here.

My query is whether validity, as we understand it, is a discovery by mathematicians, formalised to underpin consistency in mathematics, or if it's a construct developed by a specific group, in a particular context, with defined goals, to encapsulate and manage this concept of consistency.

From the outset, some mathematicians and philosophers have challenged conventional standards of validity. Consider the principle of the excluded middle. Is it inherently valid? Brouwer, along with constructive mathematicians and intuitionist logicians, crafted an alternate framework for validity that also aspires to uphold consistency. Similarly, the principle of explosion, which posits that anything follows from a contradiction, has been questioned. Relevant logicians and paraconsistent logicians have devised mathematical systems that break free from the traditional fixation on consistency.

Why this deviation? Perhaps it's because the preoccupation with consistency itself is a social construct. Returning to Aristotle, we find not a reasoned argument for non-contradiction, but rather a dogmatic declaration. His European successors echoed this sentiment, transforming a tenet into a belief, and eventually, a belief into dogma. It is this dogma that I propose is the root of the social construct of validity.

There you have it—a thought to ponder. Put it in your pipe and smoke it.