A lot of my work can be reduced to the debate on essentialism, and of course, my book comes down on the side of non-essentialism. This is the idea that there are not universal ideas or categories to to label with a word. That language is not enough for inquiry or truth-seeking.
“When we define something, then, what we are really doing is drawing a circle around a set of objects. But this circle will always have blurry edges, because our language simply cannot be infinitely precise (nor need it be, most of the time).”
This looks like my consideration of Pierce’s circle as the only mark needed to do Aristotle’s logic.
The circle in this notation is the negation operation, or distinction. And I do argue that the marks used to make circles have blurry edges. I go a little further and say that because these logical marks have blurry edges, we can actually create different kinds of marks, that still count as a kind of distinction. Its like saying you don’t have to only use a scalpel or a pen to mark the circle around logical objects or reality to create identities or logical statements. There are many other tools you could use. Intuitionist logic has a different understanding of logical negation, so the way they mark the circle is different from the way Aristotelian logician marks a circle. And these are different from the ways paraconsistent logics slice up reality, in other words, paraconsistent logicians use different tools from just scalpels or pens to do their mental arrangements.
It is true that you can reduce these different tools to a single tool, for the most part. We would not be able to begin talking about different slicers that slice reality, (extending from the nonessentialist observation that there are different ways to slice reality) if we didn’t turn our scalpel on itself, or use another scalpel on it, to tamper with it and modify it. So you could say that all these tools depend on the scalpel. Doing that is like writing computer code and only using the if, then, elseif, else code for everything, without the many other tools like loops, and so many others. Or trying to talk about computers using only algorithms and no data structures, or vice versa. Pragmatically, it is better to talk about the different logics as different tools for slicing reality, rather than reducing them all to a single kind of scalpel.