Thank you for our article on paraconsistent mathematics and for the effort to make these ideas broadly available. I am not a mathematician, but a student of Zen Buddhism., which since ancient times has explored the nature of paradox and mental constructs regarding reality. In Buddhism, a distinction is drawn between relative truth and absolute truth. Relative truth is the world of everyday distinctions, in which statements about true and false are made. The nature of that world is one of observer and objects, an ego identity which arises in the act of discrimination between, for example, "true" and "false." That is also the world of conceptual thought. The absolute, however, embraces all three elements of relativity: the self, the object of attention ("true") and the subject source of comparison ("false"). From the standpoint of the absolute, the self arises in the act of discrimination, together with subject and object. In other words, the absolute is a world of paradox that can be experienced, but which defies conceptual thought. For example, "true" and "false," from the standpoint of conceptual thought, exist as distinct entities. Something is one or the other, and such distinctions are functionally necessary for ego identity and success in such matters as crossing the street. However, from an absolute perspective, the needs of ego identity are not paramount; and "true" and "false" turn out to be matters of personal or societal convention, with no other claim to existence than comparison one to the other. All of human consciousness is like this, founded on distinctions carved out of a universe in which all paradox, all of plus and minus, add up to zero.
Regarding "This sentence is false," the phrase asserts being in the word "is," and non-being in the word "false." I suppose it is like saying, "I am dead." How can I be alive and dead at the same time? It makes no sense. And yet, from an absolute standpoint, that paradox is exactly the situation. I both "am" and I "am not." Both life and death are my nature. Both creation and destruction are happening in every moment. Indeed, it is only in accepting death that I live without fear. It is the ego self that fears dissolution that argues against such paradox.