This article is a preliminary draft. I'm publishing to help readers get a sense of the importance in understanding when traditional reasoning breaks down. This is an important issue in contemporary epistemology.
The conclusions I have come to are that Lucretius question on the limits of the knowable included a hidden (and false) assumption. When Lucretius' spear thrusts thru the boundary of the celestial sphere couldn't the celestial sphere stretch to accommodate it? My conclusions were also influenced greatly by the study of fractals. As one zooms in on a fractal boundary it retains elements of the original form yet is always changing. As if the boundaries are alive. My strong suspicion is that Aristotle's Law of the Excluded Middle is in error. The universe does not appear to me to really care about concrete true/false boundaries. In fact, as I have stated elsewhere, it seems to me that paradox must be built into the basic logical structure of reality for choice to exist. I hope to expand on this radical premise elsewhere but the corollary is that only process philosophy can resolve these issues in a meaningful manner.
Likewise re.: Göedel's Proof. Göedel's Proof states that in the set of all true theorems possible on the number field (here the term field is used in a formal mathematical sense) as rigorously described in (Saint) Alfred North Whitehead's and Bertrand Russell's seminal work, Principlia Mathematica, is either incomplete (meaning the set of all mathematically true propositions cannot be proven) or that set is inconsistent (meaning there are self contradictions within that set of true theorems). It has been a subject of some debate in the philosophy of mathematics but my conclusion is that what Goëdels proof means is that even the most rigorous intellectual treatment of logic ever devised breaks down.
"Logic? I'm sick to death of logic!", decried Spock's mother on the famous " Star Trek" series. Rightly so, I agree. Human thot & intellect incorporates more than just logic. Intuition, emotion, and paranormal phenomena all transcend the boundaries of logic. Aristotelian logic requires true premises to reach true deductions. Where do these premises come from?
I am not in any way proposing the abandonment of logic in intellectual pursuits. As a character I the often philosophical s.f. series quipped: "Science[logic] and faith[intuition, emotion] are like the shoes on your feet. You can travel farther with both than it just one." I am suggesting that there is more than just logical rigor needed in an intellectual exploration because, ultimately, logic breaks down. Temporarily adopting the term "mysticism" to incorporate these poorly defined categories of nonlinear thot such as emotion, I am hoping my fellow seekers recognize the limits of logic in their own explorations while continuing to use rigorous deduction whenever possible. Logic and Mysticism are like the two shoes on a thinker's feet. You can think farther with both than just one.
