This webpage is intended to educate in an underappreciated area, namely the field of "Trivalent Logic." There are links to related areas in parts of this page.
Western thinking goes back to the times of ancient Greece, to the times of Aristotle. Then there were two schools of thought: the school of Aristotle, or the Stoic school, and the Epicurean school. Aristotle and the Stoics held that a statement, or proposition, is either true or false; nothing else. The Epicureans, however, held that a statement can be something else beside either true or false (1). Trivalent reasoning is founded upon the traditions of the Epicureans.
Examine the self-referential statement "This statement is false." If the statement is to be believed, and if it's false, then it seems true and if it's true, then it seems false. Such absurd conclusions derive from the belief that it is either true or false and nothing else. What trivalent reasoning does in this case is resolve the thinker to not believe the statement: the statement can be viewed as irrelevant, imaginary, neither true nor false, and both true and false, or unknown. What is both beautiful and important is that all four cases are perfectly reconcilable and analogical; that is, they pattern one another.
The Stoics held a bivalent logic, which is contrasted to the trivalent reasoning of the Epicureans. Today's thinking is a mix of bivalent and trivalent patterns. Take for example the colloquial statement, "He is as dumb as a door-nail." In bivalent logic, the statement is either true or false. In the trivalent logic, the statement is true, false, or something else. Indeed, because door-nails are not alive and the person would be, the "dumb as a door-nail" clause is irrelevant; the statement is of third value. Also, so-called "flawed" questions exist only within the bivalent framework, as there are no flawed questions in the trivalent framework.
To further illustrate the zeitgeist of trivalent reasoning, take the following examples:
The above cases largely occur in the subconscious and it is little recognized that there are precisely three options in each case. Such patterns exemplify the greater part of all human reasoning. This fact is probably the reason that humans have the natural efficiency that computers lack. Additionally, the major part of neurons in the human cerebral cortex have a tendency for precisely three main dendritic projections (2), which could correspond to the trivalent thought that subconsciously occurs. If the proportion of pyramidal to non-pyramidal neurons is any indication of trivalent or transvalent thinking - thinking that ranges between two and an arbitrarily large number of values - trivalent thinking could be as high as 80 percent and non-trivalent thinking as low as 20 percent.
Some have said that transvalent reasoning/logic divides bivalent logic into a spectrum of possibilities (3). If this is true, a nexus between the quantal probalistic realm and the microscopic realm of neurons could be found. Specifically, if both types of neurons function in multivalued logic, all neural activity could be classified and analyzed in terms of quantum mechanics. It happens that the statistics of quantum mechanics is a multivalued logic itself. For speculation about how this relates to psychosis, click "No psychosis".
It is predicted that the minimum number of projections in a neuron in an adult brain be limited to precisely two. Indeed, bivalent logic is predicted to correspond to the minimum number of projections since bivalent logic is the most minimalistic type.
All reasoning is a series of steps in a chain of conclusions. It turns out that Trivalent Reasoning reduces the average number of steps needed to reach any random conclusion. It thus streamlines thought into greater efficiency. It turns out that reforming thinking into precisely three intermediate possibilities per step greatly increases thinking efficiency (3). In other words, making trivalent reasoning more conscious, or direct, could also greatly improve thinking.
Here are some examples of the current trivalent subconscious zeitgeist that could realize great unifications:
The first example relates to Science. The second two examples relate to Humanity. The third two relate to the Universe. It is the author's opinion that such double-fold triunity is beautiful and it is not to the author's knowledge that such double-fold triunity has been ever noticed before.
With regard to the second case, the normal duality of Question and Answer is resolved into Truth - for that is exactly what that is - a fusion of a particular answer to a particular question. Also, the answer aspect lends an concretion to the Truth and the question aspect lends an abstraction to it. Thus, Truth is necessarily both objective and subjective. Possibly in the Future schools and colleges will administer tests based on not being necessarily true or false, but rather both being true and/or false. Also, perhaps being given two possibilities one will be able to provide the other missing one.
With regard to the third to last case, there ordinarily exist a series of dualities in Philosophy about the nature of Spirit and Matter. Some philosophers think that all can be resolved into Spirit, whereas others think that all can be resolved into Matter, or the physical. The impulse to unify exists in both cases, but it leaves two unresolved schools of thought. The school of the the Monists hold that all resolves into a third substance, or Energy. This is probably right, except for the impulse to unify. Yet others hold that all is already one and all is that left is to realize that.
For information on Philosophy and Metaphysics in a vein similar to the above, see Triunism
Questions? Comments? Objections? Please send any/all/none to mcampbell421 (at) yahoo.com.
(2) Refers to pyramidal neurons. See http://en.wikipedia.org/wiki/Pyramidal_cell
(3) Based on the principle that precisely three leaves per branch reduces the number of average steps to result in any average terminal leaf. See telephone menu system described on page four of Brian Hayes' "Third base": http://www.americanscientist.org/content/AMSCI/AMSCI/ArticleAltFormat/20035214317_146.pdf