Posted By Confutus

My attempted change to more political blogging didn't go well. I also switched from working directly on my knowledge base to more computer programming. Then I decided to move from West Virginia to Phoenix, Arizona, and getting moved and established took higher priority than blogging.

 

One of the things I've been wanting to do for a while was to resume my studies in logic. I e-mailed a professor at ASU, who didn't sound very interested. That..peeves me, every time. So I decided to begin with reviewing my research.  I went out to ASU to the library to look up some old references, and take some notes.

My work is a new extension of the 3-valued logic of Jan Lukasiewicz, which he presented in 1921, so I looked up where I could find it. There are a couple of sources for an English translation, the better one was:

Jan Lukasiewicz: Selected works

Ed. Ludwig Borkowski

North Holland, Amsterdam, 1970

 

The paper "On Three Valued Logic"  (p 87-88 in Selected Works) provides conventional definitions for the conditional, logical equivalence, conjunction (and) and disjunction (or), and negation, and then three-valued versions of the same. I have determined that these definitions are inadequate, but they can be supplemented based on concepts he describes later. 

One thing he notes immediately is that some of the laws of classical two-valued logic do not hold in the three-valued version, notably principles of bivalence and the excluded middle, and makes the claim that "in three valued logic there are no antimonies", (or paradoxes). This is not quite the case; there are numerous problems with statements that are true and useful in classical logic that fail in the three valued version. Why they fail is work examination. For instance, he notes that  the common rule "If A implies B and B implies C then A implies C, which applies in classical logic,  fails in the three valued logic. In order for this logic to be useful for logical purposes, common rules of reasoning need to be at least explored and explained.


 
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