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    May 2008
    The word "homology" (from Greek for "agree") once meant a relation
    between for terms, say, A:B::C, "A is to B as C is to D".
    Equivalent ratios have this form: "1:2::3:6" for "1/2 = 3/6".--As
    such, it is a powerful tool for TESTING, say, MULTIPLE-CHOICE
    TESTING. Thus, "___ is to human body as wheel is to vehicle", and
    among "choices" is "leg".--But, stated as "leg is to human body as
    wheel is to vehicle", a child is TAUGHT that "just as the leg
    propels bodily motion so the wheel propels a vehicle".--Knowing
    that ENERGY activates the PHYSICAL, one may look for and DISCOVER
    that which activates the BIOLOGICAL.--But (alas!) the term
    "homology" has been taken over for an advanced concept in ALGEBRAIC
    TOPOLOGY. So I have relabeled the above "prescriptions" as
    "homalence" for "homology equivalence". (I rejected my first choice
    of "homolence" because of the pejorative use of "homo".)--I've done
    so after finding, online, the idea that humans may have a cognitive
    ability for explicating EQUIVALENCE RELATIONS between pictograms or
    logograms. Apparently the idea derives from M. Sidman as explained
    in his 1994 book, "Equivalence Relations and Behavior: A Research
    Story". This has motivated many tests, listed online, apparently
    providing evidence of this cognitive ability. In one online article,
    "Equivalence Relations in Invividuals with Limited Verbal Repertoires",
    by D. Carr, et al, it is remarked, "In Sidman's view, language learning
    may depend in part upon the emergence of equivalence relations."--My
    connection is that testees are presented with sets of four pictograms
    or logograms or mixtures to see if they can explicate what are,
    essentially, homalences of them. That is, the testers look to see if
    testees, in matching, implictly achieve homalences which, in turn,
    explicitly satisfy SYMMETRY and TRANSITIVITY conditions on EQUIVALENCE RELATIONS. (The REFLEXIVITY condition is assumed as understood.)--In another online article, "General Symbol Machines" by Thomas E. Dickins, School of Psychology, University of East London, U. K., a cognitive mechanism in each human is proposed, described, defended. Dickins cites "The Symbolic Species: The Co-evolution of Language and the Human Brain" by T. W. Deacon (1997). From semiotist C. S. Peirce, Deacon takes sequence of icon, index (indicator), symbol as development of language process. (Wikipedia ays, "Language is the medium of symbolic thought, but how can one master language withou being able to think symbolically first? The solution of this ...
    problem, according to Deacon, is the subtle evolutionary process
    of co-evolution".)--The critical sign is symbol (with assigned reference)
    which allows humans to overcome space-time limits and imagine as yet
    unknown possibilities or even impossibilities. Deacon goes beyond
    Peirce, who regards Symbol as Sign With Assigned Reference, to consider a RELATING OF SYMBOLS. A reviewer said he should connect this with SENTENCE. This, in Grammar, is what logicians-mathematicians call a WELL-FORMED-FORMULA (WFF). Wikipedia notes, a Formal Language is equivalent to its WFFs. A proof is a sequence of WFF, ending with the WFF to be proven. In the logic of statements (declarative sentences capable of verifying as "true" or "false'), a simple statement (lacking conjuction, disjunction, conditional, biconditional, negation) is a WFF; a conjunction, disjunction, conditional, bicobditional of two WFFs is a WFF; the negation of a WFF is a WFF. Nothing is a statement WFF unless subsumed under the prevous Rules (Closure).--So it's suggested that Deacon needs the equivalent of WFF to achieve CLOSURE on his Symbolic Process.--Deacon thought of the Symbolic Process as a CHAIN OF ICONS equivalent to the CONDITIONED RESPONSE of Ivan Pavlov. The latter has the structure of a LOGICAL CONDITION: IF cONDITIONED STIMULUS, THEN CONDITIONED RESPONSE.--This CONDITIONAL structure connects with another of my work, described herein as "ASSERBILITY" and in a website, Google("asserbility+jonhays"). The ASSERBILITY Measure relates to
    STATMENTS as PROBABILITY MEASURE relates to EVENTS (a homalence!), so these measures are interchangeable. Given tatuology MODUS PONENS (MP) as ((If Hypothesis then Prediction) and H. is true) then P. is true. This is varied: ((If Hypothesis then Prediction) and P. is confirmed) then P is true. An ASSERBILITY FORMULA allows multiple Hypotheses and Predictions. (MP equals 1.) But, for ONE HYPOTHESIS yielding many CONFIRMED PREDICTIONS, the A. Measure is approaching the TOTALITY of 1, that pf MP. Various Theorems follow from the FORMULA.--Then a COMMUNICABILITY Measure can be formed.--Hence, HOMALENCE FOR TESTING, LEARNING, TEACHING, DISCOVERY, COMMUNICABILITY.

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