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Revision as of 15:24, 26 January 2009
, 15:24, 26 January 2009→Syntactic Transformations: math markup + clarify new form of annotation
A large stock of rules can be derived in this way, by chaining together segments that are selected from a stock of previous rules, with perhaps the whole process of derivation leading back to an axial body or a core stock of rules, with all recurring to and relying on an axiomatic basis. In order to keep track of their derivations, as their pedigrees help to remember the reasons for trusting their use in the first place, derived rules can be annotated by citing the rules from which they are derived.
A large stock of rules can be derived in this way, by chaining together segments that are selected from a stock of previous rules, with perhaps the whole process of derivation leading back to an axial body or a core stock of rules, with all recurring to and relying on an axiomatic basis. In order to keep track of their derivations, as their pedigrees help to remember the reasons for trusting their use in the first place, derived rules can be annotated by citing the rules from which they are derived.
In the present discussion, I am using a particular style of annotation for rule derivations, one that is called ''proof by grammatical paradigm'' or ''proof by syntactic analogy''. The annotations in the right hand margin of the Rule Box interweave the ''numerators'' and the ''denominators'' of the paradigm being employed, in other words, the alternating terms of comparison in a sequence of analogies. Taking the syntactic transformations marked in the Rule Box one at a time, each step is licensed by its formal analogy to a previously established rule.
For example, the annnotation <math>X_1 : A_1 :: X_2 : A_2\!</math> may be read to say that <math>X_1\!</math> is to <math>A_1\!</math> as <math>X_2\!</math> is to <math>A_2,\!</math> where the step from <math>A_1\!</math> to <math>A_2\!</math> is permitted by a previously accepted rule.
This can be illustrated by considering the derivation of Rule 3 in detail.
<pre>
<pre>
R3a. "u C X" is to R1a, namely, "u C X",
R3a. "u C X" is to R1a, namely, "u C X",
as
as
