involved in creating them . Luckily , others were sufficiently straightforward to be analysed in the space available , while still demonstrating a to reasonable degree the true power of Dodd ’ s system .
An example of one of Dodd ’ s 85 rules for creating a formula is shown below : Rule # 8 : Are different combinations of T , I , L or P involved ? An index ( I ) may be written when such a combination is further aggregated by other indices [ with any necessary subscripts and / or superscripts ]. ( Dodd 1942 , 904 )
This rule is crucial to S-theory ’ s power and flexibility , but hides its true ingenuity . What Dodd is saying here is that any component of an S-formula can itself be an S-formula as a subcomponent of a larger , more complex formula , creating the opportunity to use recursion to any depth . To give an analogy from English , if a sentence uses a noun , the noun can be substituted by a noun phrase , and any nouns present in the noun phrase can be further substituted by other noun phrases . This process can be carried out without limit , and is a feature of natural languages , such as English , Mandarin and Hindi , but also of all of the five to ten thousand other languages known . Critically , it is what creates the expressive power which they all share , and intriguingly forms a developmental change in the language acquisition of children , Before the age of around 30 months , a child uses a very simple linguistic structure in which subclauses are absent , exemplified by ungrammatical requests such as “ Give me bottle ” and in this case representable as < imperative verb >< subject >< object >. After about this age , however , each component of a request can itself have an inner structure , for example becoming “ Give me bottle on table ”, in which the original noun had been substituted by a phrase , and , crucially , which itself can have further substitutions . In the example above ‘ table ’ could instead be ‘ little table ’. Recursion therefore turns a finite set of words , or symbols in the case of S-theory , into an infinite set of possible combinations and associated meanings . Dodd ’ s detractors dismissed S-theory without grasping this fundamental aspect .
Dodd ’ s unfinished project : Brief-S
S-formulae are extremely concise relative to the textual ‘ output ’ of academic sociologists working in the natural language tradition , such as in English . Even so , an even more concise form of symbolic expression , which Dodd termed ‘ Brief-S ’, clearly appealed to him , and although many