Mark D. Roberts

A common method of improving how well understood a theory is, is by comparing it to another theory which has been better developed. Radical interpretation is a theory which attempts to explain how communication has meaning. Radical interpretation is treated as another time dependent theory and compared to the time dependent theory of biological evolution. Several similarities and differences are uncovered. Biological evolution can be gradual or punctuated. Whether radical interpretation is gradual or punctuated depends on how the question is framed: on the coarse-grained time scale it proceeds gradually, but on the fine-grained time scale it proceeds by punctuated equilibria. Biological evolution proceeds by natural selection, the counterpart to this is the increase in both correspondence and coherence. Exaption, mutations, and spandrels have counterparts metaphor, speech errors, and puns respectively. Homologous and analogs have direct counterparts in specific words. The most important differences originate from the existence of a unit of inheritance (the traditional gene) occurring in biological evolution - there is no such unit in language.

A common method of making a theory more understandable is to compare it to another theory that has been better developed. Radical interpretation is a theory that attempts to explain how communication has meaning. Radical interpretation is treated as another time-dependent theory and compared to the time-dependent theory of biological evolution. The main reason for doing this is to find the nature of the time dependence; producing analogs between the two theories is a necessary prerequisite to this and brings up many problems. When the nature of the time dependence is better known it might allow the underlying mechanism to be uncovered. Several similarities and differences are uncovered, and there appear to be more differences than similarities.

It is argued that colour name strategy, object name strategy, and chunking strategy in memory are all aspects of the same general phenomena, called stereotyping, and this in turn is an example of a know-how representation. Such representations are argued to have their origin in a principle called the minimum duplication of resources. For most the subsequent discussions existence of colour name strategy suffices. It is pointed out that the BerlinA- KayA universal partial ordering of colours and the frequency of traffic accidents classified by colour are surprisingly similar; a detailed analysis is not carried out as the specific colours recorded are not identical. Some consequences of the existence of a name strategy for the philosophy of language and mathematics are discussed: specifically it is argued that in accounts of truth and meaning it is necessary throughout to use real numbers as opposed to bi-valent quantities; and also that the concomitant label associated with sentences should not be of unconditional truth, but rather several real-valued quantities associated with visual communication. The implication of real-valued truth quantities is that the Continuum Hypothesis of pure mathematics is side-stepped, because real valued quantities occur ab initio. The existence of name strategy shows that thought/sememes and talk/phonemes can be separate, and this vindicates the assumption of thought occurring before talk used in psycho-linguistic speech production models.

Standard linguistic analysis of syntax uses the T-model. This model requires the ordering: D-structure > S-structure > LF, where D-structure is the sentences deep structure, S-structure is its surface structure, and LF is its logical form. Between each of these representations there is movement which alters the order of the constituent words; movement is achieved using the principles and parameters of syntactic theory. Psychological analysis of sentence production is usually either serial or connectionist. Psychological serial models do not accommodate the T-model immediately so that here a new model called the P-model is introduced. The P-model is different from previous linguistic and psychological models. Here it is argued that the LF representation should be replaced by a variant of Frege'sA three qualities (sense, reference, and force), called the FregeA representation or F-representation. In the F-representation the order of elements is not necessarily the same as that in LF and it is suggested that the correct ordering is: F-representation > D-structure > S-structure. This ordering appears to lead to a more natural view of sentence production and processing. Within this framework movement originates as the outcome of emphasis applied to the sentence. The requirement that the F-representation precedes the D-structure needs a picture of the particular principles and parameters which pertain to movement of words between representations. In general this would imply that there is a preferred or optimal ordering of the symbolic string in the F-representation. The standard ordering is retained because the general way of producing such an optimal ordering is unclear. In this case it is possible to produce an analysis of movement between LF and D-structure similar to the usual analysis of movement between S-structure and LF. The necessity of analyzing corrupted data suggests that a maximal amount of information about a language's grammar and lexicon is stored.

Phrase structure trees have a hierarchical structure. In many subjects, most notably in {\bf taxonomy} such tree structures have been studied using ultrametrics. Here syntactical hierarchical phrase trees are subject to a similar analysis, which is much simpler as the branching structure is more readily discernible and switched. The occurrence of hierarchical structure elsewhere in linguistics is mentioned. The phrase tree can be represented by a matrix and the elements of the matrix can be represented by triangles. The height at which branching occurs is not prescribed in previous syntactic models, but it is by using the ultrametric matrix. In other words the ultrametric approach gives a complete description of phrase trees, unlike previous approaches. The ambiguity of which branching height to choose, is resolved by postulating that branching occurs at the lowest height available. An ultrametric produces a measure of the complexity of sentences: presumably the complexity of sentences increases as a language is acquired so that this can be tested. All ultrametric triangles are equilateral or isosceles. Here it is shown that \={X} structure implies that there are no equilateral triangles. Restricting attention to simple syntax a minimum ultrametric distance between lexical categories is calculated. A matrix constructed from this ultrametric distance is shown to be different than the matrix obtained from features. It is shown that the definition of {\sc c-command} can be replaced by an equivalent ultrametric definition. The new definition invokes a minimum distance between nodes and this is more aesthetically satisfying than previous varieties of definitions. From the new definition of {\sc c-command} follows a new definition of of the central notion in syntax namely {\sc government}.