Author Archives: Jon Awbrey

It is useful to examine the relation between syntactic production and logical implication with one eye to what they have in common and another eye to how they differ. The production says the appearance of the symbol in a sentential … Continue reading →

There is a curious sort of diagnostic clue which often serves to reveal the dominance of one mode or the other within an individual thinker’s cognitive style.  Examined on the question of what constitutes the natural numbers, an additive thinker … Continue reading →

It is possible to trace the divergence of formal grammar styles to an even more primitive division, distinguishing between the additive or parallel styles and the multiplicative or serial styles.  The issue is somewhat confused by the fact that an … Continue reading →

Along with the distinctions we see evolving among different styles of grammar and the preferences different observers display toward them, there naturally arises the question:  What is the root of that evolution? One dimension of variation in formal grammar style … Continue reading →

The questions about boundary conditions we keep encountering betray a more general issue.  Already by this point in the discussion the limits of a purely syntactic approach to language are becoming visible.  It is not that one cannot go a … Continue reading →

Having broached the distinction between objective propositions and syntactic sentences, its analogy to the distinction between numbers and numerals becomes clear.  What are the implications of that distinction for the realm of reasoning about propositions and its representation in sentential … Continue reading →

The pragmatic theory of sign relations is called for in settings where everything that can be named has any number of other names, that is to say, the usual case.  Of course we’d like to replace the multiplicity of signs … Continue reading →

Expanding our perspective on the options for formal grammar style brings us to questions about the manner in which the abstract theory of formal languages and the pragmatic theory of sign relations interact with each other. Formal language theory can … Continue reading →

Perhaps I ought to comment on the differences between the present and the standard definition of a formal grammar, since I am attempting to strike a compromise with several alternative conventions of usage, and thus to leave certain options open … Continue reading →

Before the capacity of a language to describe itself can be evaluated, the missing link to meaning must be supplied for each of its expressions.  That means opening a dimension of semantics to be navigated by means of interpretation, topics … Continue reading →