Category Archives: Visualization

One insight arising from Peirce’s work on the mathematics underlying logic is that the operations on sets known as complementation, intersection, and union, along with the corresponding logical operations of negation, conjunction, and disjunction, are not as fundamental as they … Continue reading →

A moment’s reflection on the issue of style, giving due consideration to the received array of stylistic choices, ought to inspire at least the question:  “Are those the only choices there are?” There are abundant indications that other options, more … Continue reading →

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 →