Category Archives: Cactus Graphs

Stricture, Strait, Constraint, Information, Complexity To give a concrete example of strictures and straits in action, let us institute a frame of discussion where the number of places in a relation is bounded at two and the variety of sets … Continue reading →

Stricture, Strait, Constraint, Information, Complexity Within the framework of a particular discussion, it is customary to set a bound on the number of places and to limit the variety of sets regarded as being under active consideration and it is … Continue reading →

The concatenation of the formal languages and is just a cartesian product of the sets and but the relation of cartesian products to set‑theoretic intersections and thus to logical conjunctions is not immediately clear.  One way of seeing a type … Continue reading →

I am throwing together a wide variety of different operations into the bins labeled additive and multiplicative but it’s easy to observe a natural organization and even some relations approaching isomorphisms among and between the members of each class. The … Continue reading →

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 →