0032 The hylomorphe does not really “unfold” into a category-based nested form.

A better word might be “expands”.

The hylomorphe expands into a category-based nested form.

The category-based nested form encourages an impulse to “fill in the blanks”.  On one hand, an actuality₂ demands a corresponding normal context₃ and potential₁.  On the other hand, a normal context₃ and its potential₁ draw in an appropriate actuality₂.

0033 For example, here is a picture of the Positivist Judgment as a category-based nested form.

How does this apply to the character of scientific discovery?

On one hand, a scientist investigates an actuality₂, calling for a corresponding normal context₃ and potential₁.

On the other hand, the normal context of the positivist intellect₃ is extremely aware of the potential of phenomena₁ to attract the curiosity of a scientist₂.

0034 Are there other ways to expand Saussure’s semiology, whose core claim is presented here as a hylomorphic structure?

0035 Another way for Saussure’s dyad of parole [stipulates] langue to worm its way into Peirce’s category of thirdnesscomes by way of A Primer on Sensible and Social Construction, by Razie Mah, available at smashwords and other e-book venues.

Parole_2a is a content_a-level actuality₂.

Langue_2b is a situation_b-level actuality₂.

Here is the resulting two-level interscope.

0036 On the content level, the normal context of speaking_3a brings the actuality of parole_2a into relation with the potential of ‘a vocal system of differences’_1a.

On the situation level, the normal context of thinking_3b brings the actuality of langue_2b into relation with the potential of ‘a mental system of differences’_1b. 

Going down the column for actuality₂, langue_2b virtually situates (and emerges from) parole_2a.

0037 This expansion is more than a passage from secondness into thirdness.  Unlike the direct expansion into a category-based nested form, discussed earlier, the two-level expansion enters the terrain of sign.

0038 Basically, a sign is a triadic relation, where a sign-vehicle stands for a sign-object according to a sign-interpretant.  Three elements are required: a sign-vehicle, a sign-object and a sign-interpretant.  Peirce uses his categories to create typologies of signs, based on the categorical-character of sign-vehicles, sign-objects and sign-interpretants.  Diagrams of category-based nested forms allow an alternate way to depict sign-relations.

Saussure’s two-level interscope contains (what I call) a “stipulating” sign.  Scholastics use the label “specifying”.  So the following figure exhibits extrinsic specificative formal causality.

0039 Of course, these associations are speculative.  They are consistent with Comments on John Deely’s Book (1994) New Beginnings, where the specificative and exemplar signs are diagrammed using category-based nested forms.

One attraction of this transition from Saussure’s dyad into Saussure’s specifying sign is that a finite system of differencesmay be called (in Peirce’s terminology) “a symbolic order”.  Consequently, grammar (for parole) corresponds to symbolic operations among elements within a symbolic order (for langue).