0012 Okay, the Positivist’s judgment uses the empirio-schematic judgment as a tool for generating models.  For this reason, what ought to be belongs to secondness.

At this point, the reader may see a method to the madness of the seventeenth century mechanical philosophers.  Truncated material and efficient causes permit the construction of mathematical and mechanical models, based on observations and measurements of phenomena.  Final and formal causes cannot be regarded as data, since they are metaphysical.  Metaphysical causalities cannot be regarded as physical.

Mathematical and mechanical formula represent the physical world as models (what ought to be, secondness).  Disciplinary language (relation, thirdness) couches these formula (what ought to be, secondness) in terminology that applies to observations and measurements of phenomena (what is, firstness).  Phenomena belong to firstness (the realm of possibility) because they have the potential to be observed and measured.

0013 In regards to what is, a dyadic relational structure belongs to the category of firstness.

What is the nature of this dyad, a noumenon [&] its phenomena?

0014 When an Aristotelian approaches a thing, the first abstraction sees the thing in terms of matter and form.  Typically, matter raises questions in regards to material and formal causalities.  Form raises questions in regards to efficient and final causalities.

Aristotle’s hylomorphe is a premier example of Peirce’s category of secondness.  Secondness consists of two contiguous real elements.  The contiguity, which is placed in brackets for proper notation, should signify the… um… how one real element accounts for the other real element.

Here is a picture of Aristotle’s hylomorphe and Peirce’s category of secondness.

0015 Yes, both these figures associate to Peirce’s category of secondness, the realm of actuality.

Now, according to the Positivist’s judgment, the noumenon (the thing itself) and its phenomena (the observable and measurable facets of the noumenon) belong to the category of firstness.

Here is a picture of a slogan that may be attributed to the German philosopher, Immanuel Kant (1724-1802 AD), even though he may never have actually said it.

0016 Isn’t that how philosophy operates?

A lifetime of dedicated thinking gets alchemically distilled into a slogan propounded by people who claim to be dedicated to philosophy, but are only gossips spreading unwarranted attributions.

0017 Well, maybe not “unwarranted”.

How so?

Kant’s slogan makes a crucial point.

No matter how many observations and measurements of phenomena that one makes, the resulting model does not fully objectify the thing itself.

0018 Kant’s slogan is anathema for any scientist who is convinced that science is the only reliable way to approach reality.

But, scientists are a hearty sort, even when wounded by technically appropriate statements that are anathema.  One hundred years after Kant (and I suspect, even during Kant’s lifetime), triumphalist scientists have a response-at-hand.  The noumenon is a philosophical construct.  Therefore, it may be regarded as the first approximation to a successful model, which can be objectified as its phenomena.  Since the model belongs to secondness in both the Positivist’s and empirio-schematic judgments, the model is more actual than the noumenon.  So, the model should replace the noumenon.

0019 If a model overlays the noumenon, then the apparent contradiction resolves.

Isn’t that cathartic?

0020 Well, it is good enough for scientists who are not much interested in philosophy.

How so?

To start, how can a mathematical or mechanical model be the source of the phenomena that is observed and measured in order to generate… um… itself, through the medium of a scientific disciplinary language?

0021 Okay, what about a college-level physics or chemistry or biology laboratory?

Have you ever noticed that some students (especially the one’s susceptible to philosophical inquiry) find each laboratory perplexing, as an instructor leads the class through a recipe that demonstrates that the principles behind the recipe are as real as well… any thing that you’d find in nature?

The laboratory recipe allows one to generate the phenomena that need to be observed and measured (please correctly fill out the experiment’s fact sheet) in order to validate that the model [can be objectified as] its phenomena.

And, the instructor never mentions Kant’s slogan, because the instructor has excluded philosophy so rigorously that things themselves can be replaced by scientific mathematical and mechanical models.

0022  From the point of view of a college instructor, the model (overlaying the noumenon) can be objectified as its phenomena.

The instructor does not realize that the phenomena have changed. They are not the observable and measurable facets of things that one encounters in nature.  They are recipes for generating observations and measurements in a laboratory.  A subtle change in the nature of the noumenon (it is now a model) changes the phenomena.  In this case, the phenomena become so routine that college sophomores can handle the equipment necessary to encounter the model overlaying the noumenon.