0051 When I read pithy summaries of the rise of science in the 7400s (remember to subtract 5800 to get Anno Domini), the enemies of the mechanical philosophers are superstitious scholastics, clinging to their Aristotelian conviction that the Earth serves as the center of the universe.

The contest centers on mathematical models of planetary motion.  The calculations are radically simplified when the Sun is taken to be the center of the system.  Jesuits, always combative, attack the elegantly simple mathematical model.  

0052 Redpath adds a crucial point.  Renaissance humanists join the assault.

Ah, the mechanical philosophers have two foils, scholastic humbugs and Renaissance geniuses.

0053 Against these two establishment foils, mechanical philosophers, such as Rene Descartes (7396-7451), extend the concept from mathematics to mechanics.  They propose (what turns out to be) the empirio-schematic judgment, which is derived in Comments on Jacques Maritain’s Book (1935) Natural Philosophy.  Disciplinary language (relation, thirdness) brings observations and measurements (what is, firstness) into relation with mathematical and mechanical models (what ought to be, secondness).

0053 Here is a diagram.

0054 In the 7400s, the empirio-schematic judgment is not yet crowned a winner.  Once crowned, it is set as a jewel in a larger triad, the Positivist’s judgment, the true paragon of authority in this Age of Ideas.

To me, this historical passage warrants a comparison among the scholastic judgment, the Renaissance judgment and the newly conceived empirio-schematic judgment.In particular, I want to compare one element: what ought to be.

0055 In standard tales of the birth of science, mechanical philosophers face off against recalcitrant scholastics.  These scholastics cling to a dozen or more causalities, all logically derived from Aristotle’s four causes and all discussed in a dead language: Latin. Do I see a small flaw that has become a large impediment?

Redpath adds a twist.  Mechanical philosophers also contend with Renaissance humanists, who propose a systemic vision of a world that can neglect logic.

0056 Perhaps, the contest is thrown at the start.

A little logic easily overthrows no logic at all.

Here are the three expressions of what ought to be for the scholastic, Renaissance and empirio-schematic judgments.

0057 Firstness is the realm of possibility, so Aristotle’s causalities have the quality of guesses, even though they are very good guesses.  In particular, final and formal causalities are entangled with firstness.

Sometimes, there remains only one possibility standing, after all other possibilities are exhausted.  This offers some comfort, but does allow final and formal causations to be reduced to causations that typify secondness, such as material and instrumental causes.  Firstness never achieves certainty.

Secondness is the realm of actuality.  Renaissance and mechanical philosophers offer the quality of certainty, even though the former neglects logic and the latter offers only the logics of mathematics and mechanics.

Hmmm.  I suspect this may be a leap.  But, do the oracular and occult beings of the Renaissance sort of look like final and formal causations?  And, do the models of the mechanical philosophers have the same categorical flavor as material and instrumental causes?

0058 Over a few generations, the mechanical philosophers eliminate the scholastic tradition, to the point where many modern histories of philosophy jump from Augustine to the Italian Renaissance.  The scholastic tradition gets no coverage.

What about Renaissance humanists?

Do the mechanical philosophers defeat the Renaissance humanists, as they do the medieval scholastics?

Or, do the mechanical philosophers subjugate the Renaissance humanists?

0060 If it is the latter, I wonder, “What does this subjugation imply?”

0061 Redpath portrays the subjugation of Renaissance humanism to the burgeoning empirio-schematic sciences as a defeat.

Renaissance humanism begins by attacking our natural abilities to form general abstract ideas (as seen in the scholastic judgment) and replacing them with oracular and occult beings of the imagination (as seen in the Renaissance judgment).  “Oracular” means “to speak as an oracle”. “Occult” means a coagulation within an induced dissolution.

Yes, there is a tiny flaw.  The disciplines of grammar, rhetoric, poetry, history and ethics neglect logic.  That flaw grows into a blind spot that cannot envision either Kepler’s mathematical models or Descartes’ mechanistic formulations. Renaissance humanists set the stage for the subjugation of the liberal arts to the empirical sciences.

Empirio-schematics considers only material and instrumental causes.  Partial logic is enough to overthrow a complete neglect of knowledge.  Or, should I say?  Material and instrumental causalities make more impact than final and formal causalitieis, at least in the short run.

The Age of Ideas begins with a small error, because empirio-schematics does not include final or formal causation.  Indeed, it seems that final and formal causalities remain alive, although subjugated, in modern humanism.

0062 Redpath says that a small flaw grows into a catastrophic undoing.

This must be avoided for the upcoming homeschooling renaissance.

0063 I introduce a slightly different opinion, by asking, “Does the subjugation of the Renaissance humanists open the door for Enlightenment humanists, who construct novel grammatical and ethical, oracular and occult beings, such as the slogan, ‘Liberty, equality and fraternity’, within the confines of their servitude to science?”

0064 The Enlightenment fosters a new rhetoric, a new poetics, and a new history, all compatible with the empirio-schematic judgment.  The social sciences are born.  The Renaissance vision of the rebirth of Rome digests in its own juices, and coagulates as designs for a New World Order, guided by its own deep grammar and imposing its own ethical demands.

The natural sciences give birth to the social sciences.  The social sciences give birth to the sciences of configuring a New World Order.

Here is a picture of this alternate ending to Redpath’s story.

0064 Is the much-advertised “Western Enlightenment” merely the historical rendering of a new Renaissance, in subjugation to the authority and prestige of the blossoming empirical sciences?

This is one implication of the alternate ending to Redpath’s tale.

0065 Here is a picture of the Western Enlightenment.

0066  Do I see a small flaw that may grow into a catastrophic unraveling?

Will political slogans reverse the inevitabilities of mathematics and mechanics and render the natural and social sciencesinto servants to a new science, occulting out of the chaos of the social sciences, just as the social sciences coalesce out of the neglected noumena of the natural sciences?

0067 Redpath does not articulate this particular scenario.

Twenty years later, his actions demonstrate that he intuitively senses its theodramatic implications.

Redpath pioneers an academy promoting “uncommon” common sense.

He proposes a return to the analytic and synthetic logics of Thomas Aquinas.

0068  Scholastic logic, Aristotelian causality, mathematical learning and abstractions are key features of what ought to befor the scholastic judgment, as shown below.

0069 What does that imply?

What ought to be works on principles available to sensible reason.

In this examination of Redpath’s essay, I phrase the implication as follows, “The world exhibits regularities in all three of Peirce’s realms: possibility (firstness), actuality (secondness) and normal context (thirdness).  Each realm manifests its own logic.  The Baroque scholastic tradition identifies the sign as a triadic relation and Peirce picks up this thread.  Peirce goes on to identify the three categories that are implicit in the arc of Thomism, from Aquinas to Poinsot.”

0070 In contrast, for Renaissance visionaries, what ought to be is a world constructed by oracular and occult beings.  Our world is composed of social constructions.  The discipline of poetic theology aims to discover those beings capable of restoring the political glory of Rome.

To this, Redpath says, “These oracular and occult beings excite our judgments.  They tingle our sensations.  They color our perceptions.  Yet, they neglect logic.”

0071 In contrast, for mechanical philosophers, what ought to be is a world that can be modeled with mathematics and mechanics.

To which I say, “Mathematics and mechanics apply to Peirce’s category of secondness, which is subject to the laws of non-contradiction.  The other categories are subject to scientific inquiry only in so far as they manifest secondness.  The logic of the empirical sciences is radically incomplete.”

0072 Redpath tells a tale in order to magnify Aquinas’s note of caution.  Small errors at the start of an enterprise produce significant errors at the end. 

Redpath’s tale concerns the Italian Renaissance, which neglects logic at its beginning, eventually falling into subjugation to the radically incomplete logic of the empirical sciences.

There is a historical sequence.  Renaissance innovators are followed by mechanical philosophers and mechanical philosophers are followed by the thinkers of the Western Enlightenment.

An alternate option, concocted here, says, “The Western Enlightenment may well be the rebirth of the Renaissance, under the conditions of its subjugation to the empirical sciences.”

0073 Here is a diagram of what the Enlightenment judgment can be.

Oh, it looks the same as the Renaissance judgment.

0074 So, what does that suggest?

Does the Enlightenment, retaining the Renaissance’s neglect of logic, cover up the radically incomplete logic of the empirical sciences, so that the normal contexts of the liberal arts₃ and scientific disciplinary languages₃ together exclude the richness of natural reason₃, available in scholastic arguments, Aristotelian causalities, mathematical learning and abstractions?

Ah, such is the Age of Ideas.

0075 Perhaps unwittingly, Redpath unveils the two contenders facing the Homeschooling Renaissance.  One disregards logic and proposes occult beings bursting with final and formal causalities.  The other channels logic into mathematics and mechanics and says that material and instrumental causalities explain all things.

No wonder Redpath calls for a return to “uncommon” common sense.

I call the alternative the Age of Triadic Relations.

0076  Twenty years ago, Redpath concludes that we need to learn from the mistakes of the founders of the last great Western Renaissance.  He addresses the upcoming Homeschooling Renaissance.  It must not devolve into a battle among the arts.  Rather, it must offer a restoration of ordinary sense experience as the foundation of reason.  Philosophy, as well as the literary and fine arts, will naturally follow.

Order will return to human learning.

0077 To me, the prior diagrams place Redpath’s lesson and tale into a new way of looking at our current condition.  Each diagram expresses a triadic relation.  All the diagrams engage one another.

At the same time, there is a center, the interscope that is formulated by scholastics, dismissed by Renaissance humanists, and ignored by mechanical philosophers.  Redpath calls the center “scholastic psychology”.  I call this interscope, “the individual in community_A“.

0078 Here is a picture.

0079 Yes, here is a picture, working on principles available to sensible reason.  Sensible reason transcends secondness, the realm of actuality, where the principle of non-contradiction applies.  Sensible reason includes thirdness and firstness.  In order to understand, we must place an actuality₂ into its appropriate normal context₃ and potential₁.

0080 Aquinas stands at the spring of a great philosophical river.  John Poinsot stands at the harbor, where this river enters the sea.  Charles Peirce plans to sail the sea.  Razie Mah is a sailor on Peirce’s ship.

0081 Twenty years ago, Redpath offers one guidance.  Watch for small flaws, for they become terrors at the end.

Today, Redpath offers another.  The enterprise begins.

0082 There is only one house open for us all.  There is only one boat navigating an ocean of deception.  Every parent knows this.  The house of God is built on revelation.  Reason, grounded in ordinary sense experience, allows us to see its designs.  The ship of God sails into both calm and storm.  Logic, grounded in triadic relations, allows us to characterize the winds.  Our creation starts with winds moving over the waters.  Our creation ends with a place that we call home.

Razie Mah offers his wares to the Big Schoolhouse.

Welcome to the Age of Triadic Relations.