0061 What is a category-based nested form?

Thirdness brings secondness into firstness.

A triadic normal context₃ brings a dyadic actuality₂ into relation with a monadic possibility of ‘something’₁.

Here is a picture.

0062 Each category expresses a different logic.

The realm of normal context₃ entails the logics of exclusivity, complementarity and alignment.

The realm of actuality₂ offers the logics of contradiction (and non-contradiction).

The realm of firstness₁ allows contradictions (as long as they cannot separate from one another) and displays the logic of inclusivity.

0063 I have already mentioned that Aristotle’s hylomorphe exemplifies Peirce’s category of secondness. Secondness consists of two contiguous real elements.  

Here is a picture of the comparison.

0064 Now, Aristotle’s material causality is confined to Peirce’s secondness.  But that is only the beginning.  Already, I demonstrated that chemical reactions may be formulated as hylomorphes.  All types of causes and effects may be presented as hylomorphes.  So, material causation entangles both the matter side of the hylomorphe and the form side.

For another example, hydrogen may be described as molecular material manifesting as a gas, a physical state.  If I keep the temperature the same, when I increase the pressure on this gas, its volume will decrease.  So, both sides of the hylomorphe are connected with materiality.

For example, the combustion of hydrogen and oxygen may be pictured as the hylomorphe, chemical reagents [change of free energy] chemical products.  Material causes may be located in both sides of the hylomorphe.  Plus, when free energy is released, chemical reagents (hydrogen and oxygen gases) seem to be like matter and chemical products (gaseous water) seem to be like form.  How so?  Well, matter enters into form.  Matter substantiates form.  So, there seems to be a directionality to hylomorphes that depict chemical reactions.

Science embraces material causation.

0065 What about formal causality?

Formal causality describes the way that a normal context₃ contextualizes its actuality₂, as well as the way that an actuality₂ conforms to its normal context₃.  When the actuality₂ is portrayed as a hylomorphe₂, formal causation touches base with the side of the form₂.

Science abhors formal causation, because one cannot observe or measure normal contexts₃.

Here is a picture.

0066 Does this explain why Tabaczek couples material and formal causalities?

Well, these pictures offer a way to appreciate the coupling.

0067 What about efficient causality?

Efficient causality describes the way that actuality₂ emerges from (and situates) its potential₁.  For Aristotle’s hylomorphe, matter has to efficiently substantiate form.  If the form is a shape, matter must efficiently fit that shape.

When Aristotle’s hylomorphe broadens to cover the wide variety of causes and effects belonging to Peirce’s secondness, efficient causes become very extensive.  Yet, despite the range of efficient causes, they tend to be portrayed as instrumental, physical and immediate. These portrayals emphasize the actuality side of efficient causality.  Science retains this side of efficient causality.  Science avoids efficient causes that emphasize the potential side of efficient causality, such as chance, malfunctions or delays.  

Here is a picture.

0068 What about final causality?

Final causation describes the way that the entire nested form comes together to satisfy the teleological component of its potential.  As such, efficient and final causes should complement one another.  Sometimes, a final cause cannot succeed because of lack of means (or instruments for efficient causation).  Sometimes, efficient causes are so effective that they mask complementary final causes.

Why do scientists eschew final causation?

Final causes cannot be observed or measured with scientific instruments.  However, they can be simulated as “factors” in computer programs.  Modern simulations allow scientists to import formal and final causes as factors in mathematical and mechanical models… er… I meant to say, “under the guise of truncated material and efficient causes”.

Here is a picture.

0069 These affiliations between Aristotle’s four causes and Peirce’s category-based nested form are discussed in Comments on Fr. Thomas White’s Essay (2019) “Thomism for the New Evangelization” available at smashwords and other e-book venues.  Similar commentaries by Razie Mah are located in the series, Peirce’s Secondness and Aristotle’s Hylomorphism, and in the series, Considerations of Jacques Maritain, John Deely and Thomistic Approaches to the Questions of These Times.

0070 In order to draw some lessons from the congruence between Aristotle’s four causes and Peirce’s category-based nested form, I return to Tabaczek’s mirror.

0071 On the science side, I see one hylomorphe, with two real elements, mathematical and mechanical models and observations and measurements of phenomena.  Each branch of science has its own contiguity, its own disciplinary language.  At the same time, all branches of science rely on modern material and efficient causes.  Disciplinary languages operate to precisely define the causalities expressed by models.  In laboratory sciences, measurements and observations become so formulaic that a practicing scientist will forget that that the lexicon of his discipline is highly specialized.

0072 On the Aristotelian side, I see two hylomorphes, with three real elements, a noumenon, dispositions and powers.  The term, “properties”, is not a real element.  It is the contiguity between the real features of dispositions (which pertain to (what I call) esse_ce and therefore go into the slot for matter) and powers (which pertain to essence and therefore go into the slot for form).

Ahem.

For proper postmodern etiquette, one may say either “dispositions and powers” or “properties”, but not both at the same time.  The same goes for “matter and form” and “substance”.

Did I say that properly?

A noumenon may be a whole, composed of parts, each with its own properties.  The natural philosopher encounters the whole.  The whole has its own dispositions and powers.

0073 Consequently, I suggest that the contiguity on one side of Tabaczek’s mirror reflects the other by serving as the site where causalities are expressed.  On the science side of Tabaczek’s mirror, the contiguity may be rendered in the way of Peirce’s category-based nested form, but the rendering is counter-intuitive, because it exposes formal and final causes that are hidden, like shadows, within truncated material and efficient causalities.  On the natural philosophy side of Tabaczek’s mirror, the contiguity is at home with Peirce’s category-based nested form.  Aristotle’s four causes are intuitive.

0074 Here is a picture.

0075 How about an application?

Consider the reaction of hydrogen and oxygen molecules.

Here is a picture of the reaction in terms of the agencies of science and of natural philosophy.

0076 These are very similar, so I do not anticipate many difficulties.

The reaction itself may be expressed as a hylomorphe, as an expression of Peirce’s secondness, as scientific process, or as a witness-able event.

0077 The materially balanced chemical reaction may be structured as a hylomorphe.  The contiguity may be described as a loss of free energy.  This free-energy release makes the reaction spontaneous.

Here is a picture.

0078 A container loaded with hydrogen and oxygen gases will not explode until a spark starts the reaction.  There is a significant “barrier” to reaction.  Once that barrier is breached, then all hell breaks loose.

In order to include the kinetic barrier, I can add an item to the list of potentials in the following category-based nested forms.

0079 Chapter one of Tabaczek’s book, Emergence, discusses the central dogma of emergence.

First, the causes of emergent phenomena do not add up.

And second, they seem to.

0080 For example, the above orthograde reaction has been well studied and its mechanism (composed of modern truncated material and efficient causes) is well established.

0081 What happens when I use this reaction in a hydrogen-oxygen fuel cell?

A hydrogen-fuel cell may serve as a case study for emergent phenomena.

Sure, the hydrogen-fuel cell is designed by humans, but that is okay, because it has what emergent natural phenomena have, a life of its own.

0082 The spontaneous explosive reaction can be “tamed” (okay, “exploited”, is a better word) by separating molecular hydrogen’s disposition to give electrons and molecular oxygen’s disposition to receive electrons.  All I have to do is find the right metal for two separated electrodes in water, where one electrode contacts H₂ (g) and the other electrode contacts O₂ (g).  The gases are funneled in by tubing from nearby gas cannisters.

0083 Now, I label this separation of the oxidation (the electron-giving) and the reduction (the electron taking) sides of the original chemical reaction, “contragrade”, because it re-directs the spontaneous release of free energy into an electric current that can do work.

Here is a picture of the circuit.

0084 At the anode, two hydrogen molecules touch the metal and separate into four hydrogen atoms which then release (because they are disposed to) their electrons into the electrode in order to become four aqueous hydrogen ions.  Hydrogen ions love water and will make the solution acidic.

At the cathode, one oxygen molecule touches the metal and separates into two atoms that will take on two electrons each.  They become ions that immediately attract hydrogen from nearby water molecules, resulting in four hydroxide ions.  For simplicity, I write that the result is O^-2 (aq).  Hydroxide makes the water basic.

To complete the circuit, the hydrogen ions and hydroxide ions recombine to form neutral water somewhere between the electrodes.

0085 To improve this setup, an engineer places a matrix of polysulfonate in the water between the cathode and anode.  Polysulfonate consists of sulfate ions covalently bonded to a carbon polymer, creating a forest of negative sulfate ions for the positive hydrogen ions to enter (for one side) and a ready supply of hydrogen ions that float out to neutralize hydroxide (on the other side).

0086 At this point, I can draw several conclusions.

First, the contragrade (fuel cell) reaction does not add up to the orthograde original, because the hydrogen and oxygen gases do not mix and explode.  Instead, a current is produced.  This current is capable of, say, running a little motor.  The contragrade set-up exploits the orthograde reaction by re-directing some (but not all) of the thermodynamic free energy released by the original (orthograde) reaction.

Second, the contragrade processes associated with this fuel-cell, as an emergent phenomenon, are novel.  They would not exist except for the dispositions and powers of molecular hydrogen and oxygen.  Plus, the homeodynamics of the contragrade processes can be optimized.  For example, the polysulfonate matrix assists in the ability of aqueous acid and base to recombine.

Third, the energy captured by homeodynamics is dissipated when the current does work.  So, the fuel-cell and its motor are morphodynamic (where “morpho” means “arrangement”).  The way the motor relies on the fuel cell in such a way that a failure of the fuel cell will stop the power to the motor.  In terms of the evolution of motors that use hydrogen-fuel cells, I suppose that means that machines with poor morphodynamics do not survive.

Fourth, the motor does not stand alone.  It will be part of a larger machine.  This introduces the concept of teleodynamics.  The fuel-cell driven motor has material, efficient, formal and final causes.

0087 Let me say that again, with diagrams.

The thermodynamic nested form looks like this.

0088 The homeodynamic level “constrains” the thermodynamic level through a contragrade arrangement.  The contragrade arrangement may be regarded as “downward causation”, because it transforms the orthograde reaction in such a manner that some of the orthograde free energy is channeled into an electric current.  The fact that the contragrade arrangement does not go haywire serves as a testimony to its homeostatic capabilities.  It can hold itself together, even though it is theoretically siphoning energy from an explosion.

Here is the homeodynamic level.

0089 One of the beauties of this diagram is that is keeps the thermodynamic level pristine, even though the reader knows that the explosion is separated into two reactions, one giving electrons and one receiving electrons, in a fairly complicated manner.  All the complexity is packed into the potential of the contragrade arrangement_1b.

I suppose that_1b is where the complexity belongs, because so many features of a hydrogen fuel cell can go wrong.  Engineers try to isolate and control situational potential_1b.

0090 The morphodynamic level capitalizes on the homeodynamic level, by providing an outlet that dissipates the re-directed energy.  In this example, the fuel cell powers a small motor.

0091 In chapter one, Tabaczek discusses the central characteristics of emergent phenomena.

So far, I use a scientifically designed product, the hydrogen-oxygen fuel cell, as an example.

Four characteristics have already been presented.

0092 The fifth characteristic is that emergent phenomena follow laws.

Now, what does this suggest in terms of this commercially available product?

0093 Material causation?

So, let me examine the virtual nested form in the realm of actuality (that is, the second column of the above interscope, displayed as a nested form).

Each of these actualities raise topics in material causation.  Everything must work correctly.  The orthograde chemical reaction must have convenient reagents.  It must provide lots of free energy.  The electrical current includes the right anode and cathode materials, wires as well as that polysulfonate matrix that provides a welcoming environment for hydrogen ions.

But, like any nested form, other causalities also come into play.

0094 The electric current_2b stands as the emergent phenomenon whose energy is dissipated in the virtual normal context of powering a motor_2c.  The match between the motor_2c and the current_2b defines engineering success and failure in term of formal causation.  The abilities of the fuel-cell to capture the orthograde reaction’s free energy_2a as current_2b defines engineering success and failure in terms of efficient causation.  The elegance of the design of the fuel-cell driven motor reflects final causation.

0095 The sixth characteristic?

Emergent phenomena cannot be deduced from the thermodynamic level.

Nor, can emergent phenomena be reduced to the thermodynamic level.

This characteristic becomes obvious when looking at the virtual nested form in the realm of normal context.

Really, this device is completely counter-intuitive.

Who would think of taming an explosion by miniaturizing it into a fuel cell that drives a motor?

Oh, I know, a human in our current Lebenswelt would.

But, what about a human in the Lebenswelt that we evolved in?

Notably, humans in the Lebenswelt that we evolved in construct intuitively natural devices.

Like stone-tipped wooden shafts for lances?

Oh, never mind.

0096 The seventh characteristic is that, emergent phenomena tend to show downward causation.

This is apparent when looking at the virtual nested form in the realm of possibility.

0097 Chapter two is titled, “Metaphysical Challenges for Emergence and Downward Causation”.

Once again, here is my human-designed example for an emergent phenomena: the hydrogen-oxygen fuel cell.

0098 Notice that the thermodynamic_a level has been adjusted_3a to account for the situational potential of a contragrade arrangement_1b, giving the appearance of downward causation.

In a similar manner, the fuel cell_3b design may be honed to maximize the potential of mechanical work_1c.

So, “downward causation” is the label applied when the potential of a higher level influences the normal context of adjacent lower level.

0099 Now, for a thought experiment.  Let me say that a motor powered by a hydrogen fuel-cell is made by corporation A and falls into the hands of corporation B, which would like to… um… “reproduce” the technology, in order to not be purchased outright by the profitable corporation A.

What falls into the hands of corporation B?

A fuel-cell powers a motor.

0100 The motor goes off to be analyzed by one technical team.

The fuel cell goes off to be analyzed by a second technical team.

0101 Funny, there are two “appearances of downward causation” and corporation B assigns two technical teams to the one project.  Plus, corporation B assigns a third team to coordinate the two technical teams.  Philosophers are assigned to this team.

Here is a picture.

0102 Here is how team one sees the problem.

The motor is material.  What are the materials?  The motor efficiently converts electrical current into mechanical work.  What are the efficient causes?  The motor is made by corporation A.  Is that an efficient cause or a final cause?  Who knows?  Well, we know that its a motor.  And what is the purpose of this motor?  Better ask team three.

0103 Here is how team two sees the challenge.

The fuel cell is material.  What are the materials?  The fuel cell produces an emergent phenomenon, an electric current, by separating the oxidation of molecular hydrogen from the reduction of molecular oxygen.  The technology is advanced, since the cathode (the hydrogen side) and the anode (the oxygen side) are specially designed as instruments for this purpose.  The materials touch base with the formal cause.  The formal cause is the generation of electricity.  We suspect that the free-energy of the overall chemical reaction is captured as an electric current, because that fits the fuel-cell’s design.  Design goes with formal causes.

How do we know for sure?  Ask team three.

0104 Here is how team three sees the challenge.

We need our spies in corporation A to tell us what specifically this device is designed to do (formal cause) as well as for what overall purpose (final cause).  

0105 Tabaczek, who seeks to introduce Aristotle’s four causes from his own, natural philosophical point of view, regards the activities of the three teams at work in corporation B, as they are reflected in the mirror of theology.

He asks, “Where do I see Aristotle’s four causes in emergence and downward causation?”

After all, this is precisely what the three teams in corporation B seem to be dealing with.  The electrical current is an emergent phenomenon that powers a motor for unknown purposes.  The potential of each higher level of analysis orders the configuration of the adjacent lower level analysis.  Can that be called, “downward causation”?

Of course!  But, if someone in team three tries to figure out the material, efficient, final and formal causation, that person is faced with two implied hylomorphes.

0106 Plus, the contiguities in Peirce’s secondness may range far and wide, but they all touch base with Aristotle’s exemplar, matter [substantiates] form, as foundational icon.  The terms, “coordinate” and “integrate” take on the characteristic of  “causes”, broadly defined as a contiguity between two real elements.

A scientist would like to simplify all this into one hylomorphe: material causes [integrate] efficient causes.  The causes that matter are physical.  The causes that form are reductive (that is, the higher-level potential is merely a manifestation of the adjacent lower-level nested form).  The scientist’s preference is called “reductive physicalism”.

0107 The metaphysicians say, “Whoa, that is a step too far.  The implied hylomorphes are both real and account for the existence of team three, which employs us.”

They label the two implied hylomorphes, “nonreductive physicalism”, in order to articulate their disagreement.

Articulate their disagreement?

Labels are important.

“Reductive physicalism” shoehorns emergence into modern truncated efficient and material causations.

“Nonreductive physicalism” acknowledges that final and formal causes cannot simply be cut out of the scientific analysis.

Note the compromise.

Typically, the term, “physicalism”, elevates modern truncated material and efficient causations.

These metaphysicians want to remain on the science side of Tabaczek’s mirror.

That is where the money is.

0108 So, I ask, “Which side of Tabaczek’s mirror does team three belong?”

0109 Tabaczek quotes Nancy Murphy, a philosopher and theologian.  In 1995, she quotes another philosopher and theologian, Austin Farrer, who, in 1957, says that, in emergent phenomena, constituents are caught, as if bewitched, by large patterns of action.

Using the motor driven by a hydrogen fuel-cell as an example, I repeat.  An electrical current catches constituents that manipulate the combustion of molecular hydrogen and molecular oxygen, as if the chemical reaction is magically commanded to power a motor that will use and dissipate the energy of the current.

0110 Team two studies (or “reverse engineers”) the way that the electric current catches the constituents of the fuel cell that manipulates the combustion of molecular hydrogen and molecular oxygen.

0111 Team one investigates the way that a motor uses and dissipates the energy manifested by the current.

0112 In order to do their job, they practice the empirio-schematic judgment.  They discuss their observations of their samples of the hydrogen fuel-cell driven motor and build models using causalities composed of truncated material and efficient causes.  

0113 Here is the problem.

Discussions of researchers in teams one and two put analytical and earnest philosophers in a bind, because these scientists neglect the question, asking, “Why is corporation A making this fuel-cell driven motor in the first place?”, while at the same time conducting their research as if the positivist’s intellect is still alive.

0114 Plus, they think that team three are on the same side as teams one and two.

But, take a look at Tabaczek’s mirror (rendered above).

0115 To me, it seems that teams one and two are agents on the science side of the mirror.

Team three has agents on the philosophy side of the mirror.

But wait, these agents want to be on the science side of the mirror as well.

Which brings me to point 0002.

Consider a sentence, found on page 273 of Emergence, midway in the final chapter, seven, saying (more or less), “I hope that my re-interpretation of downward causation and emergent systems, in terms of old and new Aristotelianism, will help analytical metaphysicians sound more credible to scientists and philosophers of science, who employ, analyze and justify methodological reductionism.”

Hmmm.

0116 This reader can barely imagine the heaps of intellectual garbage that this earnest and prayerful graduate studentstruggles through in constructing chapters one and two.

Then, at the start of chapter three, Tabaczek introduces the philosopher scientist, the guru at the top of the academic mountain (the story takes place in Berkeley, after all), the much-ballyhooed, well-published and honorably appointed, Professor Terrence Deacon.

Deacon works on the model side of Tabaczek’s mirror.  He converses with the ghost of the positivist intellect.  He fashions novel versions of Aristotle’s four causes in order to accomplish, on the science side, what any dullard would do on the philosophical side of Tabaczek’s mirror.

By “dullard”, I mean “a nerd who believes in the risen Christ”.

0117 With that in mind, I have a few caveats.

First, when I mention “Deacon”, I mean what Tabaczek says about the work of Professor Deacon.  After all, Tabaczek writes the book under examination.

Second, on both sides of Tabaczek’s mirror, spoken words mean whatever the viewing agent thinks they mean, because each viewing agent projects his own image into the mirror.

I hope that makes sense.

0118 Fortunate for me, I am already using Deacon’s terminology.  Deacon’s terms label the levels for the interscope of the hydrogen-oxygen fuel-cell.  “Thermodynamic” labels orthograde processes on the content level.   “Homeodynamic” covers the contragrade processes on the situation level.  “Morphodynamic” covers the perspective level, where the energy captured by an emergent phenomenon_2b is dissipated.

Needless, to say, there is one key term that I neglect.  “Teleodynamic” applies to the entire interscope, especially the integration of the perspective-level actuality_2c into other emergent processes.

So, my example of a fuel-cell driven motor is not complete, because the motor gets integrated into another emergent-bearing interscope.

0119 My manner of expressing the thermodynamic (content) level differs from Deacon’s manner.

I prefer to express the unconstrained orthograde reaction.

Deacon prefers to show how the situation-level potential_1b constrains the orthograde reaction in order to exploit reagent properties.

Here is a comparison using the ongoing example.

0120 Of course, since Deacon is much more clever than this examiner, Deacon’s preference allows a generalization of the adjusted thermodynamic level.

Here is a picture of the  generalization, along with the hydrogen-oxygen fuel-cell example.

0121 Almost all emergent phenomena are unique, each in its own way.

0122 Does a general description work?

0123 To me, the normal context_3a of the general description (tendency towards equilibrium) fits the normal context_3a of the example (adjusted orthograde reaction).  Without the adjustment, the thermodynamic example is a chemical reaction that releases lots of free energy.  Boom!

In Deacon’s schema, the “downward causation” of situation-level potential_1b is apparent in the content-level adjusted category-based nested form.  There is a certain pedagogic advantage to this.  The method becomes obvious.  The actuality is a contained circulation of ingredients_2a.  Specifically, this corresponds to the construction of the fuel cell itself.  The fuel cell physically separates the oxidation of hydrogen from the reduction of oxygen.

0124 Oh, did I mention that the “contained circulation” and the “physical separation” correspond to Aristotle’s material causes, not divorced from formal cause?

Yes, the material causes are integrated with the formal cause.  In general, the formal cause aims to maintain a tendency towards equilibrium_3a for the circulating ingredients_2a.  For the specific application, this requires the physical separation of the reagents, molecular hydrogen and molecular oxygen, as well as the separation of the sites where electron loss and gain occur.

Tabaczek intuitively couples material and formal causes.  He puts them into the same basket, so to speak, without explaining why.

0125 So, the tendency towards equilibrium_3a is formalized by the way that ingredients are circulated and contained_2abased on the potential of maintaining a displacement from equilibrium_1a.  One efficient cause is obvious in the specific case.  The physical separation_1a of the anode and cathode_2a forces the hydrogen to give up its electrons at the anode and the oxygen to take up its electrons at the cathode.  But, that is not the only efficient cause.  The addition of a polysulfonate barrier, creating a forest of negative charges for positively charged hydrogen ions to enter, improves “the circulation of ingredients”.

0126 The couplings of actuality_2a and potential_1a in the efficient causes cannot be divorced from the final cause, which says, “There is more to the potential that what the scientist maintains.”

Yes, the normal context_3a and potential_1a simultaneously select for and give rise to the actuality_2a.  Darwinian natural selection for multicellular organisms offers an analogy.  On one hand, natural selection selects.  On the other hand, sexual reproduction offers variation.  The logic of normal contexts is to exclude, align or complement.  The logic of potential is to include, even to allow contradictions.  So, in the scientific laboratory, a lot of failed experiments take place before the proper conditions, the proper “containment of circulating ingredients” is isolated within the constraints of the normal context_3a (the scientific question at hand) and out of the ordered chaos of the laboratory_1a (the instruments and equipment at hand).

“Final causes” label the manifestation of an actuality_2a within its normal context_3a and out of its potential_1a.  They also describe intentionality.

0127 The problem?

Final causes are metaphysical.

The ghost of the positivist intellect has a rule, “Metaphysics is not allowed.”

And, that rule spooks the agents on the science side of Tabaczek’s mirror.

That is the specter that fogs their mirror.

0128 Here is the homeodynamic (or situation) level general and specific nested forms.

0129 The fuel cell_3b is the normal context for the example.

Does the fuel cell amplify the non-equilibrium dynamics_3b of the adjusted orthograde reaction_3a?

Of course it does.

0130 Final causes come to the fore.

The normal context of a fuel cell_3b operates on the potential of ‘a contragrade arrangement for the orthograde chemical reaction of molecular hydrogen and molecular oxygen’_1b in order to produce an electric current_2b.

A normal context that amplifies a nonequilibrium dynamic_3b brings an emergent being_2b into relation with the potential of ‘constraints and biases imposed on an orthograde process’_1b.

If I, as a scientist, say, “The contragrade arrangement_1b of the adjusted orthograde reaction_3a explains the emergent phenomenon_2b, the electric current_2b, in terms of instrumental and efficient causality.”, I really am saying, “I have imported the shadow of final causality into my declaration of modern instrumental and efficient causes.”