Whitehead's Cosmology as a Fixed Schema Network Graph

[gregsharp73]

Hello forum,

I am interested in tapping into the collective wisdom of this group for feedback on the attached document prior to a wider distribution. It involves interpreting the cosmology/"philosophy of organism" presented in A. N. Whitehead's Process and Reality (1929) through the lens of a network graph having a particular schema and set of rules for its use.  It is my belief that this perspective would be an aid to anyone wrestling to apply or even simply to better understand Whitehead's philosophical contribution and its relevance today.

I am particularly interested in conversing here with anyone who may have read or heard about Whitehead's ideas and were struck by the sense that he was thinking in graphs before that really was even a thing.  What fascinates me in all of this is how remarkably ahead of his time he actually was and how we might come to recognize that his time has finally come and that in so many respects, he still points to where we need to go.

Thank you in advance for your consideration,

Greg Sharp

[Alex Shkotin]

Hi Greg,

Interesting research. Is there any chance you give us an example of the graph itself - some subgraph. The schema is not very readable for me.

I don't know how to read 

Is there any example of this part of the schema?

Alex

пн, 20 янв. 2025 г. в 01:11, gregsharp73 <gregs...@gmail.com>:

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[gregsharp73]

Hi Alex,

Thank you for the question.  

You raise an excellent point regarding the use of the word "schema".  This word has a great potential to confuse us because of its many uses. 

Whitehead titled chapter II of Part I from Process and Reality, upon which much of the document is focused, the "categoreal scheme".  I am arguing that this represents a "fixed graph schema".  These are related terms but having two distinctly different meanings, largely due to different contexts.  I suspect your question may actually be getting at a more contemporary context for "schema" (as in the modeling of data) in your request for an example.  

The whole diagram attempts to summarize Whitehead's "categoreal scheme" as a "fixed graph schema".  So I sense in your question a tendency to want to "lose the forest in seeing the trees", but I may be wrong about that.  That tendency is understandable, but unfortunately, the cosmological scope behind this scheme/schema actually makes providing examples an extremely complex exercise.  The reason for this is that the scheme/schema is presumptively present at every level of the universe in question for modeling and iterates between all of these levels.  This is a rabbit hole at any point that one chooses to jump in, so it is much safer to stand back and first take in the forest.

But I think there is an simpler answer to your question regarding your snippet of the diagram.  The elements of the diagram that you have abstracted (another dangerous word in Whitehead's vocabulary) from the schema diagram are essentially: 

1. a big gray circle called "Actual Occassion" of some type (a Multiplicity...)", 

2. a small green circle called "actual occasion", 

3. a yellow diamond called "Eternal Object",

4. an arrow called "Subjective Form: Adversion",

5. an arrow called "Ingression".  

6. some other arrows that are cut off but appear to be directed towards the big gray circle.

These terms are all Whitehead's.  They are the categories in his scheme.

The fact that these terms have been diagrammed as shapes and arrows is the graph schema part.

The meaning of the shapes from the perspective of a graph schema corresponds to the list above as follows:

1. A graph (~nexus) or subgraph (.ie a contrast) is composed of vertices (actual occasions) which may have label(s)/type(s) (multiplicities). A vertex may be either an origin or a destination for an edge.  Big circles represent the vertex as a destination.

2. Small circles represent the vertex as an origin for an edge.

3. Diamonds represent a vertex having a single property that captures a unique symbol (eternal object).  There are infinitely many of these (color might distinguish them in a graph but here they are all just shown as yellow representing their grouping as symbols)

4. A graph contains edges (prehensions) that may be directed or undirected.  The edges in this graph are directed (thus the arrow). A directed edge determines which of its two related vertices is the origin and which is the destination. An edge may also have a label/type (subjective form). This type may also have subtypes (adversion)

5. An edge whose origin vertex has a symbol and whose destination vertex is any other vertex is the second type of edge (ingression) in this graph.  All others edges not of this type are of the type above (subjective form) but this type may have many subtypes.

6. Analysis of every vertex's incoming edges is the basis for assignment of all vertex types, and the basis upon which all other rules governing this graph schema are based.

There are more Whitehead terms and rules to discuss from the document (and that's where it gets really interesting), but hopefully this explanation is a helpful start.

Greg

[Ressler, Mark R.]

Greg:

 

You may want to compare with the figures in Sherburne’s A Key to Whitehead’s Process and Reality, though with caution, since these are only Sherburne’s interpretations, and as I recall, I had objections to his Figure 1 on p. 10, though I no longer remember why.

 

One quick correction immediately occurs to me: If a society is a nexus, then it is more than just a set of edges, it must include vertices and therefore be a subgraph.

 

The other major question  I have is why you characterize Eternal Objects as symbols.  I am not sure how that clarifies anything rather than just raising additional questions.  I always understood Eternal Objects as constraints on the realization of actual occasions and the prehensions they have with other actual occasions, where each actual occasion and its prehensions would be constrained to some extent by every Eternal Object.  Additionally, Whitehead recognizes a nexus of all Eternal Objects, in which case there would be a graph of Eternal Objects constraining the graph of actual occasions.  You could combine these graphs, but since each of them is already a complete graph, the resulting complete graph would simply compound the interrelations.  For me, I think it is more helpful to keep the meta-level of Eternal Objects logically separate from the level of actual occasions, while recognizing that Eternal Objects are not in some separate Platonic heaven.

 

I did not have time to review all of your document, but I think the representation of Eternal Objects as symbols is the key aspect you need to explain and to justify.

 

Mark Ressler

 

 

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Subject: Re: [ontolog-forum] Whitehead's Cosmology as a Fixed Schema Network Graph

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Is there any example of this part of the schema?

 

Alex

 

 

пн, 20 янв. 2025 г. в 01:11, gregsharp73 <gregs...@gmail.com>:

Hello forum,

I am interested in tapping into the collective wisdom of this group for feedback on the attached document prior to a wider distribution. It involves interpreting the cosmology/"philosophy of organism" presented in A. N. Whitehead's Process and Reality (1929) through the lens of a network graph having a particular schema and set of rules for its use.  It is my belief that this perspective would be an aid to anyone wrestling to apply or even simply to better understand Whitehead's philosophical contribution and its relevance today.

I am particularly interested in conversing here with anyone who may have read or heard about Whitehead's ideas and were struck by the sense that he was thinking in graphs before that really was even a thing.  What fascinates me in all of this is how remarkably ahead of his time he actually was and how we might come to recognize that his time has finally come and that in so many respects, he still points to where we need to go.

 

Thank you in advance for your consideration,

Greg Sharp

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[gregsharp73]

Hi Mark,

You comment " If a society is a nexus, then it is more than just a set of edges, it must include vertices and therefore be a subgraph."  This statement is entirely correct.  A society is a nexus - these are Whitehead's words on p. 89 of P&R: "The term 'society' will always be restricted to mean a nexus of actual entities which are 'ordered' among themselves in the sense to be explained in this section."  

In graph-speak this is the same as a subgraph, which includes vertices and edges.  If you were to speak of just edges, the Whitehead term would be "prehension" and if just of vertices then one of its two species: "actual occasions" or "eternal objects".  

Whitehead's comment after introducing the Categories of Existence goes: "Among these eight categories of existence, actual entities and eternal objects stand out with a certain extreme finality."  I would take this "certain extreme finality" to be because they are the two highest types of vertices in the graph (the circles vs. the diamonds as discussed with Alex above). The remaining six categories of existence cover the concepts of graph, edge, symbol, defined symbol, vertex types, and subgraph.

Could you unpack your understanding of the word "constraint" for me in the context of eternal objects?  

In this context, Whitehead seems to prefer the words "determination" and "definiteness".  And I don't think he would be bothered at all by us associating his eternal objects with Plato's forms.  This is why he defines eternal objects as "Pure Potential for the Specific Determination of Fact, or Form of Definiteness" in his fifth category of existence.

Also from p. 43 of P&R: 

"For Example, the total multiplicity of Platonic forms is not 'given'.  But in respect of each actual entity there is givenness of such forms.  The determinate definiteness of each actuality is an expression of a selection from these forms."

 So if the eternal objects are chosen platonic forms purposed to determine the definiteness of actual objects/occasions, then I am taking that determination to be an act of symbolic representation drawn upon an infinite reserve of symbols.  Peirce has much more to say about the categorization of these signs/symbols than does Whitehead, but I believe there is a fundamental agreement between them.  As you indicate, Whitehead does permit us to think about a nexus of eternal objects, which we may conceive graphically as a particular subgraph if there is a desire for logical isolation of eternal objects from actual entities (see the discussion of the Category of Transmutation on page 15 of my document). In my view, such an isolation of eternal objects, while not arbitrary, is optional.

To work out or expand upon what Whitehead was getting at with his eternal objects is from my perspective, to develop a theory of semiotics.  And this can be done with graph-based thinking as well, which I believe is what both men were doing in a general sense.  This assumes that we might be able to pick their brains at the same time and place, which we can't.
Greg

[Ressler, Mark R.]

I invoke the word ‘constraint’ simply from the basic consideration that an actuality is typically understood as becoming determined in its definiteness, to use Whitehead’s phraseology, according to the potentialities available to it, where those potentialities are standardly considered to be prior in some way or other.  Consequently, actualities such as actual occasions and the prehensions between them are constrained in their actuality according to the potentialities embodied in eternal objects.  This is inherent in Whitehead’s characterization of eternal objects that you reference.

 

On ‘Platonic Forms’, see the next page, p. 44, for Whitehead’s qualifications of the use of this term, where he clearly makes a distinction.  Of course, Aristotle also invokes the notion of form, but in a distinctly different sense than Plato does, and I have always read Whitehead as following Aristotle’s lead that forms are inherent in the actual world, not in some separate realm. 

 

Your appeal to symbols continues to concern me.  Whitehead has a chapter on Symbolic Reference, but that is developed on the basis of a prior understanding of eternal objects and actual occasions and is contrasted from the start from “The pure mode of presentational immediacy…” (p.168) involved among them in their primary relations.  Whitehead does have a theory of semiotics here, but it is built on his ontology, which is prior, so you cannot properly understand eternal objects in terms of his semiotics.  Consequently, it seems you are trying to turn Whitehead on his head.  Keep in mind that actual occasions are far below the level even of fundamental particles in physics, and therefore it seems to me that the eternal objects embodying their potentialities would be difficult even for particle physicists to describe or symbolize according to the current level of the science.

 

I do not see the agreement between Peirce and Whitehead in their ontologies at all – and certainly not their aims.  I understand Whitehead in Process and Reality as elucidating the hints he dropped in Science and the Modern World, where as I recall the overall argument is that a process ontology can better accommodate the new developments in quantum and relativity theory than traditional ontologies.  That is clearly not an aim that Peirce could have had, so any alleged agreement between Peirce and Whitehead is something that needs to be demonstrated, not assumed, and that must be demonstrated on the basis of an understanding of Whitehead’s ontology that does not presuppose it.

 

Mark Ressler

 

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[Gregory Sharp]

HI Mark,

It sounds as if we are now in agreement as to Whitehead's understanding of eternal objects given your explanation of what you mean by "constraint". 

I also take Whitehead's further discussion regarding Platonic forms on page 44 to only reiterate the point I was making.  But in Whitehead's words: 

"The term "Platonic form' has here been used as the briefest way of indicating the entities in question. But these lectures are not an exegesis of Plato's writings; the entity in question are not necessarily restricted to those which he would recognize as 'forms'...Accordingly, by way of employing a term devoid of misleading suggestions, I use the phrase 'eternal object' for what in the  preceding paragraph of this section I have termed a "Platonic form'."

Just curious - could you cite where you got this impression that Whitehead was aligning his Eternal Objects with Aristotle's sense of 'form' rather than Plato's and what the significance of that might be?  If anything, it appears that Whitehead sees little difference between the two for his purpose.  From p. 96: "The appeal to Plato in this section has been an appeal to the facts against the modes of expression prevalent in the last few centuries... Both for Plato and Aristotle, the process of the actual world has been conceived as a real incoming of forms into real potentiality, issuing into that real togetherness whis is an actual thing. Also, for the Timaeus, the creation of the world is the incoming of a type of order establishing a cosmic epoch. It is not the beginning of matter of fact, but the incoming of a certain type of social order."

If my use of "symbol" has evoked connotations to "symbolic reference" for you, then I now better understand the reason for your discomfort and can commiserate.  I certainly want to avoid any such confusing association between my use of the word "symbol" as a graph schema analog of "eternal object" and Whitehead's discussion of presentational immediacy.  

Can you think of a word that might not evoke this association from "symbol" to "symbolic reference"?  The need, as regards to the document as presented, is to identify a term within the scope of network graphs that is analogous to the Platonic forms as Whitehead is employing them for his categoreal scheme?  Perhaps "variable"? or "string"?

As to my dragging of Peirce into this discussion, it is certainly tangential to the intent of the document in question.  I honestly do not mean to disparage Whitehead at all and I gladly drop the point.  You are correct to point out that employing Peirce in discussions of relativity and quantum mechanics is anachronistic, whereas with Whitehead there was clearly an interest in engaging with these topics.  But to say that Whitehead was developing his ideas simply to address particle physics does feel like an overreach.  He clearly had broader intentions than that in writing Process and Reality. 

Would it be safe to assume that by your introduction of "Peirce and Whitehead in their ontologies..." you mean to refer to Peirce's semiotics and Whitehead's cosmology (or philosophy of organism)?  I know that Whitehead stated an 'ontological principle' (see categories of explanation (xviii) on page 9 of the document) but not that he ever characterized Process & Reality as an ontology, nor did he, as far as I know, characterize any aspects of his own work as 'semiosis'.

Finally, you misread me if you think I am trying to "turn Whitehead on his head".  I am trying to preserve his ideas by moving them into the more contemporary and familiar network graph terminology.  I believe the document and the care I have taken in its serial unpacking of Whitehead's categoreal scheme follows through on this intention quite transparently.

Greg

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[Alex Shkotin]

Hi Greg,

Thank you for your detailed answer.

You pointed out my mistake: I thought we have a kind of data modeling schema.

Now I am looking at your diagram as a graph representation of some statements, sentences of Whitehead's text.

The topic requires a good knowledge of the text. Which I do not possess.

Best regards,

Alex

пн, 20 янв. 2025 г. в 20:08, gregsharp73 <gregs...@gmail.com>:

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[Ressler, Mark R.]

No, I do not have a citation for my alignment of Whitehead with Aristotle.  It has been many years since I engaged with Whitehead, and I do not have sufficient time now to research it.  The quotation you cite on p. 96 only addresses the agreement between Plato and Aristotle concerning the impact of Forms in the actual world, not their disagreement with regard to Forms themselves.  For Whitehead, I revert back to his discussions in Science and the Modern World, where if the notion of eternal objects are to support the sciences of quantum and relativity physics, then they must be the ultimate grounds for the laws of nature, and therefore they must be fully inherent in the fabric of this world, not established in their perfection in some other realm whereby actual things in this world can only participate in them to some extent or another.

 

I mean “ontologies” with regard to both Peirce and Whitehead.  Both of them refer to systems of categories, as does Aristotle, and categories are fundamental divisions of ontologies.  This is an ontology forum, after all, not a graph theory forum.  That ontologies can be expressed in graphs is an added bonus for certain purposes.

 

It is not merely the word “symbol” that bothers me in your presentation, but the presentation of eternal objects as something different than nodes.  That is why I recommended thinking of actual occasions and eternal objects in terms of two inter-related graphs, each complete graphs in themselves, and complete in their unions.  Where a nexus is recognized, a graph of nodes can be invoked, and there are nexuses among eternal objects as well as among actual occasions.  The difference is not only between the types of nodes, but also the types of relations between them.  Ingresses between eternal objects and actual occasions are different from ingresses between actual occasions and other actual occasions, and the relations among eternal objects themselves are different from both of these kinds of ingresses.

 

Mark Ressler

 

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[gregsharp73]

Hi Mark,

You are stating precisely what I am saying in the document in regards to both eternal objects and actual occasions being nodes in a graph or subgraph (nexus) (that distinction between graph and subgraph is arbitrary) and that the nature of their relationships to each other through "ingression" are distinct relationships (more generally called 'prehension') from the relationship between two actual occasions (more specifically called 'subjective form').  I can't understand what bothers you because you are simply restating my point.  I do hope you will eventually find some time to read the document, because you clearly have a good grasp of Whitehead's ideas.

Greg

[Gregory Sharp]

In response to Mark's aversion to the use of "symbol" as a proxy for Whithead's "eternal object", I am replacing "symbol" with "potential for encoding".  The "potential" part being drawn directly from Whitehead's original description of eternal objects, and the "encoding" as a nod to the computable content of a modern network graph, which always requires some process of symbolic encoding.  To reflect Whitehead's move from "pure potential" in eternal objects to "impure potential" in propositions, the latter would now be rendered "encoded potential".

The network graph schema for Categories of Existence (v) and (vi) would then read:

(v) Eternal Object: a potential for encoding

(vi) Proposition: an encoded potential

Mark's point about "and the relations among eternal objects themselves", is a topic of Whitehead's Categoreal Obligations of Conceptual Valuation and Reversion.  These would now be mapped to rules in the graph schema of:

(iv) Encoded Potential Rule: every vertex has a potential for encoding assigned to it. (conceptual valuation)

(v) Nested Potential Rule: encoded potentials may be employed in the assignment of new potentials for encoding.

"Encoding" must be understood as distinct from "ingression" in this usage.  "Ingression" remains the Whiteheadian term that is being mapped to an edge that assigns a potential for encoding (eternal object) to a vertex (actual entity). "Potential for Encoding" is analagous to something like what it would mean to be a Platonic form.

Category of Explanation (vii): Potentials for encoding (eternal objects) are carriers of meaning but are not meaningful in and of themselves without an act of assignment (ingression) to some meaning of a particular vertex.  Complex potentials for encoding are derived from combinations of other potentials for encoding but similarly only assume meaning when assigned to a particular vertex.

For "meaning" in this category, refer to the 'ontological principle' of category of explanation (xviiii) where we have associated "reasons" with "explanations of meaning and their representation - are instantiated in the graph as vertices..."

Greg

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