Archive for the ‘Aristotle’ Category

Pick Your Causation

September 10, 2015

sq_causationCausation is one of the most important ways in which we conceptualize the world and ourselves. The reasons that objects go through their motions and people perform the acts they do are explained by the causes that lead to these effects. Constitutive materials can also be causes for the effects on things and individuals. Even the form and function of things can be thought of as effects, dependent on the causes that make them come to be. These effects in turn can be causes for subsequent effects, and so on, in a complex chain or network of causation.

Four different “directions” inform discussion about causes and effects, organized by time (Forward and Backward) and space (Upward and Downward). Perhaps space is not the best word: consider size, distance, or even importance. These four directions can also remind one of Aristotle’s Four Causes, where Efficient Causation is Forward, Formal Causation is Downward, Material Causation is Upward, and Formal Causation is Backward.

Forward causation: Temporal causation, where causes happen before their effects. Ordinarily associated with a deterministic view of causation.

Upward causation: Scientific causation, where the smaller or lower cause the effects of the larger or higher. Ordinarily associated with a reductionistic view of causation.

Downward causation: Structural causation, where the larger or higher can cause the effects of the smaller or lower. Typical examples are free will, agency, intention, or volition, where the mind and not just the brain controls the actions of the body.

Backward causation: Reverse temporal causation, where causes are in the future of their effects. This is not quite the same as teleology, although the concepts are closely linked and require further study. Typical examples are purposes, goals, and ends (versus means) (although this is not the usual philosophical meaning of backward causation).


Also see these related posts:



The Marriage of Opposites

August 29, 2015

sq_marriageThe road up and the road down are the same thing.

— Heraclitus

The Marriage of Opposites, or Chemical Wedding, or Coniunctio Oppositorum, is a term from alchemy that means combining two opposite substances, or essences, or even ideas into a unity greater than the sum of its parts. This term has also meaning in Jungian psychology as Jung showed many parallels between the processes of self-understanding and alchemy. For example, the marriage of opposites is symbolized by the union of the Animus and Anima.

Opposites are everywhere in our everyday lives and language. They are also prevalent in our social institutions such as religion, politics, philosophy, and science. There are long lists of opposites of life and language and institutions: spatial, temporal, relative, linguistic, mathematical, social, normative, philosophical, and mythological.

A + A’ = ?

What does it mean to combine two opposites into one? Does it mean that the two things are no longer extant and only the combination remains, or that the thing is its own opposite (e.g. 1 + -1 = 1)? Does it mean that a new, third thing is now created that incorporates both of the originals but they still exist as well, like Hegel’s thesis, anti-thesis, synthesis (e.g. 1 + -1 = 3)? Or does it mean that the originals annihilate each other, and nothing remains (e.g. 1 + -1 = 0)?

Usually the casual causal combination of opposites leads to an averaging of the two. For example if hot and cold liquids are combined, soon you will just get a tepid mixture. This is entropy, where the difference between the hot and the cold material is soon eliminated by the blending of the parts, and in this case actually fueled by the energy of the hot molecules.

The usual meaning of this Chemical Wedding is rather esoteric or mysterious. I propose that what the term “marriage of opposites” really means is quite different. Each “opposite” is an opposing pair itself, so that the marriage is between two pairs instead of two things. Instead of a unity, I suggest that this is the root of multiplicity. Instead of simplicity, there obtains organized complexity. Two pairs of two things yields four things in many ways: 2 + 2 = 2 * 2 = 2 ^ 2 = 4.

Let A and A’ be a pair of opposites, as well as B and B’. Then we can consider a union between those pairs to be:

(A + A’)(B + B’) = AB + AB’ + A’B + A’B’

Our individual genetic material is really a marriage of opposites in that half of it comes from each of our parents. Like Mendel’s peas, the sexual union generates the possibility of four versions of each feature. Similarly, the combination between two pairs of opposites generates a fourfold of possibilities.

How should one arrange such a union on a diagram? In Aristotle’s Square of Opposition, the true opposites are at opposite corners of a square, the “contradictories” (one is true and one is false). There are also “contraries” (cannot both be true), “subcontraries” (cannot both be false) and “subaltern” (only one implies the other) relations between corners. But the square is built from the logic of quantifiers and properties, different from this fourfold.

They can be arranged as the cycle AB + AB’ + A’B’ + A’B: One can naturally consider AB and A’B’ to be opposites, as well as AB’ and A’B. One can start with the two opposite pairs crossed, and this cycle sequence arises simply between them. Also, one nice feature is that only one of A or B needs to be changed to its opposite as we move around the cycle, even as we return to the beginning of the sequence. This is called a “gray code” in terms of binary numerals.sq_marriage2

They can be arranged as the grid AB + AB’+ A’B + A’B’: Here the opposites fall across a diagonal that runs southwest to northeast. This doesn’t have the nice properties of the cycle above, but I have used it for many of my diagrams. Instead of a cyclic symmetry, we have a dynamic symmetry about this diagonal that runs from an imagined origin of separation towards greater mixing and combination. This is the usual binary numerical sequence.



Interestingly, while thinking about the next stage in the 2 + 2, 2 * 2, 2 ^ 2, … series, I found that the superexponential or exponential tower operation is called “tetration”. In fact, Tetration( 2, 2) = 4 as well.

Also, consider “Mirage of Opposites”!



The Rational Structure of Inquiring Systems

February 26, 2015

sq_engelhartWhat are the components of consciousness? In the dissertation of L. Kurt Engelhart we see a fourfold used to analyze the texts and bodies of work of both scientists and philosophers, a hermeneutical tool if you will. This tool is also styled by concepts of “systems theory”, and requires the exposition of the aspects of Content, Control, Process, and Purpose of the authors. These match closely the Four Causes of Aristotle, which are the causes of made things or the explanations of how and why they came about: material, efficient, formal, and final. In fact, this close association was one of the main reasons I dove into the world of fourfolds. Texts are made things, after all.sq_causes

Making is so fundamental to what we do, that humans have been called “Homo Faber”, man the maker. We make tools, stories, culture, and even our concept of self. What if I turned this tool onto my own work, the writings and images found here? Perhaps that will be the project of another analyst, if my efforts warrant. What if I applied this tool to Engelhart’s project? That would be interesting indeed.

Another fourfold Engelhart presents is that of the domains of conscious experience, or the self itself as system. sq_four_alsThis fourfold consists of the Real, the Actual, the Ideal, and the Literal, but my version is in disagreement with Engelhart’s as to the classification of integrative and differentiative for the Ideal and the Literal. My assignments match the conjunctive and disjunctive properties of the operators of Linear Logic. Also left out is the Universal and how it supersedes the Actual as we make a complete turn. I like my version because it is similar to Richard McKeon’s Things, Thoughts, Words, and Actions. Also T. S. Eliot’s Falls the Shadow.

Of course this is just a brief gloss of the rich ideas presented in Engelhart’s work. Another of his key concepts is that of wholeness, which I have completely omitted. I hope to return and write a better review at a later time. I’m glad to see that Engelhart’s dissertation is now available as a Kindle book for the low, low price of $1. It is much easier to read in this format! From the Amazon Book Description:

This study describes, as a single systemic model of inquiry, the context common to conscious experience of the phenomenon of inquiry. Data are the published texts of selected contemporary writers relevant to the question. The problem is to define a common systemic structure of inquiry in a context of consciousness. Research verifies that a specific structure is common to these writers and that their respective views are converging on this same structure.

Identifying a common structure involves reducing the textual descriptions of the writers to their systemically relevant essentials. Defining the essential elements and describing a reduction method depends heavily on theory of metaphor and metaphorical evolution. A history of the metaphorical structure relevant to inquiry is described and this structure is used as a basis for finding structure in the selected texts. Texts researched include evolutionary biology, sociology, psychology (phenomenology), and philosophy. This work replicates that done by Talcott Parsons in experimentally describing a voluntaristic theory of action. A wholistic theory of inquiry is described using the same systemic scheme.

The metaphysical approaches to inquiry of realism and idealism have converged on a common theoretical structure for describing inquiry. Commonalities emphasize systemic structure comprising the elements of function: purpose, process, content, and control. It has been necessary to distinguish between affectual and instrumental purposes, and between organic and mechanical function. The ontological essentiality of the structure reveals a necessary logical relationship between function, systemicity, wholeness, and rationality in human understanding. Continuing research in philosophy is crucial to expanding our understanding of the ontological and epistemological structural essentials of consciousness.

Human inquiry during the last century has specialized in the material realm of realism, objective description, and mechanical explanation. A wholistic theory of inquiry does not discount the contributions of realism-based science or idealism-based philosophy, but expands the horizons of each to include the other. Where mathematics provides essential tools for mechanical explanation, organic explanation still lacks abstract structural tools for describing conscious organic, including human, behavior. The intent of a wholistic theory of inquiry is to provide conceptual tools that support disciplined inquiry into conscious behavior.

References and Links:

L. Kurt Engelhart / Wholeness and the Rational Structure of Inquiring Systems: A Dissertation


I removed some text about the “Book of Nature”, because it needed more work. This mentioned the systems theory adage “the purpose of a system”, which can also tie into “meaning as use”. I also missed seeing an obvious thought that inquiry is making.

[*2.188, *3.104, *8.134]


Things Happen

October 9, 2013

things_happenWhen someone says “Things Happen”, we think they are being superficial. That’s because we want to hear an explanation of why the thing has happened. In fact, the “Principle of Sufficient Reason” mandates that everything must have a reason or cause. Still, you can’t argue with the fact that things do happen.

Aristotle described four causes that explain why things happen. These four causes are called the efficient, material, formal, and final causes. This classification was all the rage back before the scientific revolution, but now it has been mostly abandoned.  Still, with some modification, I believe it can be useful for the modern world.

Why do things happen? They happen by actions, from parts, into structures, and for functions.

This fourfold is a mixture of two others: Structure-Function and the prepositions I’ve associated with Aristotle’s Four Causes.


Things, Thoughts, Words, and Actions

June 6, 2013

things_thoughts_words_actionsHere are some additional fourfolds from philosopher Richard McKeon.

McKeon wrote much on the subject of rhetoric. A favorite fourfold of concepts was that of Things, Thoughts, Words, and Actions. He called these “commonplaces of inquiry” or “places of invention and memory”. Two rhetorical devices he used were amplification and schematization. Amplification can extend the scope of, for example, words to the other three, similar to the principle of indifference. “Objectivity is the inclusive principle of indifference by which it is recognized that being is grasped only in what we think, and say, and do about it.” [1] Schematization was used to identify and distiguish, for example, commonplaces. Thus I think amplification is a conjunctive device, and schematization is a disjunctive device.


Another fourfold of subjects by McKeon was Topics, Themes, Theses, and Hypotheses. McKeon wrote, “Speculation concerning discourse must avoid the fixities of categories, doctrines, methods, and assumptions which discourse assumes in any one form of philosophy or inquiry, if it is to include all the forms which discourse takes in philosophy and in inquiry, action, and production. This is possible because the variety of categories or elements is approached in discourse by way of common topics or ‘commonplaces’; the variety of facts or statements of what is the case by way of common hypotheses; the variety of arts or methods of treating problems by way of common themes; and the variety of assumptions or principles by way of common theses.” [2]

Are both these fourfolds aligned correctly with the previous Knowable, Knowledge, Known, and Knower? McKeon’s use of terms in his rhetoric was very fluid, perhaps to prevent systemization or to promote pluralism. However, his main reference to fourfolds was Aristotle’s four scientific questions, or Four Causes, which we can use to try to understand his fourfolds.


Theresa Enos (ed.) / Encyclopedia of Rhetoric and Composition: Communication from Ancient Times to the Information Age

[1] Richard McKeon / Selected Writings of Richard McKeon: Volume One: Philosophy, Science, and Culture

[2] Richard McKeon / Selected Writings of Richard McKeon, Volume Two: Culture, Education, and the Arts

H. L. Ulman / Things, Thoughts, Words, and Actions: the problem of language in late Eighteenth-Century British rhetorical theory

[*5.197, *6.140, *7.162, *7.165]


The Archic Philosophers

May 3, 2013

archic_philosophersInspired by philosopher Richard McKeon, I believe that philosophy as a whole is encompassed by four main philosophical stances, exemplified by four ancient philosophers: the Sophists (as a group), Democritus, Plato, and Aristotle. Their four systems of thought lay out principal philosophical directions, much like the compass directions east, south, north, and west lay out a complete set of primary directions.

Of course the compass directions can be subdivided into north-east, or south-south-west, and so on, and similarly each of these philosophical systems can be divided into four parts. This division into a four-by-four matrix is called the Archic Matrix and was written about at length in the separate but complementary works of Walter Watson and David Dilworth.

Watson and Dilworth described the four main philosophical directions to be perspective, reality, method, and principle: perspective for the Sophists, reality for Democritus, method for Plato, and principle for Aristotle. I have written about these philosophical perspectives previously in several ways.

Thus philosophy as a practice goes around and around and revisits the same ideas over and over. Perhaps McKeon thought his philosophical system followed in the footsteps of Aristotle, and probably Watson and Dilworth had a similar view.

Likewise, I believe that my fourfold of Structure-Function represents these four philosophical directions in the following way: Action(s) for the Sophists, Part(s) for Democritus, Structure for Plato, and Function for Aristotle.



July 3, 2012

Aristotle’s Four Causes is an important fourfold that seems to be the basis for many of the fourfolds, both original and not, presented in this blog. Two of the causes, efficient and material, are acceptable to modern scientific inquiry because they can be thought of as motion and matter, respectively, but the other two causes, formal and final, are not. Why is that?

The formal cause is problematic because the formal is usually considered to be an abstract concept, a construction of universals that may only exist in the human mind. The final cause is also problematic because it is associated with the concept of telos or purpose. There, too, only human or cognitive agents are allowed to have goals or ends. So for two causes, efficient and material, all things may participate in them, but for the two remaining, formal and final, only agents with minds may.

These problems may be due to the pervasive influence of what the recent philosophical movement of Object Oriented Philosophy calls correlationism: ontology or the existence of things is limited to human knowledge of them, or epistemology. The Four Causes as usually described becomes restricted to the human creation and purpose of things. Heidegger’s Tool Analysis or Fourfold, which also appears to have been derived from the Four Causes, is usually explained in terms of the human use of human made things: bridges, hammers, pitchers. Even scientific knowledge is claimed to be just human knowledge, because only humans participate in the making of this knowledge as well as its usage.

Graham Harman, one of the founders of Speculative Realism of which his Object Oriented Ontology is a result, has transformed Heidegger’s Fourfold so that it operates for all things, and so the correlationism that restricts ontology to human knowledge becomes a relationism that informs the ontology for all things. Instead of this limiting our knowledge even more, it is surprising what can be said about the relations between all things when every thing’s access is as limited as human access. However, this transformation is into the realm of the phenomenological, which is not easily accessible to rational inquiry.

I wish to update the Four Causes, and claim that they can be recast into a completely naturalistic fourfold operating for all things. This new version was inspired by the Four Operators of Linear Logic. Structure and function are commonplace terms in scientific discourse, and I wish to replace formal and final causes with them. It may be argued that what is obtained can no longer be properly called the Four Causes, and that may indeed be correct.

First, let us rename the efficient cause to be action, but not simply a motion that something can perform. I’m not concerned at the moment with whether the action is intentional or random, but it must not be wholly deterministic. Thus there are at least two alternatives to an action. I’m also not determining whether one alternative is better than the other, so there is no normative judgement. An action is such that something could have done something differently in the same situation. This is usually called external choice in Linear Logic (although it makes more sense to me to call it internal choice: please see silly link below).

Second, let us call the material cause part, but not simply a piece of something. Instead of the material or substance that something is composed of, let us first consider the parts that constitute it. However, a part is not merely a piece that can be removed. A part is such that something different could be substituted for it in the same structure, but not by one’s choice. Like an action, I am not concerned whether one of the alternatives is better than the other, but only that the thing is still the thing regardless of the alternative. This is usually called internal choice.

Next, we will relabel the formal cause to be structure, but not simply the structure of the thing under consideration. Ordinarily structure is not a mere list of parts, or a set of parts, or even a sum or integral of parts, but an ordered assembly of parts that shapes a form. Ideally structure is an arrangement of parts in space. However, in this conceptualization, structure will be only an unordered list of parts with duplications allowed.

Last, instead of final cause we will say function, but not simply the function of the thing as determined by humans. Ordinarily function is not a mere list of actions, or a set of actions, or a sum or integral of actions, but an ordered aggregate of actions that enables a functionality. Ideally function is an arrangement of actions in time. However, like structure, function will be only an unordered list of actions with duplications allowed.

As we transform the Four Causes from made things to all things, both natural and human-made, we will later examine how that changes them.


[*6.144, *7.32, *7.97]


The Theory of Evolution

June 8, 2012

“I have called this principle, by which each slight variation, if useful, is preserved, by the term Natural Selection”

— Charles Darwin

Can we cast the theory of evolution into a fourfold? I propose that the following four processes can serve as an abstract model for evolution: generation, variation, speciation, and selection. These four entities are similar to the fourfold of Structure-Function, currently in development. By my analogy which will be explained later, Generation is action, Variation is part, Speciation is structure, and Selection is function. A more familiar analogy matches these four processes to Aristotle’s Four Causes: Generation is efficient cause, Variation is material cause, Speciation is formal cause, and Selection is final cause.

Generation: Offspring are like their parents by and large, except when made different by processes of variation. Mainly the act of reproduction, procreation, or replication, but includes the ordinary evolutionary factors of descent and heredity.

Variation: Offspring can be different than parents. Includes the factors of genetic variation, mutation, sexual reproduction, and genetic drift.

Speciation: Includes the factors which keep species separated and differentiated from each other.

Selection: Really natural selection. I always thought this was a negative process, where species become extinct or are selected out if they are ill adapted to their environment. Apparently the original meaning was that the fittest organisms and their traits continue: that is, they are selected to survive by nature because of their adaptive traits.

As a process of change, evolution has been suggested by scientists to operate at many levels of nature, not just for the biological. One such scientist is Eric Chaisson, who has written many books on his idea of “cosmic evolution”.


Eric Chaisson / Epic of Evolution: seven ages of the cosmos (2005)


Also note the similarity between this fourfold and the fourfold I have drawn for Kevin Kelly’s Philosophy of Technology. In “What Technology Wants”, Kelly claims that technology develops in an evolutionary manner.



The Square of Opposition

May 21, 2012

Some readers may think I’ve never met a fourfold I didn’t like. However, there are several that I haven’t presented here because they don’t seem to play well with the others. The Square of Opposition, created by Aristotle, is one such fourfold. The four logical forms of the square are relations between a subject and predicate, S and P, and supposedly exhaust the possibilities of belonging: Some S are P, Some S are not P, All S are P, and No S are P (or All S are not P).

In the diagram I have removed the S and P, and the logical forms become spare and like a Zen Koan or nursery rhyme: Some Are, Some Are Not, All Are, and None Are (or All Are Not). By doing so, they resonate more brightly with the other fourfolds and how they are presented herein. Now, the logical forms can be about existence, or the subject and predicate withdraw and become implicit to the thought.

Also, consider the four edges between the four logical forms, and label the common terms. Then the important fourfold of Are, Are Not, Some, and All is shown.


Compare and contrast the Square of Opposition to the Tetralemma and the Semiotic Square.

The 3rd World Congress on the Square of Opposition is soon to convene. May the meeting be rewarding!


[*4.84, *5.82, *7.70, *7.90]


Walter Watson and David Dilworth’s Archic Matrix

December 2, 2011

Throughout the history of philosophy, there have been many conflicting stances both towards claiming what exists (ontology), and how we can know our claims are valid (epistemology). There are the oppositions between idealism and realism, between rationalism and empiricism, between thinking all is change and all is changeless, between all is many and all is one, and so on. One approach to overcome these oppositions is to combine them to form their Hegelian synthesis. Another is to deconstruct them à la Derrida. Another pluralistic approach is to consider that there is a germ of truth on each side of the conflicting stance, an aspect of reality for which that stance is valid. Some might think that pluralism is the same as relativism, but it is not. Relativism and pluralism form yet another philosophical opposition like others mentioned above.

Regardless of the validity of pluralism, it can be very useful to analyze what philosophical stances are possible and how they relate to one another. The philosopher Richard McKeon created a rich schema for philosophical semantics that deserves greater recognition. This schema was both simplified and elaborated on by Walter Watson and David Dilworth in their books about the Archic Matrix. There are four main aspects, all exemplified by ancient philosophers: the Sophists, Democritus, Plato, and Aristotle. Everything else is a combination of these original aspects, or essentially a rehashing of them. The main aspects are perspective from the Sophists, reality from Democritus, method from Plato, and principle from Aristotle. These partition “what is”, however it is conceived, into four aspects, each of which can be interpreted in four different ways.

Considering Whitehead’s Criteria, note that perspective has consistency, method has coherency, reality has applicability, and principle has adequacy.

Walter Watson / The Architectonics of Meaning: foundations of the new pluralism

David A. Dilworth / Philosophy in World Perspective: a comparative hermeneutic of the major theories