Category Archives: ontology

Writing the Book of the World

If one was writing a book that described the entire world or universe as it is, how should that book present the world to us? It is not enough to speak truly, itemizing “all that is the case”, one must also use the right notions while doing so.

Philosopher Theodore Sider wants us to accept structure as the all important fundamental notion of how to talk about the world. His idea of structure is that it reveals where the joints or articulations of the world can be carved, and that the structure of the world is real and it is objective. Structure is the right and proper way to find these joints, and go about this carving.

(Of course the structure that Sider promotes is not to be confused with the structuralism of linguistics and anthropology that was so popular before deconstruction and post-modernism critiqued it nearly to death. This post is not about structuralism because its structure is a reflection of language and the mind itself, not an attribute of the actual world.)

Chapters 1-8 are titled: Structure, Primitivism, Connections, Substantivity, Metametaphysics, Beyond the Predicate, Questions, and Rivals. Chapters 9-12 are devoted to ontology, logic, time, and modality (because I guess these are favorite topics in metaphysics) and what structure tells us about them. I don’t think Sider is saying that reality is carved naturally into these four domains, but I think it makes a rather nice fourfold.

In Metaphysics, Ontology is another word for Being, but it can also mean a classification system for the different kinds of things that exist (but I guess that’s not metaphysical). Modality is the Metaphysical or Epistemic study of necessity and possibility, so it is certainly related to time. There are also modal logics which have quantifiers for modalities such as necessity and possibility.

I closing I must say that once you carve up some structure by its joints, then you are left with parts, which may be structures in their own right. And as I’ve posited elsewhere, functions and actions are the structures and parts of time. I also wonder if there is a comparison of Sider’s structure to the metaphysics of E. J. Lowe, but perhaps I should just read each of their work.

Further Reading:

Theodore Sider / Writing the Book of the World

Some reviews:

Click to access 12-05-wtbotw-review.pdf

Review that needs registration to read:

[*9.8, *11.112]



Every Fourth Thing

What do I mean by the subtitle of this blog? If you search on Google for “every fourth thing”, after you see a few references to this blog you see mentions like: being out of something at the druggist, or saying a particular actor is appearing in a random show, or showing extra interest to a comment from a spouse, or things being requested that are forgotten by waiters, or subtexts of statements issuing from celebrities or politicians, or noting that every such organism ever discovered since the beginning of time was in fact a beetle.

So for the most part, a frequency of occurrence, like you have everything of a certain type that exists or can be named or thought about or the facts of the world in a line, and you are counting down and picking out every fourth one of them. For the usual sense of the phrase “every fourth thing”, the three things not picked are ignored because they don’t meet the condition desired, but for the sense I want, they are still “fourths” of things. They are as important as the one picked, either because they implicitly complete the wholeness in some way, or complete some other wholeness.

Or instead of the other three things passed over completing the whole, you have to count out your fourths four times, so you are looking at sixteen things but skipping twelve things to end up with four fourths. Or here is another idea, you have everything (of a certain type) in the world in a bin, and the condition of selection is that it is a fourth by its nature rather than counting it out. This is probably closer to my intention, but the ambiguity between these alternate senses is why I continue to enjoy the subtitle “every fourth thing”.

Once you’ve figured out your selection process, do any four things you select comprise a four-fold, or do only things that go together in a “special way” deserve to be called that? Do you pick with replacement, or once picked do things become unavailable for further selection? You have quite a lot of picking to do, so I would say no to replacement at first consideration; but since I do reuse fourths ad nauseam, replacement must be ok.

And one of the other amusing things that I like about “every fourth thing” is that I can pretty much talk about anything I want to with the minor condition that it has four parts to it (or some multiple of four), or that it’s four things together, or whatever. I used to be far more rigorous and selective, but now I don’t really care so much, and I’ll burden my readers with all sorts of nonsense to while away the time until the sun explodes. There’s really a never ending supply that goes on and on and on (and on).

Putting aside those questions for now, since they are evidently more complicated than my initial expectations, for this analysis I am trying to enumerate the different ways that four fourths could combine to form a unity. This list depends heavily on notions of sameness and difference. I have also discussed notions of equivalence before, but I have not returned to those considerations for a while and they may be erroneous or incomplete. But let’s soldier on and at least give it an honest try before we are exhausted by all of our doubts or side issues.

The first way that comes to mind is if each of the fourths is either identically the same thing or merely indistinguishable from each other (via replacement or being indiscernible). I’m not sure at the moment how to differentiate the two concepts so I’ll lump them together for now. Mathematically, we could represent this by the simple sum 1 + 1 + 1 + 1, or maybe the lambda expression λa.4a. For an example we could use the protons in a beryllium atom, a four leaf clover, or the sides of a square.

The second way is if each of the fourths is definitely a different thing. Then you might well ask why they are a unity and I’ll just say because I said so, that’s why! Or if I’m feeling magnanimous, I’ll try to at least give some reasons. Mathematically, we could represent this type of four-fold by a set, e.g. {a, b, c, d}, or by λa λb λc λd.a + b + c + d. As an example, a piano quartet would be nice consisting of piano, violin, viola, and cello. Also, the Four Causes, at first blush.

For the third way, we could consider the cross product of two sets, each having two elements, say {A, B} x {C, D}. Again, the linear expression λa λb.2a + 2b is different. And most real world examples have opposite relations like {A, ~A} x {B, ~B} (what I’ve called double duals before), so I’m having difficulty here. Maybe there are really 3 ways here that should be differentiated. Examples: the nucleus of a helium atom, Heidegger’s Four-fold, the Four Qualities, etc.

For the fourth way, let’s consider the fourths to be distinguishable, but there also is an order to them. Mathematically, how about the ordinal 4 = {0, 1, 2, 3} (but not the cardinal!). As an example, consider common time in music (4 4 time), having four quarter notes to a measure. The notes are different because of their order in the sequence, even if they are the same tone. Also the Four Seasons, except that it’s a double dual plus it has a sequence.

Now the fifth way. Mathematically: the Cartesian Plane, R x R, or the Complex Plane, C. Latitude and longitude, or maybe even North, South, East, West are examples. For every ordered pair (x,y) there is (-x, -y), (x, -y), and (-x, y). Or complex x + iy, -x – iy, x – iy, -x + iy.

Sixth. Three and one. Not the song “Three and One” by Thad Jones, even though it’s a great tune. Not the object (or is it the subject) of Trinitarianism, because that’s three IN one, and also the three are different. Ditto for three ingredient recipes. No on the yet to be released 4th Neon Genesis Evangelion movie 3.0 + 1.0, since that’s also three different things as far as I know (the first three movies). Perhaps ammonia (NH3) is an appropriate example with three hydrogens and one nitrogen . But I can’t say I’m very excited about this one, but it may be important due to my selection questions above. Now do the math: λa λb.3a + b.

Seventh. Two and one and one. λa λb λc.2a + b + c. I like this one even less, but at least it lets you see that the lambda expressions can be put into hierarchical order based on partitions of four. Perhaps the nuances of further structure can be teased out by different expressions, such as set theoretical or logical (instead of arithmetical).

Further Reading:

[10.156, *10.190, *11.80, *11.81]




Fourfold Physicalism

It is not enough for a wise man to study nature and truth, he should dare state truth for the benefit of the few who are willing and able to think. As for the rest, who are voluntarily slaves of prejudice, they can no more attain truth, than frogs can fly.

— From Man a Machine, by Julien Offray de La Mettrie

Further Reading:


Structures are built from parts.
Parts are reductions of structures.
Functions are assembled from actions.
Actions are the constituents of functions.

[*8.132, *9.104, *10.10]


Relations All the Way Down

There is nothing to be known about anything except an initially large, and forever expandable, web of relations to other things. Everything that can serve as a term of relation can be dissolved into another set of relations, and so on for ever. There are, so to speak, relations all the way down, all the way up, and all the way out in every direction: you never reach something which is not just one more nexus of relations.

— Richard Rorty from Philosophy and Social Hope


The ancient Greek philosopher Empedocles somehow reasoned that the world was made entirely from four basic elements: fire, earth, water, and air. Science as we know it has disproved this from being the case, but this idea still has a rich symbolic meaning even today that informs our popular culture.

A recent philosophical stance called “ontic structural realism” argues that science suggests that only relations between things are of lasting importance, that is the structural relationships within and between things, not the things themselves that bracket the relations. What we call a quark for instance is just the relations it has with other quarks and the other entities that have relationships with quarks. Perhaps then the world consists of “relations all the way down”, instead of stopping at some point on the lowest level with the things that constitute the world.

If this is so, what if the world was made completely from four basic relations, instead of four basic things? sq_structure_functionCould they be something like the four binary operators of linear logic? I have likened these four basic operators of Linear Logic to my fourfold Structure-Function, where in addition to Structures, we also have Functions, Actions, and Parts. But these three other relations are also structural, in that only the relation something has to another something makes it structural, functional, actional, or a part of a something.

Book Description for Every Thing Must Go:

Every Thing Must Go argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers’ a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, they demonstrate how to build a metaphysics compatible with current fundamental physics (“ontic structural realism”), which, when combined with their metaphysics of the special sciences (“rainforest realism”), can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, Ladyman and Ross argue, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. Every Thing Must Go also assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the author’s metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism vs. empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds.

Stuff I need to read:

James Ladyman, Don Ross / Every Thing Must Go: Metaphysics Naturalized

Jason D. Taylor / Relations all the way down? Exploring the relata of Ontic Structural Realism



Bending the Elements

You and your forefathers have devastated the balance of this world. And now, you shall pay the ultimate price!

— From Avatar: the Last Airbender

I recently finished watching the animated series “Avatar: the Last Airbender”. I know I’m a bit late with my praise, but I thought this was an excellent series. It had fascinating world-building, well thought-out plotting, and believable characterization. It had humor, drama, fantasy, even teen romance. Something for all ages!

It could be because I’ve been thinking alot about the Four Elements and how I view them as analogies for the four relations I’ve been discussing for some time on this blog. In Avatar, they are literally the four elements of the world: fire, earth, water, and air. But in addition, these elements correspond to the four peoples of this world. The people of the Fire Nation are willful, the people of the Earth Kingdom are resolute, the people of the Water Tribe are empathic, and the people of the Air Nomads are reflective. Some individuals are able to “bend” the element that is associated with the people they are born into, so that for example a member of the Fire Nation might be able to produce and control fire with thought and gesture. Not everyone has this ability, however.

The Avatar is a continuously reincarnated individual that embodies the spirit of the world. He or she is born into each of the four peoples in a repeating cycle, but the Avatar is also the only individual that can learn to bend all four elements, and even all at the same time. Because of his or her unique powers, the Avatar is known to be able to bring and restore balance to the world, and to tie the real world to another, spiritual world. Avatar: the Last Airbender is the story of Aang, a descendent of the Air Nomads, but the last of his people due to genocide. He has been in a state of suspended animation for the last 100 years and awakes to a troubled world of war and turmoil. Can Aang save his world?

Hopefully I’m not spoiling anything in saying that he does. Indeed a sequel is currently being produced called “The Legend of Korra” that is planned to run 52 episodes. This sequel takes place a number of years after the end of Avatar, and the next Avatar after Aang is Korra from the Southern Water Tribe. The world is now somewhat more advanced technologically than it was during Aang’s time, and although not at war because it is still enjoying the peace that Aang initiated, there is still some strife and unrest for Korra to eventually bring the Avatar’s balance to. I am enjoying it also!


It is interesting to note that fire is the only element that can be generated by the will ex nihilo. With enough skill, water can be extracted from living matter and the air. Of course, air is ever present and earth is seldom far away.



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]



Philippe Descola’s Four Ontologies


Philippe Descola / Par-delà nature et culture

[*7.42, *7.43, *7.44]


Walter Watson and David Dilworth’s Archic Matrix

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.

Further Reading:

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



E. J. Lowe’s Four Category Ontology


E. J. Lowe / The Four-Category Ontology: a metaphysical foundation for natural science

Lowe, Edward Jonathan

[*4.94, *6.98]


John R. Searle’s Epistemological and Ontological Senses of Objective and Subjective


John R. Searle / The Construction of Social Reality