Category Archives: Metaphysics

fourfolds, Metaphysics, ontology, Philosophy

Aristotle’s Fourfold Division of Being

Leave a comment

Aristotle’s fourfold division of being, found in his work Categories, classifies entities based on whether they are “Said of” a subject and whether they are “Present in” a subject. The four categories obtained  by these distinctions are: Accidental Particulars (not Said of but Present in), Accidental Universals (Said of and Present in), Primary Substances (or Substantial Particulars) (neither Said of nor Present in), and Essential Universals (or Substantial Universals) (Said of but not Present in) (also called Secondary Substances).

Present in Not Present in
Said of Accidental Universals Essential Universals
Not Said of Accidental Particulars Primary Substances

Or, looking at these four categories another way, with explanation:

Said of? Present in?
Essential Universals Yes No These are species or genera that are “Said of” particular substances but are not “Present in” any single subject. (i.e. the species of “humans”)
Accidental Particulars No Yes These are non-substantial particulars that are “Present in” a subject but are not “Said of” any other subject. (i.e. the wisdom of Socrates)
Accidental Universals Yes Yes These are universals that are both “Said of” and “Present in” subjects. (i.e. the wisdom that can be in some humans, such as philosophers)
Primary Substances No No These are individual, particular things that can exist on their own, such as an individual man or other type of entity. (i.e. Socrates)

Note the original term “accidental” can now be thought of as merely “non-substantial”. But Aristotle’s fourfold division wasn’t discussed at great length in the Categories, as pride of place was devoted to his ten-fold ontology, which we won’t be covering here.

The recent philosopher E. J. Lowe wrote much on essentially this same fourfold classification, which he called the Four Category Ontology. Lowe’s diagram of this, which he called “The Ontological Square”, also describes several other relationships between these four categories: Instantiation (between Kinds and Objects, and Attributes and Modes), Characterization (between Kinds and Attributes, and Objects and Modes), and Exemplification (between Attributes and Objects).

Non-substances Substances
Universals Non-substantial Universals, i.e. Attributes Substantial Universals, i.e. Kinds
Particulars Non-substantial Particulars, i.e. Modes Substantial Particulars,
i.e. Objects

Further Reading:

https://www.ancientgreekphilosopher.com/2015/08/05/aristotles-categories-four-fold-division-of-being/

https://philosophy-models.blog/2019/01/20/aristotles-categories-the-four-fold-division/

https://faculty.washington.edu/smcohen/320/cats320.htm

https://plato.stanford.edu/entries/aristotle-categories/#FouFolDiv

https://plato.stanford.edu/entries/aristotle-metaphysics/supp1.html

https://plato.stanford.edu/entries/aristotle-categories/

Ludger Jansen / Aristotle’s Categories

https://link.springer.com/article/10.1007/s11245-006-9009-1

Kevin Mulligan, Peter Simons, Barry Smith / Truth-makers in Philosophy and Phenomenological Research 44(3) 287-321 (1984)

E.J. Lowe / The Four-Category Ontology: A Metaphysical Foundation for Natural Science

https://ndpr.nd.edu/reviews/the-four-category-ontology-a-metaphysical-foundation-for-natural-science/

[*4.94, *6.98, *6.143]

<>

 

fourfolds, Metaphysics, Philosophy

Plato’s Fourfold Division in the Philebus

Leave a comment

In Plato’s dialogue the Philebus, Socrates uses a fourfold division to describe fundamental, metaphysical principles of all things: the Unlimited (ápeiron, the indefinite, boundless aspect), the Limited (péras, the definite aspect of measure and boundary), the Mixture of these two (meikton, a combined indefinite-definite), and the Cause of the mixture (aitia, which gives structure to the mixture and is responsible for unifying it).

This framework provides the foundation for the dialogue’s central argument about what constitutes the good life, and what activity is best to achieve it. In the dialogue, Socrates uses the four parts of the division to examine the natures of both pleasure and reason, determining that their mixture, brought about by some cause, is the key to a truly good life. So neither pleasure alone, nor reason alone, would suffice.

This fourfold division reminds me of Aristotle’s later schema of the Four Causes. Initially I thought that the Unbounded could be the Material Cause, the Bounded could be Formal Cause, the Mixture could be Final Cause, and finally the Cause could be Efficient Cause. That is because one might think that there is always more material to be had if you want it, and the form of a project puts shape, constraints, limits, and relationships on it.

However, I now believe that what is truly limited is the raw material (matter, energy, time, information), and what is unlimited is all possible form (and not any one particular form). The combinations or permutations that one can make from a finite set of elements are essentially unlimited in number, or at least increase exponentially with the length of the permutation or the size of the combination.

Consider the finite nature of an alphabet, and the endless number of sentences that can be formed from it. Or think about the four DNA base pairs, and the endless variety of genes and organisms that can be generated from them. Remember Darwin’s quote: “Endless forms most beautiful”. Of course many of sentences one can make are gibberish, and many of the organisms one could make are not fit or even viable.

I realize that in Plato’s dialogue the Unlimited and the Limited are more about the continuous and the discrete: the infinite and the finite, the unbounded and the bounded, the indefinite and the definite. The examples of the Unlimited given have the common aspect of “more and less”, i.e. they are indeterminant. By contrast, the examples of the Limit(ed) are of a determinant nature, a bound, a limit, a fixation, a stop to the “more and less”.

It seems that one could spent an unlimited amount of time studying the intricacies of the Philebus and thinking about the meaning of it. But I am starting to feel that my time is indeed limited and other matters require my attention. I know I am probably at odds with all others in the proper interpretation of this part of the dialogue. At least you might enjoy the limited links I have provided, and you still have the unlimited freedom to make of them what you will.

Further Reading:

https://en.wikipedia.org/wiki/Philebus

https://www.gutenberg.org/files/1744/1744-h/1744-h.htm

https://standardebooks.org/ebooks/plato/dialogues/benjamin-jowett/text/philebus

https://plato.stanford.edu/entries/plato-ethics/

Mary Louise Gill / The Fourfold Division of Beings (Philebus 23b-27c)

https://www.academia.edu/40402669/The_Fourfold_Division_of_Beings_Gill_on_Platos_Philebus_

Ashley Lascano / A critical analysis of the metaphysics of limit and unlimited in Plato’s Philebus

https://commons.lib.jmu.edu/honors201019/691/

George Rudebusch / Philebus 23c-26d: Peras, Apeiron, and Meikton as Measure Theory

https://impactum-journals.uc.pt/platojournal/article/view/10332

<>

fourfolds, Metaphysics, Philosophy, Space and Time

Four-dimensionalism

Leave a comment

Previous posts (here and here) have considered mathematical and scientific ideas about four dimensions. Here are some links about the metaphysical considerations of four-dimensionalism.

Further Reading:

Theodore Sider / Four-Dimensionalism: An Ontology of Persistence and Time

https://ndpr.nd.edu/reviews/four-dimensionalism-an-ontology-of-persistence-and-time/

https://tedsider.org/

Ludwig Jaskolla / Real Fourdimensionalism: An Essay in the Ontology of Persistence and Mind

https://ndpr.nd.edu/reviews/real-fourdimensionalism-an-essay-in-the-ontology-of-persistence-and-mind-2/

https://en.wikipedia.org/wiki/Four-dimensionalism

https://plato.stanford.edu/entries/temporal-parts/

https://en.wikipedia.org/wiki/The_Unreality_of_Time

https://en.wikipedia.org/wiki/Philosophy_of_space_and_time

Also:

https://ndpr.nd.edu/reviews/persistence-through-time-and-across-possible-worlds/

https://ndpr.nd.edu/reviews/how-things-persist/

And even:

https://ndpr.nd.edu/reviews/the-language-and-reality-of-time/

https://ndpr.nd.edu/reviews/the-elements-and-patterns-of-being-essays-in-metaphysics/

https://ndpr.nd.edu/reviews/a-materialist-metaphysics-of-the-human-person/

Maybe:

https://www.friesian.com/lieb.htm

[*10.89]

<>

fourfolds, logic, Metaphysics, Philosophy

Schopenhauer’s Four Laws of Thought

Leave a comment

The first three of Arthur Schopenhauer’s Four Laws of Thought are pretty much the same as the classical three laws of thought. Schopenhauer added a fourth law that was basically for his Principle of Sufficient Reason.

  • Identity
  • Non-contradiction
  • Excluded middle
  • Sufficient reason

These Four Laws are often given in two flavors: the first, in fairly concrete terms of subjects and predicates, and the second, more glib in terms of existence and being and such (isness).

  • A subject is equal to the sum of its predicates. Everything that is, exists. (Identity)
  • No predicate can be simultaneously attributed and denied to a subject. Nothing can simultaneously be and not be. (Non-contradiction)
  • Of every two contradictorily opposite predicates one must belong to every subject. Each and every thing either is or is not. (Excluded middle)
  • Truth is the reference of a judgment to something outside it as its sufficient reason or ground. Of everything that is, it can be found why it is. (Sufficient reason)

The phrase ‘it can be found’ sounds like a constructive method rather than a mere existence proof, but the common theological technique that combines both by saying “everything happens for a reason” avers the reason to an ineffable deity. (I bet Schopenhauer would have disliked this view because from what I understand he was an atheist.)

Moving on, I would like to represent these four laws in even more concrete terms of logical expressions. In the following attempt, let a, b be subjects (or objects), and P, Q be predicates (or qualities):

  • ∀a (a ≡ ∀P P(a))
  • ∀a ¬∃P (P(a) ∧ ¬P(a))
  • ∀a ∀P (P(a) ∨ ¬P(a))
  • ∀a ∃b (b → a)

When detailed in this way, these four laws don’t seem very complete, or don’t quite form a unity, as implication and equivalence are each in only one of them. Even though it doesn’t help that criticism, perhaps one can succinctly say:

  • Things can be reduced to (all) their qualities.
  • Qualities are disjoint from their opposites.
  • Qualities and their opposites are sufficient.
  • Things are entailed by some thing (possibly same).

In addition, I quite liked this Goodread review which aligns Aristotle’s Four Causes with Schopenhauer’s Fourfold Root. So then:

  • From Parts : Material Cause : Becoming : Identity
  • For Functions : Final Cause : Knowing : Non-contradiction
  • Into Structures : Formal Cause : Being : Excluded-middle
  • By Actions : Efficient Cause : Acting : Sufficient reason

Further Reading:

https://en.wikipedia.org/wiki/Law_of_thought

https://en.wikipedia.org/wiki/Law_of_identity

https://en.wikipedia.org/wiki/Law_of_excluded_middle

https://en.wikipedia.org/wiki/Law_of_noncontradiction

https://en.wikipedia.org/wiki/Principle_of_sufficient_reason

https://plato.stanford.edu/entries/sufficient-reason/

https://plato.stanford.edu/entries/schopenhauer/

https://en.wikipedia.org/wiki/Quantifier_(logic)

https://en.wikipedia.org/wiki/Universal_quantification

https://en.wikipedia.org/wiki/Existential_quantification

https://www.goodreads.com/review/show/1328220242

Aristotle’s Four Causes

Schopenhauer’s Fourfold Root of the Principle of Sufficient Reason

Things Happen

[*11.196, *11.197]

Notes:

At some point, I need to understand the difference between the law of the excluded middle and the principle of bivalence.

https://en.wikipedia.org/wiki/Principle_of_bivalence

https://philosophy.stackexchange.com/questions/3268/what-is-the-difference-between-law-of-excluded-middle-and-principle-of-bivalence

https://thephilosophyforum.com/discussion/1840/the-principle-of-bivalence-and-the-law-of-the-excluded-middle-please-help-me-understand

<>

fourfolds, Metaphysics

Everything is Four

10 Comments

Is everything four? Some try to prove it with a numerological trick. Take a word. Count its letters. Convert the number to words. Count letters. Repeat. Every English word seems to end up on four or 4, with nowhere else to go! Voila!

Since I’ve searched for this topic, a musician has released an album with this title. Cool!

But what do I mean by it? Everything can be divided into four parts, or has four aspects, or four sides, or what? I’m not sure, exactly.

But let’s test it against Alfred Whitehead’s Criteria for Metaphysical Theories!

  • Is it consistent? Yes! That is, nothing in the theory contradicts other parts of the theory, because there are no other parts. And if something is part of a foursome, that something can also be a foursome (even if an arbitrary one).
  • Is it coherent? Yes! That is, the theory is logically whole, such as it is. A bit boring? Perhaps…
  • Is it applicable? Yes! That is, we can apply our method to reduce something to four parts to everything, as long as we don’t care what the parts are. Plus we can combine anything with three other things, ad nauseum!
  • Is it adequate? No, not really. It does little to explain itself or the rest of the world.

So, we must continue our search for our ultimate metaphysical theory. It must be everything is four, plus something else… plus two more somethings…

Further Reading:

http://www.unterzuber.com/4our.html

http://www.marijn.org/everything-is-4/

https://en.wikipedia.org/wiki/Everything_Is_4

Whitehead’s Criteria for Metaphysical Theories

The Collatz Conjecture

[*11.140]

<>

 

 

 

fourfolds, Metaphysics, ontology, Philosophy

Writing the Book of the World

Leave a comment

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

http://tedsider.org/

Some reviews:
http://ndpr.nd.edu/news/writing-the-book-of-the-world/

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

https://en.wikipedia.org/wiki/Ontology

https://plato.stanford.edu/entries/modality-varieties/

https://plato.stanford.edu/entries/modality-epistemology/

https://en.wikipedia.org/wiki/Structuralism

Review that needs registration to read:
https://www.lrb.co.uk/v34/n16/aw-moore/carving-at-the-joints

[*9.8, *11.112]

<>

 

eightfolds, Metaphysics, Physics, Space and Time, spacetime

Noether-Pauli-Jung, V2

1 Comment

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity. And if Space-Time and Matter-Energy are both divided into Space and Time and Matter and Energy, one obtains this eight-fold.

Causality means that some action or cause in time (say a process) of things in space can have an effect (another process, say) on different things in space, and Synchronicity means that different events (say processes) separated in space can have non-causal relationships between them.  Conservation means the consistency of a quantity of matter or energy or matter-energy through time, and Symmetry means the consistency of a measure of a structure or form through space.

I am reminded of my fourfold Four Bindings, consisting of Chains, Grids, Blocks, and Cycles. Causality and Synchronicity are Chains (or non-chains for the latter) Space and Time are Grids (or flexible meshes), Matter and Energy are Blocks (or chunks of stuff), and Symmetry or Conservation are Cycles (of the group-theoretic kind or the equivalence class kind or just loops).

Further Reading:

https://en.wikipedia.org/wiki/Causality

https://en.wikipedia.org/wiki/Synchronicity

https://en.wikipedia.org/wiki/Symmetry

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

Four Bindings

This is a reworking of a previous six-fold diagram that I believe is served better as an eight-fold.

Noether-Pauli-Jung

[*10.68, *10.155, *11.55]

<>

eightfolds, fourfolds, Metaphysics, Space and Time

An Eightfold Metaphysics

4 Comments

If one juxtaposes the fourfold Space-Time-Matter-Energy with the fourfold Structure-Function-Part-Action, one sees that there are several relations between them. These are simple common-sense relations, not modern-physics types of relations. Below they are listed by Space-type relations and Time-type relations.

Space is required for the extension of Structures.
Matter constitutes Structures.
Parts in an arrangement make up Structures.

Structures extend and are organized in Space.
Matter is located in Space.
Parts occupy Space.

Time allows the expression of Functions.
Energy is required for the operation of Functions.
Actions in a sequence constitute Functions.

Functions have duration and reoccur in Time.
Energy requires and is dependent on Time.
Actions take place within Time.

Several analogies are also evident in this diagram.

  1. Space : Structures :: Time : Functions
  2. Space : Parts :: Time : Actions
  3. Space : Matter :: Time : Energy
  4. Structures : Parts :: Functions : Actions
  5. Structures : Matter :: Functions : Energy
  6. Parts : Matter :: Actions : Energy

Notice that analogies 1.-3. are “contains” relations, and 4.-6. are “part of” relations. One obtains the nesting of entities:

Space > Structures > Parts > Matter
Time > Functions > Actions > Energy

I suppose that any analogy could be shown in a figure like the one on the right (or even written as A / B // C / D) or with the two squares side by side, and that sets of four or six analogies that overlap could be nicely shown as above. If so, I wonder what can be gained by such representations? Probably individually not so much but with overlaps I think it would be interesting.

Further Reading:

The study of parts and wholes relations is called Mereology.

https://en.wikipedia.org/wiki/Mereology

https://plato.stanford.edu/entries/mereology/

[*10.157, *11.26, *11.34]

<>

 

fourfolds, Metaphysics, ontology, Space and Time

Fourfold Physicalism

Leave a comment

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:

https://equivalentexchange.wordpress.com/2012/07/03/structure-function/

https://equivalentexchange.wordpress.com/2013/10/09/things-happen/

https://equivalentexchange.wordpress.com/2014/02/01/relations-all-the-way-down/

https://equivalentexchange.wordpress.com/2015/06/09/four-primary-relations/

https://en.wikipedia.org/wiki/Man_a_Machine

Notes:

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]

<>

fourfolds, Metaphysics, Physics, Psychology, Space and Time

Atom and Archetype

2 Comments

A few weeks ago I ran across this nice review of the book Atom and Archetype: the Pauli-Jung letters 1932-1958. This is a collection of letters exchanged between psychiatrist Carl Jung and physicist Wolfgang Pauli over a course of years. Evidently, Pauli was quite the metaphysician and Jung was intrigued by Einstein’s physics of relative space and time. Together in dialectic they argued and struggled to join together the disparate notions of mind and matter.

What mainly caught my eye was a diagram that I’ve slightly altered and shown above. I’ve mainly just replaced energy with matter-energy for two reasons: first because matter and energy are inter-convertible and second because matter conditions space. This results in similarity to the fourfold diagram for Lucretius that I’ve shown before, consisting of Particles, the Void, Falling, and Swerving.

Further Reading:

https://www.brainpickings.org/2017/03/09/atom-and-archetype-pauli-jung/

Carl Jung and Wolfgang Pauli / Atom and Archetype: the Pauli-Jung letters 1932-1958, Princeton University Press; Updated edition (July 21, 2014)

https://equivalentexchange.wordpress.com/2011/10/10/lucretius-on-the-nature-of-things/

https://equivalentexchange.wordpress.com/2014/02/17/matter-energy-space-and-time/

https://equivalentexchange.wordpress.com/2015/01/16/wave-particle-duality/

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

[*10.60]

<>