Category Archives: Metaphysics

Schopenhauer’s Four Laws of Thought

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:

  • Material Cause : Becoming : Identity
  • Final Cause : Knowing : Non-contradiction
  • Formal Cause : Being : Excluded-middle
  • Efficient Cause : Acting : Sufficient reason

Further Reading:

[*11.196, *11.197]


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


Everything is Four

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:

Whitehead’s Criteria for Metaphysical Theories

The Collatz Conjecture






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]



Noether-Pauli-Jung, V2

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:

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

[*10.68, *10.155, *11.55]


An Eightfold Metaphysics

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.

[*10.157, *11.26, *11.34]



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]


Atom and Archetype

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:

Atom, Archetype, and the Invention of Synchronicity: How Iconic Psychiatrist Carl Jung and Nobel-Winning Physicist Wolfgang Pauli Bridged Mind and Matter

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



Kant’s Synthetic-Analytic Distinction, V3

One of the oldest and most problematic philosophical questions is the comparison of the a prioria posteriori distinction with that of the analyticsynthetic distinction. Both are used in epistemology to divide knowledge, or true statements, between the innate and the learned, or the immediate and the earned, so they might even be considered the same. A priori and a posteriori statements are before “experience” and after it, respectively. Analytic statements are true only by their “meaning”, whereas synthetic statements are true only when facts about the world are combined consistently with that meaning.

It seems we have complicated the issue because now we must define and understand “experience” and “meaning”. However, these concepts are not independent because we must experience meaning, and meaning in turn conditions experience. In addition, even the a priori or the analytic are not innate or immediately obvious because deductions and the rules of logic require effort just like inductions do. Otherwise we would have Fitch’s Paradox: all truths are in fact known. What a muddle! So both experience and meaning are necessarily locked into a cooperative spiral dance to improve each other.

In addition, if you search for the two pairs a priori-a posterior and analytic-synthetic, you also find that the pair necessary-contingent is associated with them. Are these three pairs independent of one another and so give rise to eight triplets, or are they dependent in some way and reduce into fewer combinations? In addition, from Wikipedia:

Thus, the relationship between aprioricity, necessity, and analyticity is not easy to discern. However, most philosophers at least seem to agree that while the various distinctions may overlap, the notions are clearly not identical: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.

The web site of Stephen R. Palmquist has a great wealth of material on fourfolds in relation to Kant’s as well as his own philosophy. From my own initial reading of his extensive material I have tried to choose a canonical Kantian fourfold which has the most relevance to my project.

The fourfold shown to the right Dr. Palmquist calls Kant’s “reflective perspectives on experience”. Consisting of the logical, the empirical, the transcendental, and the hypothetical, these facets bear a close analogical likeness to many of the fourfolds presented here.

Logical: Analytic a priori
Transcendental: Synthetic a priori
Hypothetical: Analytic a posteriori
Empirical: Synthetic a posteriorikant_table

Dr. Palmquist also has many of his own books available on his web site for the interested reader. I will certainly be returning to his web site in the future for much enjoyable study.

Further Reading:

A Priori-A Posteriori, Analytic-Synthetic, and Necessary-Contingent Distinctions

[*7.68, *7.84, *8.126, *10.54]



The Ogdoad: Unity of Eight Gods

Here’s a notable fourfold of dualities: the Ogdoad, or eightfold of deities. I usually don’t stray into ancient mythology but this cosmological system evidently led the Greeks to their idea of the four elements. These paired male and female deities were personifications of certain metaphysical concepts and their opposites.

  • Amun and Amaunet: The Hidden and its opposite
  • Nun and Naunet: The Abyss and its opposite
  • Kuk and Kauket: The Darkness and its opposite
  • Huh and Hauthet: The Boundless and its opposite

Some even conjecture that the word ANKH was formed from the initial sounds of these four or eight deities.

Further Reading:



Distinctions with and without Differences

sq_distinction2It is often asked, why is there something rather than nothing?

Instead why not ask, why is there a rich diversity of things, rather than a dull sameness? And even though the closer and the further one looks the diversity is almost without limit, one also sees the world divided into natural kinds that partition it into a differentiated but interrelated mixture.

Several ancient philosophers thought that the entire world was an indivisible whole, a solid “being”. Others thought that you can’t even step into the same river twice, thus a fluid “becoming”. The real world seems to be somewhere in-between these two poles, moving continuously back and forth to now generate difference and newness, and then returning to sameness and oldness, and next continuing on to newness again.

Why drives these generative processes? One could say evolution, but evolution merely means “change over time”. And it would need to be an evolution at all levels of the cosmos, from the physical constituents of matter to the psychological constructs of culture. What do these disparate systems have in common?

Perhaps the commonality lies in the relations between small and large ensembles of chunks of space and time. In theories of statistical thermodynamics, the associations between micro states and macro states as well as micro events and macros events may drive entropy.

Here I present a schema that divides the continuum between one and many into four: Sameness, Similarity, Distinction, and Difference.
A member of the “being” camp might say these aren’t really different, whereas one from the “becoming” camp could say there really isn’t any sameness to begin with. Here I’ve chosen neither camp but struggled to bridge the gap between them.


Also see:

Statistical Thermodynamics

One and Many