Category Archives: Philosophy

The Four Philosophy Ensemble

A woman came up to me and said
“I’d like to poison your mind
With wrong ideas that appeal to you
Though I am not unkind”
She looked at me, I looked at something
Written across her scalp
And these are the words that it faintly said
As I tried to call for help…

— From Whistling in the Dark, by They Might Be Giants

  • The Cynic
  • The Realist
  • The Optimist
  • The Apathetic

Further Reading:

The Utopian vs. the Dystopian


Since these pair up nicely (Realism and Apathy, Optimism and Cynicism), perhaps one could combine them as Optimistic Realism, Optimistic Apathy, Cynical Realism, Cynical Apathy.


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.


Tractatus Logico-Philosophicus

Just the facts, ma’am.

— Detective Joe Friday

  1. The World (Die Welt): The world is everything that is the case.
  2. The Case (Der Fall): What is the case, the fact, is the existence of atomic facts.
  3. The Picture (Das Bild): The logical picture of the facts is the thought.
  4. Thought (Gedanke): The thought is the significant proposition.
  5. Propositions (Der Satz): Propositions are truth-functions of elementary propositions.
  6. The Form (Die Form): The general form of truth-function is: [p-bar, xi-bar, N(xi-bar)].
  7. Silence (Schweigen): Whereof one cannot speak, thereof one must be silent.
  8. ( ):

The Tractatus has seven propositions, most with sub-propositions and sub-sub-propositions, etc. I have added the eighth, which is the actual silence of all one cannot speak of. Quite a large section, for all its emptiness.

I also thought it would be nice to have an internet version where you could click and expand down through the sub-sentences. There are already many such versions available for your enjoyment.

I can’t decide whether I like the English or the German version better, so here are both.

Further Reading:

The Tricky Truth about Tractatus Trees (updated)



Aristotle’s Four Questions of Inquiry

At the beginning of the second book of his “Posterior Analytics”, Aristotle claims that there are four questions for investigating the nature of things and their properties. The answers to these questions hopefully gives us “demonstrable” knowledge about them, or knowledge of a “scientific” nature.

  • That it is (to hoti) : Is it a fact that a thing has a property? (Is this that?) “the question of fact” knowing-that
  • Why it is (to dioti) : Why does a thing have a property? (Why is this that?) “the question of reason or cause” knowing-why
  • Whether it is (ei esti) : Does a thing or property exist? (Does this or that exist?) “the question of if it is or of existence” knowing-if
  • What it is (ti esti) : What is the nature and meaning of a thing or property? (What is this or that?) “the question of what it is or of being or essence” knowing-what

The original terms were innovative in their ancient Greek, and even today cause some confusion in their translation and explanation (at least for this reader, so pardon the multiplicity of phrasings). It seems these questions are more about kinds or universals and not individuals or particulars, so they aren’t really about agents or locations or times (such as who, where, when).

The questions naturally fall into two sets of pairs: the first pair being between a thing and a property (binary), with the first question leading to the second question (knowing the fact comes before knowing the reason for the fact), and the second pair being just about a thing (unary), again with the first question leading to the second question (knowing the existence comes before knowing the essence).

In order to obtain a demonstration that an answer to one of the two questions to hoti or to dioti is correct, Aristotle reasoned that a “middle thing” is needed, a “link” between question and answer. Four types of cause are given, two of which borrowed from his Four Causes (Efficient and Final), and two others (those of definition and of “an antecedent that necessitates a consequent” (does this mean logical entailment or consequence?)).

Robert Sokolowski in the article cited below calls the ei esti and ti esti questions hermeneutic in comparison with the scientific questions to hoti and to dioti, and argues that each pair of questions reciprocally compliment the other, rather than one pair being dependent on the other. That is because the existence and the essence of things being sought after are indeed the “links” being sought after in the how and the why questions.

Obviously these concepts are too deep to be understood at a simplistic level, which is all I have managed so far.

Further Reading:

Click to access McK-Hellenistic&RomanFdnsOfAristotleInWest.pdf

Robert Sokolowski / Scientific and Hermeneutic Questions in Aristotle, Philosophy & Rhetoric, Vol. 4, No. 4 (1971), pp. 242-261

Patrick Hugh Byrne / Analysis and Science in Aristotle


[*11.142, *11.144, *11.146, *11.163]




The Free Will Theorem

The Free Will Theorem of Conway and Kochen is an interesting argument that tries to suggest free will goes “all the way down”. If experimenters can make their choices freely on how to measure certain experiments then the elementary particles being measured can make “free choices” as well. But the contrapositive of this result seems more interesting to me: if some elementary particles are not free, then the experimenters aren’t either!

I’ve cheated some here because it is really based on three axioms or assumptions, and not four. All for the sake of science (and philosophy)!

  • Fin : Information transmission has a maximal (finite) speed, and obtains from causality
  • Twin : For two elementary particles, it is possible to quantum “entangle” them, separate them significantly, and measure the square of their spin in parallel directions (but “full entanglement” is not required)
  • Spin : For certain elementary particles of spin one (the vector or gauge bosons: gluons, photons, Z and W), the squared spin component (taken in three orthogonal directions) will be a permutation of (1,1,0)
  • Min : Instead of Fin, the weaker assumption Min states that the spin measurers need only be “space-like” separated and make choices independently of each other
  • Lin : Instead of Fin or Min, Lin is an even weaker assumption that rests on experimentally testable “Lorentz Covariance”

If nothing else, trying to understand this theorem teaches you a bit about elementary particles and quantum physics!

Further Reading:

Click to access rtx090200226p.pdf



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]



The Four Types of Knowledge

What types of knowledge are there?

In his Nicomachean Ethics (Book VI), Aristotle famously describes several intellectual virtues. There is Techne, or Art; Episteme, or Knowledge, Phronesis, or Prudence, Sophia, or Wisdom, and Nous, or Intellect. He considered Sophia a combination of Nous and Episteme, but some others think it stands alone. Nous also seems to be more subjective, as well as supplying Phronesis with its aims, but is complicated. So are there three types, or five? I would like there to be four, thank you very much.

In Venharanta and Markopoulos’s paper, Phronesis seems to be the balance or sum of Techne, Episteme, and Sophia. In Carsten Pedersen’s web article, Techne, Episteme, Sophia, and Phronesis form a fourfold, with Nous in the center. Jon Alan Schmidt, a member of Virtuous Engineers, distinguishes between kinds of knowledge (Techne, Episteme, and Phronesis) and forms of human activity associated with them (Poiesis, Theoria, and Praxis). I like this distinction. What is the activity associated with Sophia?

Not knowing any Greek puts me at a disadvantage. Nous is linked to Noesis as a type of knowledge and Noein which seems to be the activity. I will present the following table and see how I like it!

Forms of
Human Activity
Types of
Theoria Episteme Science
Praxis Phronesis Prudence
Poiesis Techne Craft
Noein Sophia Wisdom

Further Reading:

It’s all Greek to me: The terms ‘praxis’ and ‘phronesis’ in environmental philosophy

Knowledge for Aristotle & Plato

Kurt von Fritz / ΝΟΥΣ, Noein, and Their Derivatives in Pre-Socratic Philosophy (Excluding Anaxagoras):
Part I. From the Beginnings to Parmenides, Classical Philology, Vol. 40, No. 4 (Oct., 1945), pp. 223-242

Kurt von Fritz / ΝΟΥΣ, Noein, and Their Derivatives in Pre-Socratic Philosophy (Excluding Anaxagoras):
Part II. The Post-Parmenidean Period, Classical Philology, Vol. 41, No. 1 (Jan., 1946), pp. 12-34

Vanharanta H., Markopoulos E. / Visualization of the Wisdom Cube Scientific Knowledge Space for Management and Leadership. In: Kantola J., Nazir S. (eds) Advances in Human Factors, Business Management and Leadership. AHFE 2019. Advances in Intelligent Systems and Computing, vol 961. Springer

In Danish (English via Chrome translation):

Bent Flyvjerg / Making Social Science Matter: Why Social Inquiry Fails and How it Can Succeed Again

Interesting Anime:

[*3.34, *11.130]


The Arcane Arts of Ramon Llull : the Dignities

Oh, Ramon Llull, where have you been all my life? I’m sure he’s been there all along, death now over seven hundred years in the past, just like always. His legacy seems at first glance to be quite the essence of medieval religion and scholastic philosophy, but still significantly and obscurely different to be enticing to this one. And on further examination, much more.

My schema above has little to do with his grand elaborate figures, except for listing the sixteen attributes he called “dignities”. Llull’s diagrams are full of clock-like wheels within wheels, complicated tableau, and combinatorial patterns. He wished to create a universal model to understand reality, and who wouldn’t want to discover the same? It is said that his methods are akin to an early computer science, and I’m just now starting to understand why.

The magister based the substance of his methods on his Christian faith, although he converted in midlife from Islam. Living in Barcelona, it was probably a good place to make such a change, but felt his calling was to convert others as well, so traveling he went. The methods he developed to convince others of their errors in belief were quite remarkable, as were the volume of his writing.

Like Gottfried Wilhelm Leibniz, who lived four hundred years later and was influenced by him, Llull wished to automate reasoning. But instead of building mechanical devices, Llull built computers from paper and ink, rulers and drawing compasses, scissors and glue. And instead of numbers as the smallest tokens of his computer, he used abstractions (i.e. words) that he felt would be understood by everyone in exactly the same way.

For example, he enumerated these sixteen dignities or aspects of his Christian diety, although sometimes he used the first nine. His constructions allowed one to pose questions and then obtain answers mechanistically that would be convincing to all observers of the correctness of the result. Too bad he was ultimately stoned to death while on his missionary work, although he lived to be eighty two.

Llull’s devices remind me of some of my pitiful charts and diagrams, and make me wonder if I may either adapt some of his techniques to my own use, or be inspired to develop others. I suspect I have locked myself into limitations by my approach, or are these constraints to my advantage? It might be hard to have spinning elements, but I can envision sliding elements like Napier’s Bones, origami-style folding and pleating, and even physical constructions like linkages and abacuses.

Now a martyr within the Franciscan Order, Llull’s feast day is June 30, which I’ve now missed. I hope to remember him to repost or improve on this by next year.

Further Reading:

The memory wheel



Richard McKeon’s Aspects of Knowing, Part 3

Previously on this blog:

Each method can be associated with a discursive process: operational with debate, dialectical with dialogue, logistic with proof, and problematic with inquiry. Each method is also associated with a mode of thought which in turn has two moments and one dependency or assumption: the operational method is debate by discrimination and postulation dependent on chosen theses, the dialectical method is dialogue by assimilation and exemplification dependent on changeless models, the logistic method is proof by construction and decomposition dependent on indivisible constituents, and the problematic method is inquiry by resolution and question dependent on discoverable causes.

For this diagram, the four dependencies or assumptions are in the center, and the associated methods are adjacent to them. Filling out the outer edge are the four pairs of moments. Listed, these facets are:

  • Methods (associated discursive process): Operational (Debate), Dialectical (Dialogue), Logistic (Proof), Problematic (Inquiry)
  • Assumptions: Chosen Theses, Changeless Models, Indivisible Constituents, Discoverable Causes
  • Modes of Thought: discrimination and postulation, assimilation and exemplification, construction and decomposition, resolution and question

The second diagram comes from a chart in McKeon’s “Philosophic Semantics and Philosophic Inquiry”. Here, the four methods are in the upper left corner (Universal) and lower right corner (Particular), and four principles are in the lower left corner (Meroscopic) and upper right corner (Holoscopic). Four interpretations are in the center (the vertical pair is Ontic, and the horizontal pair is Phenomenal), and four selections are adjacent to them. Listed, these facets are:

  • Methods: Operational, Dialectical, Logistic, Problematic
  • Principles: Simple, Actional, Comprehensive, Reflexive
  • Interpretations: Existentialist, Entitative, Ontological, Essentialist
  • Selections: Knower (Types), Knowable (Matters), Knowledge (Hierarchies), Known (Kinds)

Note that the Archic Matrix of Watson and Dilworth is essentially derived from this, and even has many of the same terms. However and obviously, the sixteen-fold arrangements of the two diagrams are different.

Further Reading:

[*5.184, *5.185, *6.20, *11.102, *11.106]