T. S. Eliot: Four Quartets

August 12, 2016

sq_four_quartets5Time is a child playing dice.








The Four New Elements

August 8, 2016

sq_new_elementsFour new elements have been named! They are Nihonium (Nh 113), Moscovium (Mc 115), Tennessine (Ts 117), and Oganesson (Og 118).



Also see:




Timothy Williamson’s Tetralogue

August 5, 2016

sq_tetralogueA recent book of introductory philosophy is Timothy Williamson’s Tetralogue: I’m Right, You’re Wrong. Instead of using a dialogue with two viewpoints used by some classical philosophers, Williamson structures his book into a tetralogue, or a conversation with four viewpoints.

The viewpoints are portrayed by four individuals as they enjoy a lengthy train ride: Zac (Relativism), Sarah (Naturalism, Empiricism, Skepticism, Fallibilism, Materialism, Scientism), Bob (Culturalism, Traditionalism, Conservatism, Ancestralism), and Roxana (Rationalism, Logicalism).

Who’s right and who’s wrong? I haven’t read it yet but it looks interesting!

Several reviews:



A Twitter account to follow (I didn’t know it would do that):

Also see:



[*8.149, *9.146]


On Things, Thoughts, Words, and Actions

August 2, 2016

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

Review at:


Consequently, he closes by proposing “four principles for analyzing the relations among systems of things, thoughts, words, and actions.” As defined by Ulman, these principles are translation (the ordering of one set of relations such that it models selected aspects of other sets of relations); modeling (the creation of new relations by systematic translation); ordering (the response of one system of relations to changes in others); and autonomy (the capacity of one system of relations to resist ordering by others).

Also see:


[*5.197, *6.106, *6.140, *7.162, *8.120, *8.121]


The Semiotic Square

July 29, 2016

sq_greimasFrom Wikipedia:

The semiotic square, also known as the Greimas square, is a tool used in structural analysis of the relationships between semiotic signs through the opposition of concepts, such as feminine-masculine or beautiful-ugly, and of extending the relevant ontology.


In an earlier post I combined an unusual representation of the semiotic square with that of the Tetralemma. Please use this one instead.





The Fourfold Body

July 3, 2016

sq_tomb_templeAs an addendum to my previous post, I remembered the nice article below.

Anthony Synnott / Tomb, Temple, Machine and Self: The Social Construction of the Body, The British Journal of Sociology, Vol. 43, No. 1 (Mar., 1992), pp. 79-110


The body is socially constructed; and in this paper we explore the various and ever-changing constructions of the body, and thus of the embodied self, from the Greeks to the present. The one word, body, may therefore signify very different realities and perceptions of reality; and we consider briefly how and why these meanings changed.

Plato believed the body was a ‘tomb’, Paul said it was the ‘temple’ of the Holy Spirit, the Stoic philosopher Epictetus taught that it was a ‘corpse’. Christians believed, and believe, that the body is not only physical, but also spiritual and mystical,  and many believed it was an allegory of church, state and family. Some said it was cosmic: one with the planets and the constellations. Descartes wrote that the body is a ‘machine’, and this definition has underpinned bio-medicine to this day; but Sartre said that the body is the self.

In sum, the body has no intrinsic meaning. Populations create their own meanings, and thus their own bodies; but how they create, and then change them, and why, reflects the social body.

Also a book!

Anthony Synnott / The Body Social: symbolism, self, and society (1993)

[*6.142, *9.139]


The Fourfold Self

May 28, 2016

sq_fourfold_selfA recent post by Sandeep Gautam synthesizes several distinctions of the human being as self to come up with a nice fourfold model. These are the Materialistic (or perhaps Substantive), the Experiential or Experienced, the Remembered (or perhaps Visualized), and the Prospective or Anticipatory (or perhaps Envisioned). These can also be neatly labeled as “having”, “doing”, “being”, and “becoming”.

I have talked about Gautam before in my post The Fundamental Four of Sandeep Gautam. The fourfold discussed then was developed from evolutionary problems and drives but reminds me somewhat of this new fourfold, where Food/Foes -> Materialistic Self, Family/Friends -> Experiential Self, Focus/Frame -> Remembered Self, and Flourishing/Fun -> Anticipatory Self.

There are several other fourfold models of the self that are readily found. There is the ancient “Modes of Consciousness” from the Upanishads: Physical, Emotional, Intuitional, and Absolute. There is the anthroposophical model of Rudolf Steiner: Physical, Life/Etheric, Astral/Feeling, and Ego/“I”. There is the one by Friedrich Nietzsche: Deepest, Ego/“I”, Ideal/Higher, and True. And there is the religious or new age model: Body, Mind, Soul, and Spirit.

The problem with most of these older models of the self is the lack of consensus on the meaning and existence of the terms used in their construction, much less a way to know if the set is complete or not. Thus the fourfolds seem to be rather diverse and vague. I favor a more pragmatic and psychological approach in choice of models, plus those that can be easily mapped into Aristotle’s Four Causes, both attributes of which I see in Gautam’s models.

The comparison and contrast of these models to come up with a synthesis might still be a worthwhile future effort. There are also several fourfold models of the brain itself that could be entered in to the mix.

References and Links:







[*9.130, *9.132]


Buy One Get One Free

May 6, 2016

sq_free_group2Speaking of paradoxes, the Banach-Tarski Paradox is an interesting theorem in mathematics that claims that a solid 3-dimensional ball can be decomposed into a finite number of parts, which can then be reassembled in a different way (by using translation and rotation of the parts but no scaling is needed) to create two identical copies of the original structure. The theorem works by allowing the parts of the decomposition to be rather strange.

One of the important ingredients of the theorem’s proof is finding a “paradoxical decomposition” of the free group on two generators. If F is such a free group with generators a and b, and S(a) is the infinite set of all finite strings that start with a but without any adjacency of a and its inverse (a^-1) or similarly b and b^-1, and 1 is the empty (identity) string, then

F = 1 + S(a) + S(b) + S(a^-1) + S(b^-1)

But also note that

F = aS(a^-1) + S(a)

F = bS(b^-1) + S(b)

So F can be paradoxically decomposed into two copies of itself by using just two of the four S()’s for each copy. Both aS(a^-1) and bS(b^-1) contain the empty string, so I’m not sure what happens to the original one. One might think that aS(a^-1) is “bigger” than S(a) but they are actually both countably infinite and so are the same “size”.

The generators a and b are then set to be certain 3-dimensional isometries (distance preserving transformations which include translation and rotation). The rest of the theorem requires further constructions that may be of interest, as well as needing the Axiom of Choice or something like it. It is also curious that the paradox fails to work in dimensions of 1 or 2.

The diagram above tries to list the beginning of each of the sets S(a), S(b), S(a^-1), and S(b^-1). The empty string can be thought to occupy the center of the diagram but it is either not shown because it is empty, or it is shown as being empty. Alternatively one could create a more general fourfold with the aspects of structure, (paradoxical) decomposition, parts, and reassembly.






[*9.124, *9.125]


The Paradoxes of Zeno

April 21, 2016

sq_zeno_paradoxes5“Suppose,” said Zeno, “that Achilles and a tortoise are planning to race”.

Such is the beginning of a famous thought experiment by an ancient philosopher. Since athletic Achilles was much faster than the slow tortoise, he let the tortoise start first. But alas, he could never catch up to it, since every time Achilles made it to where the tortoise had been, the tortoise had moved just a little further ahead. Of course Achilles was faster so he had to pass the tortoise quickly unless it had started near the finish line. So, paradox!

Most of the paradoxes of Zeno were about fractions and entireties of time and space. Can an infinite series of fractions of space add up to a finite entirety of space in a finite entirety of time? Some might say that integral calculus solves these basically mathematical problems, yet others think they point to metaphysical issues as regards to the discreteness and the continuity of time and space.

This fourfold reminds me of my previous fourfold Spacetime which dealt with succession (as parts of time), location (as parts of space), extension (as wholes of space), and duration (as wholes of time). It must have been in the back of my mind.






Invention and Discovery

April 15, 2016

sq_learning2What are the differences between invention and discovery? Ever since my post Propositions as Types I’ve been trying to determine what they are. Some say that mathematics and logic are completely human inventions and they have no correspondence to the natural world. Others say that mathematics already exists in some “Platonic” realm just waiting for our discovery. Similar to convergent evolution, the parallel invention or discovery of similar notions in mathematics lends credence to the idea that there is something “out there” just waiting for us to find it, although one could also argue that it’s merely the cultural climate along with some innate functioning of the brain. For example there is the parallel development of calculus by Newton and Leibniz. The notion of effective computability in the “Propositions as Types” paradigm also has several concurrent developments.

Modern science is based on mathematics so as one goes so goes the other. Physicist Eugene Wigner wrote a famous article on the “Unreasonable effectiveness of mathematics in the natural sciences” which has inspired a host of similarly titled articles about the “unreasonable effectiveness” of one thing for another. But the key point is that we really don’t understand the origins of mathematical thinking, or why it is so useful in helping us understand the natural world. Its value and utility seems, in fact, unreasonable.

But let’s return to the differences between invention and discovery. If something is invented, it means that it is new, freshly created. If something is discovered, it means that it already exists and it’s just waiting for us to find it. Thus the difference is between the natural and artificial, or between what exists and what didn’t exist before humans created it. Some believe the natural world itself is socially constructed, so in some sense it didn’t exist before humans saw it, or will disappear when humans stop perceiving it. This is about is arrogant as believing that the world didn’t exist before a person was born or after they die; a solipsistic view if ever there was one.

Once something is discovered, one can learn about it. Once something is invented, one can make it. Thus learning and making are tied to discovering and inventing, respectively. Inventing and discovering are required for making and learning. Of course one can also learn about an invention or how something is made, or one can learn facts about a discovery.

This fourfold of inventing, discovering, learning, and making is also related to other fourfolds. The Four Hats of Creativity seem to utilize each of these special actions for each livelihood: inventing (or creating) for the artist, discovery for the scientist, and making for the engineer (but less well learning for the designer). In addition, the Psychological Types of Jung appear to emphasize a type for each special action: intuition for invention, sensation for discovering, and cognition for learning (but less clear emotion for making).

Please compare this with a related analysis on the methods of active learning at the Tetrast (link below), where the key faculties are struggle for invention, practice for discovery, value for making, and discipline for learning.








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