Archive for the ‘Philosophy’ Category

Four Philosophies, V2

August 9, 2017

Thinking some more on Popper’s Three Worlds, here is a set of philosophical disciplines that seem to resonate with the themes of this blog.

  • Phenomenology: the philosophical study or theory of phenomena as distinct from that of the nature of being
  • Epistemology: the theory of knowledge, especially with regard to its methods, validity, and scope
  • Ontology: the branch of metaphysics dealing with the nature of being
  • Axiology: the philosophical study of the nature of value and valuation, and of the kinds of things that are valuable

I believe that one could also make a case for associations with phenomenology to the subjective, epistemology to the objective, ontology to the substantive, and axiology to the normative.

Further reading:

https://www.quora.com/What-does-ontology-epistemology-and-axiology-mean

http://cognitive-edge.com/blog/phenomenology-epistemology-ontology/

(Note that the author of the article above, David Snowden, is the creator of the Cynefin Framework.)

https://en.wikipedia.org/wiki/Phenomenology_(philosophy)

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

http://www.iep.utm.edu/phenom/

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

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

http://www.iep.utm.edu/epistemo/

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

https://plato.stanford.edu/entries/logic-ontology/

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

https://plato.stanford.edu/entries/value-theory/

https://equivalentexchange.wordpress.com/2015/05/14/four-philosophies/

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The Ogdoad: Unity of Eight Gods

March 24, 2017

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 or primeval waters and its oppositional heaven
  • 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:

http://www.sacred-texts.com/afr/stle/stle12.htm

https://henadology.wordpress.com/theology/netjeru/hermopolitan-ogdoad/

http://www.kheper.net/topics/Egypt/Hermopolis.html

http://www.secretoftheankh.com/

http://www.doremishock.com/articles/thememphitetheology.htm

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Analogical Thinking

January 20, 2017

sq_analogicalIs analogy or metaphor the root of thinking? Some thinkers think so. But what exactly is analogy?

Looking at various lists of analogies of the A:B::C:D motif, I have distilled them into four groups: Relational, Hierarchical, Linguistical, and Mathematical. Are there analogies that don’t fit this scheme?

Relational

Object / characteristic
Order, sequence
Transformation
Agent / object, action
Function, purpose
Cause / effect
Source / product

Hierarchical

Classification, category, type, membership
Whole / part
General / specific

Linguistical

Meaning, definition
Synonym, antonym
Contrast, degree, intensity
Word parts
Expressions

Mathematical

Equivalence
Multiples
Negation
Patterns, geometries
Number
Size, magnitude
Direction, vectors
Spacial, temporal
Ratio, proportion

References:

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

http://www.nyjournalofbooks.com/book-review/surfaces-and-essences-analogy-fuel-and-fire-thinking

View story at Medium.com

Currently Reading:

George Lakoff, Mark Johnson / Metaphors We Live By

To Read:

Douglas Hofstadter, Emmanuel Sander / Surfaces and Essences: analogy as the fuel and fire of thinking, Basic Books (2013)

Noah Roderick / The Being of Analogy, Open Humanities Press (2016)

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

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Distinctions with and without Differences

September 24, 2016

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.

References:

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

https://en.wikipedia.org/wiki/Becoming_(philosophy)

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

Also see:

Statistical Thermodynamics

One and Many

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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:

http://ndpr.nd.edu/news/59251-tetralogue-i-m-right-you-re-wrong/

https://www.timeshighereducation.com/books/tetralogue-im-right-youre-wrong-by-timothy-williamson/2018800.article

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

Also see:

https://equivalentexchange.wordpress.com/2015/05/14/four-philosophies/

https://equivalentexchange.wordpress.com/2011/12/09/stances-towards-truth/

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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.

References:

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes

https://equivalentexchange.wordpress.com/2011/09/23/spacetime/

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Categories of Experience

March 23, 2016

sq_categoriesThe philosophy of Charles S. Peirce is chock-full of triples, but especially present are his three universal categories of experience. Threes aren’t really my specialty, but while reading a chapter of Richard Bernstein’s book on the “pragmatic turn”, I was reminded of Peirce’s relational ontology: Firstness, Secondness, and Thirdness. Wondering how these could be extended to a Fourthness, I immediately found a fair amount of work on the subject.

Of course, Peirce argued that such a Fourthness was redundant, unnecessary to the structure of his systematic philosophy. He used various reasons for his conclusions, including mathematical, logical, and semiological. There is also a wealth of subsequent work by later researchers on defending this claim, but what is interesting is that others have investigated extending his three into a four.

So, what might be Fourthness? Some of the aspects of fourfolds collected here have commonalities with some of the attributes of Firstness, Secondness, and Thirdness. For Firstness: feeling, quality, possibility; For Secondness: will, fact, existence; For Thirdness: knowledge, law, representation. I really don’t have anything to add at the present time and I have merely gathered these notions together for my future consideration.

References:

http://en.wikipedia.org/wiki/Categories_%28Peirce%29

http://en.wikipedia.org/wiki/Hypostatic_abstraction

http://www.paulburgess.org/triadic.html

http://tetrast.blogspot.com/2006/09/compare-to-aristotle-aquinas-peirce.html

Carl G. Vaught / Semiotics and the Problem of Analogy: a critique of Peirce’s theory of categories. Trans. of the Charles S. Peirce Society, Vol. 22, No. 3 (1986) 311-326

http://www.jstor.org/stable/40320143

Carl R. Hausman / Fourthness: Carl Vaught on Peirce’s categories. Trans. of the Charles S. Peirce Society, Vol. 24, No. 2 (1988) 265-278

http://www.jstor.org/stable/40320211

Donald W. Mertz / Peirce: logic, categories, and triads. Trans. of the Charles S. Peirce Society, Vol. 15, No. 2 (1979) 158-175

Richard J. Bernstein / The Pragmatic Turn. Polity (2010)

Also:

Ben Goertzel / The Hidden Pattern: a patternist philosophy of mind

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Four Transformations of Chu Spaces

November 29, 2015

sq_four_transformationsCan mathematics help us reformulate Cartesian Dualism? I have previously tried to diagram some of computer scientist Vaughn Pratt’s notions, such as a Duality of Time and Information and the Stone Gamut. Another recent attempt is the diagram above of four transformations that issue out of his analysis of Chu Spaces. Pratt’s conceptualization of these generalized topological spaces led him to propose a mathematization of mind and body dualism.

The duality of time and information was actually an interplay of several dualities, such as the aforementioned time and information, plus states and events, and changing and bearing (or dynamic and static). The philosophical mathematization in his paper “Rational Mechanics and Natural Mathematics” leads to additional but somewhat different dualities, shown in the following table:

Mind Body
Mental Physical
States Events
Anti-functions Functions
Anti-sets Sets
Operational Denotational
Infers Impresses
Logical Causal
Against time With time
Menu Object
Contingent Necessary

Pratt reveals two transformations that are “mental”: delete and copy, and two that are “physical”: adjoin and identify.

These four transformations are functions and their converses which:

  • Identify when the function is not injective.
  • Adjoin when the function is not surjective.
  • Copy when the converse is not injective.
  • Delete when the converse is not surjective.

Ordinarily we think of mind and body as being radically different in kind, but perhaps they are the same but merely viewed from a different perspective or direction. Recall what Heraclitus says, “the road up and the road down are the same thing”.

References:

https://en.wikipedia.org/wiki/Dualism_%28philosophy_of_mind%29

http://boole.stanford.edu/pub/ratmech.pdf

http://chu.stanford.edu/

http://en.wikipedia.org/wiki/Chu_space

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Pick Your Causation

September 10, 2015

sq_causationCausation is one of the most important ways in which we conceptualize the world and ourselves. The reasons that objects go through their motions and people perform the acts they do are explained by the causes that lead to these effects. Constitutive materials can also be causes for the effects on things and individuals. Even the form and function of things can be thought of as effects, dependent on the causes that make them come to be. These effects in turn can be causes for subsequent effects, and so on, in a complex chain or network of causation.

Four different “directions” inform discussion about causes and effects, organized by time (Forward and Backward) and space (Upward and Downward). Perhaps space is not the best word: consider size, distance, or even importance. These four directions can also remind one of Aristotle’s Four Causes, where Efficient Causation is Forward, Formal Causation is Downward, Material Causation is Upward, and Formal Causation is Backward.

Forward causation: Temporal causation, where causes happen before their effects. Ordinarily associated with a deterministic view of causation.

Upward causation: Scientific causation, where the smaller or lower cause the effects of the larger or higher. Ordinarily associated with a reductionistic view of causation.

Downward causation: Structural causation, where the larger or higher can cause the effects of the smaller or lower. Typical examples are free will, agency, intention, or volition, where the mind and not just the brain controls the actions of the body.

Backward causation: Reverse temporal causation, where causes are in the future of their effects. This is not quite the same as teleology, although the concepts are closely linked and require further study. Typical examples are purposes, goals, and ends (versus means) (although this is not the usual philosophical meaning of backward causation).

References:

http://plato.stanford.edu/entries/causation-backwards/

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

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

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

http://www.nbi.dk/~emmeche/coPubl/2000d.le3DC.v4b.html

Also see these related posts:

https://equivalentexchange.wordpress.com/2010/08/12/aristotles-four-causes/

https://equivalentexchange.wordpress.com/2010/08/11/a-warning/

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The Marriage of Opposites

August 29, 2015

sq_marriageThe road up and the road down are the same thing.

— Heraclitus

The Marriage of Opposites, or Chemical Wedding, or Coniunctio Oppositorum, is a term from alchemy that means combining two opposite substances, or essences, or even ideas into a unity greater than the sum of its parts. This term has also meaning in Jungian psychology as Jung showed many parallels between the processes of self-understanding and alchemy. For example, the marriage of opposites is symbolized by the union of the Animus and Anima.

Opposites are everywhere in our everyday lives and language. They are also prevalent in our social institutions such as religion, politics, philosophy, and science. There are long lists of opposites of life and language and institutions: spatial, temporal, relative, linguistic, mathematical, social, normative, philosophical, and mythological.

A + A’ = ?

What does it mean to combine two opposites into one? Does it mean that the two things are no longer extant and only the combination remains, or that the thing is its own opposite (e.g. 1 + -1 = 1)? Does it mean that a new, third thing is now created that incorporates both of the originals but they still exist as well, like Hegel’s thesis, anti-thesis, synthesis (e.g. 1 + -1 = 3)? Or does it mean that the originals annihilate each other, and nothing remains (e.g. 1 + -1 = 0)?

Usually the casual causal combination of opposites leads to an averaging of the two. For example if hot and cold liquids are combined, soon you will just get a tepid mixture. This is entropy, where the difference between the hot and the cold material is soon eliminated by the blending of the parts, and in this case actually fueled by the energy of the hot molecules.

The usual meaning of this Chemical Wedding is rather esoteric or mysterious. I propose that what the term “marriage of opposites” really means is quite different. Each “opposite” is an opposing pair itself, so that the marriage is between two pairs instead of two things. Instead of a unity, I suggest that this is the root of multiplicity. Instead of simplicity, there obtains organized complexity. Two pairs of two things yields four things in many ways: 2 + 2 = 2 * 2 = 2 ^ 2 = 4.

Let A and A’ be a pair of opposites, as well as B and B’. Then we can consider a union between those pairs to be:

(A + A’)(B + B’) = AB + AB’ + A’B + A’B’

Our individual genetic material is really a marriage of opposites in that half of it comes from each of our parents. Like Mendel’s peas, the sexual union generates the possibility of four versions of each feature. Similarly, the combination between two pairs of opposites generates a fourfold of possibilities.

How should one arrange such a union on a diagram? In Aristotle’s Square of Opposition, the true opposites are at opposite corners of a square, the “contradictories” (one is true and one is false). There are also “contraries” (cannot both be true), “subcontraries” (cannot both be false) and “subaltern” (only one implies the other) relations between corners. But the square is built from the logic of quantifiers and properties, different from this fourfold.

They can be arranged as the cycle AB + AB’ + A’B’ + A’B: One can naturally consider AB and A’B’ to be opposites, as well as AB’ and A’B. One can start with the two opposite pairs crossed, and this cycle sequence arises simply between them. Also, one nice feature is that only one of A or B needs to be changed to its opposite as we move around the cycle, even as we return to the beginning of the sequence. This is called a “gray code” in terms of binary numerals.sq_marriage2

They can be arranged as the grid AB + AB’+ A’B + A’B’: Here the opposites fall across a diagonal that runs southwest to northeast. This doesn’t have the nice properties of the cycle above, but I have used it for many of my diagrams. Instead of a cyclic symmetry, we have a dynamic symmetry about this diagonal that runs from an imagined origin of separation towards greater mixing and combination. This is the usual binary numerical sequence.

References:

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

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

Notes:

Interestingly, while thinking about the next stage in the 2 + 2, 2 * 2, 2 ^ 2, … series, I found that the superexponential or exponential tower operation is called “tetration”. In fact, Tetration( 2, 2) = 4 as well.

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

Also, consider “Mirage of Opposites”!

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