iSoul In the beginning is reality

Tag Archives: Means And Extremes

means, medians, middles, and centers vs. extremes, ranges, and spans

Capitalism and socialism

Wikipedia notes: The initial usage of the term capitalism in its modern sense has been attributed to Louis Blanc [a socialist] in 1850 and Pierre-Joseph Proudhon [an anarchist] in 1861. Karl Marx and Friedrich Engels referred to the capitalistic system (kapitalistisches System) and to the capitalist mode of production (kapitalistische Produktionsform) in Das Kapital (1867). The use of the word “capitalism” in reference to an economic system appears twice in Volume I of Das Kapital, p. 124 (German edition), and in Theories of Surplus Value, tome II, p. 493 (German edition). Marx did not extensively use the form capitalism, but instead those of capitalist and capitalist mode of production, which appear more than 2600 times in the trilogy Das Kapital.

In short, socialists invented capitalism, which is to say, they invented an ideology as a foil for their ideology. Once we step outside the ideology of socialism we do not find the ideology capitalism but instead economic liberty and attempts to deny economic liberty. Socialism is an ideology which (among other things) attempts to deny economic liberty and in its place implement an ideology called socialism.

Ideologies are inherently idealist in the philosophical sense of asserting that reality is mental or immaterial. Most ideologues are idealists as the words would imply, but some – notably Karl Marx – claimed to be materialists. Either way, ideologies are inherently anti-realist.

Realists (at least as realists) do not promote ideologies but instead independent realities that are discovered, not invented. Economic liberty was gradually discovered and matured into modern markets and finance. Over time it is inevitable that some people will accumulate more wealth than others as long as economic liberty allows people to express their talents and inclinations. That can cause social problems which may legitimate state intervention.

That is not an endorsement of the ideology socialism but a recognition of the complementarity of liberty and equality in society. A realist response on how to reconcile these two priorities would follow a dialectic of complementarity to find a satisfactory mean between the extremes. Instead what many societies are dealing with is a dialectic of contradiction which tries for an extreme of liberty or (more often) equality alone. This is a prescription for instability, unsustainability, and worse.


The problems with the two extremes of government are well known. Monarchy, oligarchy, aristocracy, plutocracy, and the like are all forms of government in which one person or a small group of people have almost all the authority, land, power, wealth, etc. The problem is that either they are not necessarily wise or competent or benevolent so that the resulting government is generally corrupt and serves the self-interest of the few rather than the interest of the many.

On the other hand the problems of democracy are also well-known, even if they are forgotten or over-shadowed by ideals of egalitarianism or libertarianism. As the ancient Greek democracies show, people exploit the public purse for private purposes, until bankruptcy ends the game. Unfortunately, poor people are inclined to vote for those who give them the most rather than consider the interest of the whole.

The solution to this lacks a word, so I’ll invent one: midocracy, rule of the middle class. The richest and most powerful people should be excluded from voting and ruling since their self-interest is too much for perpetuating their dominance rather than considering the welfare of the whole. The poorest and least powerful people should also be excluded from voting and ruling since their self-interest is too much for undermining the higher classes and impoverishing the whole.

The solution is to let the middle class alone vote and rule. Their interests are balanced between maintaining stability while allowing some change and using of the public purse for some public purposes. The middle class is the most balanced between stability and change, spending and saving, private and public interests. A healthy middle class is the best guarantee of freedom and justice, peace and prosperity for the long term.

The necessity of philosophy

The contemporary world is characterized, among other things, by the cult of the expert.  It is widely and officially accepted that the expert and only the expert can speak authoritatively on a given subject.  So extensive is this cult that once someone has become a certified expert in one field, they are often assumed to be experts in other fields, whether or not they actually have the qualifications.

How do we know who is an expert on what subject?  The experts tell us!  As long as the experts support one another’s claims to expertise, they constitute a closed system and everyone else is supposed to accept them all.  But if some experts disagree with other experts, no end of problems can result.  This is such a disastrous possibility that it is often suppressed.  If an expert disagrees with the predominant expert option, their expert status must be taken away.

So the cult of the expert becomes an all-or-nothing proposition.  Either one accepts all the certified experts or one rejects the whole idea.  And this basic proposition must be decided by people who are not experts.  That is the irony of the cult of the expert.

But it was not always this way, nor must the cult of the expert necessarily continue.  Let us briefly consider what life would be like without the cult of the expert.  That is, what if people were encouraged to think for themselves?  Would civilization crumble?  Or would it flourish in ways that no-one can predict?

The starting-point for this project must be something that is available to anyone that is close at hand, that is within the grasp of anyone who wants to think for themselves.  There must be no expertise required!  Sometimes it is called “common sense” although that is an ambiguous term.  I prefer to all it high-level thinking in contrast to the detail-level thinking that requires special education or experience.

One of the problems that experts are prone to is seeing the trees but not the forest – missing the larger picture because they are focused on details.  Of course, they can retort that the amateur sees the forest but not the trees, meaning they make mistakes by overlooking important details.  Agreed; there are potential problems either way.  In taking a high-level approach, we shall have to take care to avoid hasty generalizations and mistaken identifications.

This is the task of philosophy.  With nothing more than a love of wisdom and a curious mind, we launch out to gain sufficient understanding to live wisely – that is, to gain wisdom.

One method to approach a question is to look at extreme answers in order to frame the issue.  In common experience, extremes are rare so we make expect to find answers somewhere in between.


Extreme positions

Evolutionists are extreme “lumpers” as far as classification goes: there is only one kind of life (or stuff) and all differences are a matter of degree.  The problem for science is that differences of kind cannot be demonstrated unless one first accepts some criteria for differentiating them, which evolutionists won’t do because it would lead to the demise of evolution.

Another approach is to look at the opposite extreme that every individual is different in kind (historically called occasionalism).  By focusing on the particulars one can always find differences between two things and by exaggerating their significance they become differences in kind.

These two extreme positions (evolutionism and occasionalism) are symmetric: they are both right or both wrong.  But by symmetry if one of them is wrong, the other must be wrong, too.  So evolution cannot be right.

In Bayesian terms these are extreme priors and Bayesian calculations don’t work for extreme priors.  So Bayesianism needs to be modified to begin not with mere belief but with data and simple generalization of data.  Then new data can be used to adjust the current generalization rather than give new hypotheses equal weight to old generalizations.  It should be more like exponential smoothing with greater weight given to well-tried theories than to new data — scientific practice is more like this anyway.

Notice how our opponents keep trying to focus our attention on new evidence such as radiometric data.  Our answer should first be, What about the old data such as evidence of a world-wide deluge?  They have no right to dismiss that.  Our opponents abuse the desire for progress into denigrating the past altogether.  But it is precisely the knowledge of previous generations that is at stake here.  Our opponents can emphasize how up-to-date they are; we have the wisdom and knowledge of the ages behind us.  Only a culture that trashes its past can defeat us.

December 2014

Convergent induction

History of Chemistry, Simplified

The simplest universe has only one kind of substance, which was the first scientific theory, that of Thales (ca 585 BC) who stated that the origin of all matter is water. Then there was Anaximenes, who held that everything in the world is composed of air. Xenophanes said, It’s all Earth. No, it’s all fire, said Heraclitus.

Empedocles combined them all in his theory that all matter is made up of four elemental substances – water, air, earth, and fire – in fixed quantities. The Pythagoreans taught that all things are composed of contraries. Aristotle combined the four elements of Empedocles and the contraries of the Pythagoreans and said that every substance is a combination of two sets of opposite qualities – hot and cold, wet and dry – in variable but balanced proportions.

Leucippus and Democritus disagreed with this approach and took the opposite position that all matter is made up of imperishable, indivisible entities called atoms. The atomic approach languished until many years later it was revived during the Renaissance. It was further developed by Dalton and others in the 19th century. Basic combinations of atoms, called elements, came to be seen as the building blocks of all substances. The list of elements was expanded into the Periodic Table which is key to the very successful science of chemistry today.

The so-called Ockham’s Razor, which may be stated “entities must not be multiplied beyond necessity”, is usually understood as a preference for simplicity. But it ignores trade-offs between, for example, a plurality of substances and a plurality of entities. Which is simpler, Thales’ single substance in many forms or Democritus’ single form but many entities?

Convergent Induction

There are three related lessons to be taken from this brief historical review: (1) science starts with simple, extreme positions; (2) for every simple, extreme position there is an opposite simple, extreme position; and (3) science develops complex, intermediary positions between simple extremes.

(1) It is well-known that science follows a principle of simplicity (parsimony) which leads it to start with overly simplified ideas, find their empirical weaknesses, and then gradually add complexity. As A.N. Whitehead said, “Seek simplicity and distrust it”.

(2) Simplicity comes in pairs. This is demonstrated in the case of chemistry between the extremes of one or a few substances and the opposite extreme of many atoms. There is the simplicity of a few unique entities vs. the simplicity of many uniform entities. There is also the simplicity of simple stasis vs. simple dynamics. These contrary simplicities have loomed large in the history of science, and many other subjects.

(3) While science begins with simple, extreme positions, it does not stay there. It progresses toward complexity. In an analogue to the mathematical theorem that any bounded increasing (or decreasing) sequence is convergent, simple extremes provide the bounds that ensure progressive induction converges.

Thus science proceeds via convergent induction, which is bounded by simple extremes and seeks empirical adequacy by progressively converging toward a complex mean. The process is progressive in that each step introduces a complexity not present before. Convergence is ensured by bounding the progression with simple extremes.

It is most usual to begin with one extreme and work in the direction of the other extreme rather than to oscillate between opposites in a convergent way. In general, there are two strategies for inductive logic: (1) assume the most about what is unknown and (2) assume the least about what is unknown. Natural science takes approach (1) and statistical science takes approach (2).

There are two directions for each of these approaches. Statistical science may be approached from the direction of maximal or minimal knowledge. For example, if there is knowledge of the physical source of variability such as by examining a pair of dice, then a frequentist direction may be best. If little is known except some empirical data that are gradually available over time, then a Bayesian direction may be best.

Natural science also has two directions. The most that can be assumed about what is unknown is that it is like what is known. But that may be either because it is a different form of the same thing or because it is a different combination of the same constituents. The former direction is top-down, macrocosmic, whereas the latter direction is bottom-up, microcosmic or atomic. The atomic direction has proved to be the most fruitful for natural science.

Since the convergent is a kind of mean between the initial extremes, that leads to the question of whether it would be possible to follow means instead of extremes. One could start with a simple mean between the extremes and then adjust it to another mean as need be. Perhaps this would be more efficient.

October 2010

Means and Extremes

Means and extremes in classical mathematics have to do with proportions.

If A is to B as C is to D, we write A : B :: C : D.  This is ordered so that A is greater than or equal to B and C is greater than or equal to D.  A and D are called the extremes; B and C are called the means.

By elementary arithmetic the product of the extremes equals the product of the means:

A x D = B x C.

If B = C, then B is the mean proportional or geometric mean of A and D.  In that case B is the positive square root of A x D.

This provides a basic principle for centrism: the means are between the extremes in a principles manner.

The dialectic of extremes and means

The dialectic of extremes and means is a method of reasoning whereby one begins with extremes and reasons to means or vice versa.  If one begins with means, these are considered as unanalyzed entities, attributes, propositions, etc.  The goal is to work out the implications of them as principles or to analyze them into their constituent parts as a combination of extremes.  If one begins with extremes, these are considered as unsynthesized entities, attributes, propositions, etc.  The goal is to synthesize them into their fullness and completion as integrated means or to work from partial truths toward full truths.

We live among means, that is, we live in the middle ground, a mesosphere where things are muddled and messy but familiar and common.  Philosophy is often said to begin here, with what is commonly known rather than with specialized knowledge.  Whatever we find must come back to the middle ground where we live or else it is like a dream unrelated to our lives.

Classical deductive logic works from truths to their implications while preserving truth.  It assumes that truth is known at the beginning, that truths are known in the middle ground of life.  They may be known because they are axiomatic (worthy of assent) or because they are self-evident, or because they were given by a trustworthy source.  The outworking of such truths leads toward extremes.

The dialectic of reasoning from extremes to means is focused on the end, not the beginning.  It does not follow from truths; it leads toward truths.  One does not usually begin with truth.  One usually begins with something at hand, something muddled and messy.  Truth is something that must be sought.  This dialectic begins with partial truths and reasons toward full truth.

Extremes express simple but partial truths.  Proverbial statements often express extremes – that’s why there are often contrary proverbs.  For example, the Book of Proverbs includes these two:  Do not answer a fool according to his folly, or you will be like him yourself.  Answer a fool according to his folly, or he will be wise in his own eyes.  (Pr. 26.4-5)

There are many pairs of entities, attributes, propositions, etc., which express contrary extremes and are partially true.  For example, a preference for simplicity leads to extremes:  in classification and typology, the extremes are all elements in one class and every element in its own class.  Some people (called lumpers) tend to combine elements into fewer classes and others (called splitters) tend to split elements into more classes.  Who is right?  They are both partially right.

Reasoning from extremes to means may be deductive or inductive.  The deductive form works via a form of backward chaining.  It starts with a mean which is a hypothesis or goal and works backwards from the consequent to the antecedent to see if the extremes will support this or any of these consequents.  Instead of reasoning from truth, it is reasoning from partial truths.  The result is a combination of partial truths, which together form a complete truth.

As an illustration of reasoning from extremes to means, consider arithmetic.  Start by defining numbers recursively: if x is a number, then f(x) is a number.  For example, if x is a number then x+1 is a number.  (Addition could be left undefined at this point but let’s assume it is ordinary addition.)  Next, consider the extremes: what are the first last numbers, if they exist?

Answer A:  There is a first number; call it 0.  There is a last number; call it 2, where 2 is 0+1+1.  This is arithmetic modulo 3.

Answer B:  There is a first number.  Call it 0 (or 1, if you prefer).  There is no last number in the sense that there is no unique last number (the sequence must not converge and one can stop at any number arbitrarily).  We conclude that 0+1 is a number, as are 0+1+1, and so on in sequence without end.

Answer C: There is no first number in the sense that there is no unique first number.  There is a last number which depends on the recursion and the arbitrary first number (called the seed number).  The sequence must be convergent.  For example, let the seed number be 1 and the recursion such that if x is a number, then the reciprocal of x+1 is also a number.  This leads to the sequence 1, ½, 2/3, 3/5, 5/8, and so on.  The last number of this sequence is (-1+√5)/2, sometimes called φ (or 1/φ).  Notice that other seed numbers could lead to the same last number.

In these examples the numbers formed by the recursions are the means.  The extremes (those directly stipulated as numbers or used as seed numbers or formed by sequences) are not really numbers.  From ancient times a number has been defined as a multitude so the first number is the second member of the number sequence and there is no last number.  The extreme numbers are the limits of ordinary numbers.  Ordinary numbers are analogous to partial truths, and extreme numbers are analogous to full truths.

These examples lead to the observation that sometimes the extremes may be contrary in different and multiple ways.  First and last are natural extremes but other attributes may be contrary, too:  definite and indefinite, arbitrary and determinate, convergent and divergent, etc.

Conjecture: convergent and divergent sequences may be put into one-to-one correspondence.

November 2013

What is design?

“Design” is one of those terms many people use but few define.  Two aspects of design are: (1) to plan and (2) to make.  An evolutionist might say that “nature made man” but would never say “nature planned man.”  The theistic evolutionist might say “God planned man” but avoids saying “God made man” except in some secondary, remote way.  Design involves both planning and making.

There seems to be a third aspect: (3) to partially surprise.  Someone who does not plan their days either does the same thing over and over or else has a haphazard kind of life.  Language has an element of surprise in what is communicated and redundancy in the medium of communication.  An artist who makes something totally unique confuses people; an artist who is too conventional bores people — good art is a design between these extremes.

These two extremes have low and high entropy.  So evidence of design in this sense would be an entropy in the middle.  A mid-entropy is evidence of design.

October 2013

Science and simplicity

Scientific methodology makes extreme simplicity (or parsimony) a key quality of a hypothesis or theory. One flaw in this is that there are multiple kinds of simplicity. The cultural milieu then becomes the arbitrator of which kind of simplicity is preferred. Historically, one version of simplicity becomes dominant until another version overthrows it. Then it may take centuries for science to develop from a simple model to a composite of different explanatory variables.

For example, from classical times the simplicity was favored that the earth and the species on it are the same as they always were so no movement or speciation or extinction was thought to take place.  Discoveries in the 19th century such as extinctions discredited earth and species fixity which was then abandoned in favor of an opposite simplicity: slow, continual change with speciation of all life.

We can easily see where this is leading.  Theories of the future will be combinations of slow and fast changes, of fixity and speciation.

Whatever simplicity science starts with, it ends up in an intermediate place between extreme simplicities.  One conclusion is that simplicity is a simplistic place to start investigation.  Simplicity hurts science because scientists cling to it too tightly and mislead people with simplistic ideas about the world until centuries have passed and more sophisticated theories are developed.  Why not start from at least a combination of extremes instead of picking one and holding onto it until it is proved wrong?  That would be a more flexible and efficient method.

May 2013