iSoul In the beginning is reality

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

Alternate arithmetic

A model is a realization of a mathematical formalism.  So ordinary arithmetic is a model of ordinary algebra.  That is, the algebra of the integers, the rational numbers, and the real numbers is realized by the arithmetic of the integers, the rational numbers, and the real numbers, respectively.  Are there other models of ordinary algebra?  Yes.  One alternate model in particular is a simple opposite of ordinary arithmetic and deserves the name alternate arithmetic.

The one-to-one correspondence between ordinary arithmetic and alternate arithmetic is as follows:

Property Ordinary Arithmetic Alternate Arithmetic
Origin 0
Ultimate 0
Unity 1 1
Duality 2 1/2
Left Order < >
Right Order > <
Minimum Digit 0 9
Maximum Digit 9 0
Minimum Decimal …000.000… …999.999…
Maximum Decimal …999.999… …000.000…

What is alternate arithmetic good for?  Ordinary arithmetic implicitly assumes beginning with nothing and adding something.  So the number N means 0+N.  Alternate arithmetic assumes beginning with everything and subtracting something.  So the alternate number N means 1/N.  That is, ordinary arithmetic is additive and alternate arithmetic is subtractive.  The square of opposition in quantification logic presents something similar.  None and some form an additive logic.  All and not all form a subtractive logic.

Instead of using alternate symbols, we may reinterpret the symbols of ordinary arithmetic.  In this way, alternate arithmetic looks exactly like ordinary arithmetic but means something opposite.  Or we may simply write the alternate number 1/N as N by abuse of notation.

November 2013

Evidence of Absence

Evidence of Absence: Completeness of Evidential Datasets

Elliott Sober presents a likelihood argument about the motto “Absence of evidence is not evidence of absence” (Sober 2009).  He states the Law of Likelihood this way:

The Law of Likelihood. Evidence E favors hypothesis H1 over hypothesis H2 precisely when Pr(E│H1) > Pr(E│H2). And the degree to which E favors H1 over H2 is measured by the likelihood ratio Pr(E│H1)/Pr(E│H2).

Read more →

The Bible vs. secular historical sciences

The Bible is diachronic but secular historical sciences are synchronic.  Let me explain.

The term “diachronic” arose in the study of the development of languages over a long time, which was the focus of linguistics in the 19th century.  But to make linguistics more scientific in the 20th century this changed to study languages as systems during particular time periods. The former approach was called diachronic, the latter synchronic.  These terms have come into use in history as the study of a people or place over a long stretch of time (diachronic) vs. the study of a time period over a large area (synchronic).

The Bible follows the Hebrew people over a long stretch of time, from their beginning on, which is diachronic.  The historical sciences are strongly synchronic: they study a wide area over a distinct period (or series of distinct periods) of time.

Synchronic linguistics is unified by the premise that languages have a common origin, a genetic relationship.  So the question becomes how to explain the differences between languages.  When this synchronic premise was applied to biological species, the question became how to explain the differences between species.

The Bible presents the opposite:  that biological kinds/baramin are distinct, though they have the same Creator.  So the question for a biblical biology is how to explain the similarities between distinct kinds/baramin.  A particular study might study a baramin over a long time.  Several of such studies might lead to the discovery of parallel changes in baramin that are explained by environmental changes and similar ways of adapting.  These are diachronic studies.

So the Bible and secular historical sciences diverge, not only because they have different premises but because they have different approaches to historical science.  The Bible is diachronic and secular science is synchronic.

November 2013

Appearance and reality

There’s a common idea that science shows appearances are often wrong.  It is said science shows that earth is not flat, the sun doesn’t go around the earth, and that life is not designed, all despite appearances to the contrary.  I think this is a mistaken view of what science has done.

Surveyors work with a flat earth model that works just fine for most purposes, and the sun’s motion relative to the earth can be described geocentrically.  Newton’s laws work fine for many purposes despite their being superseded by general relativity.

What happens is that theories are extrapolated (or interpolated) too far and they break down. A theory is superseded by one with a larger scope but the old theory may be valid within a restricted domain.  What Niels Bohr called the correspondence principle is the idea that a new theory should reproduce the results of older well-established theories in those domains where the old theories work.

So the problem is over-extrapolation (or over-interpolation).  Too often people make overly broad claims for a theory.  But until the limits of a theory are found, it may not be clear what the scope of the theory really is.

What is the scope of Darwinism?  As far as I can tell its scope is “life” as a single category, without differentiation of kinds organically or temporally.  This is a very narrow perspective, one that does not support the grandiose claims made for it.  And it is not helpful in understanding different kinds of life, particularly human life, or the age of the earth.

The Bible uses the language of appearances.  This is perfectly acceptable.  The Bible also gives God’s perspective, which is not a theory but something that theories can aspire to.  This is essentially what theologies do.

Nature is not out to trick us with deceptive appearances.  Old theories that worked still work.  All theories are limited.

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

Different sciences

It’s easy to forget that “nature” means the essence or form of something.  Over the centuries this morphed into nature as a “natural world” as if only some things have a nature — which is wrong.  Every thing or being has a nature, including God.  A natural science is the study of things/beings with a common nature or essence.

There is a hierarchy of natures/essences.  People have a human nature which includes the properties of an animal nature.  Animals have an animal nature which includes the properties that living beings in general have.  This should mean that the sciences of biology, zoology, and anthropology are related as a hierarchy.

Evolutionism undermines this hierarchy.  Evolutionism makes zoology a mere subset of biology.  But zoology should be more: it should be concerned with how the natural kind called “animal” is different in kind, not merely in degree, from other living beings.  Evolutionism denies that some beings are different in kind from other beings.  In fact extreme evolutionism makes everything from molecule to man to differ only in degree, not in kind.  Hence evolutionists talk about “science” rather than “sciences” because the differences are considered minor.

Different sciences should be distinguished according to the different kinds of things/beings that are studied.  This applies to geology, for example.  If geology is merely physics applied to earth, it is different in degree but not in kind from physics.  Geology should be understood as studying a unique kind of thing, the earth.  We could we even distinguish antediluvian geology as a separate science since the earth then was different in kind, not just in degree.

October 2013


Emil Brunner in Christianity and Civilization (1948) wrote: “the popular belief that the idea of evolution and progress was first worked out within natural science, and thence affected the conception of history, is false. The reverse is true: the idea has been transplanted from an evolutionary conception of history into natural science. Lamarck and Darwin are not the pioneers but the heirs of this modern idea. The real pioneers are men like Rousseau, Lessing, Herder, Hegel. The idea of progress and evolution is a child of the optimistic philosophy of the Enlightenment.”

Darwin cannot be toppled without toppling Rousseau/the Romantics, Hegel/Marx/”the Left”, Adam_Smith/Herbert_Spencer/”the Right”, etc.  The idea that progress is natural, inevitable, unlimited, etc. is thoroughly embedded in contemporary thought. No one wants to be on “the wrong side of history.”  So shooting at Darwin does not get to the foundations of the problem.

The idea of progress is seductive and has enough association with Christianity to make Christians fall for it.  After all, there is progressive revelation, Christianity has led to moral progress, knowledge has increased, etc. But true progress requires spiritual and moral development or intervention by God.  Progress is not naturalistic.

One thing creationists can do to make a difference is supporting alternatives to naturalistic progress.  As an example, the sustainability movement is aware how the myth of progress impedes the ability of Western civilization to continue much longer.  While political interests try to co-opt movements such as this, there is the potential for creationists to provide a biblical and scientific foundation for sustainability.  To do this would require an enlarged vision about the problem and the solution.

October 2013

Scientific history

The discipline of history investigates what actually happened in the past as far as that is known from records or other evidence.  Scientific history is what could have happened in the past without being inconsistent with the data or laws of science.  Note the difference: scientific history is about possibilities; real history is about actualities.

Scientific history is open to abuse by historical ideologies which are mere possibilities but are promoted fervently by their adherents.  Such historical ideologies arose in the 19th century with Marxism and evolutionism.  Ideologues use the language of science to claim the high ground which will only be given up if others show the impossibility of their ideologies.

It is analogous to a judicial court in which the defendant is “innocent until proven guilty.”  The prosecution must show that every reasonable construal of the evidence is against the defendant; otherwise the verdict must be “not guilty.”  On their telling the only thing evolutionists need to do to defend themselves is show that evidence presented against them can be construed neutrally or in their favor.  They do not have to present any evidence that supports their case.  Judicial courts give an advantage to the defendant but science should not have an inherent bias.

The problem is one of flawed logic.  Scientific history is flawed unless it is grounded in what actually happened in the past, not merely what could have happened.  Creationists use the Bible as the source of history to ground the practice of scientific history.  Conventional scientists have nothing on which to base their historical science so they adopt ideologies instead: naturalism and scientism.  The advantage of evolution to their mind is that it is possible and consistent with “science” which they define ideologically.

It would be a mistake to accept evolutionists’ terms of the debate and try to show that evolutionism is impossible.  It should be rejected on the basis of logic and the avoidance of ideology.  Evolutionary science is captive to ideology.

The Bible is a trustworthy chronicle of history, not merely a spiritual revelation.  This is important to critics who accuse creationists of being sectarian.  The Bible is in the first place a book, not religious object.  Much of it is a chronicle of a particular people, and the earliest part chronicles universal history.  Even the first chapter of Genesis comes to us as Adam’s chronicle, and although he did not observe it all, he was in the best position to know what happened.

Evolution is not real history; it is imaginary history.  We have real history as our starting point.  That is our best argument.

October 2013

Time and biological diversity

Based on the standard biological taxonomy here is a logarithmic model of the relationship between the time it takes life to reach the diversity that is observed today and possible positions on the lowest rank of the initial taxa of life, which I shall call prototypes.

Prototypes of the species rank would take tens of years to arrive at presently observed diversity.  This represents the position of biologists a few centuries ago in which species were considered fixed and the age of the earth was immaterial.

Prototypes of the genus rank would take hundreds of years to arrive at presently observed diversity.

Prototypes of the family rank would take thousands of years to arrive at presently observed diversity. This is approximately the position of YECs today.

Prototypes of the order rank would take tens of thousands of years to arrive at presently observed diversity.

Prototypes of the class rank would take hundreds of thousands of years to arrive at presently observed diversity.

Prototypes of the phylum rank would take millions of years to arrive at presently observed diversity.

Prototypes of the kingdom rank would take tens of millions of to arrive at presently observed diversity.

Prototypes of the domain rank would take hundreds of millions of years to arrive at presently observed diversity.

A prototype of the life rank would take billions of years to arrive at presently observed diversity.  This is the position of evolutionists, who accept only a single prototype (or LUCA) for all organic life forms.

ID advocates seem to place prototypes somewhere below the kingdom rank.

This model of time and diversity provides a simple way to compare different positions in a common framework.

October 2013