Description,
Knowledge and Truth
Copyright 2016 Graham Berrisford. One of about 300 papers at http://avancier.website. Last updated 17/09/2017 11:12
Enterprise architecture is about business system planning, and is underpinned by general system theory
Before we get to general system theory - what theory underpins that?
Systems are islands of orderly behaviour, in which the logic of interactions is describable.
This paper is the second in a series on description, communication, language and logic.
To apply system theory is to express some knowledge of the world as it is observed now, or envisaged in the future.
What is our knowledge of the world? How do we know what we know is true?
The paper introduces a philosophy expressed as a description theory based on three propositions.
Contents
Description as a
biological tool
How do we know knowledge
is true?
Conclusion: a philosophy
of knowledge
Popper’s three worlds –
resolving issues in it
Premise: there was no description before life.
There could be no description before there was a describer, no concept before there was an actor able to conceive ideas.
Our philosophy can be expressed as a description theory based on three propositions.
1. Describers observe and envisage realities; they perceive it as composed of discrete things.
2. Describers create and use descriptions; which are stored in memories and conveyed in messages (using brains, speech, writing, pictures, statues and other forms).
3. Descriptions idealise realities; they mimic selected features of things, or represent them in some encoded form.
This can be expressed in a more graphical form.
|
Description theory |
|
Descriptions <create and use> <idealise> Describers <observe & envisage> Realities |
The survival of intelligent actors depends on their ability to create and use descriptions of reality.
But we cannot know the universe as it really is; only in so far as it can be described in mental/documented/other models.
Notes:
This triangle probably does not match other triangles you have come across (like the semiotic triangle).
There is recursion; the universe of realities includes describers and descriptions.
A reality is more complex and multi-faceted than a description of it.
A particular reality (an instance) may not exactly fit a description of it (a polythetic type).
Because, outside of mathematics and computing, fuzzy matching of realities/instances to descriptions/types is normal.
The descriptions we regard as “true” are ones that match (well enough) the realities they describe, which implies testing one against the other.
The following sections exemplify how fuzzy matching of realities to descriptions is common.
All animal knowledge is explainable as a by-product of biological evolution.
The survival of intelligent actors depends on their ability to create and use descriptions of reality.
Remembering descriptions helps animals to recognise food, friends and enemies.
It helps them to manipulate things in the world and predict their behavior.
Having mental models of the world helps animals to survive, thrive, and pass their genes on.
Mental models are internal descriptions of the world, which are somehow encoded in biochemistry.
Honey bees must hold mental models of pollen sources, in order to find them communicate them by dancing.
Humans are particularly adept at encoding mental models in verbal forms.
Verbalising a description is often useful, but is not always necessary or best.
E.g. A drawing of a unicorn may describe it better than a verbal description.
Humans continually translate descriptions between different forms - internal and external.
Evolutionary biology does not require us to have a perfect description of anything.
All mental models are partial and flawed models of reality.
Our descriptions need only be accurate enough to help us survive and breed.
Animal minds evolved to model reality, not exactly as the world is, but just well enough.
Enough to sense, predict and direct events that matter to survival.
Social animals evolved to share descriptions in various ways.
They inform each other where food, friends and enemies are.
That animals share descriptions well enough is empirically demonstrable.
Again, the description does not have to be exactly true, only true enough.
Your knowledge of the world is inseparable from your ability to describe and predict it.
Knowledge (along with emotions like love and fear) helps you to survive, thrive and pass your genes on.
You know you must step off a railway track to avoid be running over by an onrushing train.
That truth of that knowledge is testable by gruesome experimentation.
Knowledge as a descriptive mental model
Your knowledge is somehow encoded in your mental model of train behavior.
The bio-electro-chemical form of that mental model is deeply mysterious.
Perhaps it is a network that connects related images, symbols, sensations and experiences held in memory.
All that matters here is that the presence of that mental model is demonstrable.
You predict the outcome of staying on the track, step off and so live to tell the tale.
Knowledge as a biological phenomenon -
inherited
Animals inherit mental models that gave their ancestors an evolutionary advantage.
E.g. Kittens innately know the properties of a mouse’s tail, and respond animatedly to any long, thin, wiggly thing.
Experiment has shown that babies fear crawling over the edge of what appears (in a visual illusion) to be a cliff edge.
I have watched a seated cat rise from the road in front of my car, walk to the side of the road and sit down again.
Surely, your innate fear of onrushing objects will surely prompt you to step out of the path of an onrushing train.
Knowledge as a psychological phenomenon -
learnt through experience
You acquire some knowledge through perceiving and remembering, through conditioning, through trial and error.
Recognising similarities between (aka classifying or typifying) situations, entities and events is a mark of intelligence and essential to learning.
Perhaps, watching a train squash an apple may teach you about the danger of standing on railways tracks.
Knowledge as a social phenomenon - acquired
through social communication
E.g. Honey bees learn the location of a pollen source by watching the wiggle dance of another bee.
So, you may be told about the danger of standing on railways tracks before you ever see one.
You and I have different mental models of train behavior.
We need only share those mental models well enough.
Enough that if I tell you the train is coming, you’ll step off the railway track.
Knowledge as a linguistic phenomenon -
encoded in a language
For communication, we encode knowledge in a shared language.
Our mental model of standing on a train track includes the knowledge that it is dangerous.
In other words, it has the quality we encode in verbal language as “dangerous”.
Our knowledge is wrapped up with having a word for that quality.
And our ability to communicate qualities is massively increased by having such a rich vocabulary.
In short, you
acquire knowledge through a mixture of inheritance, experience and
communication.
|
A
knowledge triangle |
|
Knowledge <inherit and acquire> <describes and predicts> Knowing actors <observe and envisage> Realities
|
Mathematicians use logical analysis to prove conclusions drawn from axioms.
Axioms are propositions they can’t prove.
Scientists develop theories and test them.
The best kind of scientific theory
a) fits all circumstantial evidence,
b) passes all tests devised to disprove it and
c) could be disproved by a future test.
Hovering behind a good theory is always the spectre of falsification by a future test.
A theory that could never conceivably be disproved is considered weak – more a declaration of faith or belief.
Wonderful and powerful as science is, how certain is the knowledge that it gives us?
“The
half-life of knowledge is the amount
of time that has to elapse before half of the knowledge in a particular area is
superseded or shown to be untrue.”
Fritz Machlup (1962)
The Production and Distribution of Knowledge
in the United States.
There is a spectrum of precision and certainty in science - from hard mathematics and physics to softer economics and sociology.
“The half-life of a physics paper is on average 13.07 years,
in Math it’s 9.17 years, and in Psychology it’s 7.15.”
Samuel Arbesman (2012). The
Half-life of Facts: Why Everything We Know Has an Expiration Date.
In short, we never know the universe as it really is, only as it is described in mental/documented/other models.
And all our knowledge is open to doubt.
You may be thinking, surely some knowledge is certain? There are universal and incontrovertible laws?
Laws
of concrete reality (physics)
Physicists have defined laws that typify the behavior of physical matter and energy in space and time.
This triangle describes the role of physicists in creating and using laws.
|
Physics |
|
Law of space and time <create and use> <idealise> Physicists <observe and envisage> The
universe |
Surely the laws of physics - rules that apply to physical matter and energy – are certain?
The history of cosmology is interesting, since one theory was supplanted by another over several centuries
The sequence is often presented as Aristotle/Ptolemy > Copernicus > Kepler and Galileo > Newton > Einstein.
Physicists know Newton's laws of motion are not true through all space and time, but also know they are reliable at the scales of space, time and energy humans deal with.
They also know Einstein's cosmological physics is irreconcilable with quantum mechanics, but also know each is fit for its context and purpose.
Underpinning the traditional laws of space and time are three even more basic presumptions.
In the universe:
1. An object cannot both exist and not exist at a given point in space and time.
2. An object must either exist or not exist at a given point in space and time.
3. An object cannot exist at different points in space at the same time.
Newton and Einstein surely presumed these are intuitively obvious and certainly true statements.
But it turns out Newton’s laws are generalisations that only approximately describe the motion of things – in our part of the universe.
Heisenberg’s uncertainty principle says an object’s position and speed cannot both be described exactly, at the same time.
And to Einstein’s great discomfort, a bizarre property of quantum mechanics is that an electron can be two places at the same time.
Scientists recognise the limits of their models and understand when and where to apply them.
Laws
of abstract description (logic or thought)
Logicians have defined laws that generalise the properties of a proposition.
|
Logic |
|
Laws of Logic <create and use> <idealise> Logicians <observe and envisage> Propositions
|
The three basic laws of logic are premises that describe mathematical expressions and verbal propositions.
Interestingly, they can be seen as reflecting the presumed laws of concrete reality above.
1. The law of contradiction: A proposition is not both true and false.
2. The law of excluded middle (or third): A proposition is either true or false.
3. The principle of identity: A proposition true of x must be true of x; OR x is identical with x.
I guess many mathematicians see those as intuitively obvious, certainly true statements.
Indeed, they are true in most mathematical descriptions of the universe.
Yet mathematicians have debated these laws, and now allow
that a proposition might be neither true nor false.
Conclusions
with respect to human knowledge
Some believe every law has existed forever, which is to take curiously metaphysical view what it means to exist.
Here, to exist is to take a physical form, to exist as matter or energy, and every description exists in such a form.
So, although describable things existed before life, descriptions of them did not -
there were no laws, language
or systems thinking.
And though stuff happened in generalisable ways, there were no laws of physics - because all laws are man-made generalisations of stuff happening.
Also, the so-called laws of logic/thought could not have existed before life - since they are descriptions of descriptions made by people.
Suppose we try to recast the laws of logic as laws of description.
1. The law of contradiction: A description is not both true and false.
2. The law of excluded middle (or third): A description is true or false.
3. The principle of identity: A description true of x must be true of x; OR x is identical with x.
Intuition rejects at least the first two laws.
We know a natural language description might be entirely true, entirely
false, a mix of both, or uncertain.
There is so much pseudo science about that scientific journals have become an unreliable source.
“Most published scientific research papers are wrong, according to a new
analysis. … there is less than a 50% chance that the
results of any randomly chosen scientific paper are true.”
https://www.newscientist.com/article/dn7915-most-scientific-papers-are-probably-wrong
Social communication spreads exhortations, suppositions, babble, nonsense and “fake news” and pseudoscience as well as objective knowledge.
Depressingly, pseudo-scientific papers can survive longer than scientific ones, because it is impossible to disprove them.
So, how do we know knowledge is true?
A J Ayer said knowledge is “justified true belief”.
The justification must be verification by one of two means:
· Logical analysis or manipulation of descriptive elements according to agreed rules (e.g. 2 + 2 = 4).
· Empirical testing of propositions about real-world entities and events.
Logical analysis has been wildly successful in mathematics.
Some kinds of knowledge are provable as true by logical analysis with respect to initial axioms.
By this means, mathematicians may conclude their models are perfect (but see footnote).
Logical analysis is not so in successful in investigations of nature.
Instead, we judge the truth of knowledge by how well it predicts what happens in reality.
Given a proposition or model, then we might call it:
· a supposition, speculation or hypothesis if it has never been tested
· knowledge if it has been tested successfully
· babble or nonsense if it fails to pass tests we agree are important.
In practice, these distinctions are fuzzy.
Much knowledge is a proposition or model that describes or predicts a reality well enough.
We continually validate our knowledge by inspecting it and discussing it with others.
We engage in a kind of collective mental modelling, to hone the accuracy of our knowledge.
But the people we converse with may be equally deluded.
Better, we can seek to verify a proposition or model by realising and testing it.
Still, no amount of successful tests can prove a model is true, since it may fail the next test.
Karl Popper famously proposed the test of a good theory is that it can be falsified.
His idea has proved immensely useful to the progress of science.
But even falsification does not necessarily invalidate knowledge.
“As Einstein would have happily admitted [his] new physics was not a definitive answer, nor did it negate the importance of Newton’s contribution.
It was not “right” or “true”, but simply a more accurate explanation that Newton’s”, which was perfectly good for its time.
As a pragmatist would say, it was a valid explanation” Marcus Weeks
Newton’s laws of motion remain useful knowledge, they help us deal with the world we live in.
They are propositions or models that describe and predict reality well enough.
In short, knowledge is fuzzy, there are degrees of truth.
We can reasonably point to a particular circus ring and call it “circular”.
But on close inspection, no circus ring is perfectly circular; it is only near enough circular to be usefully described thus.
|
A
truth triangle |
|
True-enough propositions <create and use> <describe and predict> Rational actors <observe and
envisage> Realities |
Generally speaking, the propositions of sociologists and economists are less certain and reliable those of chemists and physicists, and the “true enough” tests are more relaxed.
Our survival depends in part on recognising when assertion is not truth, fake news is not news, correlation is not causation, and pseudo science is not science.
Philosophers have long debated the nature of truth.
In the natural sciences, truth is a fuzzy concept that can be determined with a degree of certainty rather than complete certainty.
Absolute truth
Absolute truth and falsehood does exist in the logical world mathematics and description.
You can be certain a square is a rectangle; because the description of those things is entirely in your gift.
A scientific theory may be considered true when experimental results agree with predictions made using theory.
Similarly, a description of a particular thing is considered true when the qualities of that thing match the qualities in the description.
For example, you say the sky is blue, and when tested by observation, the sky is indeed blue.
Fluid truth
Outside of very stable domains of knowledge, the types used to define qualities can be fluid.
For example: Is Pluto a planet? Once, the question was unanswerable, then the answer was true, now it is false.
To begin with, there was an unknown, unnamed and unclassified body in space.
When that body was discovered, it was named “Pluto” and classified as an instance of “planet”.
But the definition of a planet’s qualities has changed over the centuries, and changed recently such that Pluto is no longer an instance of “planet”.
The thing may have remained the same, the definitive description of it has changed.
Fuzzy truth
Remember the law of the excluded
middle?
In modern systems of knowledge, some probability logics have degrees of truth-value between truth and falsity.
Especially, or at least, when the proposition declares something will be true in the future.
In the mathematics of fuzzy logic, predicates are the functions of a probability distribution.
This replaces a strict true/false valuation by a quantity interpreted as the degree of truth.
In natural language, the words we use to describe things are fuzzy polythetic types, meaning the described thing need not wholly match the word describing it
So, we convey meaning with probability rather certainty, and interpreting the meaning of a communication is somewhat fuzzy.
Fuzziness
in physical measurement
Is the Yankees baseball ground bigger than Lords cricket ground?
Your certainty about the answer depends on how accurately you can measure them.
The truth of a proposition about the physical world is determined by how accurately you measure physical matter and energy.
Fuzziness
in social
communication
Suppose two honey bees observe a third honey bee dancing to describe where pollen can be found.
The first bee finds the pollen, and regards the first honey as telling the truth.
The second bee fails to find the pollen, and regards the first honey bee as telling a lie.
The truth as you see it depends on your mental model, but others may have different mental models of the same reality.
How to test the truth of a proposition?
We can ask observers (a judge or jury) to examine a proposition, and give us a verdict
Or else devise test cases with predicted results, and compare the predictions with the actual results of running the tests.
Either way, there is room for fuzziness, or a margin of error.
Fuzziness in classification or type definition
Again, we describe particular things by using universal types to classify or typify them.
|
A particular thing |
instantiates a named “type” when |
it gives values to property types of that
type |
|
A circus ring |
instantiates the type named “circular” when |
its diameter is the same in all directions |
|
A play |
instantiates the type named “Hamlet” when |
it follows the script written by Shakespeare |
|
The rose bush in my garden |
instantiates the type named “rosea” when |
it exhibits the property types “thorny, flowering, bushy” |
But there is fuzziness in the definition of types and in the identification of instances.
So, we often allow a margin of error.
· This circus ring is “circular”. The earth is “spherical”. This chessboard is “square”. (What margin of error is allowed in measurement?)
· This play is a “performance of Hamlet”. (How strictly must it follow the script?)
· This plant is a “rose bush”. (What if it has only two thorns and it grows sturdily to the height of a tree?
It might be that none of above statements is 100% true, yet all are true enough for practical purposes.
The distinction between realist and idealist philosophies is debatable, but is here drawn thus.
Realist philosophers say realities have descriptions, which describers can discover.
Idealist philosophers say describers create descriptions to help them deal with realities.
Descriptive attributes are created by living entities and exist only in descriptions.
This work is based on a philosophy (we call scientific idealism) based on three propositions.
1. Describers observe and envisage realities; they perceive them as composed of discrete things.
2. Describers create and use descriptions; which are stored in memories and conveyed in messages (using brains, speech, writing, pictures, statues and other forms).
3. Descriptions idealise realities; they mimic selected features of things, or represent them in some encoded form.
This work represents the philosophy in a triangle of the kind below.
|
Scientific Idealism |
|
Descriptions <create and use> <idealise> Describers <observe & envisage> Realities |
To communicate, describers must translate between descriptions encoded in different kinds of model.
They translate between organic and inorganic - internal and external – forms of description.
Internal organic mental models encode descriptions differently from external inorganic models.
And obviously, internal models are fragile, malleable and prone to decay.
But translating between internal and external forms is no different in principle from translating between external forms.
Scientific idealism gives us answers to questions that have troubled philosophers for millenia.
Don’t presume it matches any other position you may know as “idealism”;
Indeed, others may call it “realism” or “materialism”. So why call it “idealism”?
Partly because it matches a common sense reading of that term - as it is used in enterprise architecture frameworks.
And partly because it matches the summary definition of idealism below, copied from “The Problem of Universals” Wikipedia 2017.
“Taking "beauty" as example, three positions are:
· Platonic realism: beauty is a property that exists in an ideal form independently of any mind or description.
· Aristotelian realism: beauty is a property that exists only when beautiful things exist.
· Idealism: beauty is a property constructed in the mind, so exists only in descriptions of things.”
Scientific idealism does not draw a distinction between mental and physical worlds (in the way that Popper and classical philosophies do).
The premise is the reverse: that the mental world is part of the physical world.
Descriptions include models of every kind, be they in a mental, documented or any other kind of physical form.
Models are descriptions (idealisations) - created and used by describers - of things they observe or envisage.
· Mental models are physical/biological in form (the physical world includes describers and their mental models).
· Documented models are another physical form that descriptions can take.
Both mental and documented models encode descriptions of things; and both can be seen as side effects of biological evolution.
In his philosophy of science, Karl Popper split the world into three categories:
1. the universe of discrete things
2. descriptions that model the universe
3. objective knowledge.
Like many such classifications, though appealing on the surface, it is not straightforward.
Consider a portrait of the US president; does it belong in world 1 and/or world 2?
Consider the proposition that the US president is a person; does that belong in world 2 and/or world 3?
And arguably, from a psycho-biologist’s view point, Poppers' scheme draws misleading divisions.
World 1: The universe of discrete things?
We never know the universe as it really is, only as it is described in mental/documented/other models.
Was Popper’s universe already divided into discrete entities and events before it was described?
Above the level of quantum physics, physicists regard matter and energy as continuous.
The discreteness of things, one from another, is as much a matter of perception or description as reality.
· Where is the start or end of yellow in the spectrum of visible light?
· Where is the boundary in space of a hurricane? The solar system? The United States?
· When is the start or end in time of a hurricane? An ocean wave? The Wimbledon tennis tournament?
True, any solid object in space, gas or liquid appears discrete – but its boundary may be fuzzy and change over time.
Generally, the universe only becomes discrete things in our descriptions of it.
We can divide same reality in infinitely different ways; describe it in terms of differently bounded entities and events.
More importantly, perceptions and memories are part of the physical universe – they are organic bio-chemistry.
And communicated descriptions are also part of the physical universe – they inorganic matter/energy structures.
In short, the universe includes descriptions and knowledge, which can each (if required) be perceived and described.
World 2: Descriptions that model the
universe?
We never know the universe as it really is, only as it is described in mental/documented/other models.
Can Popper’s descriptions describe imaginary things, not found in the universe?
People envisage as things as well as observe them.
A description of a unicorn is a hypothetical proposition – never realised.
More importantly, description is description, whether it is organic or inorganic.
We continually translate descriptions back and forth between internal bio-chemistry and external matter/energy structures.
World 3: Objective knowledge?
We never know the universe as it really is, only as it is described in mental/documented/other models.
Which descriptions count as knowledge? And does knowledge include false propositions, such as 2 + 2 not = 4.
Verification (by logic or testing) turns a description into objective knowledge - for the moment at least.
But that same apparently objective knowledge (like Newton’s first law of motion) may later fail to pass a different test.
In short, outside of pure logic, true/false is not binary.
So, consider the distinction between objective knowledge and description.
If it is between in-brain memory and external memory or message, then it is merely between two ways to model reality.
(And to call the former objective rather than subjective seems strange.)
If it is between certainly true and uncertain, then it is a fuzzy and/or fluid distinction.
Resolution
Difficulties interpreting Popper’s model largely disappear if you accept that:
· The model is recursive – since the universe includes descriptions and knowledge, which can each (if required) be perceived and described.
· Description is description, whether it is organic or inorganic, mental or documented, it is an encoding of information in physical matter and energy.
· The distinction between description and objective knowledge is fuzzy or fluid.
The triangular model here
We never know the universe as it really is,
only as it is described in mental/documented/other models.
So, we divide the universe in a different way from Popper.
· 1 The universe: all physical matter and energy; including planets, machines, organisms, brains, memories, speech, tennis matches and computers at run-time.
· 2 Descriptions: abstract models of the universe as it is perceived and described in terms of discrete things.
· 3 Objective knowledge: descriptions that (when tested) match the universe well enough.
· Describers: biological forms (and perhaps AI machines) capable of forming and using descriptions.
In short:
·
Describers
<observe and envision> the
universe.
·
Describers
<create and verify> descriptions
of the universe.
·
Descriptions
<model> the universe; and
objective knowledge is the subset of descriptions that have been satisfactorily
verified.
This can be expressed in a more graphical form.
|
Popper’s three worlds |
|
2 Descriptions (including 3 Objective Knowledge) <create and verify> <model> Describers <observe and envision> 1 The universe |
And expressed in the words of science.
|
Science |
|
Hypotheses
& Knowledge <create and use> <conceptualise> Scientists <describe and predict> The
universe |
The law of excluded middle – the debate
The following is
lightly edited from: http://www.britannica.com/topic/laws-of-thought
[A doctrine of traditional logicians was that] the laws of thought are
a sufficient foundation for the whole of logic.
[And] all other principles of logic are mere elaborations of them.
It has been shown, however, that these laws do not even comprise a
sufficient set of axioms for the most elementary branch of logic (the
propositional calculus)...
Aristotle cited the laws of contradiction and of excluded middle as
examples of axioms.
He partly exempted future contingents, or statements about unsure
future events, from the law of excluded middle.
Holding that it is not (now) either true or
false that there will be a naval battle tomorrow.
[Rather] the complex proposition that either there will be a naval
battle tomorrow or that there will not is (now) true.
In the epochal Principia Mathematica
(1910–13) of A.N. Whitehead and Bertrand Russell, this law occurs as a theorem
rather than as an axiom.
The law of excluded middle and certain related laws have been rejected
by L.E.J. Brouwer, a Dutch mathematical intuitionist.
His school do not admit their use in mathematical proofs in which all
members of an infinite class are involved.
Brouwer would not accept, for example, the disjunction that either there occur
ten successive 7’s somewhere in the decimal expansion of π or else not,
since no proof is known of either alternative.
But he would accept it if applied, for instance, to the first 10100
digits of the decimal, since these could in principle actually be computed.
In 1920 Jan Łukasiewicz, a leading
member of the Polish school of logic, formulated a propositional calculus that
had a third truth-value,
neither truth nor falsity, for Aristotle’s future contingents, a calculus in
which the laws of contradiction and of excluded middle both failed.
Other systems have gone beyond three-valued to many-valued logics—e.g.,
certain probability logics having various degrees of truth-value between truth
and falsity.
Symbols used in "Laws of thought"
The following is lightly edited from: http://www.britannica.com/topic/laws-of-thought
The three traditional laws of logic are listed in the table below.
|
Law |
Meaning |
Or |
Symbolically |
|
The law of contradiction |
For all propositions p, it is impossible for both p and not p to be true |
A description is not both true and not true |
∼(p · ∼p) |
|
The law of excluded middle (or third) |
Either p or ∼p must be true, there being no third or middle true proposition between them |
A description is true or not true |
p ∨ ∼p |
|
The principle of identity |
If a propositional function F is true of an individual variable x, then F is indeed true of x |
A description true of x must be true of x |
F(x) ⊃ F(x) |
|
OR, a thing is identical with itself |
For every x, x is the same as x |
(∀x) (x = x) |
This table lists the symbols of logic (after the Editors of Encyclopædia Britannica).
|
Logic symbol |
Meaning |
|
∼ |
not |
|
· |
and |
|
∨ |
or |
|
⊃ |
formally implies |
|
∀ |
for every |
|
= |
is the same as |
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