Is there really no such
thing as a fish?
A chapter in
“the book” at https://bit.ly/2yXGImr. Last updated 06/10/2021 14:13
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The chapter below presents a type theory that underpins how we describe things. It is relevant to the challenge of defining a “domain-specific language” for doing business,
It declares principles related to creating and using the descriptive types we use to characterize things. To describe something(s) observed or envisaged is to typify it/them. To typify something(s) observed or envisaged is to describe it/them.
It discusses fuzziness in how well real-world things and phenomena instantiate types. People speak of the relationship between types and individuals. Arguably, the relationship is better described as between types and the (near enough) instantiations of those types by individuals.
It further explores the many-to-many relationship between types and individuals. A type (say, “unicorn”) can exist without any related individuals, or else be instantiated/realized by one or more individuals. An individual (think, a proton at the beginning of the universe) can exist with any type to describe it; today, an individual may instantiate/realize zero, one or more defined types
For those with a mathematical or philosophic
bent, this chapter answers questions like: When or where was the set of numbers
created? the set of even numbers? the set of human beings? the set of
fish?
Contents
Where does
mathematics come from?
The
discreteness of things in descriptions of the world
Abstracting
descriptions from reality
Abstracting
types from individuals
Relating
types to instances of them
Relating
descriptive types in a network structure
Relating
descriptive types in a hierarchy
Is there
really no such thing as a fish?
Mathematics
as a tool based on typification
The evolution
of formal types from fuzzy typification
For
sure, there is a reality out there. Systems thinking is much about what we know
of reality and how we describe it. That subject is more generally called
epistemology. Several authors have proposed triangular views of epistemology,
in which they relate three concepts to each other.
|
Authors |
Epistemological triangle |
|
|
Ogden and Richards |
Semiotic Triangle |
References <are symbolised by> Symbols
<stand for> Referents |
|
Charles Peirce |
Triadic sign relation |
Interpretants <understand objects
from> Signs <represent> Objects |
|
Karl Popper |
Three worlds |
Mental worlds <produce> Products of the
mind <describe/predict> Physical realities |
|
Pierre Bordieu |
Three relations of knowledge |
Knower <social> Knowledge <epistemic>
Known |
This
work is rooted in biology rather than linguistics. It uses a triangle that
seems both easier to understand and more useful than the triangles above.
First, here is an example.
·
Architects <observe and envisage>
Buildings
·
Architects <create and use> Architectural
drawings
·
Architectural drawings <represent>
Buildings
Our
triangular relation can be seen in a wide range of biological examples.
Consider what animals know of reality and how they describe it. Flies smell
food. Once mice memorize a route through your house, they will never forget it.
Birds sound alarm calls. Honey bees communicate about pollen locations.
|
From
biochemistry to symbolic language |
Example |
|
Cells
<sense> Food items Cells
<create and use> Biochemical signals Biochemical
signals <represent> Food items |
Fruit flies
<smell> Fruit odours Fruit flies
<create and use> Biochemical signals Biochemical
signals <represent> Fruit odours |
|
Animals
<observe> Things Animals
<form and recall> Memories Memories <represent> Things |
Mice
<observe> Routes Mice <form
and recall> Route Memories Route Memories
<represent> Routes |
|
Social animals
<observe> Things Social animals
<create and use> Messages Messages <represent> Things |
Birds
<observe and envisage> Predators Birds
<create and use> Alarm calls Alarm calls
<represent> Predators |
|
Observers
<observe and envisage> Aspects of reality Observers
<create and use> Descriptions Descriptions <represent> Aspects of reality |
Honey bees
<observe and envisage> Pollen locations Honey bees
<act in and read> Dances Dances
<represent> Pollen locations |
The
epistemological triangle below generalizes from the examples above.
·
Thinkers <observe and envisage> Phenomena
·
Thinkers <create and use> Models.
·
Models <represent> Phenomena.
Thinkers
“Real-time
learning, deep understanding, reasoning requires true cognitive abilities that
none of the Second Wave AI programs have.” Data economy
To
speak of AI overtaking general human intelligence is to underestimate us – not
just our sensor and motor apparatus, but our abilities to typify phenomena we
observe and envisage - to create, record, communicate and understand
descriptions of reality - to create theories about the world – to test theories
by creating and running experiments - to study and deploy knowledge of maths,
physics, mechanics, electronics, chemistry, biology and psychology.
Models
The
meaning(s) of a descriptive model, recorded in a memory or a message, are found
not in the memory or message itself, but in the encoding and decoding processes
of the encoding and decoding thinkers. A descriptive model is always subjective
in the sense it is formed by one or more thinkers. But it may also be called
objective in so far as its accuracy can be confirmed by empirical, logical and
social verification.
In many ways, this book is about common sense, but of the kind that sometimes has to be spelled out, as below.
· There was no description before life; the universe existed long before thinkers created any description of it.
· We cannot understand reality directly; we can understand only descriptions we make of it.
· Descriptions, being abstractions from what they represent, are not all equally true, valid or useful.
· There is no absolute truth, only degrees of truth; to say I am six foot tall is near enough true for most practical purposes.
· No description can be complete, because then it would be the aspect of reality it describes.
· A description typifies what it represents (Ayer).
· Having described one thing, that description applies to all other things we observe as being near-enough similar.
A description is a generic type that defines one member of a set of near-enough similar things in terms of properties they share. Even if there is one member in that set (one universe?), we can envisage more.
The meanings of words are not fixed, other than in definitions we give them and share in specific “bounded contexts”. Consider the type “human”. There between 10 and 20 or more recognised human species. Some lists don't include Denisovans while some don't have Homo naledi, a hobbit-sized human species discovered in Indonesian caves, perhaps because they look more like chimpanzees than us.
Consider the less ambiguous type “number”. Where numbers they come from? They emerged out of Darwinian evolution.
· Animals evolved to recognise similarities between things. Even honey bees can do that, perceive a quantity of similar things and communicate that quantity to other bees.
· Humans evolved to label similar things as being of a named type (e.g. "child").
· Human gave a name to the quantity of things they judge to instantiate a type (e.g. the number of children in a family); and thus invented numbers.
Our ability to typify things in words led to the development of set theory that mathematicians now see as fundamental.
· Humans defined a named type by listing properties shared by most instances; and thus invented polythetic types.
· Human so far formalized some type definitions that to be counted as an instance, an individual must have all its properties; and thus invented monothetic types.
· Humans capitalised on monothetic types by inventing set theory.
I am not convinced linguistic philosophy or semiotics have much add to the story told here. Again, the types we give names to are not fixed, other than in definitions we give them and share in specific “bounded contexts”.
The universe may be viewed as an ever-unfolding process, in which space and time are continuous. However, when perceiving, remembering and describing phenomena, we divide the universe into discrete chunks.
Differentiating
things
Most obviously, we see bounded solids (fish in a sea, planets in orbit) as discrete entities. We divide a forest into discrete trees, though some may share roots. Thousands of years ago, musicians divided the continuous spectrum of sound into the discrete notes of a musical scale. Hundreds of years ago, Isaac Newton divided the continuous spectrum of sunlight into first five, and later seven, discrete colors.
2/1. “The most fundamental concept in cybernetics is that of ‘difference’, either that two things are recognisably different, or that one thing has changed with time.” “We assume change occurs by a measurable jump.” Ashby, 1956
The concept is more generally fundamental, since for us to distinguish one sensation from another there must be what Ernst Weber (a 19th century experimental psychologist) called a “difference threshold”, that is, the minimum amount by which the intensity of a stimulus must be changed in order to produce a noticeable variation in sensory experience. Today, psychologists call it a “just noticeable difference”.
By observation and
classification, we differentiate between:
·
things
bounded physically and separated in space (fish in a sea, planets in orbit
around a sun)
·
logical
types of things that share one or more qualities (family, category, class,
species, chemical element)
·
things
of the same type (individuals of a species, atoms of a chemical element,
members of a football team)
·
quantities
of a quality (measures of height, width, depth, weight or volume)
· changes in the state of a thing (from hot to cold, or asleep to awake)
·
generations of things (from parent to child, or
version 1 to version 2).
Klaus Krippendorff, a student of Ashby, wrote that "Differences do not exist in nature. They result from someone drawing distinctions and noticing their effects.” and “Bateson's ‘recognizable change’ [is] something that can be recognised and observed."
How
to describe things?
a) types of things, or qualities (different species, or colors),
b) instantiations of a type (the different individuals of a species, or appearances of a color in different rainbows),
c) states of a thing that changes over time (the progressive baby, child and adult states of a person, the cyclical on/off states of a light).
Which of these descriptive tools we use
depends on the context. Are “caterpillar” and “butterfly” different types or
states of an insect? Does the word “yellow” signify a type of color, or an
instantiation of the color type (a member of the set of rainbow colors)? To put
it another way, those three descriptive tools are not mutually exclusive.
To describe something to others, we may encode our knowledge in a physical structure of matter or energy, a symbol, that others can read. Say, you leave your office door open to symbolize, to convey the information, that you are open to visitors. You assume visitors can a) differentiate between the open and closed states of the door and b) know the meaning of the code you used when you opened or closed the door.
Abstracting descriptions from things and phenomena
that we observe and envisage is so important to human existence that we have
many words for doing it.
|
Things
in reality |
are
represented in |
descriptive
structures we construct in
memories and messages |
|
Phenomena we observe and envisage |
embody |
concepts |
|
exemplify |
property types |
|
|
exhibit |
features |
|
|
give values to |
variables or attributes |
|
|
show |
qualities |
|
|
are characterized by |
descriptions |
|
|
instantiate |
types |
We can
understand and discuss things in reality only in terms of descriptions we
construct of them. Descriptions are
structures an animal or machine can correlate with what is described. When a bird sounds an alarm call; other birds
correlate that sound with the presence of some danger. [GB1] When we use words, many are proxies for physical entities in
the real world.
|
Description in a typifying assertion |
Things in reality instantiate the type |
|
|
Generally |
“Roses are colored” |
A display of rose varieties |
|
More particularly |
“Some roses are red” |
A bunch of red roses |
|
And more particularly |
“This rose is red” |
One red rose |
We could replace
the words in the right-hand column of the table by photographs of roses
(another kind of description) or by live broadcast pictures (still a
description). However close we get to discussing reality itself, we never quite
get there.
Here, types are individual phenomena that emerged from biological evolution, that exist fuzzily as "resemblances" in our minds, are formalized using language, are shared via social communication, and are confirmed or denied through trial and error.
In mathematics, a type is usually defined by
some properties that are necessary and sufficient to identify an individual as
exemplifying the type. E.g a triangle is three-sided polygon whose internal
angles add up to 180 degrees.
In natural language, a type is often more loosely defined. E.g. The type “mother” may be defined as “birth giver”, “child nurturer” “partner of father” and “female genetic ancestor”. No one of the four property types is sufficient to define the type, and not all are necessary to refer to an individual as a “mother”.
The looseness of type definition surfaces in Wittgenstein’s notion of “family resemblances”, in George Lakoff’s "women, fire and dangerous things" (1987), as an "idealized cognitive model", and in type theory as a “polythetic type”.
Since you and I are interacting by means of words in this document, we
will discuss descriptive types using words. A verbal type can be presented as
composed of two parts: a type name, and an explanatory definition.
|
Type name |
Type elaboration |
|
“Even number” |
“a number divisible by two”. |
|
“Triangle corner” |
“an angle between the two lines in a corner of a triangle” |
|
“Bird” |
“an animal with feathers
and a beak” |
|
“Bird of prey” |
“a bird which feeds on
other animals” |
|
“Eagle” |
“a bird of prey with a wide
wing span” |
The type name is a short-hand for the elaboration. To use the type name
is to assume your listener already knows the elaboration, or one that is similar
enough for practical use.
When we say “this bird is an eagle”, we hope the
message receiver understands what we mean. The advantage? Using type names
saves a lot of communication time and effort. The disadvantage? The risk that a
message receiver associates a different type elaboration with the same type
name.
Even if we say: “This bird is an animal with feathers
and a beak which feeds on other animals and has a wide wing span” we still
depend on our listeners sharing our understanding of the descriptive types we
use. In natural language, this shared understanding, acquired largely by trial
error, is imperfect, just good enough, often enough.
Together, the type name and elaboration make an
intensional definition or predicate statement of this form.
|
Intensional definition pattern Predicate statement type |
Intensional definition example Predicate statement instance |
|
A thing of the named type is a thing of a more general type with these particular features. |
A thing of the even number type is a number which is divisible by two. |
“No statement which refers to a ‘reality’ transcending the limits of all sense-experience can possibly have any literal significance” Chapter 1 of “Language truth and logic” A J Ayer.
How do we develop
an understanding of words? We start by associating words with sensations of
things in the world. We associate “Mum” and “Dad” with individual people. Later
we realize there are many Mums and Dads out there, so the words are type names.
Later still, we realize others define the Mum and Dad types differently,
biologically, sociologically, or both.
Gradually, we build a network that loosely relates
words we use to typify things. The word network in our minds is surely
analogous to way a dictionary is written. One word is defined by relating it to
other words, more by “family resemblances” than by strict equality.
At base or center of the word network in our brain are
words we associate with our sense-experience of the world around us. When we are taught that
“a planet is a heavy body of matter in orbit around a star”, the description would
meaningless if we could not relate it to some experience of matter and
motion.
What we don’t do is learn words by starting
from a handful of axiomatic abstract super types like “occurrent” (or event in
time) and “continuant” (or entity in space), then build up a gigantic taxonomy or ontology in which
every words we learn is defined as a more particular subtype of the generic
supertypes (or base types). An ontological hierarchy of this kind is an
artificial device we impose on words when defining a domain-specific language
We have many
words not only for types (properties, features, concepts, qualities,
characteristics and attributes) but also for instantiating a type. We
speak of embodying, exhibiting, exemplifying, manifesting or realizing a type.
|
Thing
in reality |
Descriptive type
name |
Tells
us the thing |
|
A circus ring |
“Circular” |
manifestly has a diameter the same in all directions |
|
A play |
“Hamlet” |
realizes the script written by Shakespeare |
|
A rose bush |
“Rosea” |
exhibits the features “thorny, flowering, and bushy” |
|
A bird |
“Eagle” |
embodies a bird of prey
with a wide wing span |
A bird that
instantiates the “eagle” type should embody the property type “wing span in
metres” in a particular pair of wings, which are (say) one metre in width.
Aide: sloppily
and confusingly, we tend to say “property” when referring to a general type and
when referring to a particular value of a type.
People create
and use types with no knowledge of, or reference to, set theory. Every description constructed in the mind is a type,
even if there is only one thing, or nothing, that conforms to it. Every verbal type is simply a predicate statement we use to
describe a thing or a state of a thing.
Types do
feature in set theory - a branch of logic most often applied to mathematical
concepts. There several set and type theory variations. The aim of here is
not to explain one particular theory. It is to make some general observations
about how types relate to sets.
A set theory typically begins with this assertion or
relation “a thing can be a member of a set”. The set, the collection of
members, can be described in one or both of two ways, by extension or
intension.
Extensional
definition
In basic set
theory, a set is identified with its members, and defined by listing its
members.
|
Description Set name |
Reality Extension {members} |
|
Rainbow colors |
{red, orange, yellow, green, blue, indigo, violet} |
|
My friends |
{Jo, Mary, Tom} |
|
Polygon types |
{triangle, quadrilateral, pentangle…} |
|
This triangle’s corner angles |
{60, 70, 50} |
To distinguish type from set is to distinguish description from reality.
However, when naming the members of a set (e.g. My friends) we use words in
place of real-world things. And the named set members may be descriptive types
(e.g. polygon names) or descriptive variable values (e.g. angles). In other
words, our descriptions are themselves realities we can describe.
Intensional
definition
With reference
to set theory, every type is an intensional
definition of a set member. Some say “a type
defines a set”. More accurately, it describes one member of a set. It says
nothing about the total number of set members; that property of the whole set
is invisible in the type.
Note that though every type defines a set member, there are fantastic
and impossible types like “flying elephant” that will forever be associated
with an empty set.
Moreover, there are sets definable by extension for which no
satisfactory type can be defined. Consider the set of lamp posts you
have touched (or even the set of fish discussed later). The only way to define a type for
these sets is to have, or imply, a list of all set members.
Which
came first, type or set?
The question is not whether we should take an intensional or extensional view of sets. The question is whether we place set theory ahead of type theory, or type theory ahead of set theory. And since “knowledge is a biological phenomenon” there is no doubt about the answer.
There is more than one set theory and type theory. A pure mathematician thinks of a set as having a fixed number of members, which exist forever and everywhere. Because their interest is in purely abstract types like “number” and “triangle”. An applied mathematician, stepping out into the world where we typify physical entities and events (as in data analysis), thinks of a set as a dynamic, having a variable number of members, since members can leave and join the set.
The first kind of set theory makes no sense when it comes to types like “planet” and “customer”. It forces you into a metaphysical view of the universe, which is simply unnecessary. And once you give type theory precedence over set theory, the nonsense evaporates. Describers, descriptive types, and describable things can all be placed in time and space. We’ll return to this later in the chapter.
Obviously, members of several different sets (or
subsets) can conform to one generic type.
|
One
generic type name |
Set
name |
Set
in reality |
|
Flag color |
US flag colors |
{Red, White, Blue} |
|
Chinese flag colors |
{Red, Yellow} |
|
|
Indian flag colors |
{Orange, White, Green, Blue} |
Conversely, one member of a set can conform to different types. In this example, the two different types imply different
operations for recognizing a member of the same set.
|
Type name |
Type elaboration |
Set in reality |
|
Doubled number |
A number exactly divisible by two |
{The set of even numbers} |
|
Even number |
A number greater than an odd number by one |
Fixed and variable sets
Some mathematicians speak only of sets with a fixed number of members, such as the set of angles in the three corners of a triangle, or the infinite set of prime numbers. To them, a set is fixed forever, it is the collection of all members that ever exist across all space and time.
Others speak of real-world sets with a variable number of members. And
we can, in the intensional definition of a set member, define limits in space
and time, such as the set of roses in my garden today, or the set of customers
identified in a database table.
|
Type name |
Type elaboration |
Membership |
|
Person |
A homo sapiens who has lived, is living, or will live. |
Fixed |
|
Person alive now |
Extends “Person” with the constraint that “now” is after birth
and before death. |
Variable |
|
Person of interest |
Extends “Person” with the constraint that the Person is recorded
in our database. |
Variable |
Suppose your friends
and my friends are the same people, then, when defined by extension, there is
only one set.
|
Type name |
Type elaboration |
One set in reality |
|
Your friend |
A person whose number is in your phone right now. |
{You, me, and seven other people} |
|
My friend |
A person whose number is in my phone right now. |
Now suppose
you add or remove a friend from your phone list. A purist mathematician might
say there was one set, and your new set of friends is a different set (so one
set has been divided into two). Another may say there were always two sets, and
now, your set’s membership has changed.
In describing
the natural and business world, people usually think of sets as variable or
dynamic, meaning that a set (of friends or anything else) can gain and lose
members.
Bear in mind
People
commonly think of a set as containing members that conform to an intensional
definition, and usually assume a set has several or many members. Note however:
·
there are
fantastical types with no set member (like "flying elephant")
·
there are sets
with no satisfactory type (like the fish set below)
·
there are types
that describe one and only one thing.
Above all
remember every description we construct of a thing is a type,
even if there is only one thing, or nothing, that conforms to it.
Things in the real world are relatable to each other in an extraordinary
variety of ways. This chapter does not explore how types in a given domain of
knowledge are related to each other by one-to-many and many-to-many
associations in a network structure. E.g.
· One customer <places> one or
more orders
· One order <is placed by> one
customer <for> one or more product types.
If you want to learn about entity-relationship modelling of this kind,
you probably can’t do better than study relational data analysis and common
data model patterns. If only there was space in this book to explore those!
When people are faced with a complex network of things in the world, they often impose a hierarchy on them. They do this to help them understand and/or manage the network.
A descriptive hierarchy is a tree structure that divides one node (the base or root node) into two or more nodes, and then may subdivide those nodes several times, until a last division into elementary or atomic nodes. Things in the world can be classified by assigning them to the atomic nodes.
|
Description |
Reality |
||
|
Base node |
Node 1 |
Atomic node 1.1 |
Thing Thing |
|
Atomic node 1.2 |
Thing Thing Thing |
||
|
Node 2 |
Atomic node 2.1 |
Thing Thing |
|
|
Atomic node 2.2 |
Thing Thing |
||
Three varieties of descriptive hierarchy are distinguished below.
· Body < organ < cell <
organelle < molecule
· Document < section < paragraph
< sentence < word
· Business < division <
department < team
Dividing a system into subsystems, and composing a system from
subsystems, are fundamental ideas in systems analysis and design.
A generalization (aka class) hierarchy may be constructed from the bottom up by grouping things that share one or more common features into a type, then abstracting supertypes from subtypes.
The
ideal of the classifier is to build a tree in which a type at the bottom of the
hierarchy has every feature of all the types above it. In such a strict or pure
type hierarchy, each subtype “inherits” the features of all subtypes above it,
and “extends” their features with additional ones.
|
Roadway |
Metalled road |
Single carriage way |
|
|
Dual carriage way |
Motorway |
||
|
Non-motorway |
|||
|
Railway |
Plain railway |
|
|
|
Electrified railway |
Third line railway |
||
|
Overhead line railway |
A more famous generalization hierarchy is the classification of species. This wide and deep branching tree was built by comparing the morphology (structure or shape) of living and fossil organisms. It has been refined many times since the first version constructed by Linnaeus. Here is a tiny part of it.
Order Primates
Suborder Strepsirrhini: lemurs, etc.
Suborder Haplorhini: tarsiers, monkeys and apes
Infraorder Tarsiiformes
Infraorder Simiiformes
Parvorder Platyrrhini: New World monkeys
Parvorder Catarrhini
Superfamily Cercopithecoidea
Family Cercopithecidae: Old World
monkeys (138 species)
Superfamily Hominoidea
Family Hylobatidae: gibbons (18 species)
Family Hominidae: great apes, inc. humans (8 species)
This classification was first built with reference to the physical features of organisms preserved in the fossil record. However, studying jaws, bones, scales, teeth and fin spines on their own tends to deliver a confusing signal of evolutionary relationships. This is partly due to convergence. Evolution not only produced divergences between species. Convergent evolution leads some species in different branches to share the same structural and/or behavioral features (e.g. insects, birds, pterosaurs, and bats share wings and flight).
Phylogeneticists look to construct a type hierarchy that reflects the divergence of species over time. A cladogram is a diagram, an ever-branching tree, drawn to represent a particular view of evolution. In a cladogram, the branch from fish to human usually runs more or less along these lines.
· Earlier life form < Fish < Bony fish < Lobe-finned fish < Tetrapod (four-limbed animal) < Mammal < Ape < Human.
Note that tadpoles are on a different branch from humans.
To name a branch in the diagram (say, “fish”) is to name a type. Each subsequent branch is a new type, labelled either with a newly emerged property (say, scales) or a type name we already know (say, mammal).
However, a cladogram is not like a strict generalization hierarchy, because a type at the end of the hierarchy does not inherit all the features of its ancestral types. You may understand a little of the human type (ape, mammal) by reading the diagram backwards. But humans don’t breathe through gills or have scales. Through evolution, features are lost as well as gained.
How closely does a cladogram represent biological evolution? Real-world evolution is a well-nigh continuous process of tiny, incremental, nearly imperceptible changes. A cladogram shows it as a succession of major divisions, where species diverge. Different cladograms can show coarser or finer-grained divisions, but it usual to gloss over features gained and lost by one species over time.
After a lifetime of studying fish, the biologist Stephen Jay Gould concluded that there was no such thing as a fish. He reasoned that although there are many sea creatures, most are not closely related. For example, in the ever-branching tree of evolution, a salmon is more closely related to a camel than it is to a hagfish.
However, Gould’s conclusion can mislead people. He could define a fish set, by extension, by listing its members, but could not define a fish type without including several species he did not want to call fish, and perhaps saying that humans are fish.
The difficulty here is that people confuse three ways of answering the question Gould raised.
Can
we enumerate a fish set that embraces all things called fish today?
https://www.discoverwildlife.com/animal-facts/fish/is-there-really-no-such-thing-as-a-fish
“In days gone by, the word ‘fish’ was pinned to virtually any creature that lurked beneath the waterline. Gradually, as people paid more attention to the biology of those animals, it became clear that some ‘fish’ belonged to other groups, such as reptiles or mammals. This left a motley collection of aquatic vertebrates, including sharks, stingrays, hagfish, sturgeon, lungfish, goldfish and tuna.”
So yes, we may define a fish set by extension, by listing all the animals in that collection above, along with any others we want to call fish. The trouble is that people speak loosely, and other people may have a different fish set in mind.
How to avoid debate? How to agree the fish set without listing every species we like to call fish? Can we describe every member of our fish set by intension? Can we describe what all fish have in common?
Can
we define a fish type that embraces all things called fish today?
Suppose we say fish are cold-bloodied animals that breathe through gills, have bodies covered in scales, and have limbs in the form of fins?
|
Fishy features Fishy things |
“Cold-bloodied” |
“Gill
breathing” |
“Scaly” |
“Finned” |
|
A haddock |
Cold-bloodied |
Gills |
Scales |
Fins |
|
A shark |
Cold-bloodied |
Gills |
Fins |
|
|
A hagfish |
Cold-bloodied |
Gills |
|
|
|
A tadpole |
Cold-bloodied |
Gills |
|
|
|
A dolphin |
|
|
|
Fins |
As
Gould observed there is no fish type that satisfactorily characterises every
set member he wanted to call fish. No feature is present in all things most
people call fish (hagfish
have no scales or true fins) and not in things most people don’t call fish
(tadpoles have gills).
On the other hand, we are free to construct whatever type we choose. We can define the fish type as “an animal with gills”, and so accept and allow tadpoles are fish. After all, a tadpole is indeed the fishy state or stage of an amphibian’s life.
Can
we identity a common ancestor of all fish today?
https://www.livescience.com/46262-fossil-ancestor-jawed-vertebrates.html
“A stunningly preserved, soft-bodied fish that is more than 500 million years old could be the ancestor of almost all living vertebrates. The fossilized fish, called Metaspriggina, sports characteristic gill structures that later evolved into jawbones in jawed vertebrates, according to a new study. "For the first time, we are able to say this is really close to this hypothetical ancestor that was drawn based on a study of modern organisms in the 19th century," said study co-author Jean-Bernard Caron, a paleontologist at the Royal Ontario Museum in Toronto, Canada.”
Since all tetrapods (birds, frogs, lizards, turtles, mammals) evolved from this fishy ancestor, some cladists like to say humans are a kind of fish. That is contrary to common sense, since we are not cold-blooded, we don’t breathe through gills, and our limbs are significantly different from most fish fins in their form and function.
Discussions of the question Gould raised tend to confuse these two different concepts:
· A common ancestor in an ancestral hierarchy
· A supertype in a generalization hierarchy
The
first hierarchy is a fact of history, which scientists uncover through
painstaking research, evidence collection, hypothesis, trial and error. The
second hierarchy is one we construct to classify things. So, in summary
we might use the word “fish” to mean:
·
the ancestral type of all modern-day fish and
four legged animals, including humans
·
a generic type
(say) an animal with gills and without any human-specific features.
It
doesn’t matter, as long as we are consistent about which we mean when using the
type name.
The table below defines a tiny universe with
just three observable things, and four observable features. (For now, let us gloss over ambiguity or vagueness in the features.)
Looking at the descriptions of the three things, how
many types do you observe?
|
Description Things in reality |
“Round” |
“Heavy” |
“Yellow” |
“Source
of Light” |
|
Our sun |
Round |
Heavy |
Yellow |
Source
of Light |
|
The moon |
Round |
Heavy |
|
|
|
My beach ball |
Round |
|
Yellow |
|
In the table, you can see two things
of the type “round and heavy”; and two things of the type “round and yellow”.
So, you might observe there are two types in the table. But listen to this
philosopher.
“The fact is that one cannot in language point to an object without describing it. If a sentence is to express a proposition, it cannot merely name a situation; it must say something about it. And in describing a situation, one is not merely ‘registering’ a sense-content; one is classifying it in some way or other, and this means going beyond what is immediately given.” Chapter 5 of “Language truth and logic” A J Ayer.
Ayer tells us that as soon as we
describe one thing, we define a type. Even if we have observed only one sun,
our description of it serves as a type we can compare other things with. And
having described our sun by typifying it as a “round, heavy, yellow, source of
light”, we can go on to find other suns in the universe that conform to the
same type.
Observed and envisaged types: We
can observe things and create types to describe their features. We can envisage
types we have never observed.
Fantastic and realistic types: We
can envisage fantastic types realizable only in fiction, such as “flying
elephant”, and realistic types composed of features a thing may in fact
instantiate, but we haven’t seen yet.
Simple and complex types: There are four simple types in the tiny universe above. We can envisage
a set of “round” things, a set of “heavy” things, a set of “yellow” things, and
a set of things that is each a “source of light”. Further, we can envisage 16
complex types by combining two or three of the features. Some
combinations may describe nothing in the real word, so their corresponding sets
are empty.
The conformance of a real-world thing to a type may change. Animals can change from one type to another by “morphogenesis”. E.g.
· A tadpole changes into a frog
· A caterpillar changes into a butterfly
· You change from a child to an adult.
In each of these biological examples, the entity has a continuity of identity over time. It retains the same DNA and remains a member of the same species.
· The tadpole-frog entity conforms throughout its life to the amphibian type.
· The caterpillar-butterfly entity conforms throughout life to the insect type.
· The child-adult entity conforms throughout life to the human type.
In biology, the type that
defines an animal, found in its DNA, is called its genotype. What all members
of species share is the locations in the DNA at which particular sets of genes
occur, those being the locations and the sets that define the species.
The table is below is edited from one
produced by Van Rijsbergen 1979; see also:
http://www.iva.dk/bh/lifeboat_ko/CONCEPTS/monothetic.htm.
The table below defines a universe with
eight things (1 to 8), and eight features (A to H). How many types of thing can
you observe this table?
|
Description Things in reality |
“A” |
“B |
“C” |
“D |
“E” |
“F” |
“G” |
H” |
|
1 |
A |
B |
C |
|
|
|
|
|
|
2 |
A |
B |
|
D |
|
|
|
|
|
3 |
A |
|
C |
D |
|
|
|
|
|
4 |
|
B |
C |
D |
|
|
|
|
|
5 |
|
|
|
|
E |
F |
G |
|
|
6 |
|
|
|
|
E |
F |
G |
|
|
7 |
|
|
|
|
E |
F |
|
H |
|
8 |
|
|
|
|
E |
F |
|
H |
To qualify as a thing of a monothetic type, a thing must have every feature. The quoted source observes there are three monothetic types in the second half of the table. However, we can observe several more monothetic types.
|
Description Monothetic type |
Reality Things in the set |
|
E,F |
{5,6,7,8} |
|
E,F,G |
{5,6} |
|
E,F,H |
{7,8} |
|
Moreover… |
|
|
A,B |
{1,2} |
|
A,C |
{1,3} |
|
and so on |
|
To qualify as a thing of a polythetic type, a thing need not have every feature. The source observes that there two (four-part) polythetic types. But those two sets conform also to some two and three-part polythetic types.
|
Description Polythetic type |
Reality Things in the set |
|
A,B,C,D |
{1,2,3,4} |
|
E,F,G,H |
{5,6,7,8} |
|
Moreover… |
|
|
A,B |
{1,2,3,4} |
|
B,C |
{1,2,3,4} |
|
A,B,C |
{1,2,3,4} |
|
A,B,D |
{1,2,3,4} |
|
and so on |
|
Combining the 8 features above in different
ways give us 256 types that might be instantiated in this tiny universe. In the
wider universe of human discourse, there are infinite possible types, even if
most do not or cannot possibly represent a thing in the real world.
The types discussed in mathematics (e.g. triangles) are often monothetic, meaning every set member exemplifies, exhibits or embodies every feature of the type.
The
types we use in describing nature are often polythetic, meaning different set
members exhibit different subsets of the features associated with the named
type. E.g. a fish is “a cold blooded animal with gills, scales and fins”. A fish need not have all those
features
The types we discuss in more general conversation are also often polythetic, with no particular feature required. A thing can qualify as an instance of the type by having any one of several features.
Wittgenstein suggested we recognize loose “family
resemblances” rather than types. In such a family, A is similar to B is similar to C is
similar to D; but A is not like D. For example, the things we call
“games” don’t share any particular quality. We can formalise our sense of family
resemblances by defining the polythetic verbal type below. Still, war games are
very unlike games of solitaire.
|
Description Games
in reality |
“Pastime” |
“Competition” |
“Rehearsal
for action” |
|
Solitaire |
Pastime |
|
|
|
Crossword |
Pastime |
Competition |
|
|
World
series |
Competition |
|
|
|
Archery
(middle ages) |
|
Competition |
Rehearsal
for action |
|
War
game |
|
Rehearsal
for action |
It is not clear whether or how far we
recall family resemblances in our memory, as distinct from memories of
particular things. But how the brain compares new perceptions to past memories
doesn’t matter here; it only matters it evidently does.
Even what
appears to be a monothetic type can turn out to be polythetic. Suppose we say a bird “is an animal with
feathers, two legs, wings and a beak”. That type appears to be monothetic, but the
question arises: If a bird, through disease, loses all its feathers, is it
still a bird? Surely most people would
say yes?
In a sense, we “discover” everything we “invent”. You might plausibly say tools like the axe and the wheel were always "out there" waiting to be discovered. You might say the same of the tool we call mathematics. But only in a useless metaphysical sense, which we can cut out of our philosophy using Occam's razor.
Moreover, you surely believe that different human societies, independently, were bound to invent the axe and the wheel. You might well say the same of mathematics, that people were bound to invent it. But to say “discover” rather than “invent” is sophistry.
Typification precedes enumeration. Mathematics is descriptive/modelling tool rooted in quantification. But we cannot count the instantiations of a general descriptive type (or rather count the things that near enough instantiate a type) until we have a type.
There were no shareable descriptive types before animals were able to a) recognise resemblances between discretely observable things b) group similar things in a category (e.g. "dangerous" and "mate-worthy") and c) communicate about them using symbols (e.g. alarm calls and mating calls), of which human language is a spectacular development.
The truth/usefulness of mathematical statements depends on our biologically evolved ability to differentiate types ("food" and "friend") and differentiate instances of those types (Flora, Fiona, Fred), and count the instances of types. As Maturana said "knowledge is a "biological phenomena".
In short, no life, no description, no types, no numbers, no invention of mathematics.
In this chapter, fuzzy does not mean
what you might find in more formal discussions of mathematics and logic. It
embraces several ideas: a matter of degree, ambiguous, vague and
context-dependent or subjective.
Look again at the tiny universe
described earlier.
|
Description Things in reality |
“Round” |
“Heavy” |
“Yellow” |
“Source
of Light” |
|
Our sun |
Round |
Heavy |
Yellow |
Source
of Light |
|
The moon |
Round |
Heavy |
|
|
|
My beach ball |
Round |
|
Yellow |
|
Here, the conformance of a thing to
a type may be fuzzy for any of several reasons
·
The
conformance may be a matter of degree. E.g. a circus ring is described as circular,
though it is not a perfect circle. A play is said to be a performance of
Hamlet, though it departs from the script.
· The type may be ambiguous: Does round
mean circular or spherical?
· The type may be vague: How heavy is
heavy?
·
The
type may be context-dependent or subjective. Who decides whether the sun is
rightly described as “yellow”? Might the moon be regarded as source of light?
As a result, the extent of the set
associated with the type is debatable. Different observers may associate
different sets with the same type, and vice-versa.
In social conversation, the conformance of things to types tends to be fuzzy. We might well call a plant a “rose bush” if it has only two thorns and grows sturdily to the height of a tree. The conformance of things to types may not be 100% true, yet be true enough for practical purposes. After all, it is for practical purposes that animals evolved the ability to characterize things using descriptive types.
“In describing a situation, one is not merely registering a [perception], one is classifying it in some way, and this means going beyond what is immediately given.” Chapter 5 of “Language truth and logic” A J Ayer.
Biological evolution is parsimonious. The
competition between individuals and between species favors the most efficient.
Efficiency demands we
cannot respond to every event as though it is new and unique, we must somehow
classify events. Again, how the brain compares new
perceptions to past memories doesn’t matter here; it only matters it evidently
does.
To remember just one particular thing is to remember some of its features. In effect, that set of features forms a pattern or type that future things can be compared with. In other words, every description of particular thing can serve as a type for future reference.
If a man with a gun takes a
pot shot at you, then remembering that particular situation as a type is
valuable. The type is not the situation in reality, it is only the features
describing that situation that you remember.
We can match a newly perceived thing to our memory of one particular thing. And then respond to it in the light of what we learned from the past. Thus, referring to our memory of just one particular thing can be a basis of learning by conditioning (or trial and error) in psychology.
In nature, the matching of newly-perceived things to past-remembered things must be fuzzy. In science and business, the matching of perceived things to remembered things has to be more exact.
In describing the locations of pollen
sources, honey bees describe a set of things that resemble each other. But
honey bees don’t discuss what those resemblances are.
By contrast, humans can and do discuss the resemblances between things, and
create verbal types in doing so. We invent words (such as yellow, person,
payment) to label similar things and qualities. Words enable us to can
formalise our sense of family resemblances in the form of a polythetic verbal
type.
The constructivist position is that those abstractions (descriptions, concepts, types) don’t exist until they are formed, conceived or defined.
The success of science demonstrates the effectiveness of describing phenomena using types and logic. And the success of business demonstrates the effective of designing systems using types and logic.
EA is about business roles and processes that
create and use business data. We describe particular things by using abstract
data types to classify or typify them. Say, order, invoice and payment. We
define each entity and event type in terms of attributes (quantitative and
qualitative variable types). At run-time, when a business records an entity or
event as having values for those attribute values, it formally defines it as an
instance of that type.
We
also describe abstract process types (in data structures) which sequence atomic
activities. Say, order value = order amount * unit price. At
run-time, business processes remember things of the defined types the business
needs to monitor and direct, and uses that memory to decide how to responds to
events when they happen.
We
have no direct knowledge of things in reality. We know them only
in terms of types we construct (in the mind, in speech, writing, mathematics,
whatever) to describe them. We (describers) can
understand physical reality only in so far as it is correlated with a type we
have access to, which we can correlate well enough with reality for
practical use.
|
Types in a description theory |
|
Descriptive
types <create and use> <characterize> Describers
<observe and envisage > Described things |
A described thing is
any aspect or part of reality that a describer can observe or envisage. A type
is a representation (in mind, speech, writing or other form) that is
correlatable with a described thing. A describer is any animal or
machine that can create or use (encode or decode) a type. AI software can now abstract types (patterns) from
instances (things with similar features).
Note that each pair of concepts is related in
a many-to-many way. A describer can apply several types to the
same thing, which may be compatible or in conflict. Is light rightly described
as waves or particles? Physicists do not say either model is the “true” model,
they say only that each can be useful.
Types <represent> described things.
We usually discuss types as they are defined verbally or symbolically. However, the concept of type can be extended to embrace every kind of model an animal or machine can make of the world. Described things include everything that can be observed or envisaged, including types and describers.
Describers <create and use> types.
To create a symbolic type is to encode it. To use a type involves decoding it. Symbolic types are given meanings only in the acts of encoding or decoding. To create a type is to encode a model that represents some feature(s) of a described thing. To use a type is to decode it, then use it to respond to or manipulate whatever is described.
Describers <observe and envisage>
described things.
Describers are animals or machines that can encode and decode descriptive types. A described thing is anything that can be observed or envisaged, including types and describers. In short, observing and envisaging are processes that involve encoding, decoding and comparing of types.
Describers and types are also typifiable.
Describers are physical animals or machines. Types are also physical matter/energy structures. Many copies of a type can be created and used. If all copies are deleted, then the type disappears from the cosmos. In other words, there is no ethereal type aside from what exists in one or more copies of it.
Describers can not only observe but also envisage things, which may be purely fantastic or might possibly exist. E.g. neither a unicorn, nor the next prime number beyond today’s largest known prime, exist in material reality today, but to envisage them is to typify them.
A type is an intensional definition, a description of a
set member. Here are two complex types that describe our sun in
terms of simpler types. The second is more formal than the first.
·
A yellow, spherical, source of light, more than 100 times wider than the
earth
· A G-type,
yellow-dwarf, main sequence, star.
Both types are abstractions, since we could never
define every conceivable property of the sun (and it changes over time). Other
stars conform to the same types. The two typified sets are not the same size.
In human evolution, surely, the induction of a generic type from features found in two or more descriptions was first and foremost fuzzy. Since in nature, there are usually exceptions to the rule and hybrid cases. So-called “monothetic” types - to which things conform perfectly and completely – in the world of mathematical description – are the exception rather than the norm.
“The fact is that one cannot in language point to an object without describing it. If a sentence is to express a proposition, it cannot merely name a situation; it must say something about it. And in describing a situation, one is not merely ‘registering’ a sense-content; one is classifying it in some way or other, and this means going beyond what is immediately given.” Chapter 5 of “Language truth and logic” A J Ayer.
Think of any particular
thing; a molecule, a game of chess, a galaxy, whatever. Write down a
description of it. Perhaps the thing you have described is unique. But there is
nothing to prevent your description being realized in more than one particular
thing. To describe one thing is to create a type to which other things might
conform.
In short, generalisation
is not required to define a type. Since to remember or describe even one thing
is to define a type. We can describe things we envisage just as well as things
we observe. We can inductively draw common features from similar descriptions
to create another description. A type that we create by generalization may have
no practical use.
Remember: Every
description we construct is a type, even if there is only one thing, or
nothing, that conforms to it. This view of types underpins the simpler general
description theory in the next chapter, which in turn underpins the system
theory in chapter 1.
A description is a structure to which some phenomena
(observed or envisaged) may be correlated. Every
description we construct is a type, even if there is only one phenomenon, or
none, correlated with it.
· Describers <observe and
envisage> phenomena.
· Describers <create and
use> types to help them recognize and deal with phenomena.
·
Types
<characterize> phenomena in terms of their structural and/or behavioral
attributes.
|
Types in a description theory |
|
Descriptive
types <create and use> <characterize> Describers <observe and envisage
> Described things |
Every description (however complex)
serves as a type that may conceivably be embodied or realized in many
physical instances, by many real-world things.
An abstract system (e.g. a musical score) is a
description to which a physical system (e.g. a musical performance) may
conform. Every abstract
description we construct is a type, even if there is only one physical system,
or none, that conforms to it.
· Describers <observe and
envisage > physical systems.
· Describers <create and
use> abstract systems to help them recognize and deal with physical systems.
·
Abstract
systems <represent> physical systems in terms of their structural and/or
behavioral attributes.
|
Description |
Reality |
||
|
Describer |
Abstract system A type |
Many physical
systems Instantiations |
Many physical
entities |
|
Composer |
A symphony score |
Symphony
performances |
Orchestras |
|
Building
architect |
A set of
architecture drawings |
Concrete
buildings |
Builders |
|
Business
architect |
A set of business
roles and rules |
Businesses
processes |
Business actors |
|
Software architect |
An application’s code |
Applications deployed |
Human & computer
actors |
|
Game designer |
The rules of “poker” |
Games of poker |
Card schools |
In software system
architecture, an architecture description is a complex data structure that
relates selected aspects and parts of the described system. It is an
abstraction, since an architect could never define every conceivable property
of a run-time software system (neither every line of code, nor every state of
the system in operation) And it is a type, since many software systems might
conform to same architecture.
“My life shews that I know or am
certain that there is a chair over there, or a door, and so on – I tell a
friend e.g. "Take that chair over there", "Shut the door",
etc.” Wittgenstein
We show in our thought, talk and actions that we believe the physical world exists. Modern philosophers do not deny the existence of chairs, planets, light waves or customers. The question is not: “Did describable things exist before mankind? The question is “Did the descriptive types “chair”, “planet”, “orbit”, “light wave” and “customer” exist before mankind?
|
Types in a description theory |
|
Descriptive types <create and use> <characterize> Describers
<observe and envisage> Describable things |
For sure, all describable things can be placed in the four dimensions of time and space. Moreover, we (describers) and all our descriptions are describable things. Neither we nor the descriptive types we create and use stand outside of time or space.
Plato believed differently. He thought types exist in an eternal and ethereal way. Whether you agree with Plato or not makes no practical difference to how you live your life. It is however a problem for philosophers, who speak of particulars and universals. Universals are generic descriptive types like “tall”, “circular” and “dangerous”. Particulars are the specific qualities of discrete things we observe and envisage.
|
Universals |
|
Universals <create and use> <typify> Describers
<observe and envisage> Particulars |
The “problem of universals” is the question
of whether universals exist outside of human thought and record (or else, what
it means to “exist”).
Did the “chair” type exist before life?
Different people may have different ideas of what they judge to qualify as a “chair”. But whatever they mean by the type, surely it is an invention of humankind?
Did colors exist before life?
It
turns out that animal brains manufacture the sensation of color, from a mixture
of the light they perceive and their experience. We see the same light waves as
different colors, depending on the situation. For more on color perception,
read https://www.bbc.co.uk/news/science-environment-14421303.
Did the “elephant” type exist before their
kind came to be encoded in a genotype?
Surely not. And when we define the elephant
type as “a large, grey, herbivore, mammal with a trunk” we encode that type in
a different way. We might define the elephant type in other words, selecting
different properties as being the essential ones. And eventually elephants may
evolve to depart from its genotype and some of the ways we define it.
Did the “planet” type exist before life?
The truth of the statement “Pluto is a
planet” depends on how that type is defined. And what is true has changed, as
astronomers have defined and redefined the planet type.
Did the “ellipse” type exist before life?
The orbits of real planets are pulled by
gravity in many directions, so are never perfect ellipses. The type we call
“ellipse” exists in mathematic models we construct. Does it, as Plato
believed, exist also in an ideal or ethereal sense?
Maturana said that knowledge is a biological phenomenon. In other words, descriptive types are tools constructed by life forms. A constructivist says there can be no construct without a constructor, no concept without a conceiver, no description without a describer, no type without a typifier.
There are things in reality
that we describe (typify) as “light ray”, “electron” and “electric charge”. But
we can never discuss reality as it is; and even to imagine we could makes no
sense.
We can only discuss models we
construct of reality. Every
description (type) we construct (in our minds, speech, writing or mathematics)
is only a model.
Before life, light had no name
or description; today it has a name and is described (typified) as “waves” or
“particles”. But in reality, light is
neither waves nor particles as we think of them; those are only models
constructed by scientists who found them useful – meaning the models help
people discuss, explain and predict what light does.
Before a software system is
conceived, it has no name or architecture (description); afterwards, it has
both. But in operation, it is not an architecture (description), which is only
a model constructed by architects who find it useful - meaning the model helps
people discuss, explain and predict what the system does.
At first glance, some named philosophical positions some seem to fit this constructivist view. But under those headings, people say things that make no sense to a constructivist, and seem nothing more than a confused use of language.
To say “a weight describes the
weight of a thing” is tautologous. To say “a type describes the type of a
thing” is tautologous. To say “an architecture description describes the
architecture of a system” is tautologous. It is really to say either “a
description describes the description of a thing”, or else “a description
describes the thing of a thing”.
Surely any species with human-level intelligence will sooner or later conceive of zero (the number of eggs in an empty nest) and pi (a logical consequence of drawing a circle) and curved spacetime too. But what does it mean to say these concepts exist? Did they exist before an intelligence arrived at them? There were empty nests before people conceived of zero to describe the quantity of eggs in one, but no “zero”. There were roughly circular things, but no perfect circle, which is a construct of mathematics. And the notion of spacetime being curved is merely a way of visualizing otherwise inexplicable mathematics.
There is no need to posit a type exists outside of any description encoded in a memory or message of some kind. The constructivist position is that before life (before observation, knowledge or description of things) there were:
·
many similarly-shaped groups of stars, but no
concept of a spiral galaxy.
· many more or less circular things, but no concept of a circle or pi.
·
planets in roughly elliptical orbits, but no
“ellipse” type
· many things that resemble each other, but nobody to count them or concept of number.
To a
constructivist, there
is no ethereal property, concept or type. The idea is useless,
redundant, and better cut out using Occam’s razor. When all descriptions of an
“atom”, “mountain”, “galaxy” and “ellipse” are destroyed, then, while the
things we describe thus may continue exist, the types we use to describe them
will disappear from the cosmos.
For every philosophical position there are variants that
undermine each other.
Social constructivism?
This states that we acquire knowledge through social
interaction. Yet animals held and acquired knowledge of their environment eons
before they evolved to communicate more than mating intentions to each other.
So, social constructivism can be no more than a partial explanation
of knowledge acquisition.
Radical constructivism?
This states that our knowledge is individual, and cannot be
shared. Yet clearly, a message receiver can confirm a gale warning message when
hit by the gale. So, we reject that variety of radical
constructivism that says we cannot share knowledge - along with any kind
of relativism or perspectivism that says all constructed views of the world are
equally valid.
This is one three chapters that outline compatible theories of information, description and types. Key points include: human intelligence and civilization, along with symbolic languages and the sharing of knowledge in speech and in writing, emerged from the biological evolution of animals. Types are descriptions, and descriptions are types. Outside of mathematics, there is fuzziness in how well things and phenomena exemplify descriptive types.
Here is recap of the principles so far:
· Knowledge and description evolved in biological organisms
· A good regulator has a description of what it regulates
· Consciousness is a process that enables us to compare the past, present and future.
· To describe a thing is to typify it in terms of types already understood
· Every type is a description
· Every description is a type
The pragmatic view we take here of types may seem radical or strange to mathematicians. But it has to be addressed in systems thinking. Both abstract systems and the elements in them are types. The question arises: can a physical system deviate from that type? How far can actors who play roles in a described system depart from its rules before we say the system has evaporated?
In practice, to change any type in a system description is to change the system. Where the system is a designed one, changing the description implies a need for system testing before the changed version of the system is released.