Is there really no such thing as a fish?

Earlier, it was proposed that consciousness is a process in which (from sensations, messages and memories) we construct and compare descriptions of past, present and future things. The type theory in this chapter may be seen as foundational to how we describe things – and so to what follows in later chapters. Alternatively, you can see it as an academic aside of interest to those with a mathematical bent. It declares some principles related to the creation and use of types, and discusses fuzziness in how well real-world things and phenomena instantiate types.

Contents

Preface. 1

Seeing things as discrete and describable. 1

Types. 1

Relating types to instances of them.. 1

Relating types to sets. 1

Relating descriptive types in a network structure. 1

Relating descriptive types in a hierarchy. 1

Is there really no such thing as a fish?. 1

More about types. 1

Family resemblances. 1

The evolution of formal types from fuzzy typification. 1

Our type theory. 1

The constructivist view of types. 1

Conclusions and remarks. 1

Preface

Enterprise architecture does not address the whole of an enterprise; rather, it primarily addresses those features of a business that are describable as activity systems. Enterprise architecture abstracts regular activity systems from the physical activities of an enterprise, with a focus on business roles and processes that create and use business data.

Enterprise architecture

Abstract systems

Architects <observe and envisage> Physical systems

At system design time, general entity types like customer, event types like order and payment, and process types like billing are defined. These types are related to each other in logical data structures and process structures. E.g. order value = order amount * unit price.

At run time, physical systems consume inputs that carry information about entities and events, record those entities and events with attribute values, and use remembered information to decide how to respond to events. In all these ways, an enterprise can be seen as imitating what comes naturally to animals.

Seeing things as discrete and describable

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 universe, the space-time continuum, is describable as an ever-unfolding process, in which space and time are continuous. But when perceiving, remembering and describing phenomena, we divide the universe into discrete chunks; we do this both instinctively and consciously. Thousands of years ago, musicians divided the continuous spectrum of sound into discrete notes. Hundreds of years ago, Isaac Newton divided the continuous spectrum of light into first five, later seven, discrete colours.

To distinguish one sensation from another there must be what psychologists call a “just noticeable difference”. The concept is traceable to the 19th century experimental psychologist, Ernst Weber. His “difference threshold” is the minimum amount by which the intensity of a stimulus must be changed in order to produce a noticeable variation in sensory experience.

So, to encode some knowledge in a physical structure for others to read, we make a noticeable difference in its state. Say, you leave your office door open to convey the information that you are open to visitors. You assume visitors can differentiate between the open and closed states of the door. Moreover, they know the meaning of the code you used when you set the door position.

Klaus Krippendorff (a student of Ashby) wrote as follows:

"Differences do not exist in nature. They result from someone drawing distinctions and noticing their effects.” “Bateson's ‘recognizable change’ [is] something that can be recognised and observed."

We differentiate discrete:

· physical things in space, whether the boundary is tangible (as of a solid in a fluid) or a line we draw in the sand or on a map.

· logical families of things that share a type or label, as the players in a team may share the same style of shirt.

· measures of a quality, such as the amount of a quantity like height, width, depth, weight or volume.

· changes in the state of a thing, say from hot to cold, or asleep to awake.

· generations of things: say, from parent to child, or version 1 to version 2.

To describe a discrete thing in terms of its position in space, a family it belongs to, a quality it has, a state it is in, or a generation it belongs to, we use descriptive types.

Types

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	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

Descriptions are structures that can be correlated with what they describe. Most modern scientists say all we can understand and discuss of things are descriptions we construct of them. When we discuss description and reality, we use words as proxies for physical entities in the real world.

	Description	Reality
	Typifying assertion	Instantiation of 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

In the table above, we could replace the words in the right-hand column by photographs of roses (another kind of description) or by live broadcast pictures (still a description). However, close we get to discussing reality, we never quite get there.

Since we (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”

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.

The type name is a short-hand for the elaboration. To use the type name is to assume your listener already knows the elaboration you know, or one that is similar enough for practical use. In communication, you can use either.

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.

Suppose we say instead: “This bird is an animal with feathers and a beak which feeds on other animals and has a wide wing span.” Even then, we still depend on our listeners having the same understanding of the descriptive types we use.

To describe a thing is to typify it in terms of types already understood

“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.

https://antilogicalism.com/wp-content/uploads/2017/07/language-truth-and-logic.pdf

Where do we get our understanding from? We start by associating words with sensations of things in the world. We associate “Mum” and “Dad” with individual people. Only later do we realize there are many Mums and Dads out there, so the words are type names. Later still. we realize different people define those sets differently, biologically, sociologically, or both.

Even when we learn that “a planet is a heavy body of matter in orbit around a star”, the description would pointless and meaningless if we could not relate it to some experience of matter and motion.

Gradually, we build a loose network in which the words we use to typify things are related this way and that by “family resemblances” (discussed later).

What we don’t do is start from a handful of axiomatic abstract super types like “occurrent” (or event) and “continuant” (or entity), then build a gigantic taxonomy in which every other word we use is defined as a more particular subtype of the axiomatic ones. In fact, we only understand such abstract supertypes at a relatively advanced stage of life.

Relating types to instances of them

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.

This thing	instantiates the type	when
A circus ring	“circular”	its diameter is the same in all directions
A play	“Hamlet”	it follows the script written by Shakespeare
A rose bush	“Rosea”	it exhibits the features “thorny, flowering, and bushy”
A bird	“Eagle”	it is a bird of prey with a wide wing span

A bird that instantiates the “eagle” type should exhibit or embody the property type “wing span in metres” in a particular pair of wings, which are (say) 1 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.

Relating types to sets

We can discuss types with no knowledge of, or reference to, set theory. And every description we construct in the mind can be seen as a type, even if there is only one thing, or nothing, that conforms to it.

However, 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.

Set name	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

Some say “a type defines a set”. More accurately, a type 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.

One can say every type (which is a description) is an intensional definition of a set member (provided one allows there to be empty sets, and imaginary or impossible sets like flying elephants). But there is no need to mention sets. A verbal type is simply a predicate statement we use to describe a thing or a state of a thing.

The many-to-many association between types and sets

Note first, although 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 and I have touched, or the set of roles and processes in a business, or even the set of fish (discussed later). The only way to define a type for these sets is to use words that imply listing all the set members.

Considering sets of real-world things that can be typified, there is a many-to-many relationship between sets and types. Obviously, members of several different sets (or subsets) can conform to one generic type.

One 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 several different types. In this example, the two different types imply different operations for recognizing a member of the same set.

Type name	Type elaboration	One 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	{The set of even numbers}

Fixed and variable sets

Some mathematicians speak only of sets with a fixed number of members, such as the three angles in the corners of a triangle, or the infinite set of prime numbers. To them, a set is the collection of members that 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.	{You, me, and seven other people}

Now suppose you add or remove a friend from your phone list. A purist mathematician might say your new set of friends is a different set (so what had been one set is now divided into two sets). But 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. So, in the example above there were always two sets, and now, your set’s membership has changed.

Bear in mind

Perhaps you usually think of a set as containing members that conform to an intensional definition, (rather than whatever members are listed in an extension) 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.

And remember, every description we construct of a thing is a type, even if there is only one thing, or nothing, that conforms to it.

Relating descriptive types in a network structure

Things in the real world are related to each other, this way and that, 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’d have to go a long way to better the understanding you can gain from a study of relational data analysis and an education in data model patterns. If only there was space in this book to explore those!

Relating descriptive types in a hierarchy

When people are faced with a complex network of things in the world, they often impose a hierarchy on those things. They do this primarily 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.

Composition hierarchies

A composition hierarchy is constructed by relating a larger/longer composite type or thing to smaller/shorter component types or things. E.g.

· 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.

Generalization hierarchies

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-motor way
	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 does not only produce divergences between species. Convergent evolution leads some species (e.g. insects, birds, pterosaurs, and bats) in different branches to share the same structural and/or behavioral features (e,g wings and flight).

Ancestral hierarchies

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.

Is there really no such thing as a fish?

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.

More about types

Observing and envisaging types

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?

Features Things	“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, fantastic and realistic types

We can envisage types we have never observed. There are both 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.

Types as states in the life of a thing

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.

Monothetic and polythetic types

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?

Features Things	“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.

Family resemblances

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.

Types Games	“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 a discrete memory, one that is distinct from our memory 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?

The evolution of formal types from fuzzy typification

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.

Fuzzy typification

Look again at the tiny universe described earlier.

Types Things	“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? Might you typify somebody as a friend in one context and not in another?

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 typify things in reality.

Fuzzy matching of the new to the old

“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.

Formalizing descriptions of similar things into verbal types

In describing the locations of numerous 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. And then, we can formalise our sense of family resemblances by defining polythetic verbal types.

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.

Our type theory

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, which are (ultimately) associated with our sensations of the world. 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.

Our type theory

Types

Describers <observe & 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 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.

Every type is a description

A type is an intensional definition, a description of one 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.

Every description is a type

Physicists say that there is nothing in their description of the universe that prevents parallel universes from existing.

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.

Types in description theory

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

Describers <observe and envisage > Phenomena

Every description (however complex) serves as a type that may conceivably be embodied or realized in many physical instances, by many real-world things.

Types in systems theory

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.

Describer(s)	One abstract system A type	Many physical systems Instantiations of the type	Many physical entities
Composer(s)	A symphony score	Symphony performances	Orchestras
Building architect(s)	A set of architecture drawings	Concrete buildings	Builders
Business architect(s)	A set of business roles and rules	Businesses processes	Business actors
Software architect(s)	An application’s code	Applications deployed	Human & computer actors
Game designer(s)	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.

The constructivist view of types

“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, or light waves. The question is not: “Did the things we describe as planets or light waves exist before mankind? Rather, the question is “Did the types “planet”, “orbit” and “light wave” exist before mankind?

Plato believed types exist in an eternal and ethereal sense, not only in descriptions we construct. 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

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.

E.g. 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; those are only models constructed by scientists who find them useful – meaning the models help people discuss, explain and predict what light does.

E.g. 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.

Conclusions and remarks

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.