Thursday, 10 January 2008

On the existence and composition of intrinsic value.

In an earlier post (May 2007), I began developing a theory of information and value that seems to have universal meaning. Here I expand and rather more formalise the definitions of intrinsic value, information and the link between them. The purpose is to strengthen the theoretical foundation of my claim that information is the fundamental essence of all things in the Universe and that it seems to act with a will to live.


Conventionally, value is thought to be an attribute attached to an entity by a person as an expression of their opinion about how much utility or happiness they expect to gain from it. This meaning of value is, by definition, subjective and in practice, ephemeral and subject to arbitrary change, making it an insubstantial and poor measure for public decision making. Any measure founded only on one or more people's opinion is not scientific because it is not objective and independently quantifiable. Conventionally defined value may provide a scientific measure of opinion among those making value-judgements, but cannot result in any scientific statement about the entities being valued, since it is devoid of objectivity. The work presented here is an attempt to find a basis for objective measures of value which are compatible with the conventions of scientific measurement. By implication, it is an exploration of the existence and composition of intrinsic value, since by definition, if an entity independently has an attribute which we may call value, then that attribute must be intrinsic to the entity. The familiar subjective meaning of value derives from an interaction between an observer (the valuer) and the entity under scrutiny; often it describes the observer more than the observed. An objective measure will depend strictly on the observed entity alone and can therefore be called its intrinsic value. We shall start by systematically defining various meanings of value.

Note: ‘Objective’ implies ‘A-Priori’ as used in the philosophical sense.

“I conceive that the great part of the miseries of mankind are brought upon them by false estimates they have made of the value of things”.
Benjamin Franklin 1706-1790

Different kinds of value.

“Nowadays people know the price of everything and the value of nothing.”
Oscar Wilde 1854-1900

1. Economic Value (Ve) is founded on the axioms of consumer theory:

A1.1 That consumers are 'sovereign', independent and free entities.
A1.2 That consumers always act to maximise their private utility and nothing else.
A1.3 That utility is gained from ‘consuming’ goods at rates which may differ among goods, but which are known to the consumer (also implying that the consumer is sensitive to change in utility).

The consequence of A1.2 and A1.3 is that goods can be substituted so that the maximisation of utility becomes the choice of a set (mix) of goods in proportions that yield the highest possible utility.

The consequence of A1.1 is that Ve is subjective in the sense that it arises from the properties of both the good being valued and the valuer.

Proposition 1: The result of this subjectivity is that Ve does not exist if there is no agent making a valuation.

Environmental economics defines value as the sum of use value and non-use value. The former consists of the utility derived from direct consumption and the latter is made up of passive-consumption (e.g. enjoying scenery or the pleasure of knowing the good exists) and deferred use value, including bequest value.

A consequence of Proposition 1 is that intrinsic value does not exist.

2. Innate Value (Vi).

“The things which are seen are temporal; but the things which are not seen are eternal.”
II Corinthians 4.1:18

To define Innate value, we must first define what I call Quantitative Existence (QE). Normally existence is thought of as binary (exist or not), but QE specifies the amount of existence in terms of time (how long for) and numbers (how many replicates of an entity exist). In biology QE closely approximates to reproductive fitness (lifetime reproductive success) and in Economics it may be equivalent to utility, but only for rational motivations (e.g. excluding harmful addictive behaviours).

Innate Value is now derived from the following axioms:

A2.1 Entities always act at time t so as to maximise their QE.

It is interesting to note that this matches the axiom behind the Selfish Gene Hypothesis and if genes are regarded as packets of information, then it amounts to a generalisation of that hypothesis in which information universally seeks to maximise its QE whilst the universal increase of entropy in time (2nd law of thermodynamics) is constantly diminishing the aggregate QE of information.

A2.2 For any entity x, the existence of at least one other entity y at time t enables an increase in QE(x).

Axioms A2.1 and A2.2 allow us to deduce that any entity x may attach a value Vi(t,x,y) to every other entity y in proportion to the contribution y contributes to the QE of x at time t.

Note that this definition makes no requirement for choice, or even detection of the influence of a good on QE, though it permits both.

Since choice is not necessary, sentience (in any form) is not relevant to Vi, which therefore may apply to any entity, including inanimate objects, and even non-physical entities, for example ideas.

This leads to proposition 2: All things value at least one other thing.

A hierarchy (or chain) of valuations can be conceived, leading back to the basis of all physical existence - the founding laws of the Universe (which are the laws of physics as far as we know).

3. General and specific innate value
We can divide innate value into two components which I shall call the general innate value Vig and the specific innate value Vis, respectively. Vig is the innate value of any entity with the properties needed to increase QE, for example plant food for a herbivore, whilst Vis is the value of an instance of this class of entities, for example a specific plant. More formally, Vig(x,y,t) ≥0 iff [ QE(x) | Y(t)≠0 ≥ QE(x) | Y(t)=0 AND y e Y]. In words this says positive Vig is assigned by any entity x at time t, if and only if there exists at time t, a member of a set Y of entities defined such that the existence of any member of this set y at time t leads to an increase in QE for x.

All entities in the class Y share innate value Vig and by definition may be substituted, one for another, since they all provide the same general attributes. Any additional innate value arising from specific properties of any instance of the class are unique to that instance and therefore contributes to Vis. Thus x will attach further Vis to any y having unique attributes that increase QE(x).

The composition of entities and the supremacy of information

Axiom : All things which exist are, in various proportions, composed of a) energy/matter, b) space/time and c) organised information.

Energy and matter are treated together because of their equivalence established through Einstein’s Special Relativity. Similarly space and time are treated together because of their relationship established by General Relativity. Information theory enables us to account for all bits of information as data, irrespective of whether it is meaningless noise (disorganised information) or, potentially meaningful sequence, often referred to as signal, that is organised information.

All things are what they are because and only because of the organisation of information. The forms and mix of kinds of energy/matter and space / time occupied are set by organised information and observing the form of the entity is equivalent to reading this information. In other words energy/matter and space/time are formless raw materials that are structured by organised information into entities.

From this we can deduce that class of entities Y all must share in common energy/matter and space/time, though perhaps in quantitatively different amounts. The class Y is defined by the organised information which structures these commodities and gives them form. Further, what makes instances y of Y unique is the additional information which their composition carries. Therefore Vis results strictly from organised information content. This conclusion can be generalised to Vig, by realising that a class of entities Y is simply a generalisation of the description of an entity by attributes. Information defined what was unique about y, giving it Vis, but information also defines what is different between class Y1 and class Y2 of entities, equivalently giving each a class-level Vis. Since classes can be nested in an hierarchy which eventually includes (in the broadest class) all entities, there is no intrinsic difference between Vis and Vig.

We can now say that it is the information which defines entities, gives them uniqueness and therefore which gives them innate value.

In general, both energy and matter are interchangeable and may take many forms; space and time the same (in the sense that different parts of space and time may be occupied), but each structure of organised information uniquely defines some aspect of existence and is therefore uniquely necessary and so not substitutable.

Proposition 3: Energy/matter and space/time are abundant and within their category are substitutable, but organised information is uniquely necessary for the existence of all things and is therefore not substitutable.

We now have that unique organisation of information gives rise to innate value and that it is uniquely attached to a specific entitity. This means that unique organisation of information has objective value because it is a property of the entity itself. Furthermore, this property is potentially quantifiable, leading directly to a basis for quantitative intrinsic valuation through accounting for organised information.

Proposition 4: the value of a thing can be objectively quantified by measuring the amount of unique organisation of information needed for its existence.

This leads to a definition of Organised Information Value (Vo), which is objective. Vo is proportional to the quantity of organised information contained by an entity. This remains potentially distinct from innate value and intrinsic value, but is a good substitute for both.

Note that since innate value is derived from unique information, when a package of organised information is replicated, the Vo is shared among its instances.

“What we obtain too cheap, we esteem too lightly; it is dearness only that gives everything its value.”
Thomas Paine 1737–1809

Objective value as a link between two entities.

Objectivity is not exclusive to intrinsic value; it can also measure the innate value of one entity for another. This may be objective if and only if the quantification of value is based on a measurement of the intrinsic properties of the two entities (that is, distinct from the subjective - opinion based valuation Ve). Objective value which measures the effect of one entity y on the QE of another x, I shall call the Dependent Value Vd(x,y) to distinguish it from intrinsic value.

Effective Value

For many goods, it is easy to show that Vd is infinite because dependence on them for existence is absolute. This result is of little use for practical calculations of value.

This inspires the use of effective as opposed to absolute dependent value. Effective value Vf has the meaning of how worried we should be at the loss of a good. I shall show how it gives an intuitive justification for using the concept of substitution in calculating value.

We need not worry about the fundamental laws of physics because we have no ability to threaten their existence, nor exclude ourselves from them. We can therefore define their Vf as infinity times zero, which is indeterminate - a more realistic, but perhaps no more useful conclusion. However, this calculation illustrates the principle to be used in deriving effective value. Let Vi(x,y) be the innate value of x for y and T(x,y) be the capacity of y to remove (beyond use) x, then the effective value of x to y is Vi(x,y).T(x,y).

Since all entities are assumed to maximise their QE (Axiom 2.1), none would remove a good x with positive Vi(x,y), unless this was necessary in order to substitute it with some other good z with Vi(z,y)>Vi(x,y). The extent to which a good is removed is therefore the extent to which it is substituted, which can be found simply from the ‘rate of substitution’ - a measure familiar from economics. Indeed, in consumer theory, the rate of substitution of money p for a good x is the price of x.

Effective Value of y for x is therefore substitutability of y by x multiplied by Vd(x,y).

Significantly, when this principle is applied to the intrinsic organised information value Vo, it is simple to see that the effective value is equal to Vo divided by the number of accessible instances of the organisation of information x. This leads to:

Proposition 5: Objective Effective Value of x may be measured by the amount of unique organisation of information needed for its existence, divided by the number of instances of x available.

Note, availability may be a strong limit on the divisor if location, or other limits to access are accounted for. For independently reproducing instances (e.g. biological entities, the relationship between numbers and reproductive potential (population dynamics) must also enter the calculation - see future value below).

“Earth provides enough to satisfy every man's need, but not every man's greed.”
Mahatma Gandhi 1869-1948

Collective Value: Relaxing the independence assumption

So far, definitions have assumed that entities are independent of one-another in their actions and assessments and have assumed nothing about the effect of a behaviour of one on another.
Innate value does not allow for collective concerns, neither does the classical definition of economic value. However, the doctrine of ecology is that all living things are interconnected in mutual dependencies and human beings are a part of this ‘web’. Acting as free agents, we can step beyond the proscriptions of classical economics and act in the common interest, substituting some of our private gain for the common good.

We may ask if this has an analogue in the more fundamental realm of universal values (Vi and Vo). If all the QE of all things depends on all other things, then the common good is always served by individual QE maximisation. However this is not generally true (e.g. predation, competition and parasitism). Since nature does not show significant mutualism of the kind advanced by human moral philosophy, we cannot take this as a fundamental rule in valuation (indeed it seems to be a special trait of social animals and humans in particular). Since, then, there is no such thing as universal collective value, we need to distinguish between scientifically determined objective value and socially agreed value, which remains subjective. It may be that we decide on culturally determined values which differ from the scientifically derived objective values - that is a matter for normative studies, not science.

Future Value

Removing a good at time t may affect QE for all time including and beyond t. This, though, is contained within a complete definition of QE, since it is defined for a finite-life non-reproducing entity over the its entire life, for a reproducing entity by the reproduction success of its grandchildren, but it is ill-defined for an infinite entity. Thus no additional calculation is needed for future effects as long as complete QE is used. The economic practice of 'discounting the future' is predicated upon the assumption that future substitution will be more efficient (provide higher QE) than conservation. This assumption is, in principle, testable for objective measures of value.

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