Science Of Value Science Fiction Science Fiction And Fantasy

Hartman proposes to quantify this notion by the principle that each property of the thing is worth as much as each other property, no matter on what level of abstraction or differentiation, but depending on the degree of maximum specification (The Structure of Value, page 204.) Hence, if a thing has n properties, each of them is proportionally worth 2^-n. In other words, a car having brakes or having a gas cap are weighted equally so far as their value goes, so long as both are a part of the definition of a car. If a gas cap is not part of a car's definition, it would be given no weight, but if it was, it would be weighed equally with brakes. Similarly headlights could be weighed twice, once or not at all depending on how headlights appear in the description of a car. Given the finite set of n properties, a thing is good if it has all of the properties, fair if it has more than (n+1)/2 of them, average if it comes within 1/2 of n/2 of them, and bad if it has fewer than (n-1)/2, so that a car with no brakes is probably in fact a fair car. Something is good if it has all n properties, and we can add together the number of properties of a fair version of a thing with the number of properties of the complementary bad version (which has only those properties which the fair version does not have) and also get n. The number of properties of an average verion of a thing is n/2, within 1/2. If we add together the number of properties of a good, fair and complementary bad, and average versions of a thing, we will obtain 5n/2, within plus or minus 1/2. Hartman regards it as something of a mystery that this sum has two and half times the value of the thing itself, and says that how a thing can have more properties than it has is the secret of valuation. There is similarly a value product.

Hartman goes on to consider infinite sets of properties. Hartman claims that according to a theorem of transfinite mathematics, any collection of material objects is at most denumerably infinite (The Structure of Value, page 117.) This is not, in fact, a theorem of mathematics, though it would follow from certain assumptions on the nature of the physical universe which cosmologists typically make. Starting from the claim that a person can eventually think of a countable infinity of things, Hartman concludes the intension of man is a denumerably infinite set of predicates; which means that man, according to this first definition, is appropriately to be measured by a denumerable infinity. However he quickly passes to the conclusion that we also have a countable infinity of levels of thought, and that therefore we can think of a countable infinity of things using a countable infinity of thought levels, giving us the cardinality of the continuum of thoughts. Hartman apparently believes the generalized continuum hypothesis is true, and therefore claims the intension of man consists of elements. This is the cardinality, in Hartman's system, of intrinsic value.

Further combinations are possible, leading to larger uncountable infinities; and Hartman also introduces the reciprocals of aleph numbers, which play no role in ordinary mathematics, but which Hartman employs as a sort of infinitesimal proportion, and which he contends goes to zero in the limit as the uncountable cardinals become larger. Formalizing this in such a way as to produce an extension of the real numbers is probably best achieved by means of a suitably defined ordered field of generalized formal power series, but Hartman does not do this. In Hartman's calculus, a Dear John letter ("we will always be friends") has axiological value , whereas Christmas shopping or taking a metaphor literally would do better, with a value of .

1 Evaluation of Hartman's work

Hartman's work led to the Hartman Value Profile, which is however not a description of what is valuable, but a psychological test to determine what people regard as valuable, and which therefore belongs to psychology as a disciple. A Hartman festshrift (Values and Valuation) appeared a few years after his death, but most of the articles in it are not by Hartman supporters, and some of them are by people who are known to be critics of his work. Hartman is out of the mainstream of value philosophy, and is not regarded as a significant presence. Almost all philosophers would dispute the idea that the number of properties of a thing can in any meaningful way be enumerated, and a standard argument against that is that new properties can be defined in terms of old ones. Philosophers speak of the problem of organic value as a result of the observation that the value of a whole does not seem to be a mere sum of the value of its parts, however we define parts or value, and that adding more features, even if each seems to be a good one, can lead to the overall value going down. In this way we get overengineered software or the kind of DVD remote control which has too many buttons on it.

From a mathematician's point of view much of Hartman's work seems to be more or less nonsense, and certainly not an instance of correct mathematical methodology or axiomatic reasoning. Even when the arithmetic is correct the motivation seems to be lacking; an example is adding together good, fair, average and poor. The conclusion that this comes to two and a half times good is merely an artifact of the definition of these categories, and moreover requires us to add the satisfied properties of a fair object to the satisfied properties of the complementary poor object, a fact which Hartman seemingly fails to grasp, and which seems to make no sense. Unless some reason is supplied as to why any of this makes sense or has some purpose, we lack an important element required for a mathematical model.

Hartman supporters counter that it is not necessary for properties to be actually enumerated, only that they exist and can correspond bijectively. The question of existence is a matter for the derivative science of Ontology. The attributes in the meaning of a concept only "consist" as stipulations; they don't exist. They can resemble, but are not identical to, the properties perceived by the five senses. In contrast, Mathematics is the science of hypothetical sets invariant under transformation. In Mathematics the theory and the data coincide: they are identical.

2 References

Hartman, Robert S., The Structure of Value: Foundations of Scientific Axiology, Southern Illinois University Press, 1967

Davis, John William, ed, Value and Valuation: Axiological Studies in Honor of Robert S. Hartman, The University of Tennessee Press, 1972

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1 Evaluation of Hartman's work

2 References

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