 | This article possibly contains original research .(December 2018) |
The science of value, or value science, is a creation of philosopher Robert S. Hartman, which attempts to formally elucidate value theory using both formal and symbolic logic.
| This article possibly contains original research .(December 2018) |
The science of value, or value science, is a creation of philosopher Robert S. Hartman, which attempts to formally elucidate value theory using both formal and symbolic logic.
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The fundamental principle, which functions as an axiom, and can be stated in symbolic logic, is that a thing is good insofar as it exemplifies its concept. To put it another way, "a thing is good if it has all its descriptive properties." This means, according to Hartman, that the good thing has a name, that the name has a meaning defined by a set of properties, and that the thing possesses all of the properties in the set. A thing is bad if it does not fulfill its description. If it doesn't fulfill its definition it is terrible (awful, miserable). A car, by definition, has brakes. A car which accelerates when the brakes are applied is an awful car, since a car by definition must have brakes. A horse, if we called it a car, would be an even worse car, with fewer of the properties of a car. The name we put on things is very important: it sets the norm for how we judge them.
He introduces three basic dimensions of value, systemic , extrinsic and intrinsic for sets of properties—perfection is to systemic value what goodness is to extrinsic value and what uniqueness is to intrinsic value—each with their own cardinality: finite, and . In practice, the terms "good" and "bad" apply to finite sets of properties, since this is the only case where there is a ratio between the total number of desired properties and the number of such properties possessed by some object being valued. (In the case where the number of properties is countably infinite, the extrinsic dimension of value, the exposition as well as the mere definition of a specific concept is taken into consideration.)
Hartman quantifies this notion by the principle that each property of the thing is worth as much as each other property, depending on the level of abstraction. [1] Hence, if a thing has n properties, each of them—if on the same level of abstraction—is proportionally worth n−1. . 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 one's definition of a "car." Since a gas cap is not normally a part of a car's definition, it would be given no weight. Headlights could be weighed twice, once or not at all depending on how headlights appear in the description of a car. Given a finite set of n properties, a thing is good if it is perceived to have all of the properties, fair if it has more than n/2 of them, average if n/2 of them, and bad if it has fewer than n/2.
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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. [2] This is not, in fact, a theorem of mathematics. But, according to Hartman, people are capable of a denumerably infinite set of predicates, intended in as many ways, which he gives as . As this yields a notional cardinality of the continuum, Hartman advises that when setting out to describe a person, a continuum of properties would be most fitting and appropriate to bear in mind. This is the cardinality of intrinsic value in Hartman's system.
Although they play no role in ordinary mathematics, Hartman deploys the notion of aleph number reciprocals, as a sort of infinitesimal proportion. This, he contends goes to zero in the limit as the uncountable cardinals become larger. In Hartman's calculus, for example, the assurance in a Dear John letter, that "we will always be friends" has axiological value , whereas taking a metaphor literally would be slightly preferable, the reification having a value of .
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Hartman invented the Hartman Value Profile, which is however not a description of what is valuable, but a test to determine what people regard as valuable. It measures concept-formation and decision-making capacity. A Hartman festschrift (Values and Valuation) appeared a few years after his death. Some critics would claim that most of the articles in it are not by Hartman supporters. Hartman, some critics claim, is out of the mainstream of value philosophy, but he was asked by UNESCO to summarize the state of Value Theory at Mid-Century. Many would dispute the idea that the number of properties of a thing can in any meaningful way be enumerated, but this is something Hartman never said was necessary. A standard argument against enumeration is that new properties can be defined in terms of old ones. Adding more features, a critic could object, even if each seems to be a good one, can sometimes lead to the overall value going down. In this way we get over-engineered software or a remote control which has too many buttons on it. Hartman holds that "the name (that one puts on a concept) sets the norm" so he would rejoin that a "Remote with too many buttons" is a disvalue.
From a mathematician's point of view, much of Hartman's work in The Structure of Value is rather novel and does not use conventional mathematical methodology, nor axiomatic reasoning. However he later employed the mathematics of topological compact, connected Hausdorff spaces, interpreting them as a model for the value-structure of metaphor, in a paper on aesthetics.
Hartman, following Georg Cantor, uses infinite cardinalities. As a stipulated definition, he posits the reciprocals of transfinite cardinal numbers. These, together with the algebraic laws of exponents, enables him to construct what is today known as The Calculus of Values. In his paper "The Measurement of Value," Hartman explain how he calculates the value of such items as Christmas shopping in terms of this calculus. While inverses of infinite quantities ( infinitesimals ) exist in certain systems of numbers, such as hyperreal numbers and surreal numbers, these are not reciprocals of cardinal numbers.
Hartman supporters maintain that it is not necessary for properties to be actually enumerated, only that they exist and can correspond bijectively (one-to-one) to the property-names comprising the meaning of the concept. The attributes in the meaning of a concept only "consist" as stipulations; they don't exist. Questions regarding the existence of a concept belong to ontology.
Intensional attributes can resemble, but are not identical to, the properties perceived by the five senses. Attributes are names of properties. When, even partially, the properties of a thing match the attributes of that thing in the mind of the one making the judgment, the thing will be said to have "value". When they completely correspond, the thing will be called "good". These are basic ideas in value science.
Axiology is the philosophical study of value. It includes questions about the nature and classification of values and about what kinds of things have value. It is intimately connected with various other philosophical fields that crucially depend on the notion of value, like ethics, aesthetics or philosophy of religion. It is also closely related to value theory and meta-ethics. The term was first used by Eduard von Hartmann in 1887 and by Paul Lapie in 1902.
In mathematics, specifically set theory, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. It states that
there is no set whose cardinality is strictly between that of the integers and the real numbers,
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements.
In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the Hebrew letter (aleph) marked with subscript indicating their rank among the infinite cardinals.
In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set contains 3 elements, and therefore has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them. There are two approaches to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers. The cardinality of a set may also be called its size, when no confusion with other notions of size is possible.
In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A.
In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than aleph-null, the cardinality of the natural numbers.
In mathematics, the system of hyperreal numbers is a way of treating infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form
In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of infinite sets. The term transfinite was coined in 1895 by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were, nevertheless, not finite. Few contemporary writers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as infinite numbers. Nevertheless, the term transfinite also remains in use.
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph.
In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from another cardinal by repeated successor operations. These cardinals are sometimes called simply "limit cardinals" when the context is clear.
In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers.
In set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers , sometimes called the continuum. It is an infinite cardinal number and is denoted by or .
Robert Schirokauer Hartman was a German-American logician and philosopher. His primary field of study was scientific axiology and he is known as its original theorist. His axiology is the basis of the Hartman Value Inventory (also known as the "Hartman Value Profile ", which is used in psychology to measure the character of an individual.
The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961. It states that the number of countable models of a first-order complete theory in a countable language is finite or ℵ0 or 2ℵ0. Morley showed that the number of countable models is finite or ℵ0 or ℵ1 or 2ℵ0, which solves the conjecture except for the case of ℵ1 models when the continuum hypothesis fails. For this remaining case, Robin Knight has announced a counterexample to the Vaught conjecture and the topological Vaught conjecture. As of 2021, the counterexample has not been verified.
In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. Some of the things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom. Recent developments concern combinatorics of the continuum and combinatorics on successors of singular cardinals.
Infinity is something which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals aimed to extend enumeration to infinite sets.
In the mathematical discipline of set theory, a cardinal characteristic of the continuum is an infinite cardinal number that may consistently lie strictly between , and the cardinality of the continuum, that is, the cardinality of the set of all real numbers. The latter cardinal is denoted or . A variety of such cardinal characteristics arise naturally, and much work has been done in determining what relations between them are provable, and constructing models of set theory for various consistent configurations of them.
