Sadly, known definitions are meaningless, circular, or long lists of traditional goods.
Summary of the problems:
Attempted definitions of goodness fail in known ways. Definitions generally either describe traits or properties of a real object or set of objects, or divide a concept into other, subsidiary concepts. Both approaches have failed to define goodness. As a result, desperate philosophers have tried desperate expedients to get some of the value that such a definition would provide.
Problems with definitions using traits or properties:
Most philosophers find that the traits or properties that would justify calling a thing good are different for different categories of judgment. For example, the criteria by which we judge art to be good are different from those by which we judge people to be good. A famous early discussion of this problem is by Aristotle, in his Nicomachean Ethics (at 1096a5).
Many judgments of goodness translate to prices, but this appears to be a summary or effect of judgment, not a cause. For example, a piece of art found in an attic may be sold for the price of a meal. A collector may then recognize it as a lost work of a famous artist, and sell it for more than the price of a house. The price changed because the collector had better judgment than the owner who kept it in an attic.
If goodness were a common trait or property, we should be able to abstract it, but no one has succeeded. Thus goodness is widely believed not to be a property of any natural thing or state of affairs.
Of course, this belief is open to trivial skepticism: Perhaps philosophers just haven't stumbled across the right definition. However, after several thousand years, the prospect is bleak.
One wonders where such an immaterial trait as goodness could reside. An obvious answer is "Inside people." Some philosophers go so far as to say that if some state of affairs does not tend to arouse a desirable subjective state in self-aware beings, then it cannot be good.
Although a definition of external "objective" goodness could be used to construct rational morals and legislation, a subjective definition of goodness remains useful to help one live a good life.
However, simple hedonism is rejected even by most hedonists because there seem to be pleasures that are bad (e.g. eating too much) and pains that are good (e.g. going to the dentist).
There are some problems with identifying goodness as pleasure. It's strange to say that carrying out one's duty (which is obviously good) has anything to do with pleasure. Also, the sense of achievement following completion of one's work is rarely considered pleasure, although it is clearly good to finish one's work. Aristotle even distinguished genuine happiness from amusement, and virtuous from base pleasures. This makes some sense because useful work (like the Wikipedia) is clearly better than mere amusement (such as a chat room).
The usual fix of Hedonism is to consider consequences, as well as pleasure and pain. For example. going to a dentist has a small amount of pain now, but avoids a great deal more later. However, even consequentialism is strained when considering duty.
Happiness or pleasure can often be recognized, which solves many problems for Hedonism. But there are more problems with Hedonism. No known definitions of happiness or pleasure have met objections similar to those of a definition of goodness: The situations producing the happiness or pleasure are different in different categories of action. Neither happiness nor pleasure has been conceptually divided (analyzed) in a way that permits deductive choices of real-world alternatives.
Problems with definitions dividing the concept of Goodness:
The other form of definitions of goodness is to try to divide the concept of goodness into smaller, more understandable concepts.
It has been thought that if some conception of goodness were divided, or causally regressed far enough, the process would eventually come to a logical stopping place, an "ultimate good." However all known forms of such regressions appear to be either circular, or open to skepticism.
Attempts to translate, divide or causally regress the concept of goodness usually fail in a particular way. Every such attempt seems to end up with one or more subconcepts described with the word "goodness" or related words like "pleasure," "dutiful," "praiseworthy", or "virtuous." Such definitions appear to be circular, and therefore are believed invalid.
The circularity of causal regression hits scientific definitions of goodness especially hard, because it seems to indicate that science cannot study goodness. Some philosophers have gone so far as to say that science can only study "what is", not "what should be." The clearest proponent of this viewpoint was David Hume in "A Treatise Concerning Human Understanding," who famously said that there is no logical way to convert an "ought" to an "is."
G.E. Moore[?] described this circularity clearly and called this "The Naturalistic Fallacy," because he believed that people had a sort of nonphysical intuition that could sense goodness. Few people believe in this intuition, but the term has stuck because goodness is so widely thought nonphysical.
Many philosophers tried to end the regressions by applying an auxiliary evaluation that helps the general regression to a stopping place. This auxiliary evaluation is often open to skepticism.
For example, Aristotle considered "The supreme element of happiness" to be theoretical study, because it "ruled all others." (Nicomachean Ethics, 1177a15) In this case, supremity was the auxiliary evaluation that could be doubted.
Thomas Aquinas asserted that everything sensed was an effect, with an earlier cause, and that each immediate (proximal) cause was less diluted in goodness, and that therefore, the first cause would have to be perfectly good. In this case, the concept of dilution might be doubted as an inaccurate metaphor, or that the dilution necessarily scales back to perfection (maybe the first cause was pretty good, instead of perfect). One might also doubt that the causal regression ends: It might be circular, for instance. [I don't have a copy of the Summa Theologica- can anyone find the reference and correct my (no doubt) misquote?]
Philosophers have made progress against the circularity.
Aristotle pointed out that some goods appear to have value in themselves, while others are useful only to get other goods. He called these "intrinsic goods" and "instrumental goods." For example, if health is an intrinsic good, then surgery and drugs are instrumental goods.
Another improvement is to distinguish contributory goods. These have the same qualities as the good thing, but need some emergent property of a whole state-of-affairs in order to be good. For example salt is food, but is usually good only as part of a prepared meal. Other exampless come from music and language.
Most philosophers that think goods have to create desireable mental states also say that goods are experiences of self-aware beings. These philosophers often distinguish the experience, which thay call an intrinsic good, from the things that seem to cause the experience, which they call "inherent goods."
Kant showed that many practical goods are good only in states-of-affairs described by a sentence containing an "if" clause. Further, the "if" clause often described the category in which the judgment was made (Art, science, etc.). Kant described these as "hypothetical goods," and tried to find a "categorical" good that would operate across all categories of judgment.
An interesting result of Kant's search for a categorical good was a moral command, the "categorical imperative": "Act according to those maxims that you could will to be universal law." From this, and a few other axioms, Kant developed a moral system that would apply to any "praiseworthy person." (See "Foundations of the Metaphysics of Morals," third section, -.)
It's clear that a general definition of goodness must categorically define goods that are ultimate, intrinsic, non-contributory, and at least inherent.
Desperate practical expedients:
The classic expedient is to simply make a list of all the ancient good things. This works, but it can't help find or evaluate new things, and it can't answer skeptics. The problems with such lists are that they are likely to be both incomplete, and contain difficult items with no value. One reasons about such lists using casuistry.
Some philosophers have concentrated on prioritizing real things or states-of-affairs using simplified or undefined concepts of goodness.
Jeremy Bentham's book "The Principles of Morals and Legislation" prioritized goods by considering pleasure, pain and consequences. This theory had a wide effect on public affairs, up to and including the present day. A similar system was later named Utilitarianism by John Mill.
Utilitarianism succeeds in many cases. However Utilitarianism has some questionable areas of judgment. For example, it considers all goods as interchangeable. If feeding a starving child would cause the child to feel sick, and not permanently improve his situation, a Utilitarian would prefer to spend the money on a car for a rich man.
Unhappily, the utilitarian argument to permit abortions is of the same form as this questionable type, though with changed quantities. To see this, substitute "unconscious fetus, destined for loveless poverty" for "starving, hopeless child" and "improved woman's income" for "rich man's watch."
To a humanist, who values human life above all else, the form of the judgment remains invalid, while a utilitarian might agree with the statement, based on the changed magnitudes of value.
In another widely questioned set of judgments, Utilitarians weigh the pleasures and pains of men and animals in the same scale. See PETA, an animal rights organization based firmly on Utilitarian ideals.
John Rawls' book "A Theory of Justice" prioritized social arrangements and goods based on their contribution to justice. Rawls defined justice as fairness, especially in distributing social goods, defined fairness in terms of procedures, and attempted to prove that just institutions and lives are good, if rational individuals' goods are considered fairly.
Rawls[?]' crucial invention was "the original position[?]," a procedure in which one tries to make objective moral decisions by refusing to let personal facts about oneself enter one's moral calculations.
A problem with both Kant's and Rawls' approach is that goodness appears to be both prior to and essential to fairness, and different for different beings. Procedurally fair processes of the type used by Kant and Rawls may therefore reduce the totality of goodness, and thereby be unfair.
For example, if two people are found to own an orange, the standard fair procedure is to cut it in two, and give half to each. However, if one wants to eat it, while the other wants the rind to flavor a cake, cutting it in two is clearly less good than giving the peel to the baker, and feeding the meat to the eater.
Many people judge that if both procedures are known, using the first procedurally-fair procedure to mediate between a baker and an eater is unfair because it is not as good.
Applying procedural fairness to an entire society therefore seems certain to create recognizable inefficiencies, and therefore be unfair, and therefore, by the equivalence of justice with fairness, unjust.
This strikes at the very foundation of Kantian ethics, because it shows that hypothetical goods can be better than categorical goods, and therefore be more desirable, and even more just.
Whatever goodness is, it is important.
Also see value theory.