Current Thinking on Value

How many distinct meanings does the word 'value' have? Right now, I think the answer is four, but I have the feeling this list is both incomplete and not as compact as it could be. I'd like to make sense of all uses of 'value' in as few basic meanings as possible. Here's what I have now:

Value as Attitude

Mary values her alone time.
Pavel values books printed in the year he was born.

These sentences focus on a particular attitude Mary or Pavel have toward something. If we can shift the word order and still talk about this particular type of value, we get:

Mary's alone time is valued by Mary.
  or maybe
Mary's alone time has value to Mary.
  or
Mary's alone time is valuable to Mary.
  or even
Mary's alone time has value.

In the last example, "to Mary" is not explicitly mentioned but may be discernible by context. Now what's interesting here is that we can make statements which superficially sound like things have the property of "being valuable" in themselves, but really these things "have value" purely because someone has a particular attitude toward them.

This is the sort of value people have in mind when they say "value requires a valuer" or that there can't be "value without a valuer."

Value, the Facilitating Relationship

Sobriety has value for avoiding automobile accidents.
Grass has value for slowing erosion.

No attitude necessary. This sort of value could hold true in a world without any sentient beings whatsoever.

I'm tempted to count value_attitude as a subclass of value_{facilitating relationship} with personal desire fulfillment (or similar) as the thing being facilitated, but consider this asymmetry:

Carlos values the painting Starry Night by Van Gogh.
The painting Starry Night has value for exciting Carlos' visual taste.

The painting Ecstasy by Parrish has value for exciting Carlos' visual taste.
Carlos has never seen Ecstasy and so he does not value it.

We might say that Ecstasy has value for Carlos but not value to Carlos.

Non-relational Value

Does a painting — or anything — have value "in itself" without any explicit or implicit reference to a personal attitude, facilitated outcome, etc? This notion is often called "intrinsic value" (though that same term is also confusingly used to mean end-value as opposed to means-value).

This is the sort of value that comes up, for example, in environmentalist arguments that a lush forest which no conscious being ever knows about would still have value just as itself.

I strongly suspect non-relational value is not only fictional, but a confused idea.

Quantitative Value

Math, basically. I don't know how to fit "X has greater value than Y when X is 5 and Y is negative" into any of the above categories. Maybe it came out of quantifying the strength of value_attitude in the form of monetary prices?

At any rate, I'm still ruminating on these categories and will likely revise my view in coming months.