Are quantities/amounts a state of existence?

Question

A quantity is often given like 'three metres' or 'two apples', but this seems more like a 'state' that any collection of entities can have.

We describe many things as being'two people', the couple next door, the couple across the road etc, but even though we say that are both 'two people', numerically they are different sets of people.

This language suggests to me that what we are describing in 'two people' is simply a state of being, such as 'a man' or 'sad' or 'happy' it is simply descriptive of what exists.

For example:

We might say A is B and see this as a statment of Identity such as:

A=B

But to say 'A is two people' and 'B is two people' it is wrong to say

A=two people=B as we do not necessarily know this based on identity. Any 'two people' can be different from one another.

We use forms of 'be' to express this, which suggests we see defining the amounts that constitute something describes it's existence.

Answer 1

I mean I know that more from the scientific and less from the philosophical context but as far as I can find it's not used terribly different, but there's usually the distinction between quality and quantity where a quality is a property of an object or state, which is often more of a vague phenomenological description while the quantity is more or less something concretely measurable.

Like often times you have a quantum (a minimal unit of something) and a quantity is just how many of those you've got. Now to treat a quantity as a quality you'd probably move from the definition of a set of individual items to a description of an entity. Like 2 people would be two people where 2 is the quantity of people, whereas if you define them as couple you might argue that being two people is just a feature of the couple.

Being quantitative basically moved science to the next level because that means you can compare things and use math whereas a pure qualitative discussion of properties often lacks the ability to compare things. Like if you state that it is "hot" or "cold" or even that it gets "hotter" or "colder" that could mean different things to different people and in different contexts and things like a middle ground, twice as hot or mixing a hot and a cool environment would difficult to theoretically describe as you'd need the experiment to tell you the result or allow for predictions.

So no the quantity is usually something very concrete while the quality may very well be an abstraction.

Answer 2

I would say we build structures of progressive abstraction & metaphor, as rooted in ideas like interchangeability (do apples equal pears? do decomposed apples count? context decides), and abstraction of numberlines from continuous symmetries under transformation (ie how we can make rulers from a standardised reference length). Space and time also have these symmetry qualities where things stay the same when we move them or repeat them later, and that leads to the power of math in physics - but not so much elsewhere, like in biology.

As described in more detail here

• What do we explictly refer to in mathematical expressios

& here:

• The Unreasonable Ineffectiveness of Mathematics in most sciences

Answer 3

We know physical quantities as the result of measurements.

Measurement in quantum mechanics is really very complicated. So, let us restrict to classical physics.

In classical physics, measurements come in two basic forms.

The easy one is just counting. You count some unit. The units do not have to be identical. The count is understood to include this variation in the reporting of the quantity. So, twelve cookies includes the variation in cookies. And so on.

In effect, counting establishes an integer ratio between a standard item (possibly somewhat sloppily designated) and a group of items that are considered similar.

The harder one is measurement of some quantity that has a dimension. Length, for example. Measurement has these parts. A standard is established. Then a ratio is established between the standard and the measured quantity. The quantity is the ratio, and the unit of the quantity is the standard.

Previously, standards were established less formally. Such things as the length of the King's foot was "a foot." Or the length of your forearm was "1 qubit." Lately we have established more and more formal standards, and these have become more and more repeatable.

Some easy examples: (These are a bit outdated because the current standards are based on modern physics.)

• The standard is the Standard Meter held in the standards place in Paris, France. A measurement consists in establishing that a distance is so-many times as long as the standard meter, giving so-many meters as the quantity. This relationship can be established through a number of methods from simple things like putting a meter stick beside the thing being measured. Or laser range finders, etc.
• The standard is the Standard Kilogram. The rest is similar to distance.
• The standard second is a certain fraction of a particular year. The rest goes similarly to distance.
• For other quantities such as temperature, power, density, etc., compound standards are established based on simple standards. Density is mass per volume, volume is distance cubed. Mass and distance are simple. Then the rest is similar.

Some other quantities can be dealt with in this fashion. Color, for example, can be dealt with as a wavelength of light, a distance. Color perception is quite different and depends on many factors besides wavelength. Loudness can be done as energy in the sound. Perception of sound is likewise very complicated.

Qualities or characteristics are not automatically able to be expressed as quantity. "Happy" as a characteristic is not able to be straightforwardly converted to a number. It is possible to do surveys and attempt to coarsely give numerical values. This gets into a related but distinct idea, that of affine characteristics. These are things that can be established as larger or smaller, but not to have numerical values. One thus gets "affine time" where you can determine before and after, longer and shorter, overlapping or not overlapping, and similar things. But not actual numerical values of duration. This is what you experience in the absence of any sort of thing to treat as a clock. A clock would act as a standard, and the numerical value would be the ratio between the clock's standard and the measured duration.

So to summarize: physical quantity consists of a measured amount, and this means determining a relationship to some sort of standard.