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Suppose 2 hypothetical fruits A and B. A's mass is 10 g and B's mass is 15 g. In addition, A only contains vitamin A and B only contains vitamin B. Each vitamin A molecule weighs 200 picogram and each vitamin B molecule also weighs 200 picogram. However vitamin A is a biologically different molecule than vitamin B (they have different functions; say vitamin A is an immune system booster and vitamin B is a clotting factor component).

Quantitatively, mass-wise, fruit A is different from fruit B (A weighs less than B).
Quantitatively, mass-wise, vitamin A is identical to vitamin B (they both weigh 200 picogram), but they're biologically distinct (one acts on the immune system and the other participates in the clotting cascade). Is this quality (nonmathematical/non-quantity), the difference between vitamin A and vitamin B?

Are there any real-world examples like this?

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The real numbers are uncountably infinite. If we were to take this as unqunatifiable (irreducible to mathematics), do we have warrant to say the real numbers are either pure quality or, at a minimum, not as much of a quantity as say the number 329?. Compare real numbers to, for instance, odd numbers; the latter is in bijection with the natural numbers. I guess I'm trying to draw the distinction qualitative infinity vs. quantitative infinity.

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Pseudoquality: "It does not matter whether the cat is black or white, so long as it catches mice" ~ Deng Xiaoping.
In essence, the color of the cat (although quantitative in terms of wavelenght/frequency) doesn't matter, which is to say a black cat is neither better/worse (quantitative comparison) than a white cat. In this particular instance, for Deng Xiaoping, color is nonquantitative, it is a (pseudo)quality. Of course this is a partial (pseudo)quality since the black cat = the white cat (same).

Ergo, for an X to be a quality it has to be neither same nor not same (greater/lesser). What could be such a thing? I wonder ...

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  • You describe their having distinct biological effects as “non mathematical.” I would just point out that that’s not a reasonable characterization. The relationship between their biological effects is no less “mathematical” than the relationship between their masses. The former may not be expressible numerically, but one could certainly represent it in terms, say, of a directed graph (or network). Commented Nov 9, 2023 at 17:28
  • Vitamin A and vitamin B molecules are also quantitatively different on a bunch of other characteristics, mass is not the only one molecules have. Biological difference is just a consequence of different chemical composition, C20H30O vs C₆₃H₈₈CoN₁₄O₁₄P. What does "like this" mean, like what "this"?
    – Conifold
    Commented Nov 9, 2023 at 21:02

4 Answers 4

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they're biologically distinct (one acts on the immune system and the other participates in the clotting cascade). Is this quality ... the difference between vitamin A and vitamin B?

The difference in biological effects is a difference between vitamin A and vitamin B. There are other differences as well:

  • the chemical composition
  • the physical molecular structure
  • the response to light
  • the interaction with other molecules
  • etc.

Things can be alike on one metric (e.g. mass) but different on another metric (e.g. structure). Which metric (or metrics) matters depends on the purpose of making a distinction.

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What you are asking about seems to sit squarely in the middle of the metaphysical term 'identity of indiscernibles'. From WP:

The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa. It states that no two distinct things (such as snowflakes) can be exactly alike, but this is intended as a metaphysical principle rather than one of natural science. A related principle is the indiscernibility of identicals, discussed below.

You ask after the quality that distinguishes vitamin A from B:

Is this quality (nonmathematical/non-quantity), the difference between vitamin A and vitamin B?

Therefore, that is one normative decision that can be used in judgement to distinguish A from B. What is important to note is that 1) it is but one that you have chosen and 2) there are other possibilities.

For instance, presuming mass is identical, A can be distinguished from B by chemical structure. Or, as you have already conceded, A and B have different effects on the body, the former an immune booster and the latter affects clotting. If they have different chemical structure, then they also have necessarily different geometries, in size or shape or both. They might also be produced by different chemical pathways. Or as part of differences in chemical structure, they might have different bonds or have different sorts of electrochemical properties.

The reasonable position then is that ALL of these differences serve as a basis to claim that A is different B.

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The measurement 200 picograms is a description of how each object interacts with the world, just as a fact like "it's a clotting agent" is a description of how an object interacts with the world. An object's mass is the quality related to how hard it pushes back on the body accelerating it when accelerated at a known acceleration. We know from many experiments that when an object has this quality, it can be expressed as a mathematical relationship of many other qualities. While some of the mathematical relationships are the various mass-related laws of physics you're familiar with from physics class, one that comes before any of those can make sense is the relationship of linearity: the property of a quality that if you have two objects which have that quality, the two objects put together have twice that quality. Linearity allows us to use a number multiplied by a well-defined reference interaction (in this case the kilogram) to describe the way that the object will interact, or to use an algebraic variable (rather than a function or a natural-language description) to represent that quality. The selection of the reference interaction, and hence the number used to multiply it, is arbitrary.

To say that two objects have the same value for some observable is to say that there is one way that an object can interacts with other objects that is the same for both objects.

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Perhaps I am off topic, but since I see you persist in your question, I will address it from a quite different perspective.

Another aspect of this (quantity vs quality) is the problem of when/how consecutive quantitative changes constitute a qualitative change. For example is you watch a child 24/7 grow, when exactly is this child considered a teenager? Obviously there isn’t a specific moment when the qualitative change (of being a teenager) is actualized, but certainly at some point in time this will be a fact. Also notice the fact that even if two children have the exact same age, one may be described as a teenager and the other not, based on their behavior.

For example color red is a qualitative aspect of frequency. Beauty is a qualitative aspect of likeness. A physical object is a qualitative aspect of matter. Pain is a qualitative aspect of stimulus etc. Good and bad are also qualitative aspects of behavior.

In this way, I consider the qualitative aspect of things as a property closely related to consciousness; it's just the way someone perceives things. It’s not easy or straightforward to compare qualitative states. A qualitative comparison cannot be objectified.

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