What's a difference between 'units' and 'things'?

A unit is merely a thing (an existent) that is regarded from a certain perspective -- the "unit perspective", where you are relating this thing and other things as essentially interchangeable. For example, these three quarters in my hand are distinct things, but for many purposes they are interchangeable with one another. They are essentially identical as units of money.

This is why Rand would say that units like these quarters don't exist qua units: they don't exist as units in themselves -- "unitness" is not built in to things because it is a perspective on things, an observed relationship among things. (And it is important to note that the unit perspective isn't arbitrary: the characteristics of things which we are attending to in [legitimately] regarding them as units are of course built in to those things. This quarter isn't a unit simply because I happen to feel like regarding it as one, but because I need to regard it this way in lieu of how its material and shape and so on relate to those of other things -- and such characteristics are what they are independent of my awareness of them.)

A "thing" is just an "existent" -- some thing which exists.

A "unit" is a thing regarded as one of a kind of thing.

A concept is a notion of a kind of a thing.

Unit means "one". When I look at a quarter, and say it is "a quarter" I mean it is "one quarter" or "a unit of the concept 'quarter'". The process of counting quarters requires regarding each quarter as one quarter -- of recognizing each quarter as a unit of 'quarter' .

Greg said, above: "Material things are units of the concept 'matter'" . I wonder about that. Is a loaf of bread a unit of the concept "loaf", or of the concept "bread"? Perhaps both, but in different respects. It's certainly "a" loaf, or "one" loaf. But it is made of "a" bread or of "one" bread (such as rye, or wheat, or white).

Matter (or bread) is a substance. Our regard for substances is different from our regard for units. A substance is regarded as continuous, homogeneous, and arbitrarily divisible -- that is, without present regard for whether it is ultimately made up of small entities (such as "kernels" or "molecules").

To measure a substance, you must choose a unit. As in quarts of milk, or pounds of meat.

You cannot measure a substance without mentally dividing it into units, because, qua substance, its units are by convention, and its amount given a chosen unit can be fractional.

The difference between units and substances is exactly the difference between "how many" and "how much".

I think an investigation into concepts of substances is in order. I have long thought that the alternative to the unit perspective is the substance perspective. If you don't view something as units, you regard it as a substance.

A thing is an individual concrete we perceive, such as a given object. We perceive it in its own right, independently of any other perceptions of other objects. This is perceptual level.

A unit is our recognition that an object we perceive is in fact a member of a group of related objects. We no longer treat it as an isolated object but identify it as similar to other objects we have seen before and that it has characteristics that make this object part of a type-set, of which set the particular one we are looking at we recognise as being a unit instance. To be a unit means to be "one of" that type-set. This is conceptual level.

For instance, we pick up an individual thing, notice that is generally rounded but has dimply bits at bottom and top with a short stick-like-thingamajig poking out one end, has a shiny outer surface that is red in colour yet we see has whitish insides after we bite out a chunk, and when we do so we find that it has a tart but sweet taste. That is perceptual level identification of an individual thing. We later learn that there are heaps of these things in the world, that while there are some variations in shape and skin colour they all have the same general physical layout, the same basic taste profile and are grown the same way, and that in English they are all called "apples". It is when we realise the connection of the actual apple in hand to the rest of the apples in the world that we recognise that the thing we have in hand is also a unit instance of a whole class of things, ie that we form the concept of apple and recognise that what we have in hand as being an individual apple.

What "things not existing qua units" means is that classification systems do not exist independently of our own minds. What exists in the world are all the individual red-coloured sweet-tasting roundish and dimply thingamajigs. The concept of "apple" is something that a mind has to create, based on observations of commonalities among individual things: "hey, this thingamajig is like those other thingamajigs, so I'll treat them all as members of the same one group and thus treat each individual thingamajig as a unit instance of my grouping of these thingamajigs". What stops groupings from being inherently subjective is that they can only properly be formed on the basis of actual shared characteristics and common causal connections that justify the grouping. For apples, this means recognising that each of the sweet-tasting thingmajigs has the same useful properties for our nutritional needs and for how to eat them. See ItOE for more details about this.

The same basic principle applies to all concepts, including matter. What exists and what we perceive directly is lots and lots of individual things. As it happens most of them are made of matter, but we don't start out knowing that and don't need to know that in order to use each of these things as actual things. Our identification of these things as being made of matter is a much later achievement (also preceded by us having formed a wide variety of intermediate concepts first), and does not arise until we recognise that each of the individual things we perceived share the common feature of being made of material stuff and hence recognise each individual thing as a unit example of matter.