So a layman can keep up with the reading in this topic can someone please define "Abstract concept" in the context of its current use by everyone.
This is my understanding. If anyone wants to offer a better explanation, please do so.
An "abstract" concept is a concept that is exists only in the mind. But, by definition, all "concepts" must exist only in the mind (as in, you will never find a physical thing called "concept" lying around in your room somewhere, for example). So the term "abstract concept" is actually a tautology, because it basically means "a mental construct that exists in the mind". Where else can a
mental construct exist?
Outside the mind???
Nevertheless, some abstract concepts have real, physical counterparts. For example, we know that apples exist. We can see them, touch them, eat them, so there are real, physical things that we call "apples". However, there is also the concept of apples in our minds. We can conceive of apples in our mind even when there is no actual apple that is being perceived through our senses. This mental conception of the apple is the "abstract concept" of this apple; a concept that we can neither see, nor touch, nor eat.
An obvious example of an "abstract concept" that has no real counterpart is a unicorn.
The issue being discussed in some of the earlier posts on this thread is whether or not the concept
zero has a real counterpart. A bit of confusion is being caused here because there are two different kinds of zeros. One is the zero of nothingness (the
quantitative zero) ; the other is the zero of relation (the
qualitative zero).
The zero of nothingness is that by which you attribute the quantity of zero to a set. For example, I can say that this basket has zero apples. This simply means that there are no apples in this basket. This zero basically negates the existence of the item to which it is applied. Hence, it is also called the zero of negation.
The zero of relation (or the qualitative zero) is that by which you ascribe a value to an item
relative to those beside it. For example, when I say that the temperature of a thing is zero degrees Celsius, I am not denying the existence of temperature in that thing (unlike the zero of nothingness), I am simply saying that relative to +1 degree C, this thing is cooler, and relative to -1 degree C, this thing is warmer. So
this zero refers to the
quality of the thing it is being used in reference to, not the quantity. Another example is the year 0 (according to any calendar system), where we are describing that particular period (year 0) in terms of those before it and after it. Year 0 in any calendar system is not denial of the existence of time at that moment (since it is the qualitative 0 being used).
So, coming back to the actual issue, when we use the term 'zero', does this have a real counterpart? If we are referring to the zero of nothingness, then it's real counterpart would be non-existence or absence (of a thing).
But if we are referring to the zero of relation, then the question of whether or not it has a real counterpart becomes absurd, since, with this definition, we do not refer to zero as a
thing, but rather as a
relation. And a relation is a
mental connection, not a physical one. For example, when we say that an object is heavier than another, we have formed a
mental relation between the two objects, even though those two objects might be completely physically unrelated. So when we say that a certain thing has a qualitative value of zero in
relation to some particular scale that we have agreed to use (like the temperature of a thing being zero in the Celsius temperature scale), then we are defining this zero to be a quality (or set of qualities) of that thing
relative to other similar qualities. So, by defining this zero to be a relative or relational quality, the question of whether or not this zero has a real counterpart becomes absurd, since relations necessarily exist only in the mind, not in reality.