The resolution of realityon január 14th, 2011
Words that identify a chunk of reality (an object, a complete unit) should also indicate that the chunk as a whole may be further broken down or not, and if yes, then into how many chunks. As the process of chunking is continuous over history, the number of chunks at a given point of time is not always known. What can be known however, what the initial chunk was and how many chunks of the same sort were first created. It is always the beginning, the whole or one that is certain and can be used for drawing a path on which you can place yourself related to that beginning. With subsequent objects it is easy with objects such animals or plants that show individuality, i.e. that have their own boundaries and represent a whole, a unit, a specimen.
Neverthelss they remain part of one, the whole, that theythemselves have become when identified as objects.
The resolution of reality is derived from physical analysis resulting in various physical objects with qualities and quantities. But qualities (properties) and relations (operations or verbs) are abstractions and do not exist on their own. They are like the vapour state of water.
The resolution of such objects derived from thinking or abstraction results in properties and relations which do not have the same autonomy as objects. Therefore their number is likely to differ from time to time subject to the people who perform the mental operations (such as abstraction) and the willingness to distribute, share, accept and reinforce such properties as knowledge. But it is not usual to keep a count of such properties, only that of the objects. This is not appropriate, because if an object is represented as a totality of properties, then the properties must also be counted and shown. If it is not done, you cannot align your knowledge with other people’s knowledge systematically.
Actually, set theory applied to concepts as members of sets shows a problem that may be clarified. In most representations of sets Venn diagrams are used showing a single object instead of a multiplicity of objects. This may be misleading, especially when you talk about sets once as a total of unknown quantity and once as a single unit (set). This is a change of the subject in terms of the scale used, and it is not legitimate to call the two representations the same name. You either see something as a whole and ONE at the same time, or as a complex of a multitude, in which case you had better give the total number of the constituents to equal the object (the set) as a whole, like on conversion of a digit in a numeral system. But obviously, there is an operation between the two ways of seeing a set – once as a name for a single unit, and once meaning a name that should show that it refers to members (other objects) and therefore it should be used with the name of the members in plural.
So the use of words like family once with a singular then with a plural form of verb illustrates the situation of a single word meaning plural and singular depending on context in the sentence refering to the reality of two kinds.
If it is still not clear then, please accept the following explanation. Objects are form and content, where form is also the name given to an object and content is its properties not detailed as yet here. An obejct is also quality and quantity, where its quantity is one, and its quality is usually a property that makes it different from any other objects. If the object is a word or a sign representing a concept, then this word as a unique identifier is its quality as it does that job for the object. Now as a default an object has the property of being a quantity of one, it is not possible that an object is not one or a whole, otherwise the object ceases to exist. By definition it cannot be more than one, or a fraction of one either. This means that an object is always complete, it is one, it is not a fraction or a part and it has no components or members. It cannot be a set, unless this set has one member in which case the set is the same as its member.
Now you can say that a set is a concept, an abstraction, just as numbers. But we are only dealing with objects that are represented by real numbers in the real world, so the concept of a set that is abstracted to display properties that are not real, not integer or irrational is useless. If a set contains more than one members, then it is not one object, but an object with a quality of plurality and a quantity of the number of objects contained in or making up that quality. Normally it means a number plus an object combined, if the number of the members or the objects contained in is known. If it is not known, then it is an undefined, indeterminate noun with a very vague meaning. And it it has no content, i.e. it is an empty set, then it is fiction, has no grounding in reality, no ontological commitment whatsoever.