Concepts

All distinguishable and identifiable "things" in DSB are called concepts. In hypergraph terms, concepts are the nodes between which there are hyperarcs that give the relationship between concepts.

Concept Characteristics

• Created to represent distinct "things".
• Are empty, they do not have any properties or contents.
• They may be treated as if they exist and be referred to using singular terms.
• Need not refer to any real "thing" as they may refer to abstract "things".
• There can be an unbounded number of them, but not an actual infinity of concepts.
• All objects are just concepts and their relationships.
• Concepts are not objectively real but are constructed by abstraction.

Concept Identify

Within a single fabric, each concept must be involved in the tail of a relation that the other is not involved in for the concept to have been originally distinguished at all. Therefore, no concepts within a single fabric can be identical/equivalent except to themselves (Leibniz's Law). Equivalence of concepts is only meaningful between fabrics -- disconnected hypergraphs -- where again the notion of individual concept equivalence is impossible to determine without reference to the entire fabric. Concept equivalence can only be established by finding an isomorphism between one fabric and another. If one fabric is larger than the other then any such mapping is an extension and so the concept in the larger is an instance of that found in the smaller fabric. Only if two fabrics are identical in size and have an isomorphic mapping can the concepts be said to be equivalent.