What relationships does a pattern have within the system of pattern recognition?
On this page we are going to explore the ways in which patterns meaningfully connect to each other and how new relationships can be inferred from existing ones.
Relationships in Pattern will always have a directionality to them. They may be symmetric, in which the same thing is said regardless of where the relationship starts and ends. For instance to say that 'Alpha IS EQUAL TO Beta', I would expect that 'Beta IS EQUAL TO Alpha'.
But often relational patterns will be asymmetric and this has implications about the coherence of the relationship. Interpreting a relationship in one direction must be coherent with the interpretation in the opposite direction. For example, if 'Alpha IS INCLUDED IN Beta', then 'Beta INCLUDES Alpha'. Sometimes, saying just one of these two interpretations captures the whole relationship and the other can be inferred. But this is not always so intuitive.
If I say that 'Alpha IS A PROPER PART OF Beta', this relationship is interpreted in the opposite direction as 'Beta IS NOT PART OF Alpha'. While we can see that even though this is logically coherent, it is not necessarily the intuitive conclusion we would naturally derive. Rather, we might conclude from 'Alpha IS A PROPER PART OF Beta' simply, 'Beta INCLUDES Alpha'. But recall that the opposite relationship for 'Beta INCLUDES Alpha' was 'Alpha IS INCLUDED IN Beta'. That is a different pattern and a different relationship.
Although our common speech about parts and wholes can be ambiguous, it is not ambiguous in pattern language. At one level, every unique pattern has a distinct meaning. Interpretations of patterns can be synonymous but that doesn't make them the same pattern.
The point is that interpreting relationality in pattern has its own set of rules that drive the precise meaning of any given relationship and these patterns are coherent in both directions of interpretation.
Aristotle's contribution of syllogistic logic and taxonomy is widely appreciated, but the fact that he set the stage for a pattern logic is not. His two forms of predication: to be 'present in' a subject or to be 'said of' a subject are often taken simply as an exercise in semantics rather than the identification of a fundamental pattern.
We can see that Aristotle is working out four combinations of two possible relational components: 'present-in' and 'said-of' (the latter is also translated as 'predicable of'). These two components are the starting point for all of pattern logic. When taken together, the 'subject' becomes the relationship of inclusion.
Take Aristotle's example of when these two components are working together: "Thus while knowledge is present in the human mind, it is predicable of grammar."
In pattern language, these two statements are actually expressing a single pattern whose 'subject' can be stated as "Knowledge = Grammar BELONGS TO The Human Mind". In English, we overload the linking verb "to be" in understanding this something like "the subject Knowledge = The Human Mind IS Grammar" but this conflates Aristotle's distinction between the two forms of predication. More closely maintaining Aristotle's formulation of inclusion, we describe it not as "being", but rather, as "belonging".
'Present-in' captures the individual component that belongs, and 'said-of' (or 'predicable-of') captures the general component of which the belonging is in. In Aristotle's words: "But, to speak more generally, that which is individual and has the character of a unit is never predicable of a subject. Yet in some cases there is nothing to prevent such being present in a subject. Thus a certain point of grammatical knowledge is present in a subject."
Knowledge is 'present-in' the Human Mind,
The Human Mind is the individual aspect of the relational 'subject' knowledge.
Grammar is predicable-of Knowledge.
Grammar is the general aspect of the relational 'subject' knowledge.
The relational subject Knowledge = Grammar BELONGS TO the Human Mind
Or, 'The Human Mind KNOWS Grammar'