Discreteness and Continuity

Discreteness and Continuity

Traditionally, logic is identified with reasoning, and thus considered as essentially discrete. Normally, people distinguish one thing from another, and act step by step, thus revealing the discrete side of their activity. However, this does not mean that human activity is entirely discrete, and there is no place for continuity. Indeed, the distinct operations are embedded in a continuous state of action that lasts from the beginning of the action to its end. The action is also a part of some activity, which does not have a definite beginning or end and might be thought of as purely continuous motion, so that all the apparent discreteness should be treated as limited and virtual.

In the hierarchical approach, one finds the idea of hierarchical conversion revealing discrete structures and functionally differentiated systems in a larger whole that cannot be reduced to any of its particular positions (outer manifestations). Human activity is essentially hierarchical, as it reflects the hierarchy of the world in general. The distinction between its discrete and continuous aspects is relative, depending on the particular position of hierarchy. To adequately reproduce (and control) the organization of human activity, logic must incorporate certain means powerful enough to embrace its continuity as well.

And, indeed, we can discover intrinsic continuity in any logical form.

For instance, every logical scheme is discrete since it contains a finite number of logical positions and junctions. However, both logical positions and logical junctions can be unfolded in different ways, which makes them essentially continuous, though the inner continuity of logical positions is different in kind from the outer continuity of logical junctions, which gives the two complementary aspects of continuity. However, due to universal reflectivity, logical positions and junctions are interchangeable in any scheme, so that internal continuity can be made external, and vice versa. In this way, logic integrates both the continuity of activity and its divisibility into separate actions, accounting for the possible shifts of the motives onto the goals, with actions developing into activities.

The discrete aspect of logic reflects the hierarchy of activity as it has objectively developed in a particular cultural context. The two kinds of logical continuity correspond to the infinity of the ways that could lead to the present level of development and the infinity of directions of further development. The present is different from the past and the future, but it is never isolated from them, implementing one of the possible transitions from one to another.

The level of logical reasoning implies the existence of the lower-level intuitive logicality, as well as the higher level of comprehension. One could observe that intuition and comprehension are essentially continuous, as compared to the discreteness of reasoning. However, logic is the unity of discreteness and continuity on every level, and it is only the relative dominance of one or another that varies from one position of its hierarchy to another.

[Logic] [Hierarchies] [Unism]