摘要
THINK OF A child learning how to catch a ball repeatedly thrown to her by her father.As the child practices or continues with this activity, she becomes better at it.Through a process of trial and error and across several attempts, the child, in essence, is gathering more data on what works well and what does not work and, in this manner, mapping what she learns to the outcome (ball catching).If the child could possibly articulate what she learned, the result could be represented as a function: an extensional mathematical device mapping ball paths to the appropriate actions.With better and more and more trials, the accuracy of the function increases.Nonetheless, the function remains dependent on the available data (ball catching experiences).Now, suppose that, after growing up, the child is able to understand what occurs when ball throwing, in terms of concepts and properties of relevant things in the world, e.g., gravity, the initial force of throwing the ball, throwing angles, air resistance, distance, and so on.That understanding could then be synthesized in one single equation (a symbolic artifact).Moreover, understanding (in terms of concepts) gives meaning to the elements in the equation, and it also explains why that equation (now an intentional artifact) can account for all the previous trials (data points) and all possible future trials.At that point, the data points themselves are no longer needed.The equation, as a symbolic intentional artifact, is all that one needs to predict how to behave in possible ball-throwing/catching circumstances.Note that the equation describing the possible movements of the ball describes this class of events but does not explain it.For the explanation, we need to refer to laws of nature and the concepts and properties populating the ontology of the domain.