Today I posted “Answers to Questions from Introduction by Dr. Peokioff to THE LOGICAL LEAP - INDUCTION IN PHYSICS”
Sharing sample answer for wider audience.
Q4. What relationship is established here between concept formation and induction?
Ans: From TLL
A theory of generalizations presupposes a theory of concepts. One must grasp how the constituent concepts of a generalization are related to reality before one can grasp how the generalization itself is related to reality.
…[For inductive generalization] although she[Ayn Rand] did not provide the solution, she did provide the key to it. Mr. Harriman shows that valid concepts, in her definition of concepts, not only make possible but also guide our search for true generalizations… Every major aspect of the Objectivist view of concepts - including the role of similarities and differences, of integration, of hierarchy, of context - has a counterpart in the theory of generalizations. Indeed, generalization, Mr. Harriman explains, “is nothing more(or less) than an essential form of the method of concept formation.”
[italics in above TLL text are mine]
MY FURTHER ANALYSIS
In seeking inductive generalizations, we seek causal connections in abstract form. I can see essentially two types of causal connections. One that we seek between entity and action, more specifically between relevant characteristics of entity that make the action possible. This type I think covers a broad range of generalizations that involve gravity, chemical reaction or Political revolution. The second is seeking connection between essential characteristic of the entity identified, and other attribute(property to be exact) identified in the entity. Like for example checking “All swans are white”. Here white is not an action, but we seek connection between an entity and attribute. Likewise, there might be middle case, where particular characteristic is treated like an attribute, but it is action. Like in “Man speaks language”, while for all practical(mostly syllogistic) purposes we can consider speaking language as an attribute. Strictly speaking it is action that is caused by the rational nature of man.
So in generalization, as in concept formation, we have to first observe various concretes subsumed by the generalization. Like for generalization “Ball rolls on pushing”, observing instance or instances of various balls rolling on being pushed. While in concept formation we abstract essential characteristic(s) after grouping units that are subsumed, in forming an inductive generalization there is psychologically similar step where we need to identify concepts that subsume entities involved in the actions we observe(that is, as in abstraction, here we selectively focus on the percept of generalization. We selectively focus to infer entities and attributes involved in action).
So any inductive generalization I think can be specified as follows.
Symbol - Sentence like “Pushing rolls ball” or Picture of man sitting on chair for early form of generalization “Chair can support man”.
Concepts - {Ball, rolling, pushing}
(Not just the symbols of these concepts, but indirectly also the units these concepts subsume and their characteristics ).
units of generalization - {Percepts involving ball rolling on being pushed in bowling, in tennis court, in cricket match etc.}
For generalization also there can be CCD. Like for “pushing rolls the ball”, CCD can be “man causing motion” which includes foils like “ball not rolling when not pushed” and “ball rolling further when pushed harder”.
Further, it might be possible to subsume same existent perceived for generalization into different concepts. For e.g. percept of particular soccer-ball can be subsumed by soccer-ball, spherical ball or solid movable object. As in concept formation, what concept subsumes percept in mind is determined by the purpose or CCD of inducing generalization. If the purpose like Galileo is to reduce friction in experiment, then the ball can be subsumed under the concept spherical ball. And if the purpose is for soccer player to perfect passing technique, percept of same ball can be subsumed under the concept soccer ball.
(Though Galileo uses metal balls to reduce friction, he would have to first observe regular play balls to conceive the idea of reducing friction using metal balls).
Further, while forming inductive generalization also there can be existent, identity and unit stages.
For generalization “Ball rolls on pushing” existent stage might be same as existent stage for concept of action rolling. That is pushing rolling the ball.(the existent stage will be different if first time rolling observed is “rolling of rocks in valley due to natural forces”). However, while identity stage for rolling will include percepts of rolling, sliding, walking etc. The identity stage of generalization can have more elaborate each element and a more delimited set. It will be percepts of “ball not rolling on not being pushed”, “ball rolling on being pushed”, “ball rolling more distance on being pushed harder”. And unit stage of generalization, as described before, will involve Symbol, Concepts and “units subsumed”.
Why conceptual framework is necessary for formulating generalizations, and exact steps leading to this and higher generalizations will be described later. But briefly, if there were no concepts, identity stage of inductive generalization would have to include many more perceptual instances. Like sliding, walking, rolling of cubicle blocks, kicking, pushing, rolling due to invisible actor, rotation only, etc. But most of these percepts are omitted while formulating concepts of rolling, ball, or pushing. Thus a smaller set during identity stage of induction(due to conceptual framework) enables better focus on induction.