What is the purpose of concept formation?
What are concepts?
What is the structure of a concept?
How do concepts relate to mathematical sets? (Set Theory)
How do concepts relate to mathematical categories? (Category Theory)
How do concepts relate to other concepts?
How do we form concepts?
What are the fundamental mental operations underlying human concept formation?
What is the relationship between concept formation and analogy making?
What is the purpose of concepts? To organize sense perception?
I first came across theories of concept formation through Ayn Rand's philosophy of Objectivism. Concept formation forms the essence of Objectivism, it is the core of the Objectivist approach.
To Rand, concept formation was a mathematical - connection between measurement and conceptualization.
Both are quantitative?
How do other men differ from the men you have perceived? Rand: In principle they differ in the same way the distance of the moon differs from the distance of an inch - in measurement.
Concretes within a concept differ from one another in what way?
Integration of concretes into a concept consists in maintaining their characteristics but omitting their measurements. WE recognise the identity of all of these instances.
All the instances under a certain concept are commensurable - they can be related quantitatively to the same unit.
The mind's recognition of similarity is the recognition of a fundamental mathematical .
Doesn't need to know specific numerical measurement.
The concept "man" represents all men past, present and future.
Perceived concretes are the base - reduction of what we don't perceive to what we do perceive.
Perceived concretes are the base.
Differentiation and integration.
NOT attribute ommission but measurement ommission.
"The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition." - Introduction to Objectivist Epistemology
"The relationship of concepts to their constituent particulars is the same as the relationship of algebraic symbols to numbers. In the equation 2a = a + a, any number may be substituted for the symbol “a” without affecting the truth of the equation. For instance: 2 X 5 = 5 + 5, or: 2 X 5,000,000 = 5,000,000 + 5,000,000. In the same manner, by the same psycho-epistemological method, a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes. Let those who attempt to invalidate concepts by declaring that they cannot find “manness” in men, try to invalidate algebra by declaring that they cannot find “a-ness” in 5 or in 5,000,000." - Introduction to Objectivist Epistemology
What does mathematics have to say about concept formation?
Can spaced repetition be used to form new concepts, or is it only used to maintain concepts already formed?