INDUCTIVE REASONING
Contents:
The essence of induction is the inference of generalisations (universals) from perceived instances (particulars). Deduction requires universals, and thus, presupposes induction; induction, thus, is the primary process of reasoning. Hence, human cognition without generalisation is a self-contradiction as it would have to be human cognition without induction, and thus, without deduction — hence, it would have to be cognition without reason, i.e. non-cognition.
A proposition that ascribes an attribute to every member of an unlimited class (if the class were limited, it would be enumerable, making inference unnecessary since you can learn about each member individually). In formal terms, a generalisation is a proposition of the form:
All S is P
NOTE: No metaphysical proposition is a generalisation, since a metaphysical proposition only reaffirms the fact of existence and identity as such; no metaphysical proposition abstracts and ascribes attributes of particulars to every member of an unlimited class. Corollaries of metaphysical propositions are clearly also not generalisations, as they are merely recontextualisations of the metaphysical propositions.
Both concepts and generalisations are means of extending cognition beyond perception. Concepts are the means of integrating a range of concretes; integration here means to make a range of concretes retainable and accessible by a single mental unit. Concepts by themselves serve to organise existing knowledge (ex. to organise existing perceptions into a potentially unlimited category), not to claim new knowledge. Generalisations, on the other hand, are the means to gain new knowledge about the referents of concepts. Thus, while a concept is either valid or invalid but not true or false, a generalisation is either true or false rather than valid or invalid.
Can observations of particulars ever lead to knowledge — with certainty — about the broader category under which the particulars lie? If so, how?
A method of reasoning must begin with axioms, i.e. propositions irreducible by logic (as they are the basis of logic). Such axioms must be (1) self-evident and (2) sufficient to cover every area the method of reasoning can explore.
For any method of reasoning, we begin — before any generalisation — at the laws of logic and perceptions (which are self-evident). For deduction, we are also given generalisations as premises and — often — observations of particulars. However, we are not given generalisations at the start of induction, since induction is the method of reaching generalisations. To move from perceptions to generalisations, we need a means to integrate an unlimited class of perceptions, i.e. we need concepts. First-level concepts are concepts whose referents are perceptions, and thus, this is where we begin inductive reasoning.
However, concepts by themselves are not new knowledge but the integration of knowledge already acquired and that can be acquired. Hence, to say something new, we need to apply concepts to observations that reveal the attributes and actions of one or more entities not previously integrated into the concept (since attributes and actions are the aspects of an entity or a class of entities that describe parts or the whole of its identity in some context). In other words, we must observe the expression of an entity’s identity (through attributes or actions) that reveal something more about the identity of a class of entities than was previously known in the concept alone.
Example:
The concept of swans may be integrated by essentials that do not include their colour (since their colour is not key causal factors in their nature and are not necessitated by other similarities). If we find that, for some reason inherent in the nature of the swans, they have to be white, then the generalisation would be “all swans are white” (which is not true of course, but this is just an example), which is knowledge that goes beyond the concept of swan itself.
The law that relates facts of reality to each other is the law of causality, which says that things can only act by their nature. Hence, it is through the discovery of causality that we discover something beyond known facts about a kind of thing so as to discover something that is necessitated by the nature of that kind of thing but was not evident in perception alone. Thus, generalisation must begin with applying concepts to perceived causal relationships.
Can causal relationships be perceived? If so, to what extent?
A perceptual causal relationship is the perception of an action of an entity or an interaction between two or more entities necessitated by the nature of the entities involved. If I push an object and the object moves, these actions are not only sequential but also causal, since it is self-evident that solid matter (which my hand and the ball both consist of) resists — and thus can impact — other solid matter. A first-level generalisation is a generalisation of a perceptual causal relationship, and it is formed by applying concepts to the causal relationship, i.e. retaining its essence and omitting its measurements. Hence, the axioms of induction are first-level generalisations, which — through a similar method of abstraction — can lead to higher-level generalisations.
NOTE: Applying concepts only lead to a generalisation if the essence of the causal relationship is retained by the concepts being applied. For example, I can validly say, “fire burns paper” upon observing it, but it is invalid and thus false to say, “orange, waving things burn white, flat things”; the former retains the essence of the causal relationship (the heat and the material) whereas the latter omits it.