I’m proud to introduce my theory of induction, a systematic, rigorous method of proving generalizations from observation. In this short summary, I’ll indicate the essential features and benefits of my theory to motivate you to read my book.
Overview
Like other objectivist philosophers, I conceptualize a generalization as a proposition of the form, “All S is P.” For example, “all metals conduct electricity.” Since most important scientific conclusions are generalizations, a method for proving generalizations is critical for achieving certainty in the sciences. My theory can be used to prove new discoveries and to formulate an inductive proof of past discoveries. Proof of past discoveries will give scientists certainty and clarity in many established conclusions and will uncover flaws in foundational beliefs accepted in the past. The immediate application and testing ground for my theory is to overhaul the flawed foundations of modern physics and use the clarified context of knowledge to break the stagnation in that field.
Proof Through Inductive Narrative
Inductive proof must proceed in a proper order. One must reason only with direct observation and ideas that have been proven by a chain leading back to direct observation. My theory of induction proves conclusions in the form of a story following a possible process of discovery, the observations and reasoning steps forming a plot where each discovery is made possible by discoveries made earlier. Inductive proof requires that one reason with one’s full context of knowledge (more on this below); stories aid the mind in keeping track of this total in the form of a plot. Further, stories provide a natural framework for maintaining logical order; characters in the narrative cannot come to a conclusion until they have made the required observations and reasoning steps, they cannot test a hypothesis until they have observed evidence for it. Violations of logical order are experienced by the reader as plot holes.
Proper Conceptualization Justifies Generalizations
What proves a generalization? The view of many objectivists, including Leonard Peikoff, is that a generalization is proven by grasping a causal connection. E.g. “Balls are round, roundness requires that an object roll when it is pushed, therefore balls roll.” This kind of reasoning does not prove a generalization; it simply kicks the can down the road. Such proofs always reason from some existing generalization, in this case, “balls are round,” which itself must be proven. You might object that we don’t need to prove this, that roundness is just part of what it means to be a ball, but this misses the fact that concepts are objective.
When we form a concept, its distinguishing characteristics are generalizations. When we conceptualize roundness as a distinguishing characteristic of “ball,” we implicitly form the generalization, “all balls are round.” These generalizations must be proven because man can err when forming concepts. Although concepts for perceptual-level existents like “ball” are rarely flawed, conceptualization of higher abstractions is not always so easy. The faulty mainstream concept of selfishness packages together 1. concern for one’s own interests and 2. disregard of others. Such a concept leads to false generalizations like, “People concerned chiefly with their own interests will steal when they can get away with it.” If a concept contradicts itself the way “selfish” does, any generalizations made by connecting the nature of its units to its actions will not be generally true. Causal connections on their own do not prove generalizations because such connections rely on the validity of the concepts they reason from.
What validates concepts then? When a conceptual framework is flawed, it will prevent the grasp of certain facts. Those with the mainstream concept of “selfish” will struggle to grasp that stealing is self-destructive, not selfish, even when you get away with it. In contrast, learning the objectivist concepts “selfish” and “parasite” brings this fact, and many others, into sharp focus. The purpose of concepts is to effectuate a grasp of the known facts. As a result, a conceptual framework is validated when it is shown to form a non-contradictory grasp of the full set of known facts in one’s context of knowledge.
When a conceptual framework is shown to meet this standard, the generalizations implicit in their distinguishing characteristics are proven. Statements of the form “all S is P” are justified by the fact that P is part of what it means to be an S, and when our conceptual framework forms a non-contradictory grasp of all the facts, the distinguishing characteristics of those concepts form universally true statements (true generalizations) in our context of knowledge. Generalizations are proven by constructing a comprehensive conceptual framework. To achieve this, my theory provides detailed norms for crafting such a framework.
When this is achieved, generalization by enumeration becomes possible so long as the new generalization integrates with one’s existing conceptual framework. The generalization “water is a conductor,” is proven by observing instances where electric current flows through it. After enough* instances, one validly concludes that, “conduction is a property of this kind of material, it’s part of what it means to be water. If I later come across some liquid that has all the properties of water, but does not conduct, I will form new concepts to differentiate the two different liquids, but for now, ‘water,’ means this kind of thing, with these properties, including conduction.” (*I explain how many is “enough” below.)
As more is learned, concepts and their associated generalizations must be changed over time. Once “water” is reconceptualized to be a very specific molecule, H2O, instead of “the clear liquid found in lakes and streams,” one can grasp that it is the minerals commonly found in water, not H2O itself, which are conductive. My theory gives specific norms for changing concepts and generalizations as one’s context of knowledge evolves.
When a known factor could condition the subject matter of the generalization (such as known impurities in conductive samples of water) that factor and its effects on the generalization must be investigated before the generalization is proven. My theory gives detailed norms for identifying such halts to generalization.
*How many instances are enough to conceptualize around? To answer that question, future editions of my theory will make use of Ron Pisaturo’s book, A Validation of Knowledge, to formulate a mathematically exact account of how the number of instances observed so far (e.g. the number of samples of water found to be conductive) improves the likelihood that similar instances will be observed in the future (that liquids with all the same properties of water will also have the property of conduction.) This helps determine how many instances scientists should observe in order to gain confidence that their generalizations are likely to hold in the future.
Inference: The Method of Going Beyond the Senses
I have indicated how to prove generalizations, integrations of known facts, but how do we validly apprehend facts to begin with? There are essentially two ways; direct observation and inference from direct observation. When a plastic rod is rubbed with a cloth, it will attract bits of paper. When scientists saw this, they concluded that the rod has a new property (charge). How did they know this? The rubbing is directly perceived; the rod’s new property is not. The property must be inferred— deduced from observations and earlier principles. Specifically, it is inferred from the principle that entities act in accordance with their properties, and that if an entity acts differently from others, it must have properties that others lack. Going further, some scientists made the hypothesis that these bodies contain a new kind of entity by reasoning from the principle that an entity can gain new properties by gaining new constituent entities. Such inferences are the first steps toward discovering the electron. Notice that these inferences make use of certain broad concepts like “entity,” “action,” “property,” and principles like, “the properties of entities are affected by their constituent entities.” My theory presents a clear, interconnected system of fundamental concepts and principles that form the foundation of inference in the sciences. These concepts enable a validation of well-known methods of inference such as Mill’s methods, an explication methods used implicitly in the history of physics, and an identification of brand new methods of inference that may have never been used before.
Certainty Through Top-Down Integration
To understand induction, one must understand the difference between logical inductive order (explained above) which proceeds “bottom-up,” and an order of integration, like that of Euclid’s Elements or OPAR, which proceeds “top-down.” In these works, the broadest principles (like Euclid’s 5 postulates) are developed first, then narrower principles (like the Pythagorean theorem) are explained using these broader principles. These great works of integration do not constitute inductive proof in themselves, but are instead the crown of an inductive proof; a final step which facilitates certainty.
In OPAR, the virtues are developed only after man’s life as the moral standard is explained, since the nature of virtue is a result of the proper moral standard. When concepts and their associated generalizations are structured in this top-down way, it allows the scientist to efficiently see every concept and generalization in the light of all the facts that condition it. This makes it much easier to form a conceptual framework which forms a non-contradictory grasp of the full set of facts in one’s context of knowledge, making it much easier to prove one’s generalizations. My theory gives specific norms for integrating one’s knowledge by constructing these top-down hierarchies.
Preview the Future
My ambition for this theory of induction is to enable certainty in the sciences. By following this procedure and meeting these standards, scientists can understand nature with more clarity and confidence than ever before. If discoveries achieved by a few geniuses have lifted mankind from the swamp to the stars in a mere 400 years, imagine what will be possible once the method of inductive certainty is just as common as literacy is today! To preview the current draft of A Theory of Induction, you can support my project at patreon.com/inductica, or contact us at inductica.org/contact.