Understanding the World: Expressing Levels of Certainty
Note: Research and Ghostwriting by LLM AI; shaped by my fevered brain – Ephektikoi
Introduction
In the pursuit of knowledge, various terms express different levels of certainty and evidence. These terms—"axiom," "theory," "hypothesis," "conjecture," "assumption," "supposition," and "speculation"—range from the most concrete and established to the loosest and most tentative. Below, these concepts are explained in order of their concreteness, noting how some are similar or distinct in their application.
Axiom
An axiom is a statement or principle accepted as true without proof, serving as a foundation for further reasoning or theories. Axioms are self-evident truths primarily used in mathematics and logic. For instance, in Euclidean geometry, the statement "through any two points, there is exactly one straight line" is an axiom (Hilbert, 1899). Axioms are the most concrete of these concepts because they are universally accepted within their domain.
Theory
A theory is a well-substantiated explanation of some aspect of the natural world, supported by substantial evidence and consistently validated through observation and experimentation. Theories are widely accepted as true until new evidence challenges them. For example, Einstein's theory of general relativity explains gravity as a curvature of spacetime and remains a cornerstone of modern physics (Einstein, 1916). Theories are nearly as concrete as axioms but differ because they can be disproven with new evidence.
Hypothesis
A hypothesis is a testable statement or prediction that serves as the starting point for scientific inquiry. Unlike a theory, a hypothesis is more tentative and meant to be tested and potentially falsified through experimentation. For example, the hypothesis "If plants receive more sunlight, they will grow faster" can be empirically tested (Popper, 1959). Hypotheses are building blocks for forming theories, making them less concrete than theories but more specific and testable than conjectures or speculations.
Conjecture
A conjecture is an unproven statement based on incomplete information. Conjectures are often educated guesses that may lead to hypotheses or theories but are not yet supported by sufficient evidence to be considered true. In mathematics, conjectures like the Riemann Hypothesis propose ideas that, while reasonable, have not been proven (Riemann, 1859). A conjecture is less concrete than a hypothesis because it lacks the requirement of being testable and remains speculative until proven or disproven.
Assumption
An assumption is something accepted as true without proof, often as a basis for reasoning or argument. Assumptions are similar to axioms but are usually context-dependent and not universally accepted as self-evident. In economics, for example, the assumption of rational behavior is foundational for many models, even though it may not always hold true in real-life situations (Friedman, 1953). Assumptions are less concrete than axioms but more structured than suppositions or speculations.
Supposition
A supposition is a tentative assumption made for the sake of argument or investigation. It is similar to an assumption but is often used in a more hypothetical or exploratory context. Suppositions are employed in theoretical discussions, such as thought experiments, to explore potential outcomes without committing to the truth of the premise (Rescher, 1976). A supposition is looser than an assumption because it is more hypothetical and less foundational.
Speculation
Speculation involves forming ideas or theories without firm evidence, making it the loosest and most tentative of all the concepts listed here. Speculation is often used to generate new ideas or hypotheses but lacks the evidence to be taken as reliable. For example, in finance, speculation refers to making high-risk investments based on the hope, rather than certainty, of future returns (Malkiel, 1973). Speculation is similar to conjecture in its uncertainty but is even less structured, often lacking any formal basis in logic or evidence.
Relationship Among the Terms
Axiom and Assumption: Both serve as starting points for reasoning, but axioms are universally accepted, while assumptions are context-specific.
Theory and Hypothesis: A theory is a well-substantiated explanation, whereas a hypothesis is a testable prediction that can lead to the development of a theory.
Conjecture, Supposition, and Speculation: These terms represent increasing levels of uncertainty. A conjecture is an educated guess, a supposition is a tentative assumption for exploration, and speculation is the least certain, often without firm evidence.
References
Hilbert, D. (1899). Grundlagen der Geometrie (Foundations of Geometry). https://books.google.com/books/about/Foundations_of_Geometry.html?id=91LvAAAAMAAJ
Einstein, A. (1916). The Foundation of the General Theory of Relativity. Annalen der Physik. https://www.scirp.org/reference/referencespapers?referenceid=1362677
Popper, K. (1959). The Logic of Scientific Discovery. Routledge. http://philotextes.info/spip/IMG/pdf/popper-logic-scientific-discovery.pdf
Riemann, B. (1859). On the Number of Primes Less Than a Given Magnitude. Monthly Notices of the Royal Astronomical Society. https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-translation.pdf
Friedman, M. (1953). Essays in Positive Economics. University of Chicago Press. https://press.uchicago.edu/ucp/books/book/chicago/E/bo25773835.html
Rescher, N. (1976). Theory and Decision: Essays in Honor of Werner Leinfellner. Springer. https://books.google.com/books/about/Theory_and_Decision.html?id=aNSfLjj_rAsC
Malkiel, B. G. (1973). A Random Walk Down Wall Street. W.W. Norton & Company. https://yourknowledgedigest.org/wp-content/uploads/2020/04/a-random-walk-down-wall-street.pdf
This structured explanation clarifies the differences between these terms, helping to understand their place in reasoning and the scientific process, with appropriate in-line citations and a clear ordering from the most concrete to the loosest concept.