Thinking Scientifically/Communicating Uncertainty

Science is not a stronghold of certainties; it is a disciplined practice of measured doubt.^[1] The words we choose signal how solid—or tentative—our claims are. Unfortunately, everyday usage often scrambles these signals (“it’s just a theory”), blurring the difference between a passing idea and a well-supported explanation. This essay clarifies five key rungs on the ladder of claims—speculation, conjecture, hypothesis, theory, and law—and offers guidance on how to use them to communicate uncertainty honestly and precisely.

Speculation is the seed stage: an idea posed with little to no evidentiary support. It can be insightful or wild, but by itself it bears no warrant. Speculation is valuable when it opens lines of inquiry (“Could life exist in Europa’s subsurface ocean?”) and problematic when it is dressed up as established knowledge. Responsible communication pairs speculation with clear disclaimers (“This is an informed guess; we lack data.”) and with next steps (“Here’s what would count as evidence.”).

A conjecture is more disciplined than speculation. It is a plausible claim shaped by pattern recognition or partial evidence but not yet demonstrated. In mathematics, a conjecture is a precisely stated proposition believed true but unproven (e.g., the Goldbach Conjecture). In empirical sciences, a conjecture narrows the idea to a sharply framed claim consistent with current observations but not yet operationalized for decisive tests (“A ninth planet could account for observed clustering of Kuiper Belt objects.”). Communicating a conjecture means emphasizing plausibility, not proof, and identifying what would convert it into testable hypotheses.

A hypothesis is a testable proposition. It states an expected relationship or mechanism and specifies operational definitions, measurements, and conditions under which it can be falsified or supported. Good hypotheses generate predictions that risk being wrong: “If photosynthetic pigments are present on this exoplanet, its reflected light will show a ‘red edge’ at wavelength λ.” Hypotheses often come in pairs (null and alternative), are pre-registered when possible, and are evaluated with statistical or Bayesian methods. Communicating a hypothesis means stating exactly what was predicted, how it was tested, how strong the evidence is, and what uncertainties remain (confidence or credible intervals, effect sizes, assumptions).

A theory is not a guess. It is a well-substantiated, integrative explanation that unifies diverse facts, laws, mechanisms, and confirmed hypotheses, and that continues to make accurate, risky predictions. Evolution by natural selection, plate tectonics, germ theory, and the kinetic-molecular theory qualify because they explain broad domains, cohere with independent evidence, and successfully anticipate novel findings. Theories carry deep explanatory power (“why” and “how”), not merely “what.”

Communicating a theory means emphasizing the web of converging evidence, its predictive successes, its scope and limits, and where active uncertainties lie (e.g., parameter values, boundary conditions, unresolved anomalies).

A scientific law is a concise generalization—often mathematical—describing regular patterns in nature (e.g., the inverse-square law, Boyle’s law, Mendel’s law of segregation). Laws typically tell us what happens under specified conditions, not why it happens. They can be local in scope (Hooke’s law holds for small elastic deformations) and can be subsumed or refined by broader theories (Newton’s laws are limits within general relativity). Crucially, theory does not “graduate” into law; they play different roles—explanation vs. description. Communicating a law means stating the relationship, its domain of validity, and its precision.

It is tempting to rank these categories as steps from “less true” to “more true.” That picture misleads. Speculation → conjecture → hypothesis does describe a path from idea to testability, but theory and law are not higher or lower rungs; they are complementary. A mature science often contains both: laws that summarize regularities, and theories that explain and connect them.

1. Name the claim type. Say explicitly whether you are speculating, proposing a conjecture, testing a hypothesis, presenting a theory, or citing a law. This anchors audience expectations.
2. Quantify uncertainty where possible. Use error bars, confidence/credible intervals, likelihoods, Bayes factors, or model ensembles. Replace “may” and “could” with calibrated probabilities when feasible.
3. State assumptions and scope. Every claim has a domain of validity. Declare boundary conditions, model assumptions, and known failure modes (e.g., where a law becomes an approximation).
4. Separate evidence from inference. Distinguish observed facts (measurements) from interpretations (what the theory says they mean). This reduces overclaiming.
5. Report tests and their severity. Explain what would have counted against your hypothesis and how close the evidence came to doing so. Severe testing earns credibility.
6. Update visibly. When new data arrive, show your priors and your update. Revisions are a strength, not a weakness, in a cumulative enterprise.

• Speculation → Hypothesis: “Fast radio bursts might be produced by magnetars” (speculation). Hypothesis: “Newly discovered FRB X will show a millisecond burst coincident with an X-ray flare from a known magnetar, detectable by instrument Y.”
• Conjecture in math vs. science: The Riemann Hypothesis (a mathematical conjecture) awaits proof. In climatology, the early-stage claim that aerosols offset some greenhouse warming began as a conjecture and evolved into quantified hypotheses and then model components with stated uncertainties.
• Theory and law together: The greenhouse effect is explained by radiative transfer theory and summarized by Stefan–Boltzmann and Planck laws applied to Earth’s atmosphere. The theory tells us why increasing CO₂ changes the energy balance; the laws quantify how radiation behaves.
• Scope caveat: Hooke’s law (F=kx) is accurate in the elastic regime; beyond that, materials yield or fracture. Communicating the law responsibly means naming the regime and the uncertainty in k.

In public debates, words can be weapons or bridges. Calling a well-corroborated theory “just a theory” erodes understanding; presenting speculation as fact breeds distrust. Analysts, journalists, and advocates should preserve these distinctions, pair qualitative labels with numbers, and resist false balance: uncertainty about details is not uncertainty about direction (e.g., the exact magnitude of sea-level rise by 2100 is uncertain; the fact of ongoing rise under continued warming is not).

Clear thinking deserves clear signaling.

• Speculation invites imagination.
• Conjecture sharpens plausibility.
• Hypothesis invites a decisive test.
• Theory unifies and explains.
• Law describes dependable regularities.

Communicating which kind of claim we are making—and how confident we are—doesn’t just tidy our prose; it earns trust, focuses inquiry, and helps communities act wisely amid uncertainty.

1. ↑ ChatGPT generated this text responding to the prompt: “Write an essay called ‘communicating uncertainty’ that accurately describes the use of the terms speculation, conjecture, hypothesis, theory, and law.”