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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Scientific method | 7/13 | https://en.wikipedia.org/wiki/Scientific_method | reference | science, encyclopedia | 2026-05-05T03:43:09.265477+00:00 | kb-cron |
An example for how inductive and deductive reasoning works can be found in the history of gravitational theory. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic, and European astronomers, to fully record the motion of planet Earth. Kepler(and others) were then able to build their early theories by generalizing the collected data inductively, and Newton was able to unify prior theory and measurements into the consequences of his laws of motion in 1727. Another common example of inductive reasoning is the observation of a counterexample to current theory inducing the need for new ideas. Le Verrier in 1859 pointed out problems with the perihelion of Mercury that showed Newton's theory to be at least incomplete. The observed difference of Mercury's precession between Newtonian theory and observation was one of the things that occurred to Einstein as a possible early test of his theory of relativity. His relativistic calculations matched observation much more closely than Newtonian theory did. Though, today's Standard Model of physics suggests that we still do not know at least some of the concepts surrounding Einstein's theory, it holds to this day and is being built on deductively. A theory being assumed as true and subsequently built on is a common example of deductive reasoning. Theory building on Einstein's achievement can simply state that 'we have shown that this case fulfils the conditions under which general/special relativity applies, therefore its conclusions apply also'. If it was properly shown that 'this case' fulfils the conditions, the conclusion follows. An extension of this is the assumption of a solution to an open problem. This weaker kind of deductive reasoning will get used in current research, when multiple scientists or even teams of researchers are all gradually solving specific cases in working towards proving a larger theory. This often sees hypotheses being revised again and again as new proof emerges. This way of presenting inductive and deductive reasoning shows part of why science is often presented as being a cycle of iteration. It is important to keep in mind that that cycle's foundations lie in reasoning, and not wholly in the following of procedure.
=== Certainty, probabilities, and statistical inference === Claims of scientific truth can be opposed in three ways: by falsifying them, by questioning their certainty, or by asserting the claim itself to be incoherent. Incoherence, here, means internal errors in logic, like stating opposites to be true; falsification is what Popper would have called the honest work of conjecture and refutation — certainty, perhaps, is where difficulties in telling truths from non-truths arise most easily. Scientific measurements include uncertainty estimates, calculated through repeated measurements, error propagation from underlying quantities, or sampling limitations. uncertainty. Counts of things may represent a sample of desired quantities, with an uncertainty that depends upon the sampling method used and the number of samples taken. In the case of measurement imprecision, there will simply be a 'probable deviation' expressing itself in a study's conclusions. Statistics are different. Inductive statistical generalisation will take sample data and extrapolate more general conclusions, which has to be justified — and scrutinised. It can even be said that statistical models are only ever useful, but never a complete representation of circumstances. In statistical analysis, expected and unexpected bias is a large factor. Research questions, the collection of data, or the interpretation of results, all are subject to larger amounts of scrutiny than in comfortably logical environments. Statistical models go through a process for validation, for which one could even say that awareness of potential biases is more important than the hard logic; errors in logic are easier to find in peer review, after all. More general, claims to rational knowledge, and especially statistics, have to be put into their appropriate context. Simple statements such as '9 out of 10 doctors recommend' are therefore of unknown quality because they do not justify their methodology. Lack of familiarity with statistical methodologies can result in erroneous conclusions. Foregoing the easy example, multiple probabilities interacting is where, for example medical professionals, have shown a lack of proper understanding. Bayes' theorem is the mathematical principle lining out how standing probabilities are adjusted given new information. The boy or girl paradox is a common example. In knowledge representation, Bayesian estimation of mutual information between random variables is a way to measure dependence, independence, or interdependence of the information under scrutiny. Beyond commonly associated survey methodology of field research, the concept together with probabilistic reasoning is used to advance fields of science where research objects have no definitive states of being. For example, in statistical mechanics.
== Methods of inquiry ==