Editing Scientific method (section)

==Methods of inquiry==
===Hypothetico-deductive method===

The [[hypothetico-deductive model]], or hypothesis-testing method, or "traditional" scientific method is, as the name implies, based on the formation of [[hypotheses]] and their testing via [[deductive reasoning]]. A hypothesis stating implications, often called [[prediction]]s, that are falsifiable via experiment is of central importance here, as not the hypothesis but its implications are what is tested.{{sfn | Voit | 2019}} Basically, scientists will look at the hypothetical consequences a (potential) [[theory]] holds and prove or disprove those instead of the theory itself. If an [[experiment]]al test of those hypothetical consequences shows them to be false, it follows logically that the part of the theory that implied them was false also. If they show as true however, it does not prove the theory definitively.

The [[logic]] of this testing is what affords this method of inquiry to be reasoned deductively. The formulated hypothesis is assumed to be 'true', and from that 'true' statement implications are inferred. If the following tests show the implications to be false, it follows that the hypothesis was false also. If test show the implications to be true, new insights will be gained. It is important to be aware that a positive test here will at best strongly imply but not definitively prove the tested hypothesis, as deductive inference (A ⇒ B) is not equivalent like that; only (¬B ⇒ ¬A) is valid logic. Their positive outcomes however, as Hempel put it, provide "at least some support, some corroboration or confirmation for it".<ref name="Hempel 1966">{{cite book | title=Philosophy Of Natural Science | date=1966 | first=Carl Gustav | last=Hempel | author-link=Carl Gustav Hempel | page=7 | url=https://archive.org/stream/1966PhilosophyOfNaturalScienceCarlGHempel1/1966--Philosophy-of-Natural-Science--Carl-G-Hempel%20%281%29_djvu.txt | access-date=30 April 2024}} Hempel illustrates this at [[Ignaz Semmelweis|Semmelweiss]]' experiments with childbed fever.</ref> This is why [[Frank Popper|Popper]] insisted on fielded hypotheses to be falsifieable, as successful tests imply very little otherwise. As [[Donald A. Gillies|Gillies]] put it, "successful theories are those that survive elimination through falsification".{{sfn | Voit | 2019}}

Deductive reasoning in this mode of inquiry will sometimes be replaced by [[abductive reasoning]]—the search for the most plausible explanation via logical inference. For example, in biology, where general laws are few,{{sfn | Voit | 2019}} as valid deductions rely on solid presuppositions.<ref name="Gauch Jr 2002 p30/ch4"/>

===Inductive method===

The [[inductivism|inductivist approach]] to deriving scientific truth first rose to prominence with [[Francis Bacon]] and particularly with [[Isaac Newton]] and those who followed him.<ref name= novOrganon >[[Francis Bacon]], ''[[Novum Organum]]''</ref> After the establishment of the [[hypothetico-deductive model|HD-method]], it was often put aside as something of a "fishing expedition" though.{{sfn | Voit | 2019}} It is still valid to some degree, but today's inductive method is often far removed from the historic approach—the scale of the data collected lending new effectiveness to the method. It is most-associated with data-mining projects or large-scale observation projects. In both these cases, it is often not at all clear what the results of proposed experiments will be, and thus knowledge will arise after the collection of data through inductive reasoning.{{efn| name= keplerNewton }}

Where the traditional method of inquiry does both, the inductive approach usually formulates only a [[research question]], not a hypothesis. Following the initial question instead, a suitable "high-throughput method" of data-collection is determined, the resulting data processed and 'cleaned up', and conclusions drawn after. "This shift in focus elevates the data to the supreme role of revealing novel insights by themselves".{{sfn | Voit | 2019}}

The advantage the inductive method has over methods formulating a hypothesis that it is essentially free of "a researcher's preconceived notions" regarding their subject. On the other hand, inductive reasoning is always attached to a measure of certainty, as all inductively reasoned conclusions are.{{sfn | Voit | 2019}} This measure of certainty can reach quite high degrees, though. For example, in the determination of large [[prime number|primes]], which are used in [[encryption software]].{{sfnp|Gauch|2003|p=159}}

===Mathematical modelling===

[[Mathematical modelling]], or allochthonous reasoning, typically is the formulation of a hypothesis followed by building mathematical constructs that can be tested in place of conducting physical laboratory experiments. This approach has two main factors: simplification/abstraction and secondly a set of correspondence rules. The correspondence rules lay out how the constructed model will relate back to reality-how truth is derived; and the simplifying steps taken in the abstraction of the given system are to reduce factors that do not bear relevance and thereby reduce unexpected errors.{{sfn | Voit | 2019}} These steps can also help the researcher in understanding the important factors of the system, how far parsimony can be taken until the system becomes more and more unchangeable and thereby stable. Parsimony and related principles are further explored [[#Confirmation theory|below]].

Once this translation into mathematics is complete, the resulting model, in place of the corresponding system, can be analysed through purely mathematical and computational means. The results of this analysis are of course also purely mathematical in nature and get translated back to the system as it exists in reality via the previously determined correspondence rules—iteration following review and interpretation of the findings. The way such models are reasoned will often be mathematically deductive—but they don't have to be. An example here are [[Monte Carlo method|Monte-Carlo simulations]]. These generate empirical data "arbitrarily", and, while they may not be able to reveal universal principles, they can nevertheless be useful.{{sfn | Voit | 2019}}