Decision theory (or the theory of choice) is the study of the reasoning underlying an agent's choices. Decision theory can be broken into two branches: normative decision theory, which gives advice on how to make the best decisions, given a set of uncertain beliefs and a set of values; and descriptive decision theory, which analyzes how existing, possibly irrational agents actually make decisions.
Closely related to the field of game theory,
decision theory is concerned with the choices of individual agents
whereas game theory is concerned with interactions of agents whose
decisions affect each other. Decision theory is an interdisciplinary
topic, studied by economists,
statisticians, psychologists, biologists, political and other social scientists, philosophers, and computer scientists.
Empirical applications of this rich theory are usually done with the help of statistical and econometric methods, especially via the so-called choice models, such as probit and logit models. Estimation of such models is usually done via parametric, semi-parametric and non-parametric maximum likelihood methods.
Normative and descriptive
Normative
decision theory is concerned with identifying the best decision to
make, modelling an ideal decision maker who is able to compute with
perfect accuracy and is fully rational. The practical application of this prescriptive approach (how people ought to make decisions) is called decision analysis, and is aimed at finding tools, methodologies and software (decision support systems) to help people make better decisions.
In contrast, positive
or descriptive decision theory is concerned with describing observed
behaviors under the assumption that the decision-making agents are
behaving under some consistent rules. These rules may, for instance,
have a procedural framework (e.g. Amos Tversky's elimination by aspects model) or an axiomatic framework, reconciling the Von Neumann-Morgenstern axioms with behavioral violations of the expected utility hypothesis, or they may explicitly give a functional form for time-inconsistentutility functions (e.g. Laibson's quasi-hyperbolic discounting).
The prescriptions or predictions about behaviour that positive
decision theory produces allow for further tests of the kind of
decision-making that occurs in practice. There is a thriving dialogue
with experimental economics,
which uses laboratory and field experiments to evaluate and inform
theory. In recent decades, there has also been increasing interest in
what is sometimes called "behavioral decision theory" and this has
contributed to a re-evaluation of what rational decision-making
requires.
What kinds of decisions need a theory?
Choice under uncertainty
The area of choice under uncertainty represents the heart of decision theory. Known from the 17th century (Blaise Pascal invoked it in his famous wager, which is contained in his Pensées, published in 1670), the idea of expected value
is that, when faced with a number of actions, each of which could give
rise to more than one possible outcome with different probabilities, the
rational procedure is to identify all possible outcomes, determine
their values (positive or negative) and the probabilities that will
result from each course of action, and multiply the two to give an
"expected value", or the average expectation for an outcome; the action
to be chosen should be the one that gives rise to the highest total
expected value. In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox to show that expected value theory must be normatively
wrong. He gives an example in which a Dutch merchant is trying to
decide whether to insure a cargo being sent from Amsterdam to St
Petersburg in winter. In his solution, he defines a utility function and computes expected utility rather than expected financial value.
The revival of subjective probability theory, from the work of Frank Ramsey, Bruno de Finetti, Leonard Savage
and others, extended the scope of expected utility theory to situations
where subjective probabilities can be used. At the time, von Neumann
and Morgenstern’s theory of expected utility proved that expected utility maximization followed from basic postulates about rational behavior.
The work of Maurice Allais and Daniel Ellsberg showed that human behavior has systematic and sometimes important departures from expected-utility maximization. The prospect theory of Daniel Kahneman and Amos Tversky renewed the empirical study of economic behavior
with less emphasis on rationality presuppositions. Kahneman and Tversky
found three regularities – in actual human decision-making, "losses
loom larger than gains"; persons focus more on changes in their
utility-states than they focus on absolute utilities; and the estimation
of subjective probabilities is severely biased by anchoring.
Intertemporal choice
Intertemporal choice is concerned with the kind of choice where
different actions lead to outcomes that are realised at different points
in time. If someone received a windfall of several thousand dollars,
they could spend it on an expensive holiday, giving them immediate
pleasure, or they could invest it in a pension scheme, giving them an
income at some time in the future. What is the optimal thing to do?
The answer depends partly on factors such as the expected rates of interest and inflation, the person's life expectancy,
and their confidence in the pensions industry. However even with all
those factors taken into account, human behavior again deviates greatly
from the predictions of prescriptive decision theory, leading to
alternative models in which, for example, objective interest rates are
replaced by subjective discount rates.
Interaction of decision makers
Some
decisions are difficult because of the need to take into account how
other people in the situation will respond to the decision that is
taken. The analysis of such social decisions is more often treated
under the label of game theory,
rather than decision theory, though it involves the same mathematical
methods. From the standpoint of game theory most of the problems treated
in decision theory are one-player games (or the one player is viewed as
playing against an impersonal background situation). In the emerging
field of socio-cognitive
engineering, the research is especially focused on the different types
of distributed decision-making in human organizations, in normal and
abnormal/emergency/crisis situations.
Complex decisions
Other
areas of decision theory are concerned with decisions that are
difficult simply because of their complexity, or the complexity of the
organization that has to make them. Individuals making decisions may be
limited in resources or are boundedly rational
(have finite time or intelligence); in such cases the issue, more than
the deviation between real and optimal behaviour, is the difficulty of
determining the optimal behaviour in the first place. One example is the
model of economic growth and resource usage developed by the Club of Rome to help politicians make real-life decisions in complex situations. Decisions are also affected by whether options are framed together or separately; this is known as the distinction bias.
In 2011, Dwayne Rosenburgh explored and showed how decision theory can
be applied to complex decisions that arise in areas such as wireless communications.
Heuristics
The heuristic approach to decision-making makes decisions based on
routine thinking, which, while quicker than step-by-step processing,
opens the risk of introducing inaccuracies, mistakes and fallacies,
which may be easily disproved in a step-by-step process of thinking. One example of common and incorrect thought process is the gambler's fallacy,
or believing that a random event is affected by previous random events
(truth is, there is a fifty percent chance of a coin landing on heads
even after a long sequence of tails). Another example is that
decision-makers may be biased towards preferring moderate alternatives
to extreme ones; the "Compromise Effect" operates under a mindset driven
by the belief that the most moderate option, amid extremes, carries the
most benefits from each extreme.
Alternatives
A highly controversial issue is whether one can replace the use of probability in decision theory by other alternatives.
Probability theory
Advocates for the use of probability theory point to:
the Dutch book paradoxes of Bruno de Finetti as illustrative of the theoretical difficulties that can arise from departures from the probability axioms, and
the complete class theorems, which show that all admissible decision rules are equivalent to the Bayesian decision rule for some utility function and some prior distribution
(or for the limit of a sequence of prior distributions). Thus, for
every decision rule, either the rule may be reformulated as a Bayesian procedure (or a limit of a sequence of such), or there is a rule that is sometimes better and never worse.
Alternatives to probability theory
The proponents of fuzzy logic, possibility theory, quantum cognition, Dempster–Shafer theory, and info-gap decision theory
maintain that probability is only one of many alternatives and point to
many examples where non-standard alternatives have been implemented
with apparent success; notably, probabilistic decision theory is sensitive to assumptions about the probabilities of various events, while non-probabilistic rules such as minimax are robust, in that they do not make such assumptions.
Ludic fallacy
A general criticism of decision theory based on a fixed universe of
possibilities is that it considers the "known unknowns", not the "unknown unknowns": it focuses on expected variations, not on unforeseen events, which some argue (as in black swan theory) have outsized impact and must be considered – significant events may be "outside model". This line of argument, called the ludic fallacy,
is that there are inevitable imperfections in modeling the real world
by particular models, and that unquestioning reliance on models blinds
one to their limits.
The history of scientific method considers changes in the methodology of scientific inquiry, as distinct from the history of science itself. The development of rules for scientific reasoning
has not been straightforward; scientific method has been the subject
of intense and recurring debate throughout the history of science, and
eminent natural philosophers and scientists have argued for the primacy
of one or another approach to establishing scientific knowledge. Despite
the disagreements about approaches, scientific method has advanced in
definite steps. Rationalist explanations of nature, including atomism, appeared both in ancient Greece in the thought of Leucippus and Democritus, and in ancient India, in the Nyaya, Vaisesika and Buddhist schools, while Charvaka
materialism rejected inference as a source of knowledge in favour of an
empiricism that was always subject to doubt. Aristotle pioneered
scientific method in ancient Greece alongside his empirical biology and
his work on logic, rejecting a purely deductive framework in favour of
generalisations made from observations of nature.
Some of the most important debates in the history of scientific method center on: rationalism, especially as advocated by René Descartes; inductivism, which rose to particular prominence with Isaac Newton and his followers; and hypothetico-deductivism, which came to the fore in the early 19th century. In the late 19th and early 20th centuries, a debate over realism vs. antirealism
was central to discussions of scientific method as powerful scientific
theories extended beyond the realm of the observable, while in the
mid-20th century some prominent philosophers argued against any
universal rules of science at all.
There are few explicit discussions of scientific methodologies in
surviving records from early cultures. The most that can be inferred
about the approaches to undertaking science in this period stems from
descriptions of early investigations into nature, in the surviving
records. An Egyptian medical textbook, the Edwin Smith papyrus, (c. 1600 BCE), applies the following components: examination, diagnosis, treatment and prognosis, to the treatment of disease, which display strong parallels to the basic empirical method of science and according to G. E. R. Lloyd played a significant role in the development of this methodology. The Ebers papyrus (c. 1550 BCE) also contains evidence of traditional empiricism.
By the middle of the 1st millennium BCE in Mesopotamia, Babylonian astronomy
had evolved into the earliest example of a scientific astronomy, as it
was "the first and highly successful attempt at giving a refined
mathematical description of astronomical phenomena." According to the
historian Asger Aaboe, "all subsequent varieties of scientific astronomy, in the Hellenistic world, in India, in the Islamic world, and in the West – if not indeed all subsequent endeavour in the exact sciences – depend upon Babylonian astronomy in decisive and fundamental ways."
The early Babylonians and Egyptians developed much technical knowledge, crafts, and mathematics used in practical tasks of divination, as well as a knowledge of medicine, and made lists of various kinds. While the Babylonians in particular had engaged in the earliest forms of an empirical
mathematical science, with their early attempts at mathematically
describing natural phenomena, they generally lacked underlying rational
theories of nature. It was the ancient Greeks who engaged in the earliest forms of what is today recognized as a rational theoretical science,
with the move towards a more rational understanding of nature which
began at least since the Archaic Period (650 – 480 BCE) with the
Presocratic school. Thales
was the first to use natural explanations, proclaiming that every event
had a natural cause, even though he is known for saying "all things are
full of gods" and sacrificed an ox when he discovered his theorem. Leucippus, went on to develop the theory of atomism – the idea that everything is composed entirely of various imperishable, indivisible elements called atoms. This was elaborated in great detail by Democritus.
Similar atomist ideas emerged independently among ancient Indian philosophers of the Nyaya, Vaisesika and Buddhist schools. In particular, like the Nyaya, Vaisesika, and Buddhist schools, the Cārvāka
epistemology was materialist, and skeptical enough to admit perception
as the basis for unconditionally true knowledge, while cautioning that
if one could only infer a truth, then one must also harbor a doubt about
that truth; an inferred truth could not be unconditional.
Towards the middle of the 5th century BCE, some of the components
of a scientific tradition were already heavily established, even before
Plato, who was an important contributor to this emerging tradition,
thanks to the development of deductive reasoning, as propounded by his
student, Aristotle. In Protagoras (318d-f), Plato
mentioned the teaching of arithmetic, astronomy and geometry in
schools. The philosophical ideas of this time were mostly freed from the
constraints of everyday phenomena and common sense. This denial of reality as we experience it reached an extreme in Parmenides who argued that the world is one and that change and subdivision do not exist.
In the 3rd and 4th centuries BCE, the Greek physicians Herophilos (335–280 BCE) and Erasistratus of Chios
employed experiments to further their medical research; Erasistratus at
one time repeatedly weighing a caged bird, and noting its weight loss
between feeding times.
Aristotle
Aristotle's philosophy involved both inductive and deductive reasoning.
Aristotle's inductive-deductive method used inductions from
observations to infer general principles, deductions from those
principles to check against further observations, and more cycles of
induction and deduction to continue the advance of knowledge.
The Organon (Greek: Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logic. The name Organon was given by Aristotle's followers, the Peripatetics. The order of the works is not chronological (the chronology is now difficult to determine) but was deliberately chosen by Theophrastus to constitute a well-structured system. Indeed, parts of them seem to be a scheme of a lecture on logic. The arrangement of the works was made by Andronicus of Rhodes around 40 BCE.
The Organon comprises the following six works:
The Categories (Greek: Κατηγορίαι, Latin: Categoriae)
introduces Aristotle's 10-fold classification of that which exists:
substance, quantity, quality, relation, place, time, situation,
condition, action, and passion.
On Interpretation (Greek: Περὶ Ἑρμηνείας, Latin: De Interpretatione) introduces Aristotle's conception of proposition and judgment, and the various relations between affirmative, negative, universal, and particular propositions. Aristotle discusses the square of opposition or square of Apuleius in Chapter 7 and its appendix Chapter 8. Chapter 9 deals with the problem of future contingents.
The Prior Analytics (Greek: Ἀναλυτικὰ Πρότερα, Latin: Analytica Priora) introduces Aristotle's syllogistic method (see term logic), argues for its correctness, and discusses inductive inference.
The Topics (Greek: Τοπικά, Latin: Topica)
treats of issues in constructing valid arguments, and of inference that
is probable, rather than certain. It is in this treatise that
Aristotle mentions the predicables, later discussed by Porphyry and by the scholastic logicians.
The Sophistical Refutations (Greek: Περὶ Σοφιστικῶν Ἐλέγχων, Latin: De Sophisticis Elenchis) gives a treatment of logical fallacies, and provides a key link to Aristotle's work on rhetoric.
Aristotle's Metaphysics has some points of overlap with the works making up the Organon
but is not traditionally considered part of it; additionally there are
works on logic attributed, with varying degrees of plausibility, to
Aristotle that were not known to the Peripatetics.
Aristotle introduced what may be called a scientific method. His demonstration method is found in Posterior Analytics. He provided another of the ingredients of scientific tradition: empiricism.
For Aristotle, universal truths can be known from particular things via
induction. To some extent then, Aristotle reconciles abstract thought
with observation, although it would be a mistake to imply that
Aristotelian science is empirical in form. Indeed, Aristotle did not
accept that knowledge acquired by induction could rightly be counted as
scientific knowledge. Nevertheless, induction was for him a necessary
preliminary to the main business of scientific enquiry, providing the
primary premises required for scientific demonstrations.
Aristotle largely ignored inductive reasoning in his treatment of
scientific enquiry. To make it clear why this is so, consider this
statement in the Posterior Analytics:
We suppose ourselves to possess unqualified scientific
knowledge of a thing, as opposed to knowing it in the accidental way in
which the sophist knows, when we think that we know the cause on which
the fact depends, as the cause of that fact and of no other, and,
further, that the fact could not be other than it is.
It was therefore the work of the philosopher to demonstrate universal truths and to discover their causes.
While induction was sufficient for discovering universals by
generalization, it did not succeed in identifying causes. For this task
Aristotle used the tool of deductive reasoning in the form of syllogisms. Using the syllogism, scientists could infer new universal truths from those already established.
Aristotle developed a complete normative approach to scientific
inquiry involving the syllogism, which he discusses at length in his Posterior Analytics.
A difficulty with this scheme lay in showing that derived truths have
solid primary premises. Aristotle would not allow that demonstrations
could be circular (supporting the conclusion by the premises, and the
premises by the conclusion). Nor would he allow an infinite number of
middle terms between the primary premises and the conclusion. This leads
to the question of how the primary premises are found or developed, and
as mentioned above, Aristotle allowed that induction would be required
for this task.
Towards the end of the Posterior Analytics, Aristotle discusses knowledge imparted by induction.
Thus it is clear that we must get to know the primary
premises by induction; for the method by which even sense-perception
implants the universal is inductive. [...] it follows that there will be
no scientific knowledge of the primary premises, and since except
intuition nothing can be truer than scientific knowledge, it will be
intuition that apprehends the primary premises. [...] If, therefore, it
is the only other kind of true thinking except scientific knowing, intuition will be the originative source of scientific knowledge.
The account leaves room for doubt regarding the nature and extent of
Aristotle's empiricism. In particular, it seems that Aristotle considers
sense-perception only as a vehicle for knowledge through intuition. He
restricted his investigations in natural history to their natural
settings, such as at the Pyrrha lagoon, now called Kalloni, at Lesbos. Aristotle and Theophrastus together formulated the new science of biology, inductively, case by case, for two years before Aristotle was called to tutor Alexander.
Aristotle performed no modern-style experiments in the form in which
they appear in today's physics and chemistry laboratories.
Induction is not afforded the status of scientific reasoning, and so it
is left to intuition to provide a solid foundation for Aristotle's
science. With that said, Aristotle brings us somewhat closer an
empirical science than his predecessors.
Some philosophers held that there are only atoms and void; others that the atoms are divine fire, others only wind, others only water, others only earth.
Epicurus
In his work Kαvώv ('canon', a straight edge or ruler, thus any type of measure or standard, referred to as 'canonic'), Epicurus laid out his first rule for inquiry in physics: 'that the first concepts be seen, and that they not require demonstration '.
His second rule for inquiry was that prior to an investigation, we are to have self-evident concepts,
so that we might infer [ἔχωμεν οἷς σημειωσόμεθα] both what is expected
[τò προσμένον], and also what is non-apparent [τò ἄδηλον].
Epicurus applies his method of inference (the use of observations as signs, Asmis' summary, p. 333: the method of using the phenomena as signs (σημεῖα) of what is unobserved) immediately to the atomic theory of Democritus. In Aristotle's Prior Analytics, Aristotle himself employs the use of signs. But Epicurus presented his 'canonic' as rival to Aristotle's logic.
Emergence of inductive experimental method
During the Middle Ages
issues of what is now termed science began to be addressed. There was
greater emphasis on combining theory with practice in the Islamic world
than there had been in Classical times, and it was common for those
studying the sciences to be artisans as well, something that had been
"considered an aberration in the ancient world." Islamic experts in the
sciences were often expert instrument makers who enhanced their powers
of observation and calculation with them. Muslim scientists used experiment and quantification to distinguish between competing scientific theories, set within a generically empirical orientation, as can be seen in the works of Jābir ibn Hayyān (721–815) and Alkindus (801–873) as early examples. Several scientific methods thus emerged from the medieval Muslim world by the early 11th century, all of which emphasized experimentation as well as quantification to varying degrees.
Ibn al-Haytham
"How
does light travel through transparent bodies? Light travels through
transparent bodies in straight lines only.... We have explained this
exhaustively in our Book of Optics." —Alhazen
Experimental evidence supported most of the propositions in his Book of Optics
and grounded his theories of vision, light and colour, as well as his
research in catoptrics and dioptrics. His legacy was elaborated through
the 'reforming' of his Optics by Kamal al-Din al-Farisi (d. c. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).
Alhazen viewed his scientific studies as a search for truth:
"Truth is sought for its own sake. And those who are engaged upon the
quest for anything for its own sake are not interested in other things. Finding the truth is difficult, and the road to it is rough..."
Alhazen's work included the conjecture that "Light travels
through transparent bodies in straight lines only", which he was able to
corroborate only after years of effort. He stated, "[This] is clearly
observed in the lights which enter into dark rooms through holes. ...
the entering light will be clearly observable in the dust which fills
the air." He also demonstrated the conjecture by placing a straight stick or a taut thread next to the light beam.
Ibn al-Haytham also employed scientific skepticism and emphasized the role of empiricism. He also explained the role of induction in syllogism, and criticized Aristotle
for his lack of contribution to the method of induction, which Ibn
al-Haytham regarded as superior to syllogism, and he considered
induction to be the basic requirement for true scientific research.
Something like Occam's razor is also present in the Book of Optics.
For example, after demonstrating that light is generated by luminous
objects and emitted or reflected into the eyes, he states that therefore
"the extramission of [visual] rays is superfluous and useless." He may also have been the first scientist to adopt a form of positivism
in his approach. He wrote that "we do not go beyond experience, and we
cannot be content to use pure concepts in investigating natural
phenomena", and that the understanding of these cannot be acquired
without mathematics. After assuming that light is a material substance,
he does not further discuss its nature but confines his investigations
to the diffusion and propagation of light. The only properties of light
he takes into account are those treatable by geometry and verifiable by
experiment.
Al-Biruni
The Persian scientist Abū Rayhān al-Bīrūnī introduced early scientific methods for several different fields of inquiry during the 1020s and 1030s. For example, in his treatise on mineralogy, Kitab al-Jawahir (Book of Precious Stones), al-Biruni is "the most exact of experimental scientists", while in the introduction to his study of India,
he declares that "to execute our project, it has not been possible to
follow the geometric method" and thus became one of the pioneers of comparative sociology in insisting on field experience and information. He also developed an early experimental method for mechanics.
Al-Biruni's methods resembled the modern scientific method,
particularly in his emphasis on repeated experimentation. Biruni was
concerned with how to conceptualize and prevent both systematic errors
and observational biases, such as "errors caused by the use of small
instruments and errors made by human observers." He argued that if
instruments produce errors because of their imperfections or
idiosyncratic qualities, then multiple observations must be taken, analyzed qualitatively, and on this basis, arrive at a "common-sense single value for the constant sought", whether an arithmetic mean or a "reliable estimate." In his scientific method, "universals came out of practical, experimental work" and "theories are formulated after discoveries", as with inductivism.
Ibn Sina (Avicenna)
In the On Demonstration section of The Book of Healing (1027), the Persian philosopher and scientist Avicenna (Ibn Sina) discussed philosophy of science and described an early scientific method of inquiry. He discussed Aristotle's Posterior Analytics
and significantly diverged from it on several points. Avicenna
discussed the issue of a proper procedure for scientific inquiry and the
question of "How does one acquire the first principles of a science?"
He asked how a scientist might find "the initial axioms or hypotheses of a deductive
science without inferring them from some more basic premises?" He
explained that the ideal situation is when one grasps that a "relation
holds between the terms, which would allow for absolute, universal
certainty." Avicenna added two further methods for finding a first principle: the ancient Aristotelian method of induction (istiqra), and the more recent method of examination and experimentation (tajriba).
Avicenna criticized Aristotelian induction, arguing that "it does not
lead to the absolute, universal, and certain premises that it purports
to provide." In its place, he advocated "a method of experimentation as a
means for scientific inquiry."
Earlier, in The Canon of Medicine (1025), Avicenna was also the first to describe what is essentially methods of agreement, difference and concomitant variation which are critical to inductive logic and the scientific method.
However, unlike his contemporary al-Biruni's scientific method, in
which "universals came out of practical, experimental work" and
"theories are formulated after discoveries", Avicenna developed a
scientific procedure in which "general and universal questions came
first and led to experimental work." Due to the differences between their methods, al-Biruni referred to himself as a mathematical scientist and to Avicenna as a philosopher, during a debate between the two scholars.
Robert Grosseteste
During the European Renaissance of the 12th century, ideas on scientific methodology, including Aristotle's empiricism and the experimental approaches of Alhazen and Avicenna, were introduced to medieval Europe via Latin translations of Arabic and Greek texts and commentaries. Robert Grosseteste's commentary on the Posterior Analytics places Grosseteste among the first scholastic thinkers in Europe to understand Aristotle's
vision of the dual nature of scientific reasoning. Concluding from
particular observations into a universal law, and then back again, from
universal laws to prediction of particulars. Grosseteste called this
"resolution and composition". Further, Grosseteste said that both paths
should be verified through experimentation to verify the principles.
Roger Bacon
Roger Bacon was inspired by the writings of Grosseteste. In his account of a method, Bacon described a repeating cycle of observation, hypothesis, experimentation, and the need for independent verification.
He recorded the way he had conducted his experiments in precise detail,
perhaps with the idea that others could reproduce and independently
test his results.
About 1256 he joined the Franciscan Order and became subject to the Franciscan statute forbidding Friars from publishing books or pamphlets without specific approval. After the accession of Pope Clement IV
in 1265, the Pope granted Bacon a special commission to write to him on
scientific matters. In eighteen months he completed three large
treatises, the Opus Majus, Opus Minus, and Opus Tertium which he sent to the Pope. William Whewell has called Opus Majus at once the Encyclopaedia and Organon of the 13th century.
Part I (pp. 1–22) treats of the four causes of error: authority,
custom, the opinion of the unskilled many, and the concealment of real
ignorance by a pretense of knowledge.
Part VI (pp. 445–477) treats of experimental science, domina omnium scientiarum.
There are two methods of knowledge: the one by argument, the other by
experience. Mere argument is never sufficient; it may decide a question,
but gives no satisfaction or certainty to the mind, which can only be
convinced by immediate inspection or intuition, which is what experience
gives.
Experimental science, which in the Opus Tertium (p. 46) is
distinguished from the speculative sciences and the operative arts, is
said to have three great prerogatives over all sciences:
It verifies their conclusions by direct experiment;
It discovers truths which they could never reach;
It investigates the secrets of nature, and opens to us a knowledge of past and future.
Roger Bacon illustrated his method by an investigation into the nature and cause of the rainbow, as a specimen of inductive research.
Renaissance humanism and medicine
Aristotle’s
ideas became a framework for critical debate beginning with absorption
of the Aristotelian texts into the university curriculum in the first
half of the 13th century.
Contributing to this was the success of medieval theologians in
reconciling Aristotelian philosophy with Christian theology. Within the
sciences, medieval philosophers were not afraid of disagreeing with
Aristotle on many specific issues, although their disagreements were
stated within the language of Aristotelian philosophy. All medieval
natural philosophers were Aristotelians, but "Aristotelianism" had
become a somewhat broad and flexible concept. With the end of Middle
Ages, the Renaissance
rejection of medieval traditions coupled with an extreme reverence for
classical sources led to a recovery of other ancient philosophical
traditions, especially the teachings of Plato.
By the 17th century, those who clung dogmatically to Aristotle's
teachings were faced with several competing approaches to nature.
The discovery of the Americas at the close of the 15th century showed
the scholars of Europe that new discoveries could be found outside of
the authoritative works of Aristotle, Pliny, Galen, and other ancient
writers.
Galen of Pergamon (129 – c. 200 AD) had studied with four schools in antiquity — Platonists, Aristotelians, Stoics, and Epicureans, and at Alexandria, the center of medicine at the time. In his Methodus Medendi,
Galen had synthesized the empirical and dogmatic schools of medicine
into his own method, which was preserved by Arab scholars. After the
translations from Arabic were critically scrutinized, a backlash
occurred and demand arose in Europe for translations of Galen's medical
text from the original Greek. Galen's method became very popular in
Europe. Thomas Linacre, the teacher of Erasmus, thereupon translated Methodus Medendi from Greek into Latin for a larger audience in 1519.
Limbrick 1988 notes that 630 editions, translations, and commentaries
on Galen were produced in Europe in the 16th century, eventually
eclipsing Arabic medicine there, and peaking in 1560, at the time of the
scientific revolution.
By the late 15th century, the physician-scholar Niccolò Leoniceno was finding errors in Pliny's Natural History. As a physician, Leoniceno was concerned about these botanical errors propagating to the materia medica on which medicines were based. To counter this, a botanical garden was established at Orto botanico di Padova,
University of Padua (in use for teaching by 1546), in order that
medical students might have empirical access to the plants of a
pharmacopia. Other Renaissance teaching gardens were established,
notably by the physician Leonhart Fuchs, one of the founders of botany.
The first published work devoted to the concept of method is Jodocus Willichius, De methodo omnium artium et disciplinarum informanda opusculum (1550).
Skepticism as a basis for understanding
In 1562 "Outlines of Pyrrhonism" by Sextus Empiricus
(c. 160-210 AD) appeared in print and in Latin, quickly placing the
arguments of classical skepticism in the European mainstream. Skepticism
either denies or strongly doubts (depending on the school) the
possibility of certain knowledge. Descartes' famous "Cogito"
argument is an attempt to overcome skepticism and reestablish a
foundation for certainty but other thinkers responded by revising what
the search for knowledge, particularly physical knowledge, might be.
The first of these, philosopher and physician Francisco Sanches, was led by his medical training at Rome, 1571–73, to search for a true method of knowing (modus sciendi), as nothing clear can be known by the methods of Aristotle and his followers — for example, 1) syllogism fails upon circular reasoning; 2) Aristotle's modal logic was not stated clearly enough for use in medieval times, and remains a research problem to this day. Following the physician Galen's method of medicine, Sanches lists the methods of judgement and experience, which are faulty in the wrong hands, and we are left with the bleak statement That Nothing is Known (1581, in Latin Quod Nihil Scitur).
This challenge was taken up by René Descartes in the next generation
(1637), but at the least, Sanches warns us that we ought to refrain from
the methods, summaries, and commentaries on Aristotle, if we seek
scientific knowledge. In this, he is echoed by Francis Bacon who was
influenced by another prominent exponent of skepticism, Montaigne; Sanches cites the humanist Juan Luis Vives
who sought a better educational system, as well as a statement of human
rights as a pathway for improvement of the lot of the poor.
"Sanches develops his scepticism by means of an intellectual
critique of Aristotelianism, rather than by an appeal to the history of
human stupidity and the variety and contrariety of previous theories." —Popkin 1979, p. 37, as cited by Sanches, Limbrick & Thomson 1988, pp. 24–5
"To work, then; and if you know
something, then teach me; I shall be extremely grateful to you. In the
meantime, as I prepare to examine Things, I shall raise the question anything is known, and if so, how, in the introductory passages of another book, a book in which I will expound, as far as human frailty allows, the method of knowing. Farewell.
WHAT IS TAUGHT HAS NO MORE STRENGTH THAN IT DERIVES FROM HIM WHO IS TAUGHT.
WHAT?" —Francisco Sanches (1581) Quod Nihil Scitur p. 100
Francis Bacon's eliminative induction
"If a man will begin with
certainties, he shall end in doubts; but if he will be content to begin
with doubts, he shall end in certainties." —Francis Bacon (1605) The Advancement of Learning, Book 1, v, 8
Francis Bacon (1561–1626) entered Trinity College, Cambridge
in April 1573, where he applied himself diligently to the several
sciences as then taught, and came to the conclusion that the methods
employed and the results attained were alike erroneous; he learned to
despise the current Aristotelian philosophy. He believed philosophy must
be taught its true purpose, and for this purpose a new method must be
devised. With this conception in his mind, Bacon left the university.
Bacon attempted to describe a rational procedure for establishing
causation between phenomena based on induction. Bacon's induction was,
however, radically different than that employed by the Aristotelians. As
Bacon put it,
[A]nother form of induction must be devised than has
hitherto been employed, and it must be used for proving and discovering
not first principles (as they are called) only, but also the lesser
axioms, and the middle, and indeed all. For the induction which proceeds
by simple enumeration is childish. —Novum Organum section CV
Bacon's method relied on experimental histories to eliminate alternative theories. Bacon explains how his method is applied in his Novum Organum
(published 1620). In an example he gives on the examination of the
nature of heat, Bacon creates two tables, the first of which he names
"Table of Essence and Presence", enumerating the many various
circumstances under which we find heat. In the other table, labelled
"Table of Deviation, or of Absence in Proximity", he lists circumstances
which bear resemblance to those of the first table except for the
absence of heat. From an analysis of what he calls the natures (light emitting, heavy, colored, etc.) of the items in these lists we are brought to conclusions about the form nature,
or cause, of heat. Those natures which are always present in the first
table, but never in the second are deemed to be the cause of heat.
The role experimentation played in this process was twofold. The
most laborious job of the scientist would be to gather the facts, or
'histories', required to create the tables of presence and absence. Such
histories would document a mixture of common knowledge and experimental
results. Secondly, experiments of light, or, as we might say, crucial experiments would be needed to resolve any remaining ambiguities over causes.
Bacon showed an uncompromising commitment to experimentation.
Despite this, he did not make any great scientific discoveries during
his lifetime. This may be because he was not the most able experimenter. It may also be because hypothesizing plays only a small role in Bacon's method compared to modern science.
Hypotheses, in Bacon's method, are supposed to emerge during the
process of investigation, with the help of mathematics and logic. Bacon
gave a substantial but secondary role to mathematics "which ought only to give definiteness to natural philosophy, not to generate or give it birth" (Novum Organum XCVI).
An over-emphasis on axiomatic reasoning had rendered previous
non-empirical philosophy impotent, in Bacon's view, which was expressed
in his Novum Organum:
XIX. There are and can be only two ways of searching into and
discovering truth. The one flies from the senses and particulars to the
most general axioms, and from these principles, the truth of which it
takes for settled and immoveable, proceeds to judgment and to the
discovery of middle axioms. And this way is now in fashion. The other
derives axioms from the senses and particulars, rising by a gradual and
unbroken ascent, so that it arrives at the most general axioms last of
all. This is the true way, but as yet untried.
Lastly, we have three that raise the former discoveries by
experiments into greater observations, axioms, and aphorisms. These we
call interpreters of nature.
Descartes
In 1619, René Descartes began writing his first major treatise on proper scientific and philosophical thinking, the unfinished Rules for the Direction of the Mind.
His aim was to create a complete science that he hoped would overthrow
the Aristotelian system and establish himself as the sole architect of a new system of guiding principles for scientific research.
This work was continued and clarified in his 1637 treatise, Discourse on Method, and in his 1641 Meditations.
Descartes describes the intriguing and disciplined thought experiments
he used to arrive at the idea we instantly associate with him: I think therefore I am.
From this foundational thought, Descartes finds proof of the
existence of a God who, possessing all possible perfections, will not
deceive him provided he resolves "[...] never to accept anything for
true which I did not clearly know to be such; that is to say, carefully
to avoid precipitancy and prejudice, and to comprise nothing more in my
judgment than what was presented to my mind so clearly and distinctly as
to exclude all ground of methodic doubt."
This rule allowed Descartes to progress beyond his own thoughts
and judge that there exist extended bodies outside of his own thoughts.
Descartes published seven sets of objections to the Meditations from various sources
along with his replies to them. Despite his apparent departure from the
Aristotelian system, a number of his critics felt that Descartes had
done little more than replace the primary premises of Aristotle with
those of his own. Descartes says as much himself in a letter written in
1647 to the translator of Principles of Philosophy,
a perfect knowledge [...] must necessarily be deduced
from first causes [...] we must try to deduce from these principles
knowledge of the things which depend on them, that there be nothing in
the whole chain of deductions deriving from them that is not perfectly
manifest.
And again, some years earlier, speaking of Galileo's physics in a letter to his friend and critic Mersenne from 1638,
without having considered the first causes of nature,
[Galileo] has merely looked for the explanations of a few particular
effects, and he has thereby built without foundations.
Whereas Aristotle purported to arrive at his first principles by
induction, Descartes believed he could obtain them using reason only. In
this sense, he was a Platonist, as he believed in the innate ideas, as
opposed to Aristotle's blank slate (tabula rasa), and stated that the seeds of science are inside us.
Unlike Bacon, Descartes successfully applied his own ideas in
practice. He made significant contributions to science, in particular in
aberration-corrected optics. His work in analytic geometry was a necessary precedent to differential calculus and instrumental in bringing mathematical analysis to bear on scientific matters.
During the period of religious conservatism brought about by the Reformation and Counter-Reformation, Galileo Galilei
unveiled his new science of motion. Neither the contents of Galileo’s
science, nor the methods of study he selected were in keeping with
Aristotelian teachings. Whereas Aristotle thought that a science should
be demonstrated from first principles, Galileo had used experiments as a
research tool. Galileo nevertheless presented his treatise in the form
of mathematical demonstrations without reference to experimental
results. It is important to understand that this in itself was a bold
and innovative step in terms of scientific method. The usefulness of
mathematics in obtaining scientific results was far from obvious. This is because mathematics did not lend itself to the primary pursuit of Aristotelian science: the discovery of causes.
Whether it is because Galileo was realistic about the
acceptability of presenting experimental results as evidence or because
he himself had doubts about the epistemological status of experimental findings is not known. Nevertheless, it is not in his Latin
treatise on motion that we find reference to experiments, but in his
supplementary dialogues written in the Italian vernacular. In these
dialogues experimental results are given, although Galileo may have
found them inadequate for persuading his audience. Thought experiments
showing logical contradictions in Aristotelian thinking, presented in
the skilled rhetoric of Galileo's dialogue were further enticements for
the reader.
Modern
replica of Galileo's inclined plane experiment: The distance covered by
a uniformly accelerated body is proportional to the square of the time
elapsed.
As an example, in the dramatic dialogue titled Third Day from his Two New Sciences,
Galileo has the characters of the dialogue discuss an experiment
involving two free falling objects of differing weight. An outline of
the Aristotelian view is offered by the character Simplicio. For this
experiment he expects that "a body which is ten times as heavy as
another will move ten times as rapidly as the other". The character
Salviati, representing Galileo's persona in the dialogue, replies by
voicing his doubt that Aristotle ever attempted the experiment. Salviati
then asks the two other characters of the dialogue to consider a
thought experiment whereby two stones of differing weights are tied
together before being released. Following Aristotle, Salviati reasons
that "the more rapid one will be partly retarded by the slower, and the
slower will be somewhat hastened by the swifter". But this leads to a
contradiction, since the two stones together make a heavier object than
either stone apart, the heavier object should in fact fall with a speed
greater than that of either stone. From this contradiction, Salviati
concludes that Aristotle must, in fact, be wrong and the objects will
fall at the same speed regardless of their weight, a conclusion that is
borne out by experiment.
In his 1991 survey of developments in the modern accumulation of knowledge such as this Charles Van Doren
considers that the Copernican Revolution really is the Galilean
Cartesian (René Descartes) or simply the Galilean revolution on account
of the courage and depth of change brought about by the work of Galileo.
Both Bacon and Descartes wanted to provide a firm foundation for
scientific thought that avoided the deceptions of the mind and senses.
Bacon envisaged that foundation as essentially empirical, whereas
Descartes provides a metaphysical foundation for knowledge. If there
were any doubts about the direction in which scientific method would
develop, they were set to rest by the success of Isaac Newton. Implicitly rejecting Descartes' emphasis on rationalism in favor of Bacon's empirical approach, he outlines his four "rules of reasoning" in the Principia,
We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
Therefore to the same natural effects we must, as far as possible, assign the same causes.
The qualities of bodies, which admit neither intension nor remission
of degrees, and which are found to belong to all bodies within the
reach of our experiments, are to be esteemed the universal qualities of
all bodies whatsoever.
In experimental philosophy we are to look upon propositions
collected by general induction from phænomena as accurately or very
nearly true, notwithstanding any contrary hypotheses that may be
imagined, until such time as other phænomena occur, by which they may
either be made more accurate, or liable to exceptions.
To explain all nature is too difficult a task for any one
man or even for any one age. 'Tis much better to do a little with
certainty, and leave the rest for others that come after you, than to
explain all things.
Newton's work became a model that other sciences sought to emulate,
and his inductive approach formed the basis for much of natural
philosophy through the 18th and early 19th centuries. Some methods of
reasoning were later systematized by Mill's Methods
(or Mill's canon), which are five explicit statements of what can be
discarded and what can be kept while building a hypothesis. George Boole and William Stanley Jevons also wrote on the principles of reasoning.
Integrating deductive and inductive method
Attempts to systematize a scientific method were confronted in the mid-18th century by the problem of induction, a positivist logic formulation which, in short, asserts that nothing can be known with certainty except what is actually observed. David Hume
took empiricism to the skeptical extreme; among his positions was that
there is no logical necessity that the future should resemble the past,
thus we are unable to justify inductive reasoning itself by appealing to
its past success. Hume's arguments, of course, came on the heels of
many, many centuries of excessive speculation upon excessive speculation
not grounded in empirical observation and testing. Many of Hume's
radically skeptical arguments were argued against, but not resolutely
refuted, by Immanuel Kant's Critique of Pure Reason in the late 18th century.
Hume's arguments continue to hold a strong lingering influence and
certainly on the consciousness of the educated classes for the better
part of the 19th century when the argument at the time became the focus
on whether or not the inductive method was valid.
Hans Christian Ørsted, (Ørsted is the Danish spelling; Oersted in other languages) (1777–1851) was heavily influenced by Kant, in particular, Kant's Metaphysische Anfangsgründe der Naturwissenschaft (Metaphysical Foundations of Natural Science). The following sections on Ørsted encapsulate our current, common view of scientific method.
His work appeared in Danish, most accessibly in public lectures, which
he translated into German, French, English, and occasionally Latin. But
some of his views go beyond Kant:
Ørsted observed the deflection of a compass from a voltaic circuit in 1820
"In order to achieve completeness in our knowledge of nature, we
must start from two extremes, from experience and from the intellect
itself. ... The former method must conclude with natural laws, which it
has abstracted from experience, while the latter must begin with
principles, and gradually, as it develops more and more, it becomes ever
more detailed. Of course, I speak here about the method as manifested
in the process of the human intellect itself, not as found in textbooks,
where the laws of nature which have been abstracted from the consequent
experiences are placed first because they are required to explain the
experiences. When the empiricist in his regression towards general laws
of nature meets the metaphysician in his progression, science will reach
its perfection."
Ørsted's "First Introduction to General Physics" (1811) exemplified the steps of observation, hypothesis, deduction and experiment. In 1805, based on his researches on electromagnetism
Ørsted came to believe that electricity is propagated by undulatory
action (i.e., fluctuation). By 1820, he felt confident enough in his
beliefs that he resolved to demonstrate them in a public lecture, and in
fact observed a small magnetic effect from a galvanic circuit (i.e.,
voltaic circuit), without rehearsal.
In 1831 John Herschel (1792–1871) published A Preliminary Discourse on the study of Natural Philosophy,
setting out the principles of science. Measuring and comparing
observations was to be used to find generalisations in "empirical laws",
which described regularities in phenomena, then natural philosophers
were to work towards the higher aim of finding a universal "law of
nature" which explained the causes and effects producing such
regularities. An explanatory hypothesis was to be found by evaluating
true causes (Newton's "vera causae") derived from experience, for
example evidence of past climate change could be due to changes in the
shape of continents, or to changes in Earth's orbit. Possible causes
could be inferred by analogy to known causes of similar phenomena.
It was essential to evaluate the importance of a hypothesis; "our next
step in the verification of an induction must, therefore, consist in
extending its application to cases not originally contemplated; in
studiously varying the circumstances under which our causes act, with a
view to ascertain whether their effect is general; and in pushing the
application of our laws to extreme cases."
William Whewell (1794–1866) regarded his History of the Inductive Sciences, from the Earliest to the Present Time (1837) to be an introduction to the Philosophy of the Inductive Sciences
(1840) which analyzes the method exemplified in the formation of ideas.
Whewell attempts to follow Bacon's plan for discovery of an effectual
art of discovery. He named the hypothetico-deductive method (which Encyclopædia Britannica credits to Newton); Whewell also coined the term scientist. Whewell examines ideas and attempts to construct science by uniting ideas to facts. He analyses induction into three steps:
the selection of the fundamental idea, such as space, number, cause, or likeness
a more special modification of those ideas, such as a circle, a uniform force, etc.
the determination of magnitudes
Upon these follow special techniques applicable for quantity, such as the method of least squares, curves, means, and special methods depending on resemblance (such as pattern matching, the method of gradation, and the method of natural classification (such as cladistics).
But no art of discovery, such as Bacon anticipated, follows, for "invention, sagacity, genius" are needed at every step. Whewell's sophisticated concept of science had similarities to that
shown by Herschel, and he considered that a good hypothesis should
connect fields that had previously been thought unrelated, a process he
called consilience. However, where Herschel held that the origin of new biological species
would be found in a natural rather than a miraculous process, Whewell
opposed this and considered that no natural cause had been shown for adaptation so an unknown divine cause was appropriate.
John Stuart Mill (1806–1873) was stimulated to publish A System of Logic (1843) upon reading Whewell's History of the Inductive Sciences. Mill may be regarded as the final exponent of the empirical school of philosophy begun by John Locke,
whose fundamental characteristic is the duty incumbent upon all
thinkers to investigate for themselves rather than to accept the
authority of others. Knowledge must be based on experience.
In the mid-19th century Claude Bernard was also influential, especially in bringing the scientific method to medicine. In his discourse on scientific method, An Introduction to the Study of Experimental Medicine
(1865), he described what makes a scientific theory good and what makes
a scientist a true discoverer. Unlike many scientific writers of his
time, Bernard wrote about his own experiments and thoughts, and used the
first person.
William Stanley Jevons' The Principles of Science: a treatise on logic and scientific method
(1873, 1877) Chapter XII "The Inductive or Inverse Method", Summary of
the Theory of Inductive Inference, states "Thus there are but three
steps in the process of induction:
Framing some hypothesis as to the character of the general law.
Deducing some consequences of that law.
Observing whether the consequences agree with the particular tasks under consideration."
Jevons then frames those steps in terms of probability, which he then applied to economic laws. Ernest Nagel notes that Jevons and Whewell were not the first writers to argue for the centrality of the hypothetico-deductive method in the logic of science.
Charles Sanders Peirce
In the late 19th century, Charles Sanders Peirce
proposed a schema that would turn out to have considerable influence in
the further development of scientific method generally. Peirce's work
quickly accelerated the progress on several fronts. Firstly, speaking in
broader context in "How to Make Our Ideas Clear" (1878),
Peirce outlined an objectively verifiable method to test the truth of
putative knowledge on a way that goes beyond mere foundational
alternatives, focusing upon both Deduction and Induction.
He thus placed induction and deduction in a complementary rather than
competitive context (the latter of which had been the primary trend at
least since David Hume
a century before). Secondly, and of more direct importance to
scientific method, Peirce put forth the basic schema for
hypothesis-testing that continues to prevail today. Extracting the
theory of inquiry from its raw materials in classical logic, he refined
it in parallel with the early development of symbolic logic to address
the then-current problems in scientific reasoning. Peirce examined and
articulated the three fundamental modes of reasoning that play a role in
scientific inquiry today, the processes that are currently known as abductive, deductive, and inductive inference. Thirdly, he played a major role in the progress of symbolic logic itself – indeed this was his primary specialty.
Charles S. Peirce was also a pioneer in statistics.
Peirce held that science achieves statistical probabilities, not
certainties, and that chance, a veering from law, is very real. He
assigned probability to an argument’s conclusion rather than to a
proposition, event, etc., as such. Most of his statistical writings
promote the frequency interpretation of probability (objective ratios of cases), and many of his writings express skepticism about (and criticize the use of) probability when such models are not based on objective randomization. Though Peirce was largely a frequentist, his possible world semantics introduced the "propensity" theory of probability. Peirce (sometimes with Jastrow) investigated the probability judgments of experimental subjects, pioneering decision analysis.
Karl Popper
(1902–1994) is generally credited with providing major improvements in
the understanding of the scientific method in the mid-to-late 20th
century. In 1934 Popper published The Logic of Scientific Discovery,
which repudiated the by then traditional observationalist-inductivist
account of the scientific method. He advocated empirical falsifiability as the criterion for distinguishing scientific work from non-science.
According to Popper, scientific theory should make predictions
(preferably predictions not made by a competing theory) which can be
tested and the theory rejected if these predictions are shown not to be
correct. Following Peirce and others, he argued that science would best
progress using deductive reasoning as its primary emphasis, known as critical rationalism.
His astute formulations of logical procedure helped to rein in the
excessive use of inductive speculation upon inductive speculation, and
also helped to strengthen the conceptual foundations for today's peer review procedures.
Critics of Popper, chiefly Thomas Kuhn, Paul Feyerabend and Imre Lakatos, rejected the idea that there exists a single method that applies to all science and could account for its progress. In 1962 Kuhn published the influential book The Structure of Scientific Revolutions
which suggested that scientists worked within a series of paradigms,
and argued there was little evidence of scientists actually following a
falsificationist methodology. Kuhn quoted Max Planck
who had said in his autobiography, "a new scientific truth does not
triumph by convincing its opponents and making them see the light, but
rather because its opponents eventually die, and a new generation grows
up that is familiar with it."
These debates clearly show that there is no universal agreement as to what constitutes the "scientific method". There remain, nonetheless, certain core principles that are the foundation of scientific inquiry today.
Mention of the topic
In Quod Nihil Scitur (1581), Francisco Sanches refers to another book title, De modo sciendi (on the method of knowing). This work appeared in Spanish as Método universal de las ciencias.
In 1833 Robert and William Chambers
published their 'Chambers's information for the people'. Under the
rubric 'Logic' we find a description of investigation that is familiar
as scientific method,
Investigation, or the art of inquiring into the nature of
causes and their operation, is a leading characteristic of reason [...]
Investigation implies three things – Observation, Hypothesis, and
Experiment [...] The first step in the process, it will be perceived, is
to observe...
In 1885, the words "Scientific method" appear together with a description of the method in Francis Ellingwood Abbot's 'Scientific Theism',
Now all the established truths which are formulated in
the multifarious propositions of science have been won by the use of
Scientific Method. This method consists in essentially three distinct
steps (1) observation and experiment, (2) hypothesis, (3) verification
by fresh observation and experiment.
The Eleventh Edition of Encyclopædia Britannica did not
include an article on scientific method; the Thirteenth Edition listed
scientific management, but not method. By the Fifteenth Edition, a
1-inch article in the Micropædia of Britannica was part of the
1975 printing, while a fuller treatment (extending across multiple
articles, and accessible mostly via the index volumes of Britannica) was
available in later printings.
Current issues
In the past few centuries, some statistical methods
have been developed, for reasoning in the face of uncertainty, as an
outgrowth of methods for eliminating error. This was an echo of the
program of Francis Bacon's Novum Organum of 1620. Bayesian inference acknowledges one's ability to alter one's beliefs in the face of evidence. This has been called belief revision, or defeasible reasoning:
the models in play during the phases of scientific method can be
reviewed, revisited and revised, in the light of further evidence. This
arose from the work of Frank P. Ramsey
(1903–1930), of John Maynard Keynes
(1883–1946), and earlier, of William Stanley Jevons (1835–1882) in economics.
Science and pseudoscience
The question of how science operates and therefore how to distinguish genuine science from pseudoscience has importance well beyond scientific circles or the academic community. In the judicial system and in public policy controversies, for example, a study's deviation from accepted scientific practice is grounds for rejecting it as junk science
or pseudoscience. However, the high public perception of science means
that pseudoscience is widespread. An advertisement in which an actor
wears a white coat and product ingredients are given Greek or Latin
sounding names is intended to give the impression of scientific
endorsement. Richard Feynman has likened pseudoscience to cargo cults
in which many of the external forms are followed, but the underlying
basis is missing: that is, fringe or alternative theories often present
themselves with a pseudoscientific appearance to gain acceptance.
