Effective Reasoning/A History of Reasoning

This page presents a (comparatively) brief history of the development of reasoning techniques.

  • 1) The history of the philosophy of reasoning follows definite cycles.
  • 2) Despite the complexity and capriciously fashionable nature of this endeavor, particular tools of reasoning have developed and endured because they have been found to be reliable.

Essentially, this Wikibook is about these "tools of reasoning" and their effective applications.

(Note: there are links at the bottom of this page to both the Great Books and Project Gutenberg sites which contain copies of the works of many of the people mentioned on this page. You may want to read what they actually said and that is certainly recommended for a fuller understanding of some of the different ways we can compile reliable data and make reasonable decisions.)

The start of Reason edit

Although very little was written about how we reason before the time of Plato, it is apparent that we did reason. The Egyptians had arithmetic and algebra by 4000 B.C. It is hard to imagine the engineering feats of the ancient world or the discovery of fundamental principles such as the Pythagorian theory without the aid of reason, but we turned to the introspection of the process of reasoning around the fifth century B.C.

And it is probably wrong to say that no one wrote about reasoning before Plato. It is simply a fact that none of the earlier writings survived (or have been found). For instance, although none of the writings of Heracleitus, who lived around 500 B.C., have been found, he was widely quoted (even by the founders of the Christian church) and fragments have survived. He was interested in the workings of the human mind. He was quoted as saying, "Opposition brings men together, and out of discord comes the fairest harmony, and all things have their birth in strife." The creative capacity of conflict is still seen as a central tenet of reasoning theory and it is certainly central to processes such as dialectic and debate.

The study of reasoning was born from strife.

The Bronze Age Thinkers edit

The death of the tyrant Thrasybulus in 388 B.C. created a need for citizens of Greece to know how to conduct themselves in court so as to recover property that had been seized by the government during the Peloponnesian War. The Sophists, for a price, filled that need. They were itinerate teachers in Athens and the surrounding area who taught, among other things, rhetoric - the art of persuasive speaking. They were popularizers of existing knowledge. The Sophistic school had been founded as early as 450 B.C. Although there was a variety of positions held by the sophists, the hallmarks of sophistic philosophy was a thoroughgoing skepticism and realism. They tended toward moral relativism and taught practical subjects.

The early sophist, Protagoras, born around 480 B.C. taught that knowledge could only be the result of sense perceptions. He may have originated the idea that man is the measure of all things. He believed that the only reality there is, is that expressed by human individuals.

The younger Gordias (born around 425 B.C.) did not believe that people could obtain any certainty in any field because real things are different from our sensory impressions of them and it is too difficult to frame an exact verbal description of them.

Many of the works of Plato (c. 427 - 347) did survive and, although he did not write about the correct way to reason effectively, he used his teacher, Socrates, to illustrate effective arguments. The general methods used by Socrates are called "dialectic". Dialectic is the use of dialogue - questions and answers - as a means of intellectual investigation. Most of Plato's surviving works has Socrates as a foil for some popular philosophy, often propounded by a Sophist. His method was to ask leading questions which ultimately demonstrated the fallacy of the belief under investigation.

Whereas the Sophists often argued with the purpose of winning a case or beating an opponent, Plato demonstrated the use of argument as a method of discovering truth. Plato saw discussion as a way to clarify and organize thought.

Unlike Gordias, Plato believed that things could be known (see his Theatetus) but, unlike Protagoras, Plato mistrusted sensory perceptions (see his Meno, Phaedrus, and The Republic). He believed that what we see around us is not the Real but only shadow images of the actually Real (called "forms"). We attain true knowledge, not through our perception but through reason and the source of true knowledge is remembrances called up from our soul which extends far back before we were born. The soul is already in possession of knowledge.

Plato also recognised the importance of the imagination. He believed that it could replace reason when reason fails to supply the necessary connection between the ideal and the actual (see his Timaeus).

Plato's student, Aristotle (384-322 B.C.), took a considerably different approach to philosophy. He was very interested in perception. He, in fact, wrote many books based on his observations of the world. He was also concerned with finding ways of making our perceptions more trustworthy. His Organum, a set of works presenting his ideas on logic were the primary texts on the subject for centuries. His system of logic is still valid and represents the first formalization of the subject. Perhaps his greatest accomplishment was the extensive conceptual development of categorical logic and the syllogistic argument.

Propositional logic, somewhat closer to modern logic than Aristotle's version, actually had a false start in the Megarian School founded by a student of Socrates, Euclid of Megara (~400 B.C.) - not to be confused with the more famous author of The Elements.

Iron Age Thinkers edit

The study of logic progressed very little for almost 1000 years after Aristotle. A bright spot was Euclid who lived around 300 B.C. and developed the axiomatic approach to logic, especially as it concerned geometry and whose masterwork, Elements, survives today.

The Romans were very practical people and focused on rhetoric. They were more interested in means of influencing others than the pursuit of truth. The ideal of the learned man in the Roman world was the citizen-orator. Argumentation formed the basis of rhetoric.

Rhetoric was one of the major courses taught in the Roman and Medieval schools (the seven liberal arts were divided into two groups of subjects - the trivium (grammar, rhetoric, and dialectic) and the quadrivium (geometry, arithmetic, astronomy, and music)). Rhetoric was composed of invention, arrangement, style, memory, and delivery. The first two were closely related to argumentation.

The Golden Age of Islam edit

The Dark ages (around 450 ACE wrecked agriculture and stable economies, and allowed the hunters to prey on the civilized world. One of these marauding bands developed a vast empire which evolved into a highly cultured society, without whose academic excellence, all the work of the Greek and Roman world would have been lost in the mists of time.

During the Middle Ages, the dominant social and educational institution was religion: therefore, rhetoric became associated with preaching.

The Islamic age - 600 - 750 ACE bought reason to a very high standard. After the sack of Baghdad and 'reconquest' of Spain there was very little advance in the study of reasoning during the Middle Ages. An exception was the development of Supposition Theory, which was concerned with the semantic relationship between a term and its referent.

Christian Universities edit

Peter Abelard (1079-1142) revived human reason as an effective tool for the discovery of truth. A sharp dialectic practitioner, he effectively confronted the predominant Realism of the day and replaced it with his own Conceptualistic philosophy. Conceptualism (and the related Nominalism) rejected the reality of universals. Nominalists considered universals to be merely names; conceptualists believed them to be concepts, which were real, but only in the mind.

Roger Bacon (1214-1294) was an early pioneer of scientific inquiry, expanding the methods that lie at the heart of modern science - experimentation and induction.

William of Ockham (1280-1349) made some strides in logic and is most famous for his "razor" - his idea that an explanation should contain no more than is necessary to explain a phenomena. He also made some preiminary discoveries toward the development of DeMorgan's Laws and explored ternary (three state) logics.

Petrus Ramus (1515-1572) popularized "everyday logic". He also introduced the convention of dividing the canons of rhetoric so that invention and arrangement were associated with philosophy. Thereafter, rhetoriticians were less involved with argument and more interested in style (gesture, delivery, figures of speech, etc.).

The Enlightenment edit

Sir Francis Bacon (1561-1626) rejected Aristotolean logic and Scholasticism in favor of a new framework for discovery published in his Novum Organum in 1620. The new approach consisted of the careful observation and collection of data, their correct interpretation, and experimentation - in other words, modern science.

The Port-Royal Logic was an important textbook of logic published anonymously in 1662 by Antoine Arnault and Pierre Nicole. It was written in the common language, contained many new notions, and was very popular.

The French matematician Blaise Pascal (1623-1662) probably contributed to the Port-Royal textbook. In response to a friend's question about gambling and in collaboration with Pierre de Fermat (1601-1665), he also developed probability theory which later gave birth to statistics.

Since the time of René Descartes (1596-1650) until very recently, "logic" meant formal, symbolic logic. The Frenchman had an enomous impact on logic.

He instituted the idea of systematic doubt - doubt any idea that can be doubted. He searched for the basis of reasoning - that which could be accepted axiomatically, without doubt. He found one idea that met that criterion. "I think, therefore, I am" (cogito ergo sum, which he wrote in French je pense, donc je suis).

Thought is beyond doubt. Even if you doubt that you are, that doubt itself is thought. Even if you are an element in someone else's dream, you at least are. If you think, then you have some form of existence. One other thing is beyond doubt. There is other. Although the accuracy of sensory perception can be doubted, it is not totally under self's control, so there must be something else that is involved in sensation.

Everything else can be doubted. Sensations are unreliable. We often see things which are not and even more often erroneously interpret things that we sense. You may see a bug on the wall and find out, on closer inspection, that it's only a spot. A bag in the road is perceived as road kill. How often have we heard people say things that they did not actually say - remembered things that never happened?

For Decartes, revelation is also unreliable. How do we know that the divine knowledge that we receive is from God? It could be from some "evil genius" who only wishes to deceive us.

Descartes inserted one other thing into logic - mathematics. He reasoned that God exists from a consideration of Euclid's exposition of geometry. He required that reasoning must proceed from unassailable axioms to conclusions. And then he translated position and motion into mathematical entities.

His rectilinear system of coordinates is named the Descartian system of coordinates in his honor. By setting up an arbitrary system of perpendicular axes, one can numerically describe the position of any point by reference to those axes. Analytical geometry is based on this concept. With Descarte began the notion that everything in the universe should be explainable formulaically. He wrote, in his Discourse on Method, "Give me extention and motion and I will construct the world."

These ideas were dominant in the sciences and in logic for the next 300 years. Reasoning became identified with formal logic. People began looking for ways to translate informal reasoning into formal logic and, thereby, to infuse reasoning with the certainty of formal thought. Science began looking for axiomatic bases for their investigations. Argumentation became the demonstration of self-evident proof.

Thomas Hobbes (1588-1679), a contemporary of Descartes and Francis Bacon's last secretary, was the founder of scientific materialism and ethical hedonism. He believed that, once fundamental propositions are laid down, everything else follows deductively. "All that exists is body [matter]; all that occurs is motion." Beyond that, we can know nothing about the external world through philosophical speculation. It could be real, but we have no way of finding it out or proving it. All we can know is what our senses tell us.

John Locke (1632-1704) believed that ideas are the products of experience and reflection on those experiences, in other words, reason.

Descartes reserved the self as the only defensible foundation for reason. Bishop George Berkeley (1685-1753) refuted that by showing that there were alternatives to Descartes' "I", such as the mind of God. Immanuel Kant (1724-1804) codified philosophical agnosticism in his Critique of Pure Reason. He did maintain, however, that it is practical to assume that true knowledge of reality is available.

David Hume (1711-1776) proposed the most devastating attack on science up to his own time. Science relies on the fact that 1) nature is causative in essence (Things happen in an orderly sequence of causes and effects), 2) nature is uniform (Genralization relies on the belief that repeated observation of a particular event makes that event predictable), and 3) things are associated naturally on the basis of similarity, proximity, contrast, temporal association, etc.

Hume showed that:

1) Causation is not an element of nature but our way of making sense of patterns that we sense in the world. Those patterns are very much conditioned by our own mental filters which are, in turn, conditioned by our culture, habits, memories, mind sets, etc. We cannot directly sense causality as such, therefore, our presumption of causality assumes that there are relationships involved that are not accessible to our senses.

2) The only way we can show that nature is uniform is by pointing out that it always has been, but that argument itself would presume the uniformity of nature. In other words, uniformity of nature can't be demonstrated without circular arguments.

3) The associations that we notice in nature are the result of the human mind's tendency to see order, even when it's not there. It is too easy to find instances where regularities are not really causal. For example, there are plenty of instances of drinkers of alcohol living to advanced age. That does not mean that drinking alcohol is good for you.

Both Gottfried Leibniz (1646-1715) and Isaac Newton (1643-1727) developed calculus independently. It is Leibniz' notation that is in use today. He investigated the use of symbols and the relations of sets.

Newton developed many of the foundations of the scientific method.

Carl Friedrich Gauss (1777-1855) did extensive work in theoretical mathematics. In seeking to minimize errors in census data, he developed the method of least squares and the normal distribution, both central to modern statistics. He claimed to have discovered alternatives to Euclid's fifth axiom of geometry, thereby discovering non-Euclidean geometries, but he never published the ideas. His pupils, Georg Riemann (1826-1866) and Janos Bolyai (1802-1860) claimed the honor.

While Guass was developing the normal distribution, Simeon-Dennis Poisson (1781-1840) was developing the theory behind the probability distribution that was ultimately named after him, the Poisson distribution, which describes the probability of lightning strikes, arrival of customers at a checkout counter, and the chance of finding a particular number of predators in a large area of forest.

Nineteenth Century edit

Augustus DeMorgan (1806-1871) perfected mathematical induction and made many contributions to symbolic logic including the DeMorgan's laws which allows one to transform a conjunction into a disjunction or vice versa.

John Stuart Mill (1806-1873), in an attempt to provide a firm basis for scientific reasoning, formalised inductive logic in his book A System of Logic (1843). His work in logic very much influenced later logicians such as Bertrand Russell (who was, by the way, his godson).

George Boole (1815-1864) noticed a striking similarity between algebra and logic and developed a "calculus of reasoning" which was published in his An Investigation of the Laws of Thought. It later became known as two-valued or Boolean algebra and became the basis, seventy years later, for the mathematics and logic used by digital computers.

Twentieth Century edit

John Venn (1834-1923) significantly extended Boole's logic and invented the Venn diagrams which make syllogistic logic so much easier to analyze.

Friedrich Frege (1848-1925) invented and axiomatized predicate logic. He was a major advocate of logicism, the position that arithmetic is reducible to logic.

In counterpoint to logicism, which held that logic was a means of discovering truth, two other conceptual frameworks arose around the turn of the century. Luitzen Egbertus Jan Brouwer (1881-1966) held, what came to be known as Intuitionism, that mathematics and logic were not about truths (characteristics of reality), but were about mental consistencies. Internally consistent methods are used to manipulate simple concepts to realize more complex mental constructs.

David Hilbert (1862-1943) laid the groundwork for Formalism, the idea that mathematics is a meaningless exercise (a game) using symbols according to formal rules which are agreed to by consensus a priori.

Karl Pearson (1857-1936) was a prodigious inventor of statistical techniques. Among his inventions are linear regression, correlation, and the chi square test. He also unified many of the most useful probability distributions by showing that they were all members of a larger class of mathematical functions.

Sir Ronald Fisher (1890-1962) was another giant of modern statistics. He invented analysis of variance, maximum likelihood techniques, linear discrimination functions, and nonparametric procedures (the first was his randomization tests). He also did pioneer work in statistical information theory.

In 1910, Bertrand Russell (1872-1970) and Alfred Whitehead (1861-1947) published their Principia Mathematica which outlined pretty much everything that had been produced in symbolic logic plus quite a lot of original material. In it, the authors proported to create an axiomatic system on which all of mathematics can be constructed. (Kurt Godel corrected that naivete a few years later.)

Rudolph Carnap (1891-1970) insisted that many of the questions addressed in philosophy were meaningless and amounted to an abuse of language. He was fascinated by the problem of formalizing semantics and developed a logical treatment of relations. He also did considerable early work in modal logics. He was a member of the Vienna Circle who institutes logical positivism which was the idea that the only authentic knowledge is scientific knowledge. They held that a statement is meaningful only if it can be verified empirically.

Ludwig Wittgenstein (1889-1951) was not a logical positivist nor was he a member of the Vienna Circle, but he influenced them greatly and was on close terms with several of them. He is the inventor of the logical truth table. He believed that the world is compose of independent logical facts that constitute more complex facts.

Albert Einstein (1879-1955) along with being an incredibly gifted physicist demonstrated that "armchair experimentation" (the use of mental exercises in developing theories) could be very productive for science. Much of his theories of relativity were developed outside the laboratory using such purely mental exercises.

Werner Heisenberg (1901-1976) called Newtonian ideas about causation and predictability into question, especially on a subatomic level.

Karl Popper (1902-1994) repudiated the traditional observationist-inductivist position of science by proposing an alternative, empirical falsifiability criterion. In it, no statement (theory, hypothesis, proposition) should be considered scientific if it does not admit the possibility of a contrary statement.

Kurt Godel (1906-1978) proved the completeness of first order logics and the incompleteness of arithmetic. His proofs show that there is no set of axioms sufficient for all mathematics and not all mathematical questions are computable. Russell and Whitehead's dream of completely axiomatizing mathematics was ended forever.

Willard V. O, Quine (1908-2000) was a major factor in the decline of logical positivism. He effectively rejected the analytical-synthetic distinction so important in empirical orthodoxy and proposed ontological relativity. Analytical statements are those that are true or false by virtue of the meaning of the words used (e.g. "A diamond is a gemstone"). Synthetic statements are those that are true or false by virtue of facts about reality (i.e. The median age of Internet users is 25"). According to ontological relativism, theories are not sufficiently determined by observed data and relies on other theories; no theory is complete in isolation. All theories are open to revision.

Quine also developed prime implicant theory that lead to the discovery by Edward J. McCluskey (1929- ) of the Quine-McCluskey algorithm for minimizing logical statements.

Although there had been some work done with modal logics since the time of Aristotle, the founder of modern modal logic was Clarence Lewis (1883-1964). Modal logics are systems for dealing with modalities such as possibility, necessity, and, by extension, similar concepts such as temporality, morality, supposition, etc.

John Tukey (1915-2000) was one of the workhorses of modern Statistics turning out many invaluable procedures such as jackknife estimation, several methods of group comparison in analysis of variance, and exploratory data analysis (using many graphical procedures such as the boxplot). He also coined the terms "bit" (from binary digit) and "software".

H. P. Grice (1915-1988) analyzed ordinary conversation and came up with the rules of language that are understood by participants in successful dialogues.

C. L. Hamblin (1922-1985) persuasively questioned the traditional fallacy classification by showing that "fallacies" are not always fallacious and must be analyzed on a case-by-case basis. Douglas Walton (1942- ) further clarified the situations in which classical fallacies may be valid arguments.

Chaim Perelman (1922-1984) introduced many concepts that are standard principles of modern rhetoric.

Maurice Karnaugh (1924- ) developed the Karnaugh map in 1950 that is used to simplify conjunctive or disjunctive logic and is used quite a lot in simplifying digital electronic circuit designs.

Chaos theory, developed in the late 1800s and through the 20th Century by scientists such as Henri Poincare (1854-1912), Jacques Hadamard (1865-1963), and Edward Lorenz (1917- ), demonstrated that there were processes in nature that could not be predicted to any fine degree of accuracy by any amount of calculation or instrumentation. Weather is one of those phenomena.

Thomas Kuhn (1922-1996) wrote very probing and influential works on the philosophy of science and asserted that science does not evolve gradually but progresses in jumps by undergoing occasional paradigm shifts.

Postmodernism, as a reaction to the modernism of the industrial revolution, was first recognized as a theoretical discipline in the 1970s. It held that meaning can only be experienced by individuals and can only be understood relative to the culture it came from. Experience is personal and cannot be generalized. Modern cultural, ethical, and religious relativism is an outgrowth of the postmodernist movement.

Stephen Toulmin (1922- ) held that formal logic is inappropriare as a model for argumentation. He developed a new and more adaptable model for nonformal reasoning. He also developed a way to diagram arguments widely in use today.

Rob Grootendorst (1943-2000) and Frans H. van Eemeren (1946- ) developed the pragma-dialectical model of argument analysis.

Michael Gilbert (1945- ) proposed a model in which argumentation is essentially a cooperative endeavor with the common goal of reaching the best possible conclusion/decision under the circumstances.

It is beneficial to note that Western logic which sprang primarily from ancient Greek philosophy is only one of three great systems of logic. Pretty much in isolation from the West, both India and China developed traditions of logic that differ in quite a few ways from Western logic.

Recent popularizers of Eastern Philosophy such as Alan Watts, Benjamin Hoff, Paul Reps, and Thomas Cleary and the use of Oriental classics such as Laozi - The Way (Tao Te), Myamoto Musachi - The Book of Five Rings, and Sun Tzu - The Art of War by business men and politicians have brought Eastern logic to the Western world.

Gotama (2nd century) can be called "the Aristotle of India". Indian logic is derived from his works much in the same way that Western logic is derived from the works of Aristotle. His Nyaya Sutras posit that there are four ways of knowing: percption, inference, comparison, and testimony and much of Nyayan logic are investigations of ways to make knowledge valid, since the followers of Nyaya believe that the only release from suffering is by obtaining valid knowledge.

The works of Genesa Upadhyaya (13th century) and the Navya-Nyaya school of Indian philosophy lead to refinements of Indian logic. Henry T. Colebrooke (The Philosophy of the Hindus, 1824) investigated the Indian system of inference and concluded that it could not be accounted for by Aristotlean logic. It is possible that such logicians as Augustus DeMorgan and George Boole were influenced by Eastern logic.

A contemporary of Confucius, Mo Ti (470-391 BC), is credited with founding the Mohist school in China. They dealt with means of valid inference. Mohist logic was based on analogical instead of deductive reasoning. Chinese logic derived from reflections on the competing and controversial philosophies of Confucianism, Taoism, and Mohism.

Chinese logic was repressed by the Qin Dynasty (221 BC) and was replaced later by the introduction of Indian philosophy with the influx of Buddhism into China in the 1st century AD.