1469DDDDDDDDD "IMAGINATION IS NOT TO BE DIVORCED FROM THE FACTS"

Today's post was penned last summer:

"In formal logic, a contradiction is the signal of defeat
But in the evolution of real knowledge
It marks the first step in progress toward a victory"
                                 —Alfred North Whitehead

Alfred North Whitehead OM FRS FBA (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy,^[18] which today has found application to a wide variety of disciplines, including ecology, theology, education, physics, biology, economics, and psychology, among other areas.

In his early career Whitehead wrote primarily on mathematics, logic, and physics. His most notable work in these fields is the three-volume Principia Mathematica (1910–13), which he wrote with former student Bertrand Russell. Principia Mathematica is considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library.^[19]

Beginning in the late 1910s and early 1920s, Whitehead gradually turned his attention from mathematics to philosophy of science, and finally to metaphysics. He developed a comprehensive metaphysical system which radically departed from most of western philosophy. Whitehead argued that reality consists of processes rather than material objects, and that processes are best defined by their relations with other processes, thus rejecting the theory that reality is fundamentally constructed by bits of matter that exist independently of one another.^[20]Today Whitehead's philosophical works – particularly Process and Reality – are regarded as the foundational texts of process philosophy.

Whitehead's process philosophy argues that "there is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have consequences for the world around us."^[20] For this reason, one of the most promising applications of Whitehead's thought in recent years has been in the area of ecological civilization and environmental ethics pioneered by John B. Cobb Jr.

Principia Mathematica (1910–1913) is Whitehead's most famous mathematical work. Co-written with former student Bertrand Russell, Principia Mathematica is considered one of the twentieth century's most important works in mathematics, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library.^[19]

Principia Mathematica's purpose was to describe a set of axioms and inference rules in symbolic logicfrom which all mathematical truths could in principle be proven. Whitehead and Russell were working on such a foundational level of mathematics and logic that it took them until page 86 of Volume II to prove that 1+1=2, a proof humorously accompanied by the comment, "The above proposition is occasionally useful."^[54]

Whitehead and Russell had thought originally that Principia Mathematica would take a year to complete; it ended up taking them ten years.^[55] To add insult to injury, when it came time for publication, the three-volume work was so long (more than 2,000 pages) and its audience so narrow (professional mathematicians) that it was initially published at a loss of 600 pounds, 300 of which was paid by Cambridge University Press, 200 by the Royal Society of London, and 50 apiece by Whitehead and Russell themselves.^[55] Despite the initial loss, today there is likely no major academic library in the world which does not hold a copy of Principia Mathematica.^[56]

The ultimate substantive legacy of Principia Mathematica is mixed. It is generally accepted that Kurt Gödel's incompleteness theorem of 1931 definitively demonstrated that for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced from them, and hence that Principia Mathematica could never achieve its aims.^[57] However, Gödel could not have come to this conclusion without Whitehead and Russell's book. In this way, Principia Mathematica's legacy might be described as its key role in disproving the possibility of achieving its own stated goals.^[58] But beyond this somewhat ironic legacy, the book popularized modern mathematical logic and drew important connections between logic, epistemology, and metaphysics.

Metaphysics is a branch of philosophy exploring the fundamental nature of reality

Unlike Whitehead's previous two books on mathematics, An Introduction to Mathematics (1911) was not aimed exclusively at professional mathematicians, but was intended for a larger audience. The book covered the nature of mathematics, its unity and internal structure, and its applicability to nature.^[45] Whitehead wrote in the opening chapter:

"The object of the following Chapters is not to teach mathematics, but to enable students from the very beginning of their course to know what the science is about, and why it is necessarily the foundation of exact thought as applied to natural phenomena."^[60]

The book can be seen as an attempt to understand the growth in unity and interconnection of mathematics as a whole, as well as an examination of the mutual influence of mathematics and philosophy, language, and physics.^[61] Although the book is little-read, in some ways it prefigures certain points of Whitehead's later work in philosophy and metaphysics

Whitehead showed a deep concern for educational reform at all levels. In addition to his numerous individually written works on the subject, Whitehead was appointed by Britain's Prime Minister David Lloyd George as part of a 20-person committee to investigate the educational systems and practices of the UK in 1921 and recommend reform.^[63]

Whitehead's most complete work on education is the 1929 book The Aims of Education and Other Essays, which collected numerous essays and addresses by Whitehead on the subject published between 1912 and 1927. The essay from which Aims of Education derived its name was delivered as an address in 1916 when Whitehead was president of the London Branch of the Mathematical Association. In it, he cautioned against the teaching of what he called "inert ideas" – ideas that are disconnected scraps of information, with no application to real life or culture. He opined that "education with inert ideas is not only useless: it is, above all things, harmful."^[64]

Rather than teach small parts of a large number of subjects, Whitehead advocated teaching a relatively few important concepts that the student could organically link to many different areas of knowledge, discovering their application in actual life.^[65] For Whitehead, education should be the exact opposite of the multidisciplinary, value-free school model^[64][66] – it should be transdisciplinary, and laden with values and general principles that provide students with a bedrock of wisdom and help them to make connections between areas of knowledge that are usually regarded as separate.

Whitehead argued that curriculum should be developed specifically for its own students by its own staff, or else risk total stagnation, interrupted only by occasional movements from one group of inert ideas to another.

Above all else in his educational writings, Whitehead emphasized the importance of imagination and the free play of ideas. In his essay "Universities and Their Function", Whitehead writes provocatively on imagination:

"Imagination is not to be divorced from the facts: it is a way of illuminating the facts. 

It works by eliciting the general principles which apply to the facts, as they exist, and then by an intellectual survey of alternative possibilities which are consistent with those principles. It enables men to construct an intellectual vision of a new world."^[68]

Whitehead's philosophy of education might adequately be summarized in his statement that "knowledge does not keep any better than fish."^[69]In other words, bits of disconnected knowledge are meaningless; all knowledge must find some imaginative application to the students' own lives, or else it becomes so much useless trivia, and the students themselves become good at parroting facts but not thinking for themselves.


Saturday, November, 11, 2017

If you ask me to summarize Whitehead's philosophy of education in a sentence, I'd reply:
"Bits of disconnected knowledge are meaningless", implying that puzzlements concerning conflicts, which remain unresolved, are due to the fact that 'the bigger picture' has not yet been constructed with clarity in your mind or mine ... for example:

"There is nothing in a caterpillar that tells you it's going to be a butterfly."
                 — R. Buckminster Fuller

PS
A meaningful thought, concerning imagination, was added, this morning, beneath the last photo published in yesterday's post