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Bertrand Russell (Philosopher and Mathematician) on Philosophy of Science

Updated on March 13, 2014

Russell has enhanced the philosophy of science.

Bertrand Russell was a British mathematician and philosopher. He was a recipient of Nobel Prize in literature.


To start with, we imagine a universe where there is no human being. Nobody makes a mental symbol of something; who writes a symbol of anything; who invents an alphabet and writes a word.

Enter a human being, cromagnon, who scratches on the wall of the cave “d” to represent a deer. The moment he writes “d” he starts to define deer. “d” defines a fact. Then every time cromagnon hunts a deer, he calls it “deer.” So he has given a name “deer” to a fact in the universe.

Cromagnon becomes more sophisticated and gives more names to a lot of facts. It comes to a point that he gives a name to something he had imagined, that is, a figment of his mind.

Russell said a fact is anything in the universe that is undefined. This definition is unlike the common one that consists of words.

This definition of fact does not assume an absolute. It does not assume something unknowable.

Our knowledge of the external world is by means of our senses, or experience (Russell, B. Our Knowledge of the External World). So far, we know matter to be composed of atoms, that an atom consists of electrons, protons, nucleus, positrons, quarks, and more that are very small. Our bare eyes are aided by the optical microscope and the electron microscope.

Definite description

Some ordinary people and scientists give names to figments of the mind. “Mermaid” for example.

A science, to be solid and stable, must start with facts. For convenience, a scientist deals with symbols and names of facts.

In this situation comes in the concept of definite description in the philosophy of science. It is a concept that insures that the scientist is not dealing with figments of the mind. We allow that “imagination” is among the stuff that psychology deals with. An insane man who says he talking to a ghost is fact for psychology.

A definite description is verifiable. A description that is not verifiable is fictitious. It is rejected as a stuff in doing science.

“The king of France who was guillotined during the French revolution of 1799,” is verifiable. The verifier is King Louis XIV.

“Bonaparte” is fictitious in the sense that there were several rulers of France named Bonaparte. “The ruler of France who crowned himself,” is verifiable. The verifier is Napoleon Bonaparte. The tradition had been that the pope places the crown on the head of a king.

A scientist who applies the concept of definite description is assured of doing sound experiments.

Definite description also applies in taxonomy. Take Oryza sativa L. which is the scientific name of rice. L. means that it was Linnaeus who gave this name. Now rice is described as having a soft stem, with roots, with slender leaves, with several grains when matured. In formal taxonomy, the descriptions are called keys that are used to identify rice. Somebody who had not seen a rice plant can identify a rice plant the first time s/he encounters a real plant with the use of keys, or definite descriptions.


What is the practical utility of definite description?

Russell says existence is to be asserted on a definite description. It is not to be asserted on a name or label.

For example, “Napoleon exists.”

Russell showed that a logical analysis of this statement results in contradiction.

Definite description also has application in composition. One should not say “France exists.” One should say “A country where once lived Joan of Arc” exists.”

In taxonomy the scientific name cannot be substituted for the keys in the identification of species. For example, in two species of pines. Keys distinguishes one from the other. Pinus mindorensis Jung and de Vries has two needles in a leaf, Pinus insularis Endl. has three needles in a leaf.

In the same manner, one should say: “A pine with two needles in its leaf exists in Mindoro, Philippines.” Not: “Pinus mindorensis Jung and de Vries exists in Mindoro, Philippines.” Several a scientist commits this kind of error.

Occam’s razor

“It is vain to do with more that can be done with less,” and “Entities should not be multiplied beyond necessary” (Russell, B. Wisdom of the West. 1954: 204). This is called Occam’s razor. Russell did not invent Occam’s razor; it was invented by William of Occam sometime in 1340s.

Russell emphasized the importance of Occam’s razor in doing science. It is a principle that helps in reducing confusion thus enhance economy and certainty.

With Occam’s razor the whole of Euclidean geometry can be reduced to point, line and plane, according to Russell.

With Occam’s razor, one comes to a minimum vocabulary of a science or discipline. As mentioned earlier Euclidean geometry’s minimum vocabulary are point, line and plane. Minimum vocabulary insures against confusion and contradiction. It is required that the axioms that serve as foundations of a science do not have a term derived from another.

Law of excluded middle

This concept simply means that there is a sentence or proposition that is neither true nor false.

For example: “A genetically modified organism is safe.”

Bt corn is a modified organism (GMO). Bt means Bacillus thuringiensis, a bacterium. A Bt corn is one whose chromosomes contain genes of this bacterium, inserted by means of biotechnology. The genes of the bacterium that controls resistance to pests (like corn borer) was isolated and inserted to the chromosome of of Bt corn. This plant is resistant to stem borer of corn. (Bt corn was made and being marketed by Monsanto).

Is it safe for humans to eat Bt corn? The issue is an ethical one. Will the genes of bacterium get incorporated into the chromosomes of a human being who had eaten Bt corn? Will it badly affect that human being?

For the present, no side effect is seen. However, will a side effect show in the long future?

There is no evidence. A proposition belongs in the law of excluded middle if there is no evidence in its favor or against it in the long future, according to Russell.

How about the creation of the universe?

A proposition goes: “The universe started as a big bang of a small matter 13.7 billion years ago.”

This is derived from the studies of Edwin Hubble, derived, in turn, from the prediction made by Einstein in his generalized theory of relativity..

To some this proposition is far from certain. The Higg's boson appears to prove it: the universe started as a negative sign that gathered mass from space.

If the Higg’s boson is not enough evidence, the the proposition above belongs in the law of excluded middle. That is, it is a sentence that has no evidence in its favor or against it in the long past.

A sentence or proposition that belongs in the law of excluded middle is not knowledge, according to Russell. It does not belong in science.


The test of mathematics is validity. Russell may not have been the first to say this. However, he clarified it further. Fundamentally, mathematics consists of maxims and rules that do not contradict each other. Mathematics belongs in pure knowledge, in the words of philosopher Emmanuel Kant. So one says, "two plus two equals four" is valid.

In a higher plane, for example, his special theory of relativity that Einstein couched in mathematical language. That language is valid so long as it follows the rules of Euclid's geometry or Riemannian geometry that Einstein used.

In a more mundane application, chess is valid. This game uses rules that do not contradict each other and it is played in a logical manner that a win is incontrovertible.

The test of science is truth. The test of a statement "The earth revolves around the sun" is truth. We are using the correspondence theory of truth that is unlike the monistic theory. In monism there is only one truth. Correspondence theory is verifiable by means of observation.

Interplay of validity and truth. Einstein couched his special theory of relativity and generalized theory of relativity in mathematical language. We say that the mathematical expressions are valid.

How do we know that the special theory of relativity, valid as it is, is also true?

Russell explained in plain language the method of Einstein in showing that this theory is true. Einstein derived from his mathematical language of the special theory a statement of fact: E = mc2. "Energy is equal to mass times the speed of light squared" is a statement of fact. It is true because it corresponds to a fact about the universe.

What is the proof that it is true? Einstein issued this statement in 1906. In 1936 Enrico Fermi did an experiment of bombarding uranium with the neutron of a weak element. He found that uranium split into two. He could not decipher his results. In 1938, Liese Mietner and company verified Fermi's results. They called the process fision. The formula was used in the manufacture of atomic bomb, two of which were dropped over Japan in 1945. Their destructive power proved that the formula is true.

These are some of the contributions of Russell in the philosophy of science.


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