Lord Bertrand Russell

A solution to Russell’s paradox

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Bertrand Russell was one of the world’s most influential philosophers. His most famous writings were often about paradoxes and contradictions that seemed to defy logic, imagination, and reason.

The example of mathematics helped persuade him to accept the teachings of Christianity. Russell once said: “I believe, therefore, that if I make myself believe otherwise, I shall be unwise.”

As an aristocrat and a scientist, Lord Russell was extraordinarily enlightened, and as a philosopher, he was essentially right on the mark and unusually intelligent and productive. He was a devoted follower of Lord Alfred Mitchell. Mitchell came from Australia to the United Kingdom in 1889, and his beliefs later evolved to become Christian, and Lord Russell followed suit.

The oldest known depiction of a paradox
The oldest known depiction of a paradox

The paradox

Russell’s paradox is a famous paradox in mathematics discovered by Bertrand Russell in 1901. It is based on the concept of a set, a collection of objects, demonstrating that some sets cannot be defined or constructed within the framework of classical set theory.

The paradox is based on the idea of a set that contains all sets that are not members of themselves. If such a set exists, then it must be either a member of itself or not a member of itself. If it is a member of itself, then it must not be a member of itself, and if it is not a member of itself, it must be a member of itself. This reasoning leads to a contradiction, which shows that such a set cannot exist.

One way to resolve Russell’s paradox is to adopt a different axiomatic foundation for set theory, such as the Zermelo-Fraenkel axioms or the von Neumann-Bernays-Gödel axioms, which are constructed in a way that avoids the paradox. These hypotheses provide a consistent foundation for set theory and allow for constructing of many sets that are important in mathematics, including infinite sets and sets of sets.

Alternatively, some philosophers and mathematicians have proposed approaches that reject the idea of sets altogether in favor of more flexible or non-classical foundations for mathematics. These approaches, such as type theory or category theory, offer different ways of understanding and constructing mathematical objects and may provide a different perspective on the paradox.

We have come to understand what science is. Science is a branch of philosophy that is very complicated because science uses mathematics. The mathematical aspect of science is there because mathematics is supposed to be the ultimate way to explain things.

Nevertheless, mathematics is also such a widely distributed intelligence that it is not surprising to find many scientifically literate people. Moreover, science uses mathematics not only to explain scientific theories but also to predict scientific discoveries. So mathematics is not the beginning of science. It is part of it.

In science, there is no one truth, so the philosopher is not much help in finding the truth. There are only many truths in science, one of which is the truth of science, which is very complex.

We could use one of Lord Russell’s paradoxes as a tool for deciding what the truth of mathematics is. The paradox is that mathematics could not be suitable if mathematics were only about measurements. If we did not try to calculate the exact distance between the north and south poles, measurements would not be complete and mathematical theories would be useless. However, if we used measurement, we would make mistakes, and mathematics would not be good.

Absolute truth

So maybe the absolute truth is that mathematics is about things that do not depend on measurement. Moreover, it could not be good even if it was just about one measurement.

The existence of absolute truth is a complex and contentious issue that philosophers and theologians have debated for centuries, and there is no consensus on a definitive answer.

Statue of ancient philosopher
Statue of ancient philosopher

Different philosophical and religious traditions have different perspectives on the nature and accessibility of truth, and it is ultimately up to individuals to decide what they believe about the existence of absolute truth.

In 1950, Bertrand Russell was awarded the Nobel Prize in Literature. His famous paradox did not hold up, but the saga of his life is eternal.

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