Russell’s Paradox and the Law of Non-Contradiction


What is Russell’s paradox simple explanation?

Russell’s Paradox is the theory that states: If you have a list of lists that do not list themselves, then that list must list itself, because it doesn’t contain itself. However, if it lists itself, it then contains itself, meaning it cannot list itself.

What is the answer to Russell’s paradox?

The whole point of Russell’s paradox is that the answer “such a set does not exist” means the definition of the notion of set within a given theory is unsatisfactory. Note the difference between the statements “such a set does not exist” and “it is an empty set”.

What is Russell’s paradox example?

Russell’s paradox is based on examples like this: Consider a group of barbers who shave only those men who do not shave themselves. Suppose there is a barber in this collection who does not shave himself; then by the definition of the collection, he must shave himself. But no barber in the collection can shave himself.

What is Aristotle’s law of non-contradiction?

According to Aristotle, the principle of non-contradiction is a principle of scientific inquiry, reasoning and communication that we cannot do without.

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Who solved Russell’s paradox?

Russell’s paradox (and similar issues) was eventually resolved by an axiomatic set theory called ZFC, after Zermelo, Franekel, and Skolem, which gained widespread acceptance after the axiom of choice was no longer controversial.

Why is Russell’s paradox A paradox?

Also known as the Russell-Zermelo paradox, the paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself. Hence the paradox.

What is the Russell’s barber paradox?

…to be known as the barber paradox: A barber states that he shaves all who do not shave themselves. Who shaves the barber? Any answer contradicts the barber’s statement. To avoid these contradictions Russell introduced the concept of types, a hierarchy (not necessarily linear) of elements and sets such that…

Can paradoxes be solved?

A paradox is the realization that a simple problem has two apparently contradicting solutions. Whether intuitively, or using a formula, or using a program, we can easily solve the problem. However, someone challenges us with another method to solve the same problem, but that method leads to a different result.

How Russell’s paradox changed set theory?

In 1901 Russell discovered the paradox that the set of all sets that are not members of themselves cannot exist. Such a set would be a member of itself if and only if it were not a member of itself. This paradox is based on the fact that some sets are members of themselves and some are not.

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What are examples of non-contradiction?

The law of non-contradiction is a rule of logic. It states that if something is true, then the opposite of it is false. For example, if an animal is a cat, the same animal cannot be not a cat. Or, stated in logic, if +p, then not -p, +p cannot be -p at the same time and in the same sense.

What are the 3 principles of Aristotle?

Aristotle states there are three principles of persuasion one must adhere to in order to persuade another of an idea. Those principles are ethos, pathos and logos.

What is Aristotle’s law of logic?

There are three laws upon which all logic is based, and they’re attributed to Aristotle. These laws are the law of identity, law of non-contradiction, and law of the excluded middle. According to the law of identity, if a statement is true, then it must be true.

Who is Socrates philosophy?

Who was Socrates? Socrates was an ancient Greek philosopher, one of the three greatest figures of the ancient period of Western philosophy (the others were Plato and Aristotle), who lived in Athens in the 5th century BCE.

What is Aristotelian argument?

Aristotelian argument (based on the teachings of the Greek philosopher Aristotle) is made to confirm a position or hypothesis or to refute an existing argument. Using the techniques at hand, the writer attempts to persuade the reader to a particular point of view.

What is syllogistic argument?

1 : a deductive scheme of a formal argument consisting of a major and a minor premise and a conclusion (as in “every virtue is laudable; kindness is a virtue; therefore kindness is laudable”) 2 : a subtle, specious, or crafty argument.

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Is syllogism a fallacy?

A syllogism is an argument that has a major premise, a minor premise and a conclusion, and often appears in the form ‘A is B, C is D, therefore E is F’. This is a specific form of argument with very specific rules that are easy to break. In many ways, syllogistic fallacies are the ‘classic’ form of fallacy.

What is deductive syllogism?

Syllogism deductive reasoning

Syllogism refers to two statements—a major and a minor statement—join to form a logical conclusion. The two accurate statements mean that the statement will likely be true for all additional premises of that category.