Some statements are always true. That kind of statement is called tautology"." One popular classical tautology, credited to the philosopher Parmenides of Elea, says "That which is, is. That which is not, is not." This essentially means that true statements are true and false statements are false. Due to their simple nature, tautologies may not always be helpful in building logical arguments.
A tautology is represented in symbolic logic as formula_9, meaning "Either "a" or not "a"." Assuming that there are no unmentioned possibilities, this covers every possible case. Another symbol used to represent a tautology is formula_10.
Because logic is a tool used to think more rationally, it can be used in countless ways. Symbolic logic is employed far and wide, from philosophical treatises to complicated mathematical equations. Computers use the rules of logic to run algorithms, which let computer programs make decisions based on data.
Logic is critical to pure mathematics, statistics, and data analysis. Logic is also studied in philosophy. People who study math create proofs that use logical rules to show that mathematical theorems are correct. There is an area of mathematics called mathematical logic that studies logic using mathematics.
Communism
Communism is a socio-economic political movement. Its goal is to set up a version of society where the factories and farms are shared by the people, and would not have rulers or money.
According to communist writers and thinkers, the goal of communism is to create a society without a government or a system of classes, and to end capitalism. Communist thinkers believe this can happen if the people take away the power of the bourgeoisie (the ruling class, who own the factories and farms) and establish worker control of the means of production (factories and farms).
Communism is not anti-individualist. However, it does also say that decisions should be good for the population as a whole, instead of just being good for only a few of people in the country.
Since 1992, there have been five nations remaining governed officially by communist ideologies. Four of these follow different forms of Marxism-Leninism - Vietnam, China, Cuba and Laos. The fifth, North Korea, now officially follows Juche, which claims to be a better version of Marxism-Leninism. North Korea called itself Marxist-Leninist before 1991. Many other nations abandoned Marxism around that time because most people thought it had failed. In many cases Marxist governments fell to authoritarianism, mass poverty, economic collapse and violent conflict, as is the case of the Soviet Union and Yugoslavia, for example.
Some of the most well-known people that have been important in the development of communism include Karl Marx, Friedrich Engels, Joseph Stalin, Mao Zedong, Vladimir Lenin, and Leon Trotsky.
In 1848, Karl H. Marx and Friedrich Engels wrote "The Communist Manifesto". It was a short book with the basic ideas of communism. Most socialists and communists today still use this book to help them understand politics and economics. Many non-communists read it too, even if they do not agree with everything in it.
Karl Marx said that for society to change into a communist way of living, there would have to be a period of change. During this period, the workers would govern society. Marx was very interested in the experience of the Paris Commune of 1870, when the workers of Paris ran the city following the defeat of the French Army by the Prussian Army. He thought that this practical experience was more important than the theoretical views of the various radical groups.
Many groups and individuals liked Marx's ideas. By the beginning of the twentieth century, there was a worldwide socialist movement called Social Democracy. It was influenced by his ideas. They said that the workers in different countries had more in common with each other than the workers had in common with the bosses within their own countries. In 1917, Vladimir Lenin and Leon Trotsky led a Russian group called the Bolsheviks in the October Revolution. They got rid of the temporary government of Russia, which was formed after the February Revolution against the Tsar (Emperor). They established the Union of Soviet Socialist Republics, also called the Soviet Union or USSR.
The Soviet Union was the first country claiming to have established a workers' state. In reality, the country never became communist in the way that Marx and Engels described.
During the 20th century, many people tried to establish workers' states. In the late 1940s, China also had a revolution and created a new government with Mao Zedong as its leader. In 1959, the island of Cuba had a revolution and created a new government with Fidel Castro as its leader. At one time, there were many such countries, and it seemed as though communism would overtake Capitalism. However, communist party governments didn't use democracy, which is a very important component of socialism and communism. Because of this, the governments became separated from the people, making communism difficult. This also led to disagreements and splits between countries.
By the 1960s, one-third of the world had overthrown capitalism and were trying to build communism. Most of these countries followed the model of the Soviet Union. Some followed the model of China. The other two-thirds of the world still lived in capitalism, and this led to a worldwide divide between capitalist countries and communist countries. This was called the "Cold War" because it was not fought with weapons or armies, but competing ideas. However, this could have turned into a large war. During the 1980s, the United States and the Soviet Union were competing to have the biggest army and having the most dangerous weapons. This was called the "Arms Race". President Ronald Reagan called communist countries like the Soviet Union the "Evil Empire" because he did not agree with communist ideas.
Since 1989, when the Berlin Wall was torn down, most countries that used to be communist have returned to capitalism. Communism now has much less influence around the world. In 1991, the Soviet Union broke up. However, around a fifth of the world's people still live in states controlled by a communist party. Most of these people are in China. The other countries include Cuba, Vietnam, Laos, and North Korea. There are also communist movements in Latin America and South Africa.
Many people have written their own ideas about communism. Vladimir Lenin of Russia thought that there had to be a group of hard-working revolutionaries (called a vanguard) to lead a socialist revolution worldwide and create a communist society everywhere. Leon Trotsky, also from Russia, argued that socialism had to be international, and it was not important to make it happen first in Russia. He also did not like Joseph Stalin, who became the leader of the USSR after Lenin's death in 1924. Trotsky was made to leave the Soviet Union by Stalin in 1928, and then killed in 1940. This scared many people, and lots of communists argued about whether this was right and whose ideas should be followed.
Mao Zedong of China thought that other classes would be important to the revolution in China and other developing countries because the working classes in these countries were small. Mao's ideas on communism are usually called Maoism or Mao Zedong Thought. After Stalin's death in 1953, Mao saw himself as the leader of worldwide communism until he died in 1976. Today the Chinese government is still ruled by the Communist Party, but they actually have what is called a mixed economy. They have borrowed many things from capitalism. The government in China today does not follow Maoism. However, few revolutionaries in other countries like India and Nepal still like his ideas and are trying to use them in their own countries.