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# Truth-Functional Logic and Logical Atomism

## What is truth-functional logic?

Truth functional logic preserves logical truth by substituting terms according to the rules of logic. The truth or falsity of a statement can be calculated according to the truth of its parts. For example, if A or not-A (the law of non-contradiction) is a rule, then if A is true, not-A must be false; if A is false, then not-A must be true. Compound sentences are true or false depending only on whether their components are true or false. For example, the sentence "It is raining and cold" is true if "It is raining" is true and "It is cold" is true.

Truth functional logic is typically applied according to tables that indicate the truth values of sentences that contain clauses linked by the connectives "if," "and," "not," "if-then," and "if and only if." The truth or falsity of the whole sentence depends on the truth or falsity of its components, according to the rules of logic that apply to each of the connectives.

## What was logical atomism?

The main claim of logical atomists was that the world is made up of logical facts. These logical facts are like atoms because they can't be divided into smaller facts. Single logical facts can be combined by truth-functional logic into molecular facts.

To apply the theory of logical atomism to more complex statements, such as the claims of science, the method of logical construction was posited. In logical construction, any "S' represents a logical construction of "Ps" if statements about S can be reduced to atomic statements about Ps. For example, a salad is a logical construction of its ingredients, and perceptions of ordinary objects are logical constructions of sense data. Bertrand Russell (1872-1970) and Ludwig Wittgenstein (1889-1951) were the main proponents of this perspective.

## What was the influence of logical atomism?

As a philosophical doctrine, logical atomism was surpassed by logical positivism. However, its main rhetorical force did demolish what Bertrand Russell (1872-1970) termed "logical holism," or the notion that the world is a whole, no part of which can be known independently of all others. Logical holism was the epistemological doctrine associated with absolute idealism.

## Bertrand Russell

##### Who was Bertrand Russell?

Arthur William Bertrand Third Earl Russell (1872-1970), who was known to his friends as "Bertie," is hailed as the founder of analytic philosophy, along with G.E. Moore (1873-1958) and Ludwig Wittgenstein(1889-1951). He studied and lectured at Cambridge University, losing his position there between 1916 and 1944 because of his pacifist views and activism. He won the Nobel Prize in 1950. His writings on philosophical, political, scientific, and social reform topics are all in beautifully executed prose, which he was said to have been able to compose from the first draft.

Russell is now best known for his failed attempt with Alfred North Whitehead (1861-1947) to reduce mathematics to logic, his theory of descriptions, his theory of types, and his ruling doctrine that the work of philosophy is to analyze propositions (the meanings of sentences) and that the only propositions worthy of such analysis must have "constituents" with which we are acquainted (have direct knowledge of).

Russell was one of the most productive philosophical authors of all time. He published hundreds of articles and essays and scores of books. Among the most noteworthy are "On Denoting," Mind (Vol. 14, 1905); Philosophical Essays (1910); The Problems of Philosophy (1912); Principia Mathematica, with Alfred North Whitehead, three volumes (1910-1913); Why I am Not a Christian (1927); A History of Western Philosophy and Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day (1946); and The Autobiography of Bertrand Russell (1967-1969).

His pacifist activities won Bertrand Russell a Nobel Prize, while as a philosopher he was the most productive author of his day, publishing scores of books (AP).

##### What was Bertrand Russell's theory of knowledge?

Russell distinguished between two kinds of knowledge. Knowledge by acquaintance was direct knowledge of "sense data," mental states, thoughts, and feeling. More indirect "knowledge by description" was ultimately based on knowledge by acquaintance. For example, I have knowledge by acquaintance of this page as I am typing it into my computer, but knowledge by description of Burma, where I have never been.

##### What was Bertrand Russell's theory of definite descriptions?

Russell gave an account of how it is possible to talk meaningfully about things that do not exist. According to his theory of definite descriptions, what a proposition of the form "X is Q" means is: "There is exactly one thing that is X and that one thing is Q," or, "At least one thing is X and no more than one thing is X and whatever is X is Q."

Russell's theory makes it possible to distinguish between the contradiction of "X is Q" and "X is not-Q." To use Russell's example: (A) "The King of France is bald" has as its contradictory, (A') "There is no King of France, or there is more than one King of France, or there is one King of France who is not bald." But, (B) "The King of France is not-bald" means, according to Russell's theory, (B') "There is one King of France, no more and no less, and he is not bald." And, A' and B' do not have the same meaning.

##### What is Bertrand Russell's theory of types?

Russell began with a puzzle inspired by the German philosopher Gottlob Frege's (1848-1925) attempt to reduce mathematics to logic: Is the class of all classes that are

Did Russell have a humorous side?

Although he suffered from depression on and off throughout his life, this did not suppress Russell's wit, as the following quotes show:

"The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts."

"I would never die for my beliefs because I might be wrong."

"It has been said that man is a rational animal. All my life I have been searching for evidence which could support this."

"Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths."

not members of themselves, or C, itself a member of itself? This question seems valid, but Russell showed that it leads to contradictions: If C is a member of itself then it should not be in D, which is the class of classes that are not members of themselves, but if C is a member of itself, it will be in D. But if C is not a member of itself, then it should be in D, and C is a member of itself. Russell's answer was that there is a hierarchy of types of things that restricts what can be said about them. So we can say that Russell is an analytic philosopher, but not that a group of people are an analytic philosopher.

##### What did Bertrand Russell think about his use of logic?

Russell believed that logic could be used to solve both philosophical problems and everyday ones, if propositions were translated into the correct logical form. To accomplish this, he held the ideal of a "logically correct" language. For a while he thought that his student Ludwig Wittgenstein (1889-1951) was on the right path toward supplying that. But Wittgenstein only alluded to such a language in his early work and abandoned the project later on.

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