I have briefly discussed the meaning of “logic” and various parts of logic. I am now going to discuss the most important parts of propositional logic in greater detail. This will include the following chapters:
- The meaning of propositional logic.
- Truth tables
- Truth trees
- Natural deduction
What is propositional logic?
Propositional logic is a symbolic language that lacks content, and uses letters to symbolize propositions. For example, consider the statement “the sky is red or blue.” We could replace “the sky is red” with “A” and “the sky is blue” with “B.” In that case we would end up with “A or B.”
Propositional logic is used to evaluate the validity of deductive arguments and the consistency of statements. Statements that are inconsistent are said to form “contradictions.” For example, the statement “the sky is blue” contradicts the statement “the sky is not blue.”
Propositional logic consists of logical connectives, rules of inference, and axioms. These will be discussed in more detail in later chapters. However, it is important to know what “statements” and “propositions” are, so they will be discussed in greater detail here.
What are statements?
Statements are sentences that are true or false. For example, “all mammals are animals” is a statement written in English. In this case the statement is true.
What are propositions?
Propositions consist in the meaning of statements. We could say that propositions are the “conceptual content” of statements. For example, “the sky is blue” is a statement written in English that refers to the same proposition as “le ciel est bleu,” which is a statement written in French.
Another example of two statements that refer to the same proposition is “all whales are mammals” and “if something is a whale, then it’s a mammal.”
Related: What is Logic?