A deduction in formal logic is a way of proving a proposition. It is used most often in geometry, but also has its place in philosophy and law. It is often unused in science as it requires that one have certainty of truth of both the major and minor premises--something science is unwilling to make claims about.
When a conclusion is inferred from premises or facts, it is said to "follow" from previously stated propositions via certain logical rules.
The most famous rule goes as follows:
- A is true.
- If A is true, then B is true.
- Therefore, B is true.
Another type of deduction, known as "proof by contradiction", is:
- If Q is true, then R is true.
- R is not true.
- Therefore, Q is not true.
Truth Values in Sentential Logic
T implies T, True T implies F, False F implies F, True F implies T, True
The final two are rooted in the fact that the consequent following from an antecedent that is not true says nothing about the truth or falsity of the statement, it must be assumed to be true.
Aristotle codified the rules of syllogistic deduction two millenia ago in Ancient Greece. He created 256 forms of syllogisms relating to groups of things. For example, an AAA1 syllogism:
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.