In simple words, logic is “the study of correct reasoning, especially regarding making inferences.” Logic began as a philosophical term and is now used in other disciplines like math and computer science. While the definition sounds simple enough, understanding logic is a little more complex. Use logic examples to help you learn to use logic properly.
Definitions of Logic
Logic can include the act of reasoning by humans in order to form thoughts and opinions, as well as classifications and judgments. Some forms of logic can also be performed by computers and even animals.
“The study of truths based completely on the meanings of the terms they contain.”
Logic is a process for making a conclusion and a tool you can use.
- The foundation of a logical argument is its proposition, or statement.
- The proposition is either accurate (true) or not accurate (false).
- Premises are the propositions used to build the argument.
- The argument is then built on premises.
- Then an inference is made from the premises.
- Finally, a conclusion is drawn.
Definition of Logic in Philosophy
Logic is a branch of philosophy. There are different schools of thought on logic in philosophy, but the typical version is called classical elementary logic or classical first-order logic. In this discipline, philosophers try to distinguish good reasoning from bad reasoning.
Definition of Logic in Mathematics
Logic is also an area of mathematics. Mathematical logic uses propositional variables, which are often letters, to represent propositions.
Types of Logic With Examples
Generally speaking, there are four types of logic.
Informal Logic
Informal logic is what’s typically used in daily reasoning. This is the reasoning and arguments you make in your personal exchanges with others.
Premises: Nikki saw a black cat on her way to work. At work, Nikki got fired.
Conclusion: Black cats are bad luck.
Explanation: This is a big generalization and can’t be verified.
Premises: There is no evidence that penicillin is bad for you. I use penicillin without any problems.
Conclusion: Penicillin is safe for everyone.
Explanation: The personal experience here or lack of knowledge isn’t verifiable.
Premises: My mom is a celebrity. I live with my mom.
Conclusion: I am a celebrity.
Explanation: There is more to proving fame that assuming it will rub off.
Formal Logic
In formal logic, you use deductive reasoning and the premises must be true. You follow the premises to reach a formal conclusion.
Premises: Every person who lives in Quebec lives in Canada. Everyone in Canada lives in North America.
Conclusion: Every person who lives in Quebec lives in North America.
Explanation: Only true facts are presented here.
Premises: All spiders have eight legs. Black Widows are a type of spider.
Conclusion: Black Widows have eight legs.
Explanation: This argument isn’t controversial.
Premises: Bicycles have two wheels. Jan is riding a bicycle.
Conclusion: Jan is riding on two wheels.
Explanation: The premises are true and so is the conclusion.
Symbolic Logic
Symbolic logic deals with how symbols relate to each other. It assigns symbols to verbal reasoning in order to be able to check the veracity of the statements through a mathematical process. You typically see this type of logic used in calculus.
Symbolic logic example:
- Propositions: If all mammals feed their babies milk from the mother (A). If all cats feed their babies mother’s milk (B). All cats are mammals(C). The Ʌ means “and,” and the ⇒ symbol means “implies.”
- Conclusion: A Ʌ B ⇒ C
- Explanation: Proposition A and proposition B lead to the conclusion, C. If all mammals feed their babies milk from the mother and all cats feed their babies mother’s milk, it implies all cats are mammals.
Mathematical Logic
In mathematical logic, you apply formal logic to math. This type of logic is part of the basis for the logic used in computer sciences. Mathematical logic and symbolic logic are often used interchangeably.
Types of Reasoning With Examples
Each type of logic could include deductive reasoning, inductive reasoning, or both.
Deductive Reasoning Examples
Deductive reasoning provides complete evidence of the truth of its conclusion. It uses a specific and accurate premise that leads to a specific and accurate conclusion. With correct premises, the conclusion to this type of argument is verifiable and correct.
Premises: All squares are rectangles. All rectangles have four sides.
Conclusion: All squares have four sides.
Premises: All people are mortal. You are a person.
Conclusion: You are mortal.
Premises: All trees have trunks. An oak tree is a tree.
Conclusion: The oak tree has a trunk.
Inductive Logic Examples
Inductive reasoning is "bottom up," meaning that it takes specific information and makes a broad generalization that is considered probable, allowing for the fact that the conclusion may not be accurate. This type of reasoning usually involves a rule being established based on a series of repeated experiences.
Premises: An umbrella prevents you from getting wet in the rain. Ashley took her umbrella, and she did not get wet.
Conclusion: In this case, you could use inductive reasoning to offer an opinion that it was probably raining.
Explanation: Your conclusion, however, would not necessarily be accurate because Ashley would have remained dry whether it rained and she had an umbrella, or it didn't rain at all.
Premises: Every three-year-old you see at the park each afternoon spends most of their time crying and screaming.
Conclusion: All three-year-olds must spend their afternoon screaming.
Explanation: This would not necessarily be correct, because you haven’t seen every three-year-old in the world during the afternoon to verify it.
Premises: Twelve out of the 20 houses on the block burned down. Each fire was caused by faulty wiring.
Conclusion: If more than half the homes have faulty wiring, all homes on the block have faulty wiring.
Explanation: You do not know this conclusion to be verifiably true, but it is probable.
Premises: Red lights prevent accidents. Mike did not have an accident while driving today.
Conclusion: Mike must have stopped at a red light.
Explanation: Mike might not have encountered any traffic signals at all. Therefore, he might have been able to avoid accidents even without stopping at a red light.
Follow the Logic
As these examples show, you can use logic to solve problems and to draw conclusions. Sometimes those conclusions are correct conclusions, and sometimes they are inaccurate. When you use deductive reasoning, you arrive at correct logical arguments while inductive reasoning may or may not provide you with a correct outcome. Check out examples of logical fallacies to see what incorrect logical reasoning looks like.