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What is Logic? - Definition & Examples

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  • 0:01 What Is Logic?
  • 0:31 Informal Logic
  • 4:05 Formal Logic
  • 4:57 Symbolic Logic
  • 5:51 Mathematical Logic
  • 6:28 Lesson Summary
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Lesson Transcript
Instructor: Lauren Fonseca
In this lesson, we will discuss what logic is and how it is used to formulate and evaluate arguments. We will look at the flaws in reasoning and how to avoid false conclusions. We will cover informal logic, formal logic, symbolic logic, and mathematical logic.

What is Logic?

We all know in varying degrees about Mr. Spock from Star Trek. His Vulcan ancestry requires him to think logically. Logic is a tool to develop reasonable conclusions based on a given set of data. Logic is free of emotion and deals very specifically with information in its purest form.

There are many subsets in the study of logic including informal logic, formal logic, symbolic logic, and mathematical logic. We will discuss each type of logic and when it is appropriately used.

Informal Logic

Informal logic is the mode used in everyday reasoning and argument analysis. Informal logic consists of two types of reasoning: deductive and inductive.

Deductive Reasoning

One type of logical reasoning is deductive. Deductive reasoning uses information from a large set and applies that information to any member of that set.

For example:

  • All English professors are boring (major evidence or premise)
  • Lauren is an English professor (minor evidence or premise)
    • Therefore, Lauren is boring (conclusion)

The major premise makes a statement concerning members of a profession. The minor premise identifies a member of that profession. The conclusion declares that since Lauren is a member of a profession, then she must have the characteristics attributed to the profession as a whole.

Inductive Reasoning

Another type of logical reasoning is inductive. Inductive reasoning uses specific data to form a larger, generalized conclusion. It is considered the opposite of deductive reasoning.

For example:

  • Yesterday, you left for work at 7:15 a.m. and arrived at work on time.
  • Today, you left for work at 7:15 a.m. and arrived at work on time.
    • Therefore, if you leave at 7:15 a.m., you will always arrive at work on time.

In this example, we have a small set of data (two days of arriving on time), and we have concluded that this will always be the case.

Problems

You may have noticed some problems with these examples. All English professors are certainly not boring and traffic patterns are not always the same (especially if you have to drive past a major shopping area at Christmas time to get to work).

Deductive reasoning only works when both major and minor premises are true. Using words like 'all' will generally falsify your statement (only one example of the contrary is needed). However, if you use words like 'many' or 'some,' it is less likely that your premises will be rejected. So, when using this type of reasoning, make sure your premises are verifiable.

Inductive reasoning requires lots of data. The more data you present, the easier it is for your reader to make the necessary leap to your conclusion. The more data, the shorter the leap. Two data points regarding driving time are not enough. Those days happened to be sunny and clear. There were no school buses. There were no accidents.

Logical Fallacies

Logical fallacies are incorrectly reasoned facts. There are many logical fallacies, but the more popular ones are as follows:

Ad Hominem: The literal translation of this term is 'to the person.' This is when we attack people instead of attacking the argument. Instead of saying that you are stupid for believing that if you leave for work every day at the same time you will arrive on time, your lack of data should be attacked.

Stereotyping: We use stereotypes all of the time, sometimes without even knowing it. Stating that all English Professors are boring is a stereotype.

Faulty Sampling: Our argument concerning arriving on time for work uses a faulty sample. We have only two data points that are not representative of the whole. (Both days were sunny, you didn't have to shovel your car out of the snow.)

False Dilemma: Oftentimes we oversimplify. A false dilemma implies that there are only two options. For example, the statement 'You are either with us or against us' is a false dilemma. The third option is indifference.

Post Hoc/Ergo Propter Hoc: The Latin translation is 'It happened before this, therefore it happened because of this.' Statements like, 'Every time I wash my car, it rains,' is committing the post hoc fallacy.

Formal Logic

Formal logic deals with deductive reasoning and the validity of the inferences produced. For an argument to work, the conclusion must logically follow the premises and the premises must be true. For example:

  • Every cat is a mammal.
  • Some carnivores are cats.
    • Therefore, some carnivores are mammals.

or

  • Every college professor must have at least a master's degree.
  • Some of my friends are college professors.
    • Therefore, some of my friends have at least a master's degree.

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