# The Basics of Inductive vs. Deductive Reasoning

Here are a few definitions that may come in handy when considering inductive vs. deductive reasoning:

Reasoning: the process of drawing conclusions or inferences from facts or premises.

Problem Solving and Critical Thinking in regards to inductive vs. deductive reasoning

Problem Solving

Logic and reasoning are terms associated with the phrases problem solving and critical thinking. The first step in solving any problem is to define the problem in a thorough and accurate manner.

Always ask yourself, “What am I being asked to do?” Once you define the problem, all known information relative to the problem must be gathered, organized, and analyzed.

Before using any method of solution, determine if its use is valid for the situation at hand. If a past method of solution is apparent, use it. If not, explore standard options or develop creative alternatives. Applying a general rule to solve a particular problem is an example of deductive reasoning.

Deductive Reasoning

Deductive reasoning is a method for solving problems of logic and employs premises, syllogisms, and conclusions.

Deductive Reasoning: go from general case to specific case.

Premises: minor or major propositions or assertions that serve as the bases for an argument

Syllogism: an argument composed of two statements or premises followed by a conclusion.

Conclusion: the last step in a reasoning process.

An argument is the reason or reasons offered for or against something. The two statements, or premises (a major and minor premise) support the conclusion. If the conclusion is guaranteed (inescapable in all circumstances) the argument is considered valid. If not guaranteed, the argument is considered invalid.

Argument: the reason or reasons offered for or against something.

Valid Argument: the conclusion is guaranteed (inescapable in all instances).

Invalid Argument: the conclusion is not guaranteed.

Inescapable = valid = logical, always true

Not inescapable = invalid

Example of a valid argument

1. All men are mortal.

2. Socrates is a man.

Therefore, Socrates is mortal.

Example of an invalid argument

1. All men are mortal.

2. Socrates is mortal.

Therefore, Socrates is a man.

Inductive Reasoning: (go from several specific cases to the general case)

Example:

1. I did not win the lottery two weeks ago.

2. I did not win the lottery last week.

Therefore I will not win the lottery this week.

Reasoning of this type is called inductive reasoning. Although it may seem to follow and may in fact be true, the conclusions in an inductive argument are never guaranteed.

Using Venn Diagrams when working with inductive vs. deductive reasoning: Definition and Applications

Saying that an argument is valid does not mean that the conclusion is true.

An argument is valid if its conclusion is inescapable given the premises.

The validity of a deductive argument can be shown by the use of a Venn diagram.

A Venn diagram is a diagram consisting of various overlapping figures contained within a rectangle (called the “universe”).

VENN DIAGRAMS:

1. To depict a statement of the form “All A are B” we draw two circles, one within the other. The outer circle represents A, the inner circle represents B.

2. To depict “No A are B” we draw two separate circles; one for A and one for B.

3. To depict “Some A are B” we draw two overlapping circles; one depicting A and the other depicting B. The overlapping region represents both A and B.

4. In all three preceding examples, the area outside of the circles represent every premise that is neither A or B.

Therefore, the area inside the rectangle represents every possible premise or the universe.

Inductive vs. Deductive Reasoning: Venn Diagrams and Invalid Arguments

To show that an argument is invalid, you must construct a Venn diagram in which the premises are met yet the conclusion does not necessarily follow.

Example:

1. Some plants are poisonous.

2. Broccoli is a plant

Therefore, broccoli is poisonous

Saying that an argument is valid does not mean the conclusion is true.

Example:

1. All doctors are men.

2. My mother is a doctor

Therefore, my mother is a man.

Thus, if the premises are wrong, the argument may be valid but the conclusion may not be true. Logic: the science of correct thinking.

Reasoning: the process of drawing conclusions or inferences from facts or premises.

Problem Solving and Critical Thinking in regards to inductive vs. deductive reasoning

Problem Solving

Logic and reasoning are terms associated with the phrases problem solving and critical thinking. The first step in solving any problem is to define the problem in a thorough and accurate manner.

Always ask yourself, “What am I being asked to do?” Once you define the problem, all known information relative to the problem must be gathered, organized, and analyzed.

Before using any method of solution, determine if its use is valid for the situation at hand. If a past method of solution is apparent, use it. If not, explore standard options or develop creative alternatives. Applying a general rule to solve a particular problem is an example of deductive reasoning.

Deductive Reasoning

Deductive reasoning is a method for solving problems of logic and employs premises, syllogisms, and conclusions.

Deductive Reasoning: go from general case to specific case.

Premises: minor or major propositions or assertions that serve as the bases for an argument

Syllogism: an argument composed of two statements or premises followed by a conclusion.

Conclusion: the last step in a reasoning process.

An argument is the reason or reasons offered for or against something. The two statements, or premises (a major and minor premise) support the conclusion. If the conclusion is guaranteed (inescapable in all circumstances) the argument is considered valid. If not guaranteed, the argument is considered invalid.

Argument: the reason or reasons offered for or against something.

Valid Argument: the conclusion is guaranteed (inescapable in all instances).

Invalid Argument: the conclusion is not guaranteed.

Inescapable = valid = logical, always true

Not inescapable = invalid

Example of a valid argument

1. All men are mortal.

2. Socrates is a man.

Therefore, Socrates is mortal.

Example of an invalid argument

1. All men are mortal.

2. Socrates is mortal.

Therefore, Socrates is a man.

Inductive Reasoning: (go from several specific cases to the general case)

Example:

1. I did not win the lottery two weeks ago.

2. I did not win the lottery last week.

Therefore I will not win the lottery this week.

Reasoning of this type is called inductive reasoning. Although it may seem to follow and may in fact be true, the conclusions in an inductive argument are never guaranteed.

Using Venn Diagrams when working with inductive vs. deductive reasoning: Definition and Applications

Saying that an argument is valid does not mean that the conclusion is true.

An argument is valid if its conclusion is inescapable given the premises.

The validity of a deductive argument can be shown by the use of a Venn diagram.

A Venn diagram is a diagram consisting of various overlapping figures contained within a rectangle (called the “universe”).

VENN DIAGRAMS:

1. To depict a statement of the form “All A are B” we draw two circles, one within the other. The outer circle represents A, the inner circle represents B.

2. To depict “No A are B” we draw two separate circles; one for A and one for B.

3. To depict “Some A are B” we draw two overlapping circles; one depicting A and the other depicting B. The overlapping region represents both A and B.

4. In all three preceding examples, the area outside of the circles represent every premise that is neither A or B.

Therefore, the area inside the rectangle represents every possible premise or the universe.

Inductive vs. Deductive Reasoning: Venn Diagrams and Invalid Arguments

To show that an argument is invalid, you must construct a Venn diagram in which the premises are met yet the conclusion does not necessarily follow.

Example:

1. Some plants are poisonous.

2. Broccoli is a plant

Therefore, broccoli is poisonous

Saying that an argument is valid does not mean the conclusion is true.

Example:

1. All doctors are men.

2. My mother is a doctor

Therefore, my mother is a man.

Thus, if the premises are wrong, the argument may be valid but the conclusion may not be true. Logic: the science of correct thinking.