Logic is significant because it is the foundation of reason and well constructed-arguments

Review Deduction

a reasoning process that involves drawing a specific conclusion from a general statement or premise

Deduction is significant because it is a formal reasoning process that allows people to arrive at logical conclusion

Review Induction A reasoning process that involves drawing a general conclusion from specific observations.

Induction is significant because it enables people to arrive at conclusions based on their best evidence

Review The three laws of thought Developed by Aristotle, law of non contradiction, law of the excluded middle, the law of identity.

Significant because they provide the underlying structure of logic

Review Logical Consistency Statements that do not contradict each other

Significant because it is a necessary element of correct reasoning and sound judgement.

Review Logical Contradiction Statements that contradict each other or violate Aristotle’s law of non-contradiction

Significant because it helps people recognize arguments that are not sound or not reliable

Review Syllogism A form of formal deductive argument that consists of premises that lead to a conclusion

Significant because they establish a structure that can be used to test the soundness of an argument

Review Validity The correctness of the reasoning in deductive arguments.

Provides criteria for evaluating the logic of arguments

Types of Syllogisms Syllogisms are often categorized into three categories: Categorical Disjunctive Hypothetical Syllogisms can also be expressed by using letters (all A are B)

Types of Syllogisms Categorical Syllogism Aristotle was the first to use categorical syllogisms which states that things belong-or do not belong- in categories

In categorical syllogisms there is a major premise, minor premise, and a conclusion

Types of Syllogisms Categorical Syllogism All categorical syllogisms include

A middle term that appears in the major and minor premises A Predicate term that appears in the major premise and the conclusion A subject term that appears in the minor premise and the conclusion

Types of Syllogisms Categorical Syllogism All humans are mortals

Socrates is a human

Therefore, Socrates is mortal

Types of Syllogisms Categorical Syllogism All humans are mortals Socrates is a human Therefore, Socrates is mortal In letters:

All A are B C is an A Therefore, C is a B

Types of Syllogisms Categorical Syllogism All humans are mortals Socrates is a human Therefore, Socrates is mortal

Types of Syllogisms Categorical Syllogism All humans are mortals Socrates is a human Therefore, Socrates is mortal

Types of Syllogisms Categorical Syllogism All humans are mortals Socrates is a human Therefore, Socrates is mortal

Types of Syllogisms Categorical Syllogism All humans are mortals Socrates is a human Therefore, Socrates is mortal

Types of Syllogisms Categorical Syllogism All cats are pigs

Garfield is a cat

Therefore, Garfield is a pig

Types of Syllogisms Categorical Syllogism All cats are pigs Garfield is a cat Therefore, Garfield is a pig Is there anything wrong with this argument? Is it logical and sound?

Types of Syllogisms Categorical Syllogism All cats are pigs Garfield is a cat Therefore, Garfield is a pig

If either one of the premises are false the argument can’t be sound, even though it may be valid

Categorical Syllogisms Testing Validity How do we know if a categorical syllogism is valid or invalid?

Logicians have governed rules to test the validity of an argument

Categorical Syllogisms Testing Validity 1. Two negative propositions can never result in a positive conclusion

a negative proposition says that something does not belong in a class of things.

As a result the conclusion cannot go on to say that something does belong in a class

Categorical Syllogisms Testing Validity 1. Two negative propositions can never result in a positive conclusion

No cats are fashion designers No dogs are cats Therefore, dogs are fashion designers

Categorical Syllogisms Testing Validity 2. When one of the premises expresses a negative, the conclusion must also be a negative.

No cars are toys Toys are things you play with Therefore, cars are things you play with

Categorical Syllogisms Testing Validity No cars are toys Toys are things you play with Therefore, cars are things you play with

The idea of playing with cars may be appealing, but the syllogism is invalid because it draws a positive conclusion when one of the premises expresses a negative proposition.

Categorical Syllogisms Testing Validity 3. No conclusion can be drawn from two particular propositions

John is a student Some students are members of the school swim team Therefore, John is a member of the school swim team

Categorical Syllogisms Testing Validity All correct syllogisms can be shown in a Venn diagram All teachers are educators Nahla is a teacher Therefore, Nahla is an educator

Categorical Syllogisms Testing Validity All correct syllogisms can be shown in a Venn diagram

Teachers

Nahla

Educators

Disjunctive Syllogisms Open with either-or statements

In logic, the word “disjunctive” means involving a choice

A disjunctive syllogism, therefore, expresses a choice

Disjunctive Syllogisms It states that either one thing or another is true and leaves in the possibility that both could be true

When logicians do not want to mean both, they specifically say, “either, but not both”

Disjunctive Syllogisms Either Tom or Sasha (not both) is a baseball fan (Either A or B is C) Tom is not a baseball fan (A is not a C) Therefore, Sasha is a baseball fan (Therefore, B is a C)

Disjunctive Syllogisms (MP) Either Tom or Sasha (or both) is a baseball fan (MP) Tom is not a baseball fan (CON) Therefore, Sasha is a baseball fan

The major premise states that one of two things is the case The use of the word “or” includes the idea “or both”. It is understood that or both is included.

Disjunctive Syllogisms (MP) Either Tom or Sasha (or both) is a baseball fan (MIP) Tom is not a baseball fan (CON) Therefore, Sasha is a baseball fan

The minor premise of this syllogism denies one of the alternatives The conclusion then accepts the other alternative.

Disjunctive Syllogisms (MP) Either Tom or Sasha (or both) is a baseball fan (MIP) Tom is not a baseball fan (CON) Therefore, Sasha is a baseball fan

This is a valid form of the argument. Compare it to the following example:

Disjunctive Syllogisms Either Tom or Sasha (or both) is a baseball fan (MIP) Sasha is a baseball fan (CON) Therefore, Tom is not a baseball fan

Is this valid? NO…..The word or in the first statement includes the idea “or both”. Just because Sasha is a baseball fan, it does not follow that Tim is NOT a baseball fan. Both could be fans as the premise stated

Disjunctive Syllogisms Either Tom or Sasha (or both) is a baseball fan (MIP) Sasha is a baseball fan (CON) Therefore, Tom is not a baseball fan

Only one rule governs disjunctive syllogisms:

To be valid, the premises must contain a denial of one alternative, and the conclusion must affirm the other

Hypothetical Syllogisms Easy to spot because they usually contain if-then statements

At least one of the premises must be a hypothesis, which begins with the word “if”

EX…

Hypothetical Syllogisms If you water the garden, the tomato plants will grow If the plants grow, you will then have tomatoes to eat Therefore, if you water the garden, then you will have some tomatoes to eat If A, then B If B, then C Therefore If A then C

Hypothetical Syllogisms If you water the garden, the tomato plants will grow If the plants grow, you will then have tomatoes to eat Therefore, if you water the garden, then you will have some tomatoes to eat This argument is: Valid? Sound?

Hypothetical Syllogism What happens if hypothetical propositions do not express a true cause-and-effect relationship? If you buy that shirt, you will get a date If you get a date, you will be married in one year

Therefore, if you buy that shirt, you will be married within one year Valid? Sond?