Logical Reasoning

An Introduction to Logic

And Fallacious Reasoning

Definitions Related to Logic

• Logic - means correct reasoning. A logical text supports statements with reasons and evidence. A text is illogical when it does not provide reasons backed by evidence (facts and examples).

• Coherence - means “to stick together”. Reasoning is coherent (or has coherence) when ideas stick together because they are arranged in an order that makes sense to the reader. The reasons or evidence must have a connection; they can’t just jump around.

Types of Reasoning

• Deductive Reasoning – A process of reasoning from known facts to conclusions. Sometimes it can be thought of as starting from a general statement that is accepted as true to a specific statement that is “therefore” true.

• Inductive Reasoning – A process of reasoning that moves from making observations to forming conclusions. It can also be thought of as starting from specific examples and moving toward a general statement. This is also called inference.

• Fallacious Reasoning - false thinking or mistakes in logic. Fallacious reasoning leads to incorrect conclusions.

Deductive Reasoning

• Deductive Reasoning – A process of reasoning from known facts to conclusions, or from a general statement that is accepted as true to a specific statement that is “therefore” true.

• Deductive arguments often start with a categorical claim, which is simply a statement that states a relationship between two categories or events. Examples of categorical claims:

– All cats are mammals. – No cats are reptiles– Some cats are long-haired mammals– Some cats are not long-haired mammals

• You may see other words like never, sometimes, always, etc. Categorical claims are important to be analyzed to determine if they are true, and to see if they support a conclusion.

Theory of Syllogism Argument (Syllogism) – Example 1

All “x” has the characteristic of “y”.

A standard baseball game has 9 innings.

This thing is an “x”. We watched a standard baseball game.

Therefore, this “x” has the characteristic of a “y”.

Therefore, that game had 9 innings.

• Deductive Reasoning often uses a 3-step argument called syllogism, introduced by the Greek philosopher Aristotle.

• This 3-step process was the beginning of modern formal logic, or logical thinking.

Examples of Deductive Reasoning

• More examples of deductive reasoning using syllogism:

• How would you change Example 2 to have a more standard categorical claim?

Argument (Syllogism) – Example 2

Argument (Syllogism) – Example 3

The last day to register for the Disney trip is June 15.

All people are mortal.

Joe missed the registration date. Jim Carey is a person.

Therefore, Joe will not be able to register for the trip.

Therefore, Jim Carey is mortal.

Inductive Reasoning

• A process of reasoning that moves from making observations to conclusions. This is also called inference.

• Inductive reasoning can also be thought of as theory building.

• Successful inductive reasoning depends on the quality of your observations, or evidence.

• If the quality of the observations are not good enough, or if not enough observations have been made, inductive reasoning may not be as dependable as deductive reasoning.

Inductive Reasoning – Example 1

Inductive Reasoning – Example 2

Tonya is seen walking from her car to her home with a set of golf clubs.

Every swan that my family and I have ever seen is white.

Tonya’s husband Jeff loves golf and tomorrow is his birthday.

This swan is also white.

(Inference)Tonya has bought Jeff a set of golf clubs.

(Inference)All swans are white. (are they?)

• While Example 2 below is not “cohesive”, inductive reasoning is not useless. It is the basis of scientific discovery and investigation, when used correctly.

Examples of Inductive Reasoning

We Need Both Inductive and Deductive Reasoning

• In scientific discovery and in life, we use both types of reasoning.

• For example, we can use inductive reasoning to attempt to make enough observations to come up with a theory or conclusion.

• Next, we can switch back to deductive reasoning using our conclusion or theory (which is general).

• Note that sometimes it is not possible to prove something is always true, so the best we can have is a theory.

Example of Using Both Types of Reasoning

Example Using Both Types of Reasoning

A crime scene investigator gathers evidence, including fingerprints or DNA. (Inductive)

It is known that fingerprints or DNA uniquely identify a person. (Deductive)

Therefore, we know that the particular person was at the crime scene. (Conclusion, based on both inductive and deductive reasoning)

Fallacious Reasoning

• Fallacious Reasoning means false thinking or mistakes in logic.

• May be based on: mistakes in logic or incomplete information.

• Fallacious reasoning leads to false conclusions.

• Inductive reasoning is where we sometimes see examples of fallacious reasoning (black swan).

Examples of Fallacious Reasoning

Type and Definition Examples

Hasty Generalization – Conclusions made from weak or insufficient evidence

“Your friend said the concert you’re attending would have extra security. Obviously, this will be the safest concert your city has ever had.”

Stereotyping – Believing that all members of a group share a certain characteristic

“All concerts are unsafe.”

More Examples of Fallacious Reasoning

Type and Definition Examples

Personal Attack (Name Calling, or Ad Hominem) – Attacking the person making the argument, rather than the argument itself.

“Your parents don’t want you to go to the concert. They obviously don’t know anything about anything.“

False Dilemma (Either/Or) –

The assumption that a problem or situation has only one possible cause or resolution when there may be several.

“If your parents don’t let you go to the concert, then they don’t trust you.”

Yet More Examples of Fallacious Reasoning

Type and Definition Examples

False Analogy – Relying only on comparisons to prove a point rather than arguing deductively and inductively

“Education is like cake; a small amount tastes sweet, but eat too much and your teeth will rot out. Likewise, more than two years of education is bad for a student.”

Appeal to Fear –

Using a claim that is intended to produce fear instead of being actual evidence to support the claim.

“You know, Professor Smith, I really need to get an A in this class. I'd like to stop by later to discuss my grade. I'll be in your building anyways, visiting my

father. He's your dean, by the way."

Logical Arguments

• A logical argument is a group of statements, called premises, that are claimed to provide support for, or are reasons to believe, a conclusion.

• Note that these statements or premises can be either true or false.

• To reach a logical conclusion, all premises or statements leading up to the conclusion must support it.

• Some premises may be categorical claims, such as those presented earlier.

Examples of Arguments

• Argument 1:(Premise) Isaac can fix anything electric.(Premise) The electric switch in my lamp is broken.(Conclusion)Isaac can fix my lamp.

• What type of reasoning is this?

Logic Problems

Argument 2:

• Lars needs a notebook for some of his classes. Lars has three notebooks.Conclusion: Lars is in three classes.

• What type of reasoning is this?

Logic Problems

Argument 3:• (Premise) I have 5 dogs for pets.

(Premise) Three of them learned to lie down and roll over.(Premise)Three of my dogs were Scotties and two were Collies.Conclusion: My collies never learned to lie down and roll over.

• What type of reasoning is this?

Logic Problems – Cont’d

Argument 4:• (Premise)None of Barry’s sisters can do a

back dive. (This is a categorical claim)

• (Premise) Lisa can do a back diveConclusion: Lisa is not Barry’s sister.

• What type of reasoning is this?

Logic Problems, Cont’d

Argument 5:• Sometimes Joanna rides her bike when

she goes to the store. (Categorical claim)I saw Joanne riding her bike.Conclusion: Joanne was going to the store.

• What type of reasoning is this?