Logical Reasoning

1
Logical Reasoning

• An Introduction to Logic
• And Fallacious Reasoning

2
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 cant just
  jump around.

3
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.

4
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.

5

• 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.

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.
6
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.
7
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.

8
Examples of Inductive Reasoning

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

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.
Tonyas 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?)
9
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.

10
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)
11
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).

12
Examples of Fallacious Reasoning
Type and Definition Examples
Hasty Generalization Conclusions made from weak or insufficient evidence Your friend said the concert youre 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.
13
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 dont want you to go to the concert. They obviously dont 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 dont let you go to the concert, then they dont trust you.
14
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."
15
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.

16
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?

17
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?

18
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?

19
Logic Problems Contd

• Argument 4
• (Premise)None of Barrys sisters can do a back
  dive. (This is a categorical claim)
• (Premise) Lisa can do a back diveConclusion
  Lisa is not Barrys sister.
• What type of reasoning is this?

20
Logic Problems, Contd

• 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?