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Logical Reasoning

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Logical Reasoning An Introduction to Logic And Fallacious Reasoning Definitions Related to Logic Logic - means correct reasoning. A logical text supports statements ... – PowerPoint PPT presentation

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Title: 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?
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