Logic and Reasoning

Panther Prep North Central High School

Logical Proof

Logical reasoning is the easiest way to convince because the information is presented as fact.

However, not all information is common sense to the audience so the speaker has to connect the dots.

To do this, the speaker can use: – Deductive reasoning – Inductive reasoning

Introduction

Logic

– the study of reasoning – allows us to test the truth or falsity of inferences and reasoning – used in problem solving

Inference

…reaching a conclusion on the basis of evidence and reasoning – the creation of new ideas or information from existing ideas or information – the process of creating new statements from other statements • • these statements are called

Propositions Propositional Logic —

the logic of propositions the validity of propositions —analyzing

Induction

Inductive reasoning

– the inference of a general law from particular instances – the process of summarizing observations to derive a generalization about the world – we rarely observe all of the instances if a particular phenomena, so we can never be sure it is true in all cases —we can estimate probability

Induction

   A daisy is a flower.

A rose is a flower.

A violet is a flower.

Therefore, plants with colorful blooms are flowers.

Deduction

Deductive reasoning is a way for the speaker to draw a direct line from a general concept to the specific end of their purpose.

…the inference of particular instances by reference to a general law or principle Sherlock Holmes’ deductive reasoning techniques The format for these sets is called a

syllogism

Syllogisms

   All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

– – – The 1 st statement is the generalization or general rule called the

major premise

The 2 nd statement is an observation or specific fact called the

minor premise

The 3 rd statement is the inference that follows the first two statements called the

conclusion

Validity and Truth

The Rules of Inference tell us whether a syllogism is valid or not, but not if it is

true

.

– Validity is simply a matter of correct reasoning.

To determine if a conclusion of a valid syllogism is true, we have to agree that the premises are true.

– When a syllogism is both valid in reasoning and the premises are true, we say the conclusion is

sound.

Accuracy vs. Precision

Accuracy: proximity to target or true value Accurate, but not precise Precision: proximity to similar situations Precise, but not accurate

Fallacies

Fallacies are mistruths that are used to make a point.

Fallacies are generally used to dramatize a position, dramatize information or to compensate for the lack of supporting information.

While popularly used, they can lead to a destruction of the credibility of the speaker and therefore a destruction of the speech itself.

Types of Fallacies

Types of fallacies include: – Unwarranted or Hasty Generalization (Including information that does not apply.) – Errors in casual information • Post Hoc – Unproven cause-effect relationship • Non Sequitur – Stating a conclusion that does not necessarily follow the argument.

– Begging the Question (States as fact what needs to be proven.) – Ignoring the Question (Misdirection of attitude)

Types of Fallacies (Cont.)

Types of fallacies include: – False Analogy (A parallel that does not exist.) – Either/Or Fallacy (Stating only two options when more exist.) – Ad Hominem (Attack of character on the opposition) – Red Herring (Addition of information to confuse) – Ad Populum (Public opinion MUST be right, right?)

Identifying Fallacies

See if you can determine what, if any, fallacy is present in the following statements: – “The Ford Explorer is the most popular SUV on the market, so it must be the safest.” – “You were the only person working when the accident happened so it must be your fault.” – “If you don’t finish this paper, you will become a bum and live in a van down by the river.” – “The rate of crime is increasing in our schools because of the reduction of art and music programs.”

Identifying Fallacies (Cont.)

– “If you do not vote for the private school funding bill you simply do not care about children.” – “Stand back! I can help. My dad is a doctor.” – “Johnny is not fit to lead this project because he can’t even tie his shoes in the morning.” – “Mom, if you don’t buy me an iPhone, it means that you don’t really love me.” – “Would we not work harder if we made more money?” – “You either finish the project tonight or you will get eaten by a werewolf.”

Validity and Truth

Validity does not guarantee truth and truth does not guarantee validity.

In order to have a

sound

syllogism, the form must be

valid

and the premises must be

true.