Introduction to Critical Thinking

Welcome to

Critical Thinking

Unit 3

Critical & Logical

Reasoning

ISM5001 Critical Thinking and Argumentation

Logic and Reasoning

Logic – The science of correct reasoning.

Reasoning – The drawing of inferences or conclusions from known or assumed facts.

Two basic categories of human reasoning

Deduction: reasoning from general premises, which are known or presumed to be known, to more specific, certain conclusions.

Induction: reasoning from specific cases to more general, but uncertain, conclusions.

Both deductive and inductive arguments occur frequently and naturally…both forms of reasoning can be equally compelling and persuasive, and neither form is preferred over the other (Hollihan & Baske, 1994).

Deductive Reasoning Example:

When it rains, John’s old car won’t start. It’s raining. Therefore, John’s old car won’t start. (Applies a broad generalization to a specific case.)

Inductive Reasoning Example:

John’s old car won’t start. It’s raining. Therefore, John’s old car won’t start when it’s raining. (Uses a specific case to reach a broad generalization.)

To better visualize the difference between deductive and inductive reasoning imagine each as a triangle. The deductive pyramid is upside down, while the inductive pyramid is right side up:

Broad Generalization

To specific

Deductive Reasoning

Specific generalization

To broad

Inductive Reasoning

Inductive Reasoning:When detectives arrive at the scene of a crime, the

first thing they do is look for clues that can help them piece together what happened. A broken window, for example, might suggest how a burglar entered or exited. Likewise, the fact that an intruder didn't disturb anything but a painting that hid a safe might suggest that the burglar knew exactly where the safe was hidden. And this, in turn, suggests that the burglar knew the victim.

The process described above is called inductive reasoning. It consists of making observations and then drawing conclusions based on those observations.

• Like a detective, you use inductive reasoning all the time in your daily life.

• You might notice, for example, that every time you eat a hot dog with chili and onions, you get a stomachache.

• Using inductive reasoning, you could logically conclude that the chili dogs cause indigestion, and that you should probably stop eating them.

• Similarly, you might notice that your cat tries to scratch you every time you rub her stomach.

• In both examples, what you're doing is moving from the specific—a particular observation—to the general—a larger conclusion.

• Inductive reasoning starts from observation and evidence and leads to a conclusion.

Using inductive reasoning generally involves the following questions:

1. What have you observed? What evidence is available?

2. What can you conclude from that evidence?

3. Is that conclusion logical?

In deductive reasoning, on the other hand, we start with the conclusion and then see if the evidence for that conclusion is valid. Generally, if the evidence is valid, the conclusion it supports is valid as well. In other words, deductive reasoning involves asking:

1. What is the conclusion? 2. What evidence supports it? 3. Is that evidence logical?

If you can answer yes to question 3, then the conclusion should be logical and the argument sound.

Deductive Reasoning1. All students eat pizza.

Claire is a student at ASU.Therefore, Claire eats pizza.

2. All athletes work out in the gym. Barry Bonds is an athlete. Therefore, Barry Bonds works out in the gym.

3. All math teachers are over 7 feet tall. Mr. D. is a math teacher. Therefore, Mr. D is over 7 feet tall.

Deductive Reasoning

The argument is valid, but is certainly not true.

The above examples are of the form

If p, then q. (major premise)

x is p. (minor premise)

Therefore, x is q. (conclusion)

Deductive VersusInductive Reasoning

Deduction It is the form or structure

of a deductive argument that determines its validity

the fundamental property of a valid, deductive argument is that if the premises are true, then the conclusion necessarily follows.

The conclusion is said to be “entailed” in, or contained in, the premises. example: use of DNA

testing to establish paternity

Induction By contrast, the form or

structure of an inductive argument has little to do with its perceived believability or credibility, apart from making the argument seem more clear or more well-organized.

The receiver (or a 3rd party) determines the worth of an inductive argument

Deduction Versus Induction--still more

Deductive reasoning is commonly found in the natural sciences or “hard” sciences, less so in everyday arguments

Occasionally, everyday arguments do involve deductive reasoning: Example: “Two or more

persons are required to drive in the diamond lane. You don’t have two or more persons. Therefore you may not drive in the diamond lane”

Inductive reasoning is found in the courtroom, the boardroom, the classroom, and throughout the media

Most, but not all everyday arguments are based on induction Examples: The

“reasonable person” standard in civil law, and the “beyond a reasonable doubt” standard in criminal law

Inductive or deductive reasoning? A sample of fifty

motorists who were stopped by the CHP at a sobriety checkpoint on a Saturday at midnight revealed that one in four drivers were either uninsured, intoxicated, or both. Thus, if you get involved in an accident on the freeway there is a 25% chance the other motorist will be drunk or uninsured.

The Law of the Sea treaty states that any vessel beyond a 12 mile limit is in international waters. The treaty also states that any vessel in international waters cannot be legally stopped or boarded. Therefore, when the U.S. Coast Guard intercepts boats coming from Cuba or Haiti more than 12 miles from the U.S. coast, it is violating the Law of the Sea.

Sample Deductive and Inductive ArgumentsExample of

Deduction major premise: All

tortoises are vegetarians

minor premise: Bessie is a tortoise

conclusion: Therefore, Bessie is a vegetarian

Example of Induction

Boss to employee: “John has a tattoo of an anchor on his arm. He probably served in the Navy.”

Deductive Reasoning

All dogs are mammals and mammals have kidneys.

Therefore your dog has kidneys.

Deductive Reasoning

All squares are rectangles, and all rectangles have four sides.

All squares have four sides.

Inductive Reasoning

All swans we have seen have been white; therefore all swans are white.

Inductive Reasoning

All swans we have seen have been white; therefore the next swan we see will be white.

Inductive Reasoning

All known planets travel about the sun in ellipitical orbits; therefore all planets travel about the sun in ellipitical orbits.

Deductive or Inductive?

Since all men are mortal, and Socrates is a man, Socrates is mortal.

DEDUCTIVE

Deductive or Inductive?

Exploration of the surface of Mars has produced some surprising facts. Therefore exploration of the surface of Jupiter will produce some surprising facts.

INDUCTIVE

Deductive or Inductive?

Since Chris is a good athlete, Chris's sister must be a good athlete also.

INDUCTIVE

Deductive or Inductive?

The sun is a star; the sun has planets; therefore some stars have planets.

DEDUCTIVE

Advantages/Disadvantages

Advantage of deductive reasoning is the truths that it establishes are absolute

Disadvantage of deductive reasoning is that must have some truths in hand before starting

Advantages/Disadvantages

Advantage with inductive reasoning can start with nothing, make some observations, reach conclusions

Disadvantage is the conclusions are tentative

It's easy to confuse inductive and deductive reasoning, so here's something to help you remember which is which:

Inductive: Evidence · Conclusion (IEC)

Deductive: Conclusion · Evidence (DCE)

Three Fundamental Patterns of Reasoning

3. Comparative reasoning Makes interpretations, draws inferences, or

offers explanations by relying on something that is more familiar in order to understand something that is less familiar.

“This is like that” reasoning.

Useful for suggesting ideas and promising areas of inquiry and investigation

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