Deduction And Induction

Arguments can be divided into two groups:
deductive arguments- involve necessity
inductive arguments- involve probability
Remember that we are always concerned with the relation between the premise(s) and the conclusion.
In this lesson we are still only concerned with what an argument is intended to be. We are not yet concerned with evaluating arguments as good or bad.
In a deductive argument it is claimed that the premises provide necessary support for the conclusion. In logic we are dealing with a very specific meaning of necessity, absolute necessity. For example, although it is very, very likely that the sun will rise tomorrow, it is not necessary that it do so--only very probable. On the other hand, the proposition that 2+2=4 is a necessary proposition. There is absolutely no other way around it, it follows by the meaning of those terms.
Once you have internalized this sense of necessity it becomes hard to deal with "regular" people because you will have a hard time saying "certain," "sure," "always," "never" and related words that are part of your technical terminology in situations when other people expect you to use them easily (and inaccurately). I drive my kids crazy by (almost) never being sure of anything. Them: "Mom, will we get to school on time?" Me: "I think so." Them: "Well, are we almost late?" Me: "No, I think we'll get there with ten minutes to spare." Them: "So, then we'll certainly get there before the bell rings--right?--why didn't you say so?" Me: --gulp. . .
The easiest way to determine whether an argument is inductive or deductive is to recognize various specific types of arguments that fall under each of these categories. And, as in Lesson 1, there are sometimes certain indicator words that act as red flags and help us identify inductive and deductive arguments. But, note that it is risky to rely on indicator words because often an arguer will use deductive indicator words such as "certainly," "undoubtedly," etc. to embellish what is really an inductive argument. Once again, your common sense will be of great help.

*Deductive*	*Inductive*

ARGUMENT TYPES

Argument from math	Prediction
Argument from definition	Argument from analogy
Categorical syllogism	Inductive generalization
Hypothetical syllogism	Argument from authority
Disjunctive syllogism	Argument based on signs
	Causal inference

INDICATOR WORDS
necessarily	probably/improbably
certainly	plausible/implausible
absolutely	likely/unlikely
definitely	reasonable to conclude

ASSIGNMENT:
Determine whether the following arguments are inductive or deductive. State the specific type of argument. If you believe that the argument does not fall under any of the eleven types listed above, explain in your own words the basis of your decision to classify it as inductive or deductive. (10 points each)
NOTE: An argument that is set up as a deductive argument but is invalid is still a deductive argument.

1. The sum of the interior angles of any triangle is 180°. In triangle #1, angle A is 30°, angle B is 90°. Therefore, angle C is 60°.
2. If I make an A, then I will pass this course. Odds are, I will make a B. So, I probably won't pass this course.
3. The situation in America today is much like that of ancient Rome before its fall, in that the U.S. is controlled by a small group of self-serving individuals. It is inevitable that within 50 years America will suffer the same fate as Rome.
4. The platypus is not a mammal because no mammal lays eggs and the female platypus does.
5. The last time I ate here, the shrimp dish I ordered was disgusting. It must be the case that this restaurant buys lousy seafood.
6. The sign on the candy machine reads "Out of Order." The candy machine must be broken.
7. All guitar players are musicians, and some guitar players are not astronauts. It follows that some musicians are not astronauts.
8. Irene likes either coffee or tea in the morning. But she doesn't like tea. Therefore Irene likes coffee in the morning.
9. These mushrooms have a very similar appearance to the ones growing in the garden. The ones in the garden are edible. The conclusion is therefore warranted that these mushrooms are edible.
10. My birthday is six days after my sister's birthday. My birthday is on the 12th. Therefore, my sister's birthday is on the 18th.

Examples of Inductive Reasoning

The term "inductive reasoning" refers to reasoning that takes specific information and makes a broader generalization that's considered probable, while still remaining open to the fact that the conclusion may not be 100% guaranteed.

In other words, you're making an educated or informed guess based on the information or data that you have. It might sound right, but that doesn't mean it is right. Together, let's explore some examples of inductive reasoning. You'll quickly see what it's all about.

Understanding Inductive Reasoning

There are varying degrees of strength and weakness in inductive reasoning. There are also various types including statistical syllogism, arguments from example, causal inference, simple inductions, and inductive generalizations. They can have part to whole relations, extrapolations, or predictions.

Some examples of inductive reasoning include:

· Jennifer always leaves for school at 7:00 a.m. Jennifer is always on time. Jennifer assumes, then, that she if she leaves at 7:00 a.m. for school today, she will be on time.

· The cost of goods was $1.00. The cost of labor to manufacture the item was $0.50. The sales price of the item was $5.00. So, the item always provides a good profit for the stores selling it.

· Every windstorm in this area comes from the north. I can see a big cloud of dust in the distance. A new windstorm is coming from the north.

· Bob is showing a big diamond ring to his friend Larry. Bob has told Larry that he is planning to marry Joan. Bob must be surprising Joan with the diamond ring tonight.

· The chair in the living room is red. The chair in the dining room is red. The chair in the bedroom is red. All the chairs in the house are red.

· Every time you eat peanuts, you start to cough. You are allergic to peanuts.

· Every cat that you've observed purrs. Therefore, all cats must purr.

· Michael just moved here from Chicago. Michael has red hair. Therefore, all people from Chicago have red hair.

· The children in that house yell loudly when they play in their bedroom. I can hear children yelling in that house. Therefore, the children must be playing in their bedroom.

· Every chicken we've seen has been brown. All chickens in this area must be brown.

· John is an excellent swimmer. His family has a swimming pool. John's sister Mary must also be an excellent swimmer.

· All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown.

· All the children in this daycare center like to play with Legos. All children must like to play with Legos.

· Ray is a football player. All the other football players on the high school team weigh more than 170 pounds. Therefore, Ray must weigh more than 170 pounds.

· Practically every house on South Street is falling apart. Sherry lives on South Street. Her house is probably falling apart.

Deductive Reasoning Examples

Some would argue deductive reasoning is an important life skill. It allows you to take information from two or more statements and draw a logically sound conclusion.

Deductive reasoning moves from generalities to specific conclusions. Perhaps the biggest stipulation is that the statements upon which the conclusion is drawn need to be true.

If they're accurate, then the conclusion stands to be sound and accurate. Let's explore some deductive reasoning examples. See if you would've drawn the same conclusions yourself.

Examples of Deductive Reasoning

Everyday life often tests our powers of deductive reasoning. Did you ever wonder when you'd need what you learned in algebra class?

Well, if nothing else, those lessons were meant to stretch our powers of deductive reasoning. For example, if a = b and b = c, then a = c. Let's flesh that out with added examples:

· All dolphins are mammals, all mammals have kidneys; therefore all dolphins have kidneys.

· All numbers ending in 0 or 5 are divisible by 5. The number 35 ends with a 5, so it must be divisible by 5.

· All birds have feathers and all robins are birds. Therefore, robins have feathers.

· It's dangerous to drive on icy streets. The streets are icy now, so it would be dangerous to drive.

· All cats have a keen sense of smell. Fluffy is a cat, so Fluffy has a keen sense of smell.

· Cacti are plants and all plants perform photosynthesis; therefore, cacti perform photosynthesis.

· Red meat has iron in it and beef is red meat. Therefore, beef has iron in it.

· Acute angles are less than 90 degrees. This angle is 40 degrees, so it must be acute.

· All noble gases are stable. Helium is a noble gas, so helium is stable.

· Elephants have cells in their bodies and all cells have DNA. Therefore, elephants have DNA.

· All horses have manes. The Arabian is a horse; therefore, Arabians have manes.

Invalid Deductive Reasoning

Even with two solid premises, sometimes, deductive reasoning goes wrong. Here are a few examples of just that:

· All swans are white. Jane is white. Therefore, Jane is a swan.

· All farmers like burgers. Jethro likes chicken wings. Therefore, Jethro is not a farmer.

· All actors are handsome. Tom Cruise is handsome. Therefore, Tom Cruise is an actor.

In each of these examples, the premises may very well be true but the conclusions make invalid assumptions. Let's take the Tom Cruise example. Just because Tom Cruise is handsome, does that mean he must be an actor? Who's to say all electricians or writers aren't pretty too? In these examples, a + b does not necessarily equal c. Rather, "c" is an overgeneralization.

Deductive Reasoning vs. Inductive Reasoning

Inductive reasoning is akin to deductive reasoning. The main difference is that, with inductive reasoning, the premises provide some evidence for the validity of the conclusion, but not all.

With deductive reasoning, the conclusion is necessarily true if the premises are true. With inductive reasoning, the conclusion might be true, and it has some support, but it may nonetheless be false. However, your educated guess can become a hypothesis you could consider fleshing out through research and an abundance of outside sources.

Let's take a look at a few examples of inductive reasoning. After we examine the inductive reasoning, we'll flip it and see what it looks like in the form of deductive reasoning.

· Inductive Reasoning: The first lipstick I pulled from my bag is red. The second lipstick I pulled from my bag is red. Therefore, all the lipsticks in my bag are red.
Deductive Reasoning: The first lipstick I pulled from my bag is red. All lipsticks in my bag are red. Therefore, the second lipstick I pull from my bag will be red too.

· Inductive Reasoning: My mother is Irish. She has blond hair. Therefore, everyone from Ireland has blond hair.
Deductive Reasoning: My mother is Irish. Everyone from Ireland has blond hair. Therefore, my mother has blond hair.

· Inductive Reasoning: Most of our snowstorms come from the north. It's starting to snow. This snowstorm must be coming from the north.
Deductive Reasoning: All of our snowstorms come from the north. It's starting to snow. Therefore, the storm is coming from the north.

· Inductive Reasoning: Maximilian is a shelter dog. He is happy. All shelter dogs are happy.
Deductive Reasoning: Maximillian is a shelter dog. All shelter dogs are happy. Therefore, he is happy.

Notice how each example of deductive reasoning is more sound (assuming the first two premises are true)? In each instance, the inductive reasoning may be true. But, they're lacking enough evidence to be universally true. Further samplings would be required.

Don't Leave Room for Assumptions

If you proceed with facts and evidence, your deductive or inductive reasoning can quickly turn into an assumption. And that's what we typically try to avoid in life. A hypothesis, however, is a nice place to start. This is an idea that can be molded into factuality and follow the lines of deductive reasoning.

Deductive reasoning in research

Deductive reasoning is a basic form of valid reasoning. Deductive reasoning, or deduction, starts out with a general statement, or hypothesis, and examines the possibilities to reach a specific, logical conclusion, according to California State University. The scientific method uses deduction to test hypotheses and theories. "In deductive inference, we hold a theory and based on it we make a prediction of its consequences. That is, we predict what the observations should be if the theory were correct. We go from the general — the theory — to the specific — the observations," said Dr. Sylvia Wassertheil-Smoller, a researcher and professor emerita at Albert Einstein College of Medicine.

Deductive reasoning usually follows steps. First, there is a premise, then a second premise, and finally an inference. A common form of deductive reasoning is the syllogism, in which two statements — a major premise and a minor premise — reach a logical conclusion. For example, the premise "Every A is B" could be followed by another premise, "This C is A." Those statements would lead to the conclusion "This C is B." Syllogisms are considered a good way to test deductive reasoning to make sure the argument is valid.

For example, "All men are mortal. Harold is a man. Therefore, Harold is mortal." For deductive reasoning to be sound, the hypothesis must be correct. It is assumed that the premises, "All men are mortal" and "Harold is a man" are true. Therefore, the conclusion is logical and true. In deductive reasoning, if something is true of a class of things in general, it is also true for all members of that class.

According to California State University, deductive inference conclusions are certain provided the premises are true. It's possible to come to a logical conclusion even if the generalization is not true. If the generalization is wrong, the conclusion may be logical, but it may also be untrue. For example, the argument, "All bald men are grandfathers. Harold is bald. Therefore, Harold is a grandfather," is valid logically but it is untrue because the original statement is false.

Inductive reasoning

Inductive reasoning is the opposite of deductive reasoning. Inductive reasoning makes broad generalizations from specific observations. Basically, there is data, then conclusions are drawn from the data. This is called inductive logic, according to Utah State University.

"In inductive inference, we go from the specific to the general. We make many observations, discern a pattern, make a generalization, and infer an explanation or a theory," Wassertheil-Smoller told Live Science. "In science, there is a constant interplay between inductive inference (based on observations) and deductive inference (based on theory), until we get closer and closer to the 'truth,' which we can only approach but not ascertain with complete certainty."

An example of inductive logic is, "The coin I pulled from the bag is a penny. That coin is a penny. A third coin from the bag is a penny. Therefore, all the coins in the bag are pennies."

Even if all of the premises are true in a statement, inductive reasoning allows for the conclusion to be false. Here's an example: "Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald." The conclusion does not follow logically from the statements.

Inductive reasoning has its place in the scientific method. Scientists use it to form hypotheses and theories. Deductive reasoning allows them to apply the theories to specific situations.

Abductive reasoning

Another form of scientific reasoning that doesn't fit in with inductive or deductive reasoning is abductive. Abductive reasoning usually starts with an incomplete set of observations and proceeds to the likeliest possible explanation for the group of observations, according to Butte College. It is based on making and testing hypotheses using the best information available. It often entails making an educated guess after observing a phenomenon for which there is no clear explanation.

For example, a person walks into their living room and finds torn up papers all over the floor. The person's dog has been alone in the room all day. The person concludes that the dog tore up the papers because it is the most likely scenario. Now, the person's sister may have brought by his niece and she may have torn up the papers, or it may have been done by the landlord, but the dog theory is the more likely conclusion.

Abductive reasoning is useful for forming hypotheses to be tested. Abductive reasoning is often used by doctors who make a diagnosis based on test results and by jurors who make decisions based on the evidence presented to them.

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Dr Sohail Ansari

Assignment 38 for practical work in media lab: Deduction And Induction & Abductive reasoning For the Departments of Media Studies by Prof Dr Sohail Ansari