# Chapter 1: Basic Terminology -- Inferences

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The main focus of our course is reasoning and not truth.   However, students understandably get confused early in the course because we use reason to find out the truth.   We all want to have a successful life and make the right decisions that will lead to a successful life.   Ideally we will learn or figure out the truth and then reason from what is true to what else is true, and make good decisions.   The process of reasoning from what we think is true to what else is true is what we are most interested in for this class. As we will see below, we use this reasoning process everyday. Basically that is all logic is -- reasoning from what we think is true to what else must be true IF what we think is true is really true.

One of the first concepts introduced in Chapter 1 is the process of an inference.   An inference is the process of reasoning from what we think is true to what else is true.   An inference can be logical or illogical.   Important is that an inference is synonymous with the reasoning of an argument or what we call metaphorically a trail of reasoning.   A trail of reasoning example was given with the hat problem in Chapter 1.   One trail: If there were 5 hats originally, and only three used on the heads of the prisoners, and the remaining hats were put into an empty closet, then we know that there are two hats in the closet.   Notice what we mean by a "trail" - if one thing is true, then another is true, and if that is also true, then something else is true.   Notice also that simple arithmetic is a logical inference and predicts things we sometimes cannot see.   5-3=2.   We predict that there are two hats in the closet IF the closet was empty prior to putting the remaining hats in the closet.

All this terminology (reasoning , inference , argument , premises and conclusion ) is just common sense in disguise.   [Hint on terminology]

Here is a simple example, similar to the first one in Chapter 1.

## Example 1

Today, no one can beat Best Buy's prices on the new Apple iPhone.
(inference
So, the lowest price for the new Apple iPhone is only at a Best Buy store.

We make inferences like this one every day.   We get what we think or hope is good information, we think about what it means, and infer what else we think we know.   Then we often act on our inferences.

So for the term 'inference,' all we mean is coming to a conclusion about what we think we know from something else we think we know.   Above, the person who thinks this way would assume the advertisement is true and then infers that if it is true, the lowest price for the new iPhone is only at Best Buy. (Remember though inferences can be good or bad, correct or incorrect, flawless or faulty.)

We can also see how the technical terms of 'premise,' 'conclusion,' and 'argument' fit in the above example:

## Example 2

Today, no one can beat Best Buy's prices on the new Apple iPhone.   Premise
(inference)
So, the lowest price for the new Apple iPhone is only at a Best Buy store. Conclusion

The premise and the conclusion by themselves are just statements, but the whole process of having the premise or premises and then the conclusion is technically called an argument in logic.   Arguments always have premises and conclusions.  Important: See #14 in Exercise I, Chapter 1.

Next, we said above that inferences can be logical or illogical. Is Example 1 a good inference?   No, as the book explains the "no one can beat" phrase is a typical trick used in advertising.   If an Apple Store has a new iPhone for \$199 (with a contract of course), then if Best Buy's was also \$199, then the advertisement (Premise) is true, but not the inference (Conclusion).   If you lived much closer to an Apple Store than a Best Buy store, you would probably be making a mistake in wasting gas or time and effort on going to the Best Buy store. Bad inferences can cost us time and money. Add it up. Making lots of bad inferences in life could cost you a lot of grief and an unhappy life.

Let's try some inferences.   Which one of the following would be a correct inference from this advertisement?

## Example 3

Now can save up to 30% off on all the new arrival merchandise at H-Zone.

1. All the merchandise at H-Zone is 30% off.
2. About 30% of the new arrival merchandise at H-Zone is on sale.
3. At least one item of new merchandise at H-Zone is 30% off.
4. A replica of the Under Armour football Jersey warn by Colt Brennan at the 2007 Sugar Bowl, normally \$75, is now only \$52.50, 30% off.

## Example 4

No other retail store can beat Radio Shack's price on the new Samsung Galaxy phone.

1. Only Radio Shack has a low price on the new Samsung Galaxy phone.
2. Radio Shack's new Samsung Galaxy phone sale is the lowest.
3. The best buys of the new Samsung Galaxy are at Radio Shack.
4. Radio Shack's price on the new Samsung Galaxy is at least as low as that at other retail stores.

Understand why?   Radio Shack's price might be \$199.99, but if Best Buy's is also \$199.99, and no other retail store is lower, then the premise is true, but options A, B, and C would be illogical inferences.   Meaning that the advertisement (premise) could be true, but A, B, and C as conclusions could be false.   Only option D is true for sure if the advertisement is true.   Note what we mean then about a logical inference: If the premise(s) are true, the conclusion is necessarily true.   And an illogical inference: Even if the premise(s) are true, the conclusion could be false.

Inferences matter, but so does the information we use to make inferences.   Consider this example.

## Example 5

Internet Advertisement for USPlabs OxyELITE Pro with pictures of beautiful muscular men:

"Burn Fat, Increase Energy & Support Appetite Regulation! Most of us have the ultimate goal of losing belly fat and this OxyELITE pro product is very useful. OxyELITE pro is an excellent product used for reduction of fat from the body. This product contains special scientifically tested ingredients which are very helpful in burning the fat from the body. Actually I love this product, I have reduced almost 30 pounds of my weight in three months. The only thing I want to say is "wow." Want to lose weight, get that flab off in front, eat less, and have more energy?"

(inference)

In the fall of 2013, Hawaii health officials asked stores to pull this product from shelves after officials linked it to cases of liver failure and acute hepatitis in 29 people. Eventually about 50 people were hospitalized, some dying, from using this product.

By the time of the State action, two people had undergone liver transplants and one person had died, according to the Hawaii State Department of Health. Twenty-four of the people who fell ill reported using OxyELITE Pro before being diagnosed.   The patients had no other medication or supplement in common. Is having true information and using good reasoning important?   Indeed, they could save your life.

## Quiz

Let's try a few quiz items.

In logic, an inference is the thinking process from what we think is true (information) to what else we think is true.

In logic, an argument consists of statements. One or more of the statements is alleged information (premises) and one statement (the conclusion) is an inference from the alleged information (premises). Premises--> (inference to) -->Conclusion.

In an illogical inference, we always know the premise or premises (information) is not true.

In an illogical inference, even if the information (premise or premises) is true, the conclusion could be false.

Did you miss the third quiz-me? Study the iPhone example above again. Remember the advertisement (information, premise) could be true, but the reasoning to the conclusion incorrect. We will go over and over this point. Probably the hardest part of the class -- we are not judging the truth of premises. We are judging the reasoning. Illogical inference = EVEN IF the information (premise or premises) is true, the inference to the conclusion is faulty.