7 paragraph essay on the following questions

1 Basic Logic

The two most common forms of basic logic that we apply in our daily lives and our written arguments are induction and deduction. Of these two forms of reasoning, we far more frequently use induction in supporting our views. (1)

Directions: Select each header to reveal information on each topic.

Inductive Reasoning

With inductive reasoning, our aim is to arrive at conclusions about our subject based on the observations of specific supporting instances. These conclusions are often based on generalizations concerning a set of data.

As an example, consider the inductive reasoning approach one might take in recognizing which of the three local television weather forecasters was most accurate in predicting the daily high temperatures. If you studied their forecasts every day for two weeks and then compared their predictions with the official high temperatures reported by the local weather service, you could begin to arrive at a conclusion on which forecaster was the most accurate. This is inductive reasoning in a nutshell, as the observer moves from specific observations—the comparison of the daily predictions with the actual daily temperatures—to generalizations. In this case, the final conclusion might be that one of the three forecasters was better at predicting the daily high temperature. Simple, right?

This example, however, brings other questions into the discussion.

· Is two weeks of data enough to form a valid conclusion?

· Were the forecasters predicting the weather for similar geographic areas?

· Did the news agencies provide each of the forecasters with sufficiently sensitive equipment?

The reliability of an arguer’s conclusion depends on the quality and quantity of the observations, and those factors are what sometimes makes some inductive leaps logically faulty. If the sample size is too small, for instance, an arguer could be guilty of committing the common logical fallacy of “hasty generalization,” or drawing a conclusion from an incomplete or inadequate body of data.

It is important to note that induction is a reasoning process, and not necessarily a strategy for developing an essay. It is used to arrive at generalizations that suggest probabilities—not certainties. If, for instance, I go hunting for a new house in a planned subdivision here in Florida and I observe that most of the homes follow one of three basic floorplans, then it stands to reason that I will probably live in a home that follows one of those plans should I choose to buy there. That doesn’t mean, however, that there might not also be some homes which were built independently and which follow a different floorplan. Logic merely suggests that I would find myself in one of the more common models. (13)

To avoid making hasty generalizations, writers should be thorough in their research and careful in their organization and their positioning of supporting materials.

Deductive Reasoning

Deductive arguments seek a greater degree of certainty than their inductive counterparts. They often begin with a general statement that can be applied to a number of specific situations. Typically, deductive arguments take the form of the simple syllogism, which looks like this:

Major Premise: Truth about a large group.

Minor Premise: Truth about a specific member of that group.

Conclusion: Considered valid if the connections and conditions between the major and minor premises are true.

Here is an example of the simple syllogism:

Major Premise: Students scoring above a 3.0 GPA in their English classes at FSCJ need not take the CLAST exam to enter one of Florida’s public universities.

Minor Premise: Derek has a 3.5 GPA in his English classes at FSCJ.

Conclusion: Derek need not take the CLAST exam to enter a Florida public university.

Deductive arguments are only as strong as their premises, however, and while an argument may be logical, it can also be faulty. For instance, if the premises listed above are not true (Derek might have a 2.8 GPA, for instance), then the argument lacks validity. Or, perhaps Florida’s newest public university, Florida Polytechnic, has decided to independently create higher admissions standards than its state-wide counterparts. Once again, we can see that the quality of the observations is critical in determining the validity of the deductive argument.

Creating logical, reasonable arguments is often predicated on finding a sufficient body of specific, credible, and relevant supporting materials upon which to base your views. In the next pages of this learning module, we can further explore the components of basic logic and identify the many types of logical fallacies that we encounter on a daily basis. (13)

2 The Principles of Logic

So what are these principles of reasoning that are part of logic? There are many such principles, but the main (not the only) thing that we study in logic are principles governing the validity of arguments—whether certain conclusions follow from some given assumptions.

For example, consider the following three arguments:

If Tom is a philosopher, then Tom is poor. Tom is a philosopher. Therefore, Tom is poor.

If K>10, then K>2. K>10. Therefore, K>2.

If Tarragona is in Europe, then Tarragona is not in China. Tarragona is in Europe. Therefore, Tarragona is not in China.

These three arguments here are obviously good arguments in the sense that their conclusions follow from the assumptions. If the assumptions of the argument are true, then the conclusion of the argument must also be true. A logician will tell us that they are all cases of a particular form of argument known as "modus ponens":

If P, then Q.

P.

Therefore, Q.

We shall discuss validity again later on. It should be pointed out that logic is not just concerned with the validity of arguments. Logic also studies consistency, and logical truths, and properties of logical systems such as completeness and soundness. But we shall see that these other concepts are also very much related to the concept of validity. (13)

3 Formal and Informal Logic

Sometimes a distinction is made between informal logic and formal logic. The term "informal logic" is often used to mean the same thing as critical thinking. Sometimes it is used to refer to the study of reasoning and fallacies in the context of everyday life. "Formal logic" is mainly concerned with formal systems of logic. These are specially constructed systems for carrying out proofs, where the languages and rules of reasoning are precisely and carefully defined. Sentential logic (also known as "Propositional logic") and Predicate Logic are both examples of formal systems of logic.

There are many reasons for studying formal logic. One is that formal logic helps us identify patterns of good reasoning and patterns of bad reasoning, so we know which to follow and which to avoid. This is why studying basic formal logic can help improve critical thinking. Formal systems of logic are also used by linguists to study natural languages. Computer scientists also employ formal systems of logic in research relating to artificial intelligence. Finally, many philosophers also like to use formal logic when dealing with complicated philosophical problems, in order to make their reasoning more explicit and precise. (13)

4 What is a Fallacy?

Fallacies are mistakes of reasoning, as opposed to making mistakes that are of a factual nature. If I counted twenty people in the room when there were in fact twenty-one, then I made a factual mistake. On the other hand, if I believe that there are round squares, I am believing something that is inconsistent. This is a mistake of reasoning, and a fallacy, since I should not have believed something inconsistent if my reasoning is sound.

In some discussions, a fallacy is taken to be an undesirable kind of argument or inference. For example, a certain textbook explains "fallacy" as "an unreliable inference.” In our view, this definition of fallacy is rather narrow, since we might want to count certain mistakes of reasoning as fallacious even though they are not presented as arguments. For example, making a contradictory claim seems to be a case of fallacy, but a single claim is not an argument. Similarly, putting forward a question with an inappropriate presupposition might also be regarded as a fallacy, but a question is also not an argument. In both of these situations, though, the person is making a mistake of reasoning since he is doing something that goes against one or more principles of correct reasoning. This is why we would like to define fallacies more broadly as violations of the principles of critical thinking, whether or not the mistakes take the form of an argument.

The study of fallacies is an application of the principles of critical thinking. Being familiar with typical fallacies can help us avoid them. We would also be in a position to explain other people's mistakes. There are different ways of classifying fallacies. Broadly speaking, we might divide fallacies into four kinds.

· Fallacies of inconsistency: cases where something inconsistent or self-defeating has been proposed or accepted.

· Fallacies of inappropriate presumption: cases where we have an assumption or a question presupposing something that is not reasonable to accept in the conversational context.

· Fallacies of relevance: cases where irrelevant reasons are being invoked or relevant reasons are being ignored.

· Fallacies of insufficiency: cases where the evidence supporting a conclusion is insufficient or weak. (14

5 Types of Fallacies: Fallacies of Insufficiency

Limited Sampling

· Momofuku Ando, the inventor of instant noodles, died at the age of 96. He said he ate instant noodles every day. So instant noodles cannot be bad for your health.

· A black cat crossed my path this morning, and I got into a traffic accident this afternoon. Black cats are really unlucky.

In both cases, the observations are relevant to the conclusion, but a lot more data is needed to support the conclusion. These are hasty generalizations, based on small sample sizes of data.

Appeal to Ignorance

· We have no evidence showing that he is innocent. So he must be guilty.

If someone is guilty, it would indeed be hard to find evidence showing that he is innocent. But perhaps there is no evidence to point definitively in either direction, so the lack of evidence is not enough to prove guilt.

Naturalistic Fallacy

· Many children enjoy playing video games, so we should not stop them from playing.

Many naturalistic fallacies are examples of fallacy of insufficiency. Empirical facts by themselves are not sufficient for normative conclusions, even if they are relevant. (15)

6 Other Common Types of Fallacies

Directions: Select each topic below to reveal information on each one.

ad hominem

(Latin phrase for “against the man”)

A theory is discarded not because of any evidence against it or lack of evidence for it, but because of the person who argues for it.

This often takes the form of attacks against someone’s physical appearance.

Example:

A: The Government should enact minimum-wage legislation so that workers are not exploited. B: Nonsense. You say that only because you cannot find a good job.

ad ignorantiam

(appeal to ignorance)

The truth of a claim is established only on the basis of lack of evidence against it. A simple obvious example of such fallacy is to argue that unicorns exist because there is no evidence against such a claim.

At first sight, it seems that many theories that we describe as scientific involve such a fallacy. For instance, the first law of thermodynamics holds because so far there has not been any negative instance that would serve as evidence against it. But notice, as in cases like this, there is evidence for the law in the form of many positive instances, which therefore prove its existence.

ad populum

(appeal to popularity)

The truth of a claim is established only on the basis of its popularity and familiarity. This is the fallacy committed by many commercials. Surely you have heard of commercials implying that we should buy a certain product because it has made to the top of a sales rank, or because the brand is the city's "favorite.” In the middle of the twentieth century, tobacco manufacturers featured ads touting the number of doctors that approved of their cigarettes.

These appeals can be viewed as bandwagon appeals (everybody is doing it). Sometimes, they take the form of patriotic slogans (Levi’s—America’s jeans).

Begging the question

question (petito principii)

In arguing for a claim, the claim itself is already assumed in the premise. Example: "God exists because this is what the Bible says, and the Bible is reliable because it is the word of God."

Complex question or loaded question

A question can be fallacious if it is posed in such a way that a person, no matter what answer he or she gives, will inevitably commit him/herself to some other claim, which should not be presupposed in the context in question.

A common tactic is to ask a yes-no question that tricks people into agreeing to something they never intended to say. For example, if you are asked "Are you still as self-centered as you used to be?" then no matter whether you answer "yes" or "no,” you are bound to admit that you were self-centered in the past. Of course, the same question would not count as a fallacy if the presupposition of the question is indeed accepted in the conversational context.

False dilemma

Presenting a limited set of alternatives when there are others that are worth considering in the context. Example: "Every person is either my enemy or my friend. If he/she is my enemy, I should hate him/her. If he/she is my friend, I should love him/her. So I should either love him/her or hate him/her." Obviously, the conclusion is too extreme because most people are neither your enemy nor your friend.

Non sequitur

A conclusion is drawn which does not follow from the premise. This is not a specific fallacy but a very general term for a poor or incomplete argument. Many of the examples in this section illustrate qualities of the non sequitur. The term roughly translates to “it does not follow,” and it can be considered a fallacy of irrelevancy if not fully defended with reasonable premises.

Example: John has a safer car than mine because it cost $10,000 more when he bought it.

Post hoc, ergo propter hoc

(literally, "after this, therefore because of this")

Inferring that X must be the cause of Y just because X is followed by Y.

For example, having visited a graveyard, I fell ill and infer that graveyards are spooky places that cause illnesses. Of course, this inference is not warranted since this might just be a coincidence. However, a lot of superstitious beliefs commit this fallacy. Just because two events happen close to each other in terms of their timing, that doesn’t necessarily prove any causal relationship.

Red herring

Within an argument, some irrelevant issue is raised which diverts attention from the main subject. The function of the red herring is sometimes to help express a strong, biased opinion. The red herring (the irrelevant issue) serves to increase the force of the argument in a very misleading manner.

For example, in a debate as to whether God exists, someone might argue that believing in God gives peace and meaning to many people's lives. This would be an example of a red herring since whether religions can have a positive effect on people is irrelevant to the question of the existence of God. The good psychological effect of a belief is not a reason for thinking that the belief is true.

Slippery slope

Arguing that if an opponent were to accept some claim C1, then he or she has to accept some other closely related claim C2, which in turn commits the opponent to a still further claim C3, eventually leading to the conclusion that the opponent is committed to something absurd or obviously unacceptable.

This style of argumentation constitutes a fallacy only when it is inappropriate to think if one were to accept the initial claim, one must accept all the other claims.

An example: "The government should not prohibit drugs. Otherwise the government should also ban alcohol or cigarettes. And then fatty food and junk food would have to be regulated too. The next thing you know, the government would force us to brush our teeth and do exercises every day."

Straw man

Attacking an opponent by attributing to him/her an implausible position that is easily defeated when this is not actually the opponent's position. This often takes the form of a fallacy of diversion, as a speaker might abandon his or her central argument and develop a secondary argument that might seem more “winnable.” For instance, a parent might ask his or her daughter to mow the lawn. That child might argue that she has already cleaned her room, so she should be exempt from taking care of the lawn work. The point of contention in this example is the lawn work, so the other finished chores are immaterial to the argument at hand.

Example: When many people argue for more democracy in Hong Kong, a typical reply is to say that this is not warranted because it is wrong to think that democracy is the solution to all of Hong Kong's problems, or to say that one should not blindly accept democracy. But those who support democracy never suggest that democracy can solve all problems (e.g. pollution), and they might also agree that blindly accepting something is rarely correct, whether it is democracy or not. Those criticisms attack implausible "strawman" positions and do not address the real arguments for democracy. (15)

7 Conclusion

We are all guilty of brushing off these fallacies from time to time in our own discussions and arguments. In most cases, they are harmless tools in working through minor disagreements. Developing a stronger understanding of inductive and deductive reasoning and a clearer grasp of the logical fallacies will assist you in navigating these discussions and creating stronger, more convincing arguments of your own. It will also assist you with writing, researching, and developing stronger arguments in your college coursework and professional life. For more information on identifying, avoiding, and refuting flawed logic, please read the next section of this learning module, which features an essay by Dr. Rebecca Jones on various strategies for responding to arguments. (1)