Cerritos College

Many thanks to Jay VerLinden who created this document:  source site -- www.humboldt.edu/~act/HTML/

Many of the following terms which we will use may be new to you. Therefore, it is strongly suggested that you keep a separate "journal" of these words with their meanings and examples of each. These will be on quizzes, and you need to understand their meanings and how to identify them in argument essays — and how to use them in your argument essays.

Inductive reasoning draws a conclusion about something that is not already known based on knowledge about something that is known. The conclusion is not contained in the premises and cannot be certain, as it is in deductive reasoning. So, a valid inductive argument must go beyond what is contained in the premises. There is always at least some uncertainty, even when the premises are accepted. e.g. "If I do well on my final exam, I might get an A for the class. I think I did pretty well on the final, so there's a chance I'll get an A." This example draws an uncertain conclusion.

Deductive reasoning draws from the known to the known and reasons to an absolute conclusion based on what is known in the major premise and in the minor premise. If all the premises are true, the conclusion must also be true. e.g. "Trees and flowers are different from one another. The tulip is a flower. Therefore, it is not a tree."FORMAL VALIDITY concerns how well an argument conforms to the rules of logic to arrive at a conclusion that must be true, assuming the premises are true. A formally valid argument is one in which, if the premises are true, the conclusion must also be true (see deductive reasoning). Formally valid arguments are those that follow a proper pattern of reasoning.

MATERIAL TRUTH concerns whether or not the conclusion of an argument is true, at least to the extent that truth can be determined. If the premises are true and the argument is formally valid, the conclusion will be materially true. However, depending on how the argument is constructed, the conclusion may be materially true even if the premises are false and the logic is invalid. That is, a materially true argument is one that comes to a truthful conclusion, regardless of whether the reasoning is formally valid or not.

An ENTHYMEME is an argument similar to a syllogism, but may be missing one or more parts OR arrive at an uncertain conclusion, OR both. An enthymeme is similar to a syllogism, but it has either one or both of the following characteristics: (1) It leaves one or more parts (major premise, minor premise, conclusion) unstated, (2) It arrives at a conclusion that is not absolutely certain. e.g. "Most instructors at Cerritos are excellent teachers. Jay is an instructor at Cerritos. Therefore, Jay is probably a good teacher." This example has a major premise, a minor premise, and a conclusion, but arrives at an uncertain conclusion. So, an enthymeme may look like a syllogism, but comes to a probable conclusion instead of a certain conclusion. When it leaves out one or more parts of a syllogism and comes to a probable conclusion, it is called truncated.

A SYLLOGISM is an argument that has a major premise, minor premise, and conclusion and arrives at an absolutely certain conclusion, assuming the premises are true (see deductive reasoning). Words like "because" and "since" usually indicate that what follows is the premise of an argument. Depending on who is making the argument, these words can indicate that what follows is either a major premise or a minor premise.

The major premise is a statement of a general or universal nature. "My math exam had 100 questions.

The minor premise is a statement regarding a particular case, related to the subject of the major premise. All exams with at least 50 questions are good exams.

The conclusion is the inevitable result of accepting the major and minor premises. "My math exam was a good exam."

The major premise presents general categories, general alternatives, or general conditions, and the minor premise represents an instance of what is presented in the major premise.

Categorical syllogsim: if one of the premises is negative, then the other premise must not be negative and conclusion must be negative.

1) "All fruits are plants. A peach is a fruit. Therefore, a peach is a plant." The term "fruit" is the middle term, that of a category, the major premise of a categorical syllogism. In this example, peach fits into fruit which fits into plants. You can also think of the middle term as the term that appears in both premises but not in the conclusion of a categorical syllogism.

2) "All trees are plants. A redwood is a tree. Therefore, a Redwood is a plant. This categorical syllogism, has three terms (trees, plants, and redwood).

4) "American citizens must pay their taxes or they will be in trouble with the government. Susie did not pay her taxes. Therefore, she is in trouble with the government." This argument is a valid categorical syllogism if you assume that Susie is an American citizen; so, she falls within the category established in the major premise.

1) "All the people in the math classroom are students. Betty is in the math classroom. Therefore Fred is a student. A valid categorical syllogism may only have three terms, and this one has four ("All the people in the math classroom," "students," "Betty," and "Fred.")

2) "Some Americans believe in UFO abductions. I am an American. Therefore, I must believe in UFO abductions." The middle term ("Some Americans") is not used in an unqualified or universal sense, so the conclusion cannot be certain. If the conclusion was "Therefore, I might believe in UFO abductions" it would be a valid categorical enthymeme.

4) "Recreational drugs are safe to use. Cocaine is too addictive. Cocaine is not safe to use." This argument has four terms: "recreational drugs," "safe to use," "cocaine," and "too addictive."

Conditional or hypothetical syllogism:

The minor premise must either affirm the antecedent or deny the consequent.

If the minor premise affirms the antecedent the conclusion must affirm the consequent.

If the minor premise denies the consequent the conclusion must deny the antecedent.

In the major premise of a conditional syllogism, the "If . . ." phrase is known as the antecedent. The antecedent is the "if . . ." phrase and the "then . . . " phrase is known as the consequent. A conditional argument has a major premise with the form "If A, then B" and is also known as a hypothetical argument. It could be either a syllogism or an enthymeme.

The major premise of a conditional syllogism establishes only two things that you know about the universe: (1) If the antecedent happens, the consequent has to happen, and (2) if the consequent doesn't happen, the antecedent couldn't have happened, and you cannot draw a valid conclusion. Sometimes an argument that is invalid becomes valid if what was meant to be the conclusion is used as a premise, or if what was meant to be a major premise is used as a minor premise. The most common mistake people make is thinking that if an argument comes to a clearly untrue conclusion, it must be invalid, and that if it comes to a clearly true conclusion, it must be valid. Remember that truth and validity do not necessarily coincide.

1) "If the sky is blue there won't be rain. The sky is blue today. Therefore, there won't be rain." This takes the form of "If A then B," so it is a conditional syllogism. The minor premise affirms the antecedent, and the conclusion affirms the consequent.

2) "If I finish this assignment then I will eat sushi and watch the X-files. Luckily, you are reading this, so I finished. So I am leaving to go eat sushi and watch the X-files." The minor premise affirms the antecedent and the conclusion properly affirms the consequent. The wording leaves some room for doubt because the exact same phrases are not used throughout, but that is a characteristic of everyday arguments.

3) "If my English professor cancels class today, she got stuck in Fortuna because of the flood. She canceled class today. Therefore, she is stuck in Fortuna because of the flood." The minor premise affirms the antecedent, and the conclusion affirms the consequent. This one may seem to be invalid because, as a reasonable human being, you realize being stuck in a flood is not the only reason why the English professor might cancel a class. However, when determining formal validity you must accept the premises as everything you know to be true. This argument is formally valid, but it may be materially untrue.

4) If the price of seafood increases due to the affects of El Nino, then Mother Nature has an influential role in our economy. The price of seafood has increased due to El Nino. Therefore Mother Nature has an influential role in our economy." This argument is a valid hypothetical* syllogism because the minor premise affirmed the antecedent and the conclusion then affirmed the consequent. * Remember a hypothetical syllogism can also be called a conditional syllogism.

1) "If I study my homework then I will get better grades. I didn't study my homework. Therefore, I'm not going to get better grades." This argument is not valid because the antecedent is "If I study my homework," and this argument has a minor premise that denies the antecedent. The minor premise must either affirm the antecedent or deny the consequent or the argument must be invalid.

2) "If I drink beer then I will get fat. I drink beer. Therefore I am in good shape." The minor premise affirms the antecedent, but the conclusion does not affirm the consequent as it should.

3) "If we go out to dinner tonight, we will not have to do the dishes. We did not do the dishes. Therefore, we went out to dinner." The minor premise affirms the consequent, which cannot be done and reach a valid conclusion. In this example the major premise only allows you to know what will happen if you go out to dinner, not what will happen if you don't do the dishes. There could be many reasons why you did not do the dishes that have nothing to do with going out to dinner.The point of an argument is to give reasons in support of some conclusion. An argument commits a fallacy when the reasons offered do not, in fact, support the conclusion.

Toulmin's Model of Argument (see handout in class)