Deductive Reasoning

     Despite the overwhelming array of seemingly inconsistent court opinions, statutes, regulations and other rules that collectively make up our body of modern "law," much of this law can be harmonized and understood surprisingly well when approached from a logical perspective. The process of doing so is often referred to as "legal reasoning." When properly understood and applied within the framework of legal analysis, legal reasoning is, in fact, very logical. This first exercise will describe a particular analytical process known as "deductive reasoning" that forms the basis for most good legal analysis.

     Logical analysis is a process that comes naturally to the human mind. Although most of us routinely do not consciously organize each distinct thought into neat little mental compartments from which we then construct carefully articulated arguments, this very process is still much more familiar to most of us than we realize. From our earliest childhood experiences we intuitively have attempted to construct "logical" arguments.

"Mommy, Johnny's parents got him a pony. I want a pony, too!"

     Of course, the formal logic in this plaintiff request is definitely flawed (which in part explains why you never got that pony), but the basic structure of the logic is nevertheless present. As you got older, you became more adept at structuring your arguments.

"Dad, Johnny's father bought him a new car. You make as much money as Johnny's father, so you should buy me a new car also."

     The logic of this argument is definitely better (as evidenced by the fact that some of you may actually have convinced your parents to buy you that new car), but it is still flawed. It fails to identify and develop the major premise from which the conclusion is logically derived.

     In this exercise, our first goal is to learn what specific components must be present in order to construct a valid logical argument. The particular method of reasoning that we will study in this exercise is known as a syllogism. Simply stated, a syllogism is a term that describes a particular logical relationship between two arguments. It consists of three specific parts:

(1) The major premise (a broad statement of general applicability);
(2) The minor premise (a narrower statement of particular applicability that relates to the major premise); and
(3) The conclusion (a statement that follows logically from and is consistent with both the major and minor premises).

     To illustrate how a logical syllogism argument is constructed, consider the following classic example:

(1) All men are mortal.
(2) Socrates is a man.
(3) Therefore, Socrates is mortal.

     In this example, the major premise is set forth in the first statement. It is a broad statement, that relates generally to ALL men (i.e., it asserts that all men are mortal). The second statement is the minor premise. It asserts very narrowly and specifically only that SOCRATES is a man. It says nothing about other men in general. Thus, as compared to the major premise it is far more specific, since it applies ONLY to one particular man, Socrates, and not to the broader class of ALL men. Notice, however, that both the major and the minor premises do have ONE common term. They both relate to man, or men. Since both the major and the minor premises are related by this common term, the conclusion set forth in the third statement is therefore logically consistent.

     This basic form of syllogism provides an excellent example of deductive reasoning. In deductive reasoning, both the major premise and the minor premise are worded in such a way that the conclusion naturally and logically derives from combining a general statement with a more particular statement in reference to the same common terms. A conclusion that has been reached through this process of deductive reasoning is quite compelling in its simple logic.

     Applying this same form of deductive reasoning to our earlier examples, we now can produce the following logical argument:

(1) Every parent of a teenage driver in my class has provided a new car for their teenager to drive.
(2) You are the parent(s) of a teenage driver in my class (i.e., me).
(3) Therefore, you will (or at least should) provide a new car for me to drive.

     What parent(s) could resist such beautiful logic? And what student hasn't already mastered the intricacies of carefully articulating the precise content of such major and minor premise statements long before entering law school? In fact, whether we realize it or not, most of us are already quite familiar with the basic concept of deductive reasoning. We have already learned how to use and to apply it successfully in numerous situations throughout our everyday lives, and we do this without even consciously ever thinking about it.

(1) One dollar will buy three candy bars.
(2) I have one dollar.
(3) Therefore, I can buy three candy bars.

(1) All cars need gasoline to run.
(2) I have a car.
(3) Therefore, my car needs gasoline to run.

(1) All students who score "95" or higher on their History exam will get an "A."
(2) I scored a "95" on my History exam.
(3) Therefore, I will get an "A."

     Each of these syllogisms utilizes simple deductive reasoning. Anyone wishing to successfully challenge a conclusion that has been deductively reasoned in this manner must do so by attacking either the major or the minor premise (or both) from which the conclusion is derived. If both of the underlying premises withstand attack, the conclusion, itself, is logically inescapable.

     Most of us routinely apply this type of "logic" in countless ways each and every day of our lives. As you begin your formal study of the law, all you really need now is just to gain a clearer understanding of precisely how this process of deductive reasoning actually works within the context of a legal argument. Then, you can apply it intentionally to specific legal arguments as you focus more purposefully on learning how to "think like a lawyer."

     Apart from legal analysis, the process of deductive reasoning is used extensively in many other specific disciplines. Most commonly, you may be familiar with this process as it is used in science and in mathematics.

(1) A equals B.
(2) B equals C.
(3) Therefore, A equals C.

     Known in mathematical terms as the principle of transitivity, this doctrine states simply that if two different things (i.e., A and C) are equal to the same thing (i.e., B), then those two different things MUST ALSO be equal to each other. (i.e., A = C). In mathematics (and to a somewhat lesser extent science in general) conclusions deductively derived from a syllogism are absolutely true, because both the major and minor premises upon which they were based are also absolutely true (e.g., 2 + 2 is ALWAYS equal to 4). That's why mathematics is often referred to as an EXACT science. In the law, however, there are very few absolute truths. Thus, any major or minor premises that we formulate from less than absolute legal principles are still potentially subject to challenge. To illustrate this notion, consider the following logical syllogism:

(1) All attorneys are honest.
(2) Mary is an attorney.
(3) Therefore, Mary is honest.

     As with all properly constructed syllogisms, the analysis here is logically flawless. Structurally, this syllogism accurately fits our basic pattern for internal consistency. However, if all we know about Mary is that she is an attorney, we are reluctant to accept its ultimate conclusion that "Mary is" also "honest." Why? Logically, we know that the conclusion MUST be true (because we have deduced it from a proper syllogism); yet, we have little confidence that it is in fact absolutely true in this case. The answer here is simple. Unlike the classic mathematical syllogism that is derived from absolute truths (as stated by the major and minor premises), legal syllogisms are not based upon absolute truths.

     Conclusions reached by legal deductive reasoning from these less-than-absolute premises can only be as good as both the major and minor premises upon which they are based. If EITHER the major or the minor premise from which our syllogism's conclusion is derived turns out to be FALSE, then the conclusion will also be false. In this example, sadly most of us know from our own experiences in life that the major premise (i.e., "all attorneys are honest") is in fact not absolutely true. Thus, even though our syllogism is structurally accurate, we cannot accept its conclusion as true, because we know that one of the premises (in this case, the major premise) is clearly false.

     In most instances, legal reasoning, even when derived deductively, does not express absolute truths. Instead, legal reasoning deals mostly with propositions that are more likely true than not. The more likely true that both the major and the minor premises are, the more likely that the syllogistic conclusion derived from them will also be true. Thus, even though they are not based upon absolute truths, proper legal arguments based upon sound deductive reasoning still tend to be among the most persuasive types of arguments that can be made in the law.

     Applying this concept to our preceding example, we can produce the following syllogism:

(1) MOST attorneys are honest.
(2) Mary is an attorney.
(3) Therefore, Mary is MORE LIKELY THAN NOT honest.

     This conclusion is much more likely to be accepted as true, even though it is not absolute.

     To properly apply the process of deductive reasoning to legal analysis, we must carefully understand the techniques by which the major and minor premises are constructed. In a typical legal argument the major premise states a general proposition of law, and the minor premise then applies that same legal proposition to some particular circumstance unique to the individual case at issue. The results of such a legal syllogism argument typically resemble one of the following simple examples:

(1) A valid contract must be supported by some consideration between the parties (major premise statement).
(2) The contract between Bob and Sam was not supported by any consideration (minor premise statement).
(3) Therefore, the contract between Bob and Sam was not valid (conclusion).

OR

(1) A conviction for first-degree murder requires that the Defendant act with premeditation (major premise statement).
(2) There is no evidence that Defendant acted with any premeditation (minor premise statement).
(3) Therefore, Defendant cannot be convicted of first-degree murder (conclusion).

     Now that you know what a logical syllogism is, let's look a little more closely at how they are constructed. Logicians have developed six fairly basic rules for constructing valid syllogisms. Although they may be stated in many different ways, essentially they are as follows:

Rule 1: All syllogisms must contain three terms: a major term, a minor term and a transitory (or middle) term.

Rule 2: The transitory term must be "distributed" in at least one premise (either the major premise or the minor premise).

Rule 3: The conclusion cannot contain any term that is not "distributed" in at least one premise (either the major premise or the minor premise).

Rule 4: A syllogism cannot contain two negative premises.

Rule 5: If either premise in a syllogism is negative, the conclusion must also be negative.

Rule 6: A syllogism with two universal premises (both the major premise and the minor premise) cannot have a particular conclusion.

 

Now, lets look at each of these Rules in a little closer detail.

Rule 1: All syllogisms must contain three terms: a major term, a minor term and a transitory (or middle) term.

      Any argument that uses more than three terms lacks a proper basis for comparing the major and the minor terms. Thus, if there are more than three terms in the argument there can be no single transitory (i.e., middle) term to logically connect the two remaining major and minor terms. To illustrate Rule 1, consider the following argument:

(1) All men are mortal (major term).
(2) Socrates (minor term) is a Greek.

     Even though both the major premise and the minor premise are true, there is no way to logically connect the two statements together. There is no single "middle" term. In this example it could be "mortal" (used in statement 1) or it could be "Greek" (used in statement 2). Without a single connecting term, there is not any way to logically construct a single, unifying syllogism.

     One way to fix this problem would be to construct two separate, although related, syllogisms, as in the following illustration:

Syllogism 1:
(1) All men are mortal (major term).
(2) All Greeks (minor term) are men.
(3) Therefore, all Greeks are mortal.

     The conclusion in Syllogism 1 is derived from the unifying middle term, "men," that is contained in both the major and the minor premise statements.

     Syllogism 2 starts with the conclusion deduced from Syllogism 1:

(1) All Greeks are mortal (major term).
(2) Socrates (the minor term) is a Greek.
(3) Therefore, Socrates is mortal.

     The conclusion in Syllogism 2 is derived from a different unifying middle term, "Greek(s)," that is contained in both the major and the minor premise statements.

     Depending upon what you were trying to prove (i.e., either that "all Greeks are mortal," or that "Socrates is mortal") only one of these arguments would be appropriate, and not the other. Moreover, notice that both Syllogisms are logically valid because they each do contain three, but only three, terms.

Rule 2: The transitory term must be "distributed" (i.e., universal) in at least one premise (either the major premise or the minor premise).

     Under this Rule, the middle term must describe the entire class contained within either the major premise or the minor premise. Otherwise, each term in the conclusion could be connected to some different part of the class that was not included within the premise statement, thus preventing the conclusion from stating a categorical truth. To illustrate this concept, consider the following example:

(1) All Greeks (major term) are men (transitory term).
(2) All Persians (minor term) are men (transitory term).
(3) Therefore, all Greeks are Persians.

     Here, although both the major and the minor premises are true, the conclusion is obviously not valid. The reason for this is that the transitory term (men) as used in BOTH premise statements is NOT universal. The transitory term (men) is not "distributed" in either premise statement. That is, in this example neither the major nor the minor premise encompasses the entire class of men. Thus, Rule 2 is violated because both premise statements describe something less than the full class of men. Any logical comparison between only partial classes (i.e., the class of all Greeks and the separate class of all Persians) cannot produce a categorically valid conclusion as to the entire class (of all men).

Rule 3: The conclusion cannot contain any term that is not "distributed" in at least one premise (either the major premise or the minor premise).

     As we have just seen from Rule 2, a term is "distributed" when it refers to every member in its entire class. To be logically valid an argument cannot contain a distributed conclusion (e.g., "all," "every") that is derived from a non-distributed major or minor premise (e.g., "some," "many"). The reverse of this rule is also true.

     An example of this Rule is illustrated by the following syllogism:

(1) Law students who lack good reasoning skills (major term) should study logic.
(2) Many law students (minor term) lack good reasoning skills.
(3) Therefore, ALL law students should study logic.

     Statement 1 (referring to "law students who lack good reasoning skills") is not a universal (i.e., "distributed") statement, since there may be law students who do have good reasoning skills. Likewise, Statement 2 (referring to "many law students") is obviously also not a universal statement. Thus, the conclusion is invalid because it not distributed in either the major or the minor premises, yet it is distributed in the conclusion

Rule 4: A syllogism cannot contain two negative premises.

     Intuitively, some of you are already familiar with this Rule. Since your earliest days most of you have been taught that "two wrongs don't make a right!" This is nothing more than a simple truism that has been derived by application of the logic principle stated in this Rule. Consider the following example:

1. No man is a mother. (negative major premise)
2. My mother is not my father. (negative minor premise)
3. No man is my father. (conclusion)

     Even though both the major and the minor premise statements are true, the conclusion is completely nonsensical. That is because this syllogism violates Rule 4: it contains two negative premise statements. No valid logical conclusion can be derived from two negative premises. Of course, any logical syllogism can certainly have one negative premise statement (either a major premise or a minor premise), just not both.

Rule 5: If either premise in a syllogism is negative, the conclusion must also be negative.

     This Rule is simply a logical extension of Rule 4. If any syllogism has one negative premise (a result that is clearly permitted by Rule 4), then its conclusion MUST also be negative. Consider the following example:

1. No man is immortal. (major premise)
2. Socrates is a man. (minor premise)
3. Socrates is not immortal. (conclusion)

     Because one of the premises in this syllogism is negative (i.e., in this case, the major premise), the conclusion must also be negative.

Rule 6: A syllogism with two universal premises (both the major premise and the minor premise) cannot have a particular conclusion.

     Since the argument expressed by logical syllogisms typically progresses from a broad (i.e., "universal") statement to a narrower, more specific (i.e., "particular") statement, it is essential that such a logical syllogism contain both a universal and a particular premise, if a particular conclusion is the desired result. Any other combination of statements, even if their individual premises are otherwise accurate, does not fit within the structure for a valid logical syllogism. Stated somewhat differently, although a valid syllogism can certainly contain two universal premises (in both the major and the minor premises), if such is the case the conclusion must also be stated in universal terms.

     Consider the following illustration:

1. All mortals eventually will die. (universal major premise)
2. All Greeks are mortal. (universal minor premise)
3. All Greeks eventually will die. (universal conclusion)

     This conclusion is perfectly valid, since it, like both the major and minor premises from which it is derived, is expressed in universal terms. However, if we change the universal term "all Greeks" in the conclusion to "this Greek," making it a particular conclusion, the logic fails. It may in fact be true that "This Greek eventually will die," but such a conclusion cannot be logically derived from this syllogism. The use of universal terms in both the major and the minor premise statements requires that the conclusion also be stated in universal terms.

TEST YOUR UNDERSTANDING OF LOGICAL SYLLOGISMS: