**The Force of Logic: Using Formal Logic as a Tool in the Craft of Legal Argument by Stephen M. Rice (National Institute of Trial Advocacy, 2017) 290 pages, $ 75.**

**Part 2 **

It is claimed that 90% of the legal issues raised in domestic United States cases can be resolved through deductive reasoning, where the conclusion is mandated through two propositions. I would say the same is essentially true with legal issues in cases before the international(ized) tribunals and courts.

Instinctively, we tend to apply deductive reasoning in resolving legal issues, even if we are not aware of the formal rules of logic or the attendant nomenclature. The problem with acting on instinct is that it is a hit-or-miss approach to legal reasoning. There are times when a legal argument may seem incorrect but it is difficult to articulate the cause of the problem in clear and concise language and with reference to some well-accepted rules. Also, invariably, most legal decisions are made on the basis of deductive reasoning – even if such reasoning is not readily apparent. And since Judges occasionally err, identifying flawed legal reasoning based on an incorrect application of the rules of deductive logic, resulting in logical fallacies, is essential when seeking reconsideration or review by a higher instance court. Here is where logic, for most occasions involving formulating or defeating legal arguments, or supporting or attacking judicial decisions, comes into play.

In this second and final part of my review of *The Force of Logic* I will focus on the nucleus of Rice’s admirable text: *the fallacies in the logical structure of legal arguments, and how to identify, describe, and avoid them*. Rice, as I noted in my previous post, presents in user-friendly language the general concepts and terms necessary to understand what formal logic is and how it relates to legal argumentation. Continuing where I left off, I will proceed by first recapping the foundational terminology and the nomenclature of the different types of *syllogisms* and the rules governing these *syllogisms*, before turning to the fallacies that Rice so adroitly covers. My goal is modest: to show how important logic is to what we do as advocates, and why, subject to the caveat I expressed in my previous post, I find *The Force of Logic* to be useful as both a primer in understanding logical fallacies in legal argumentation and as a reference book.

*Nomenclature & Tools*

*Deduction** – *the process of reasoning from a general rule to a specific conclusion.

*Syllogism** – *a deductive argument made up of two distinct but related premises and a conclusion. The first premise is called the ** major premise** – the predicate or basis of the conclusion. Within the major premise is the

**. The second premise is called the**

*major term***– the subject of the conclusion. Within the minor premise is the**

*minor premise***. Applying the major premise to the minor premise leads to the**

*minor term***.**

*conclusion*** Hypothetical syllogism** – a syllogism consisting of two conditional propositions in the premises and a conclusion, which flows from the relationship between the propositions. The major premise in a hypothetical syllogism is formed using conditional language such as “if…, then…”, “on the condition that…”, “in the event that…”, “when…”, “assuming that…”, etc.

*Categorical* *syllogism** –* a syllogism categorizing persons, places, actions, behaviors, etc., in which the conclusion flows from the relationship between the subjects in the premises and their membership in a particular category. The major premise of a categorical syllogism typically includes qualifying language such as “all”, “some”, “none”, or “no”.

*Disjunctive syllogism** – *a syllogism presenting two alternatives in the major premise, followed by a categorical assertion that one of the alternatives is true and that the other is false. The major premise in a disjunctive syllogism is formed using the operator “or”, known in linguistic and logic terminology as a ** disjunct**.

** Truth and validity **– two distinct qualities describing a syllogistic argument.

*Truth*refers to the truth or falsity of the premises.

*Validity*describes the logical form of the argument.

** Logical fallacy** – an argument that violates a rule of logic. If the rule violated concerns the logical form of the argument (or syllogism), then it is called a

**.**

*formal fallacy**Logical Fallacies*

As mentioned in the nomenclature, a logical fallacy occurs when an argument violates a rule of logic. One description of a logical fallacy that Rice offers is “an argument that appears to be logically persuasive, but is not.”

In discussing each of the logical fallacies in Rice’s *The Force of Logic*, some further terminology and explanation is necessary for a clear appreciation of the rules.

*The Fallacy of Denying the Antecedent*

The fallacy of denying the antecedent applies to hypothetical syllogisms – the “if…, then…” arguments. Rice cautions that the arguments “sound or appear a lot like a valid argument that follows the rule.” They can easily be mistaken for a valid argument if you are unfamiliar with this logical fallacy and how it works. And because this kind of argument is so common, lawyers rarely think about the logical relationship between cause and effect. That is what precipitates the fallacy of denying the antecedent. This fallacy is one of the most commonly encountered formal fallacies in legal argumentation.

Evaluating a hypothetical syllogism is a two-step process. The first step is to identify the component terms of the hypothetical premise. I’ll start with one of Rice’s examples:

**[ Hypothetical premise] **

*If the subject of a contract is the sale of an interest in land, then the contract is within the Statute of Frauds.*

**[ Categorical premise] **

*The subject of the contract is the sale of an interest in land.*

**[ Conclusion] **

*Therefore, the contract is within the Statute of Frauds.*

The hypothetical premise in the example from Rice contains two terms: the ** antecedent term** (“sale of an interest in land”) and the

**(“within the Statute of Frauds”).**

*consequent term*The second step is to determine whether the categorical premise* affirms* or *denies* a term and which term is *affirmed* or *denied*. If the categorical premise asserts that a term is true, then it is said to *affirm* the term. Conversely, if the categorical premise asserts that a term is false, then it is said to *deny* the term.

In Rice’s example above, “the categorical proposition (the subject of the contract is the sale of interest in land) affirms the antecedent term.” It declares that the first term in the hypothetical proposition is true. We can change that categorical proposition to do three things:

(1) Instead of affirming the antecedent term, we could deny it (“the contract is not a contract for the sale of interest in land”).

(2) Instead of affirming the antecedent term, we could rather affirm the consequent term (“the contract is within the Statute of Frauds”).

(3) Instead of affirming the consequent term, we could deny the consequent term (“the contract is not within the Statute of Frauds”).

The ** fallacy of denying the antecedent** is a pattern of argument that seeks to lead to a conclusion where the categorical proposition denies the antecedent term.

Understanding the nature of this logical fallacy requires an understanding of the rule that dictates the form of the hypothetical syllogism. The rule dictates a hypothetical syllogism must take one of two forms. The first form requires that the categorical premise must affirm the truth of the antecedent of the conditional premise and the consequent term of the hypothetical premise must be asserted in the conclusion. If the form does not comply with this rule, the syllogism cannot be relied upon to ensure the truth of the conclusion and is fallacious.

This means that we must first find the two terms of the categorical premise. Remember, a hypothetical syllogism is an “if…, then…” argument. Typically, what follows the word “if” is the antecedent term, and what follows the word “then” is the consequent term. For example, if the categorical premise is “If A, then B,” “A” is the antecedent term and “B” is the consequent term.

Here is Rice’s example of a fallacious hypothetical syllogism that denies the antecedent (EXAMPLE 1):

**[ Hypothetical premise] **

*If the subject of a contract is a transfer of an interest in land, then the contract is within the Statute of Frauds.*

**[ Categorical premise] **

*The subject of the contract is not one for a transfer of interest in land.*

**[ Conclusion] **

*Therefore, the contract is not within the Statute of Frauds*.

The logical fallacy of denying the antecedent is committed here, and the argument is illogical because the categorical premise (“the subject of the contract is not one for a transfer of interest in land”) denies the antecedent term (“transfer of interest”).

If you reflect on the form of the argument, it is apparent why it is logically invalid. Rice explains: “[t]he fact that the consequent term can be inferred from the truth of the antecedent terms does not provide any basis to conclude that anything can be logically inferred from the absence of the antecedent term.”

For those of us familiar with property and contract law in the United States, contracts for the transfer of land must comply with a rule of law known as the “Statute of Frauds” (which requires certain types of contracts to be in writing). Yet, even if a contract does not involve the transfer of land, it does not necessarily mean that the contract falls outside the requirements of the Statute of Frauds. There are other types of contracts that must also comply with the Statute of Frauds (such as contracts for the sale of goods over $500 USD).

The key to identifying and explaining the fallacy of denying the antecedent is understanding the rule of logic that applies to hypothetical syllogisms. The real value of this rule is that it provides a frame of reference for evaluating the structure of the hypothetical syllogism. Knowing which pattern is faulty enables you to identify and explain what is wrong with the argument. Moreover, you can recognize this pattern without deconstructing the argument. As Rice points, it is not necessary to “spend[] substantial amounts of time deconstructing the form of an argument or learn[] the philosophical bases of logic.”

*The Fallacy of Affirming the Consequent*

The ** fallacy of affirming the consequent** is a pattern of argument that seeks to reach a conclusion when the categorical premise affirms the consequent term of the hypothetical premise.

The United States Court of Appeals for the Fourth Circuit,^{1}*See In re Stewart Foods, Inc.* 64 F.3d, 141, 145 (4th Cir. 1995). Rice summarizes the Court’s application of the fallacy to the argument involved in the case in the following way: “The district court’s reasoning roughly reduces to the following syllogism: (1) If a debtor rejects a contract, then a general unsecured claim exists. (2) A general unsecured claim exists. (3) Therefore, the debtor must have rejected a contract. The district court’s conclusion does not follow from its premises.” as Rice notes, has described the fallacy of affirming the consequent in the following way (EXAMPLE 2):

*(1) If A is true, then B is true. *

*(2) B is true. *

*(3) Therefore, A is also true. *

As Rice points out here, “[t]he conclusion that A is true does not logically follow from the premises,” because “it is not disciplined about the order of the terms in the hypothetical premise.” Here is another example from Rice, putting some facts in context (EXAMPLE 3):

[** Hypothetical premise**]

*If the motorcycle’s engine starts, then there is gas in the gas tank.*

[** Categorical premise**]

*There is gas in the gas tank.*

[** Conclusion**]

*Therefore, the motorcycle’s engine starts.*

In EXAMPLE 3, the conclusion that “the motorcycle’s engine starts” does not logically follow from the premises. Although the hypothetical premise is true (gas in the gas tank is a necessary condition to start the engine), the gas in the tank is not sufficient for the engine to start. The fallacious pattern here violates the order of the terms and attempts to reach a conclusion by affirming the consequent term.

This fallacy is often committed when lawyers/advocates confuse the meaning of the word “if”, treating it as if it means “if, and only if,” which does not have the same meaning or logical function.

According to Rice, “[t]he logic of hypothetical syllogisms is about order and inference.” The rule of logic ensures that arguments that take the form of hypothetical syllogisms follow the right order of terms and justify the logical inference. The rule manages the limits of conclusions drawn from hypothetical propositions. In an argument where a categorical premise affirms the consequent term of the hypothetical premise, the syllogism commits the fallacy of affirming the consequent and its conclusion is fallacious.

*The Fallacy of the Undistributed Middle Term*

The fallacy of the undistributed middle term applies to categorical syllogisms, which, as described in my prior post, are arguments that draw conclusions by placing people, places, things, behavior, etc. into categories. In order to be persuasive, the categorical syllogism must follow the rules of logic.

The fallacy of the undistributed middle term has been described by a Maryland Appellate Court as a “linguistic sleight-of-hand … a perennial vexation in appellate litigation.”^{2}*Cooper v. Singleton*, 94 A.3d 250, 258 (Md. Ct. App. 2014). But in order to understand this fallacy, it is necessary to discuss the structure and components of a categorical syllogism.

As I explained in my prior post, a categorical syllogism is made up of a major premise, a minor premise, and a conclusion. The conclusion contains two terms: the ** subject term** and the

**. The term that is the predicate of the conclusion is the**

*predicate**term***. The premise that contains the major term is called the**

*major term***. The term that is the subject of the conclusion is the**

*major premise***, and the premise containing the minor term is called the**

*minor term***. When the conclusion affirms the major premise, the subject term is included in the predicate term, and if the conclusion denies the major premise, it is excluded. The term that appears in both major and minor premises is called the**

*minor premise***.**

*middle term*Here is an example from Rice in my prior post to refresh your memory (EXAMPLE 5):

**[ Major premise] **

*All valid corporations are legal entities with at least one shareholder.*

**[ Minor premise] **

*Excavation Solutions, Inc. is a valid corporation.*

**[ Conclusion] **

*Therefore, Excavations Solutions, Inc. is a legal entity with at least one shareholder.*

In this example, the middle term is “a valid corporation.”

The form of a categorical syllogism must comply with certain rules:

(1) A categorical syllogism can only have three terms and three propositions.

(2) The middle term in a categorical syllogism has to be distributed at least once.

(3) Any term distributed in the conclusion of a categorical syllogism must be distributed in the premises.

(4) There can only be one negative premise in a categorical syllogism. If there is a negative premise, the conclusion must be negative.

The ** fallacy of the undistributed middle term** occurs when the middle term does not refer to all members of the category. Here is one of Rice’s examples (EXAMPLE 6):

**[ Major premise]**

*Some persons who have a personal stake in litigation are persons who are not credible.*

**[ Minor premise]**

*The respondent is a person who has a personal stake in this litigation.*

**[ Conclusion]**

*Therefore, the respondent is a person who is not credible.*

In EXAMPLE 6, “a person who has a personal stake in this litigation” is the middle term. The conclusion of this syllogism is invalid because the middle term is undistributed in the two premises. In other words, the major premise does not include *all* members of the category of “persons who have a personal stake in the litigation.” The conclusion fails because we cannot logically draw the conclusion that the respondent is not credible, because only “some” and not “all” persons who have a personal stake in the litigation are not credible.

The defect in this illogical argument can easily be cured by changing the qualifier “some” to “all.”

Breaking down the components of a categorical syllogism to confirm that they comply with the requirements of each of the rules of formal logic can be burdensome. If you know the rules, all that is required to evaluate the structure of a categorical syllogism is, as Rice explains, to identify a faulty component or discover a violation of just one logical rule:

*Simply identifying a fallacious pattern of unreliable argument conclusively defuses the logical force of the argument and leaves its proponent to return to the hard work of finding one alternative argument to support their conclusion.*

*The Fallacy of the Illicit Process*

The fallacy of the illicit process is similar to the fallacy of the undistributed middle term in that it applies to categorical syllogisms. The ** fallacy of the illicit process** occurs when either the major or minor term is distributed in the conclusion, but not in the argument’s premises.

The first step in spotting this fallacy is finding the major and minor terms in the argument’s structure. As explained above, the major term is the predicate to the conclusion. The subject term in the minor premise is the minor term. Here is one of Rice’s examples (EXAMPLE 7), where the major term is italicized and the minor term is underlined:

[** Major premise**] Every [person who is a] seller of a residential property in South Dakota is [

*a person who is*]

*required to comply with the residential property disclosure requirements*under South Dakota statute.

[** Minor premise**]

__The defendant__was not a [person who is a] seller of residential property in South Dakota.

[** Conclusion**] Therefore,

__the defendant__was not [

*a person who is] required to comply with the residential property disclosure requirements*.

The second step is to test whether one or both of the minor or major terms are distributed in the conclusion, and whether their distribution is confirmed in one of the premises. Let’s look at another example from Rice (EXAMPLE 8):

[** Major premise**]

*No evidence denying the plaintiff’s allegations of libel is evidence that creates a genuine dispute as to any material fact.*

[** Minor premise**]

*Some of the plaintiff’s evidence is evidence denying the plaintiff’s allegations of libel.*

[** Conclusion**]

*Therefore, none of the plaintiff’s evidence is evidence that creates a genuine dispute as to any material fact.*

EXAMPLE 8 commits a ** fallacy of the illicit minor term**, because the conclusion distributes the minor term (“plaintiff’s evidence”) and the major term (“evidence that creates a genuine dispute as to any material fact”), but the qualifier “some” indicates that the minor term is not properly distributed in the minor premise. The rules of logic, as Rice notes, “prohibit a litigant from drawing any universal conclusion about the entirety of the plaintiff’s evidence from a few examples of the plaintiff’s evidence.”

Conversely, when the conclusion distributes the major term without distributing it in at least one of the premises, the argument commits the ** fallacy of the illicit major term**.

Knowing how to detect this fallacy helps to uncover fallacious logical structures that are not readily apparent. Logically fallacious arguments are generally made with seemingly true premises:

*[T]he fact that the arguer claims a conclusion results from two truthful premises suggests that there is something sound about the conclusion. While logic tells us this is not the case, there seems to be a psychological tendency in some cases to find a conclusion “truthful by association.”*^{3}*See *Stephen M. Rice,* The Force of Logic: Using Formal Logic as a Tool in the Craft of Legal Argument *(National Institute of Trial Advocacy, 2017, Chapter 8.4, referring to Deborah J. Bennett, Logic Made Easy 88 (2004) and N.E. Wetherick & K.J. Gilhooly, *‘Atmosphere’, Matching, and Logic in Syllogistic Reasoning*, 14 Current Psychology 169, 2 (1995).

Syllogistic arguments tend to have some credibility by their argumentative structure alone. Understanding the rules of logic allows us to test the logical structure of a syllogism and determine whether it “merely sounds good” or is it “logically reliable.”

*The Fallacy of the Negative Premise*

The ** fallacy of the negative premise** occurs when a negative premise – describing how one categorical term is excluded from another – is used to support an affirmative conclusion about any categorical term. The rules of logic dictate that in a categorical syllogism there can only be one negative premise. A negative premise must be paired with an affirmative one. If the premise is negative, the conclusion must likewise be negative. Any other combination of premises and conclusions (two negative premises, or a negative and affirmative premise and an affirmative conclusion) are always invalid.

In order to spot this fallacy, it is necessary to determine whether the respective premises and conclusion are affirmative or negative. Rice notes that “determining whether a proposition is affirmative or negative, sometimes referred to as its *quality*, is generally apparent from the language of the proposition and is rarely difficult to identify.” Here is one of Rice’s examples (EXAMPLE 9):

[** Major premise**]

*No life insurer less than one year after default in payment of any premium is a life insurer that may declare lapsed any policy without first providing notice.*

[** Minor premise**]

*No defendant is a life insurer less than one year after default in payment.*

[** Conclusion**]

*Therefore, the defendant is a life insurer that may declare lapsed any policy without first providing notice.*

This logical pattern violates the rules of logic because there are two negative premises (“no life insurer” and “no defendant”) leading to an affirmative conclusion (“the defendant is a life insurer”). In other words, both the major and minor premises are ** universal** (terms like “all,” “none,” or “no”) negative propositions, and the conclusion is a universal affirmative proposition. Aptly noted by Rice:

*[O]ne might be tempted to believe that logic compels this conclusion. However, there are likely other circumstances that limit an insurer’s ability to declare a life insurance policy lapsed. It would be a leap of logic to conclude that because one category of insurers cannot declare a policy lapsed without notice that another category of insurers can declare a policy lapsed without notice**.*

The fallacious pattern in the ** fallacy of the negative premise** is easy to spot. Syllogisms that commit this fallacy infer the pattern of an affirmative conclusion from one or two negative premises. Understanding this rule allows us to test the structure of an argument that otherwise might be seemingly valid.

*The Fallacy of Affirming a Disjunct*

The ** fallacy of affirming a disjunct** applies to disjunctive syllogisms. To recap (

*see*the nomenclature above), a disjunctive syllogism is an argument that typically contains the logical operator “or”, known in linguistics terminology as a

**. The disjunctive syllogism is made up of a disjunctive premise, a categorical premise, and a conclusion. The two terms of a disjunctive premise are called**

*disjunction***.**

*disjuncts*Here is one of Rice’s examples of a valid disjunctive argument (EXAMPLE 10):

[** Disjunctive premise**]

*The driver was watching the car in front of him or he was texting his client.*

[** Categorical premise**]

*The*

*driver was not texting his client.*

[** Conclusion**]

*Therefore, the driver was watching the car in front of him.*

A valid disjunctive syllogism occurs, as Rice explains, “where the categorical premise denies one disjunct to affirm the other in the conclusion.”

The first step in identifying the ** fallacy of affirming a disjunct** is to assess whether the argument affirms or denies one of the disjuncts.

The second step is to determine whether the disjunction is inclusive or exclusive. An ** inclusive** disjunction is true if one or both disjuncts are true. The

**disjunction is false only if both disjuncts are false. An exclusive disjunction is true only if one disjunct is true and the other is false. If the disjunction is inclusive, potentially, the argument could commit the fallacy of affirming the disjunct.**

*inclusive*Let’s look at another example from Rice (EXAMPLE 11):

[** Disjunctive premise**]

*The driver was watching the car in front of him or he was texting his client.*

[** Categorical premise**]

*The driver was texting his client.*

[** Conclusion**]

*Therefore, the driver was not watching the car in front of him.*

In this example, the categorical premise affirms one of the disjuncts and attempts to negate the remaining disjunct in the conclusion. The rule governing the structure of a disjunctive syllogism does not assume that the disjunction is exclusive. Going back to the example, a driver can both text his client and watch the car in front of him at the same time. The argument in EXAMPLE 11 is only valid if it is made clear that the disjunction is exclusive; put differently, if the driver could only be doing one of those two activities (and not the other).

The ambiguous nature of the disjunction is the primary source of confusion among lawyers in deconstructing illogical and invalid disjunctive syllogisms. The ** fallacy of affirming a disjunct** provides a tool to test the structure of an argument and spot the invalid one. According to Rice:

*Those who draft legal language sometimes fail to define the nature of the disjunction involved in the language of statutes, regulations, policies, contracts, and opinions they draft. Sometimes problems with the logic of disjunction in legal argument are as much about resolving the question of intent in ambiguous usages of the word “or” as they are about applying the simple rules for valid disjunctive syllogisms.*

*The Rules of Formal Logic – A Summation*

To summarize, there are six rules of formal logic discussed by Rice that apply to each specific type of syllogism discussed above and in my prior post – hypothetical, categorical, and disjunctive.

The first rule is two-fold and applies only to hypothetical syllogisms:

(1) A hypothetical syllogism must take one of two forms. First, a hypothetical syllogism is valid where the categorical premise affirms the truth of the antecedent term of the hypothetical premise and the consequent term of the hypothetical premise is the conclusion. Alternatively, a hypothetical syllogism is valid where the categorical premise affirms the falsity of the consequent term of the hypothetical premise, and the conclusion asserts the falsity of the antecedent term of that hypothetical premise.

The next four rules apply only to categorical syllogisms:

(2) A categorical syllogism can only have three terms and three propositions.

(3) The middle term in a categorical syllogism has to be distributed at least once.

(4) Any term distributed in the conclusion of a categorical syllogism must be distributed in the premises.

(5) There can only be one negative premise in a categorical syllogism. If there is a negative premise, then the conclusion must be negative.

The sixth rule applies only to disjunctive syllogisms:

(6) A valid disjunctive syllogism is one where the minor premise denies one of the disjuncts of the major premise and the conclusion affirms the remaining disjunct.

*Fallacy-Based Perspectives on Legal Argumentation and the Value of Logic for Lawyers*

Each of the rules of logic and the logical fallacies presented in Rice’s *The Force of Logic* should provide you with some of the necessary tools to craft well-reasoned, well-supported, and logical arguments. They should also assist you in deconstructing the arguments of your opponent or the court’s findings of facts and conclusions of law, explaining why and how certain arguments, findings, or conclusions are persuasive or unpersuasive.

Though useful, deductive reasoning and the rules of formal logic do have limits. The fact that an argument commits a logical fallacy does not necessarily mean the conclusion is false; it merely means that the argument does not comport with the formal rules of logic. A logical fallacy says nothing about the *truth* or *falsity* of the assertion being made, it merely concerns the logical form of the argument.

Formal logic is just one of the many tools in a lawyer’s tool-box in developing arguments and deconstructing the opponent’s arguments, but it does not supplant legal reasoning and the requisite understanding of the rules of law.

*The Force of Logic* is worth a careful, thorough study to sharpen one’s legal arguments and expand the arsenal of tools to craft and deconstruct legal arguments. I could not agree more with Rice when he says:

*Lawyers who master the logical framework of the arguments they make and respond to empower themselves to leverage logic [are able to] be more creative, to manage complex factual and legal problems, and to translate legal concepts into arguments that will be understood by and persuasive to the clients, judges, and jurors in their audience.*

Footnotes