Basic categories of argumentation in legal reasoning

Handbook for Judicial Officers

Basic categories of argumentation in legal reasoning

The significance of logic for law
Basic logic terms and concepts
Basic categories of argumentation
Inductive reasoning
Deductive reasoning
Conclusion

Basic categories of argumentation in legal reasoning¹

Professor Douglas Lind²

While many factors such as public policy, science, psychology, moral values, ideals of justice, etc, permeate the deliberations and decision-making of lawyers and judges, such considerations are intertwined inextricably with reason and logic. This article provides an introduction to the principles of logic and methods of argumentation most common to law and legal discourse. By way of introduction, the author provides a useful overview of the basic terms and concepts used in the study of logic. He then focuses his discussion on the two broad categories of logical reasoning: inductive reasoning (analogy and inductive generalisation) and deductive reasoning (especially deductive syllogisms in their various forms), and explains how these categories differ. The author contends that although the latter form of reasoning has not been prominent in legal thinking since early in the 20th century, an understanding of it will give judicial officers an invaluable tool for assessing whether arguments found in submissions or judicial opinion are sound and warrant acceptance. The author explains the various forms of reasoning, exposes the fallacies in reasoning of each form of argument and, considers the criteria against which inductive reasoning is assessed. He provides useful illustrations of the forms of argument discussed, including some case law examples.

The essence of the rule of law is that the logic of private force be replaced by the public force of logic.³

The significance of logic for law

Around the turn of the 20th century, those at the forefront of the Legal Realist movement decried over-reliance on logic in law and judicial decision. Ever since, judges and lawyers in common law jurisdictions have minimised the importance of formal logic for understanding law and legal reasoning.

Many legal practitioners have feared that to acknowledge logic as central to law would risk a return to the rationalistic excesses of the formalistic jurisprudences that proliferated in 19th century legal thought. For it was against that formalist tradition that the Legal Realist jurists, along with their Free Law counterparts on the European continent, directed much of their critical energies early in the 20th century. It was in spirited opposition to that tradition that Oliver Wendell Holmes, Jr, penned his most famous aphorism: “[t]he life of the law has not been logic: it has been experience”.⁴

There is good reason to retain a sceptical attitude towards overly rationalistic accounts of law and judicial practice. The weave of historical doctrine, legal principle, and factual circumstances that comprises judicial decision-making is far too intricate to allow critical appraisal under any single evaluative method, including the principles of logic. So we are rightfully uneasy when we are reminded of the formalistic visions of the 19th century jurists — visions that perceived the essence of adjudication as reducible to simply the logical derivation of conclusions required necessarily by predetermined legal principles.

Somewhere between the extremes of strict formalistic jurisprudence and an outright disregard for logic and argumentative form, however, lies the mid-range of practice where law and judicial decision-making do their work. The pithy remark quoted above is all that is typically given to represent Holmes J’s view towards the role logic plays in judicial decision. Yet a broader look at his jurisprudential writings together with his judicial opinions reveals that he fully considered logic to be a central aspect of law and judicial decision-making.⁵ In this regard Holmes was not alone. For a number of other major 20th century writers on jurisprudence, such as Benjamin Cardozo,⁶ John Dewey,⁷ Julius Stone,⁸ and HLA Hart,⁹ agreed that evaluating and creating arguments sits at the core of the crafts of judging and lawyering. Edwin Patterson stated it well when he suggested that the rules of logic “are so ingrained in the pattern of legal reasoning that … [p]erhaps formal logic has as much to do with (articulated) legal reasoning as Euclidean geometry has with building houses”.¹⁰

Practitioners of the law thus can well benefit from possessing an understanding of the principles of logic that regularly are used in legal reasoning and judicial decision-making. Such an understanding requires, in important part, skill in working with the processes of inductive reasoning — the logical methods of analogy and inductive generalisation — by which inferences are drawn on the basis of experience and empirical observation. The common law method of doctrinal development through case law, as well as the general norm known as “the Rule of Law” — that like cases should be decided alike — are grounded logically in inductive reasoning.

Equally important for legal reasoning is a second general category of argumentation — deductive logic, especially the forms of argument known as “syllogisms”. These are the familiar forms of deductive argument consisting of two premises and a conclusion. This is the aspect of logic that early in the 20th century stirred such spirited opposition to formalism. It is also the aspect of logic that has been so minimised in legal thought ever since. That is unfortunate. For even a modest understanding of deductive logic gives those engaged in legal practice — especially judicial officers — an invaluable tool for assessing whether an argument found in a set of submissions or a judicial opinion is sound and warrants rational acceptance or suffers from a logical fallacy that makes it unworthy of further consideration.

The purpose of this article is to provide an overview of the principles of logic and methods of argumentation that are most common to law and judicial practice. The article concentrates on the two general categories of logical reasoning: inductive reasoning (analogy and generalisation) and deductive reasoning (especially deductive syllogisms). In his Rhetoric, Aristotle wrote that “every one who proves anything at all is bound to use either syllogisms or inductions”.¹¹ Modern logic has moved in directions more complex and symbolic than those two general categories. Still, deductive syllogisms and inductive reasoning remain remarkably useful for understanding the basic structures and forms of reasoning used in law and legal discourse. For that reason, this article focuses on setting forth a number of key considerations for developing a good working knowledge of those two categories of argumentation.

Basic logic terms and concepts

A number of terms and concepts central and craft-bound to the study of logic appear in this article. Among the most basic are the following:

Proposition or statement: A proposition or statement is an assertion or claim which is either true or false, and which can be either asserted or denied. Propositions differ in these respects from questions, exclamations, and commands.
Argument: An argument is a group of propositions wherein one proposition is claimed to follow logically from the others. The others are treated as providing grounds or support for the truth of that one. An argument is not just a collection of propositions, but a group with a particular structure.
Conclusion: The conclusion of an argument is the one proposition that is arrived at and said to follow from the other propositions of the argument.
Premises: The premises of an argument are the propositions which are assumed or otherwise accepted as providing reasons or support for accepting, as true, the one proposition which is the conclusion.
Premise and conclusion are “relative” terms: A proposition can serve as the conclusion of one argument while it is a premise in another argument. Moreover, premises and conclusions require each other. A proposition standing alone is neither a premise nor a conclusion. Only when it serves as an assumption in an argument is a proposition a premise. A proposition is a conclusion only when it is said to logically follow from other propositions with which it is joined to form an argument.
Inference: The term “inference” refers to the logical process that takes place in an argument. The premises of the argument are said to “infer” the truth of the conclusion. That is to say the premises provide reasons, grounds, support, or justification for accepting the conclusion’s truth.
Valid/validity: Validity is an evaluative concept that expresses approval of the form or structure of an argument. A valid argument is one with a form that allows for the drawing of a necessarily true conclusion. The concept of validity applies only to deductive arguments.
Truth: Truth is an evaluative concept that expresses approval of the content or subject matter stated in the individual propositions in an argument. The concept of truth applies to propositions or statements found in both inductive and deductive arguments. However, its application is limited to the individual propositions themselves. An argument, taken as a whole, does not have truth value.
Sound/soundness: Soundness is an evaluative concept that expresses full approval of a deductive argument. A sound deductive argument has both valid form and true premises. Its conclusion is necessarily true.
Fallacy: A fallacy is a logical error in reasoning. All fallacious reasoning produces conclusions that are not logically justified. Fallacies can be either “formal” or “informal”. A formal fallacy is a logical error found in the form or structure of a deductive argument. A deductive argument that commits a formal fallacy is both invalid and unsound. Informal or material fallacies are logical errors in reasoning that do not go to the form of an argument but to its content or subject matter. Arguments that commit informal fallacies are often valid in form and may be intuitively or psychologically compelling. They are fallacious in that they attempt to draw unjustified inferences from premises that do not provide sufficient, reliable grounds for their conclusions. Informal fallacies can be divided into the categories of fallacies of relevance and fallacies of language or rhetoric.

Premise indicators: Certain words and phrases frequently signal the premises of an argument. These terms, sometimes called “premise indicators”, typically indicate that what follows is a premise. Not uncommonly, the conclusion of an argument is stated immediately preceding a premise indicator. Common premise indicators include:

because	follows from	insofar as
given that	for	in virtue of
since	for the reason that	may be inferred from
as	in view of the fact	may be deduced from
as shown by	inasmuch as	may be derived from

Conclusion indicators: There are also several words and phrases that commonly mark the conclusion of an argument. These “conclusion indicators” typically indicate that what follows is the argument’s conclusion. Common conclusion indicators include:

therefore	as a result	finally
thus	so	follows that
hence	in conclusion	implies that
accordingly	in consequence	entails that
consequently	may infer	shows that

Arguments without indicators: While indicator terms are present in many arguments and tend to be very helpful in identifying premises and conclusions, not every argument contains these versatile logical expressions. It is common, especially in oral communication, for arguments to proceed without indicator terms. The nature and immediacy of verbal exchange, particularly face-to-face dialogue, together with the interpretive aids that come from gestures and inflections make indicator terms often unnecessary. Consider the following verbal exchange between three patients in an asylum:¹²

NEWTON: But damn it all, we’re not mad.

MÖBIUS: But we are murderers.

They stare at him in perplexity.

NEWTON: I resent that!

EINSTEIN: You shouldn’t have said that, Möbius!

MÖBIUS: Anyone who takes life is a murderer, and we have taken life …

No indicator terms are needed here for Dr Möbius to clearly make his point: that from the premises — “Anyone who takes life is a murderer”, and “We have taken life” — it logically follows that, “We are murderers”. The context makes indicator terms unnecessary.

Basic categories of argumentation

Stated most generally, there are two basic categories of argumentation — deductive arguments and inductive arguments. It can be helpful to think of these two categories as differing from one another in the following ways:

Inferential strength of the relation between premises and conclusion: Every argument involves a claim that its premises provide some support or justification for accepting the truth of the conclusion. Deductive and inductive arguments differ in terms of the inferential strength the premises provide for the conclusion.

(i)

In deductive arguments, the premises, if true, are treated as providing conclusive grounds for the truth of the conclusion, that is, that the conclusion must be true or is necessarily true. The inferential strength of the relation between premises and conclusion is one of necessity.

(ii)

In inductive arguments, the premises, if true, are treated as providing some grounds or support for the truth of the conclusion, that is, that the conclusion is probably true, or more likely true than not. The inferential strength of the relation between premises and conclusion is one of probability.
Containment of the conclusion within the premises: Another way of looking at the different premises-conclusion relationships involved in deductive and inductive reasoning is to consider whether the conclusion asserts something to be true that “goes beyond” what is implicitly stated or “contained within” the premises.

(i)

The premises of a valid deductive argument, if true, entail the necessary truth of the conclusion. This makes deductive reasoning a powerful logical tool, for it provides a basis for accepting the truth of a conclusion where there is no room left for rational doubt. Yet this inferential relationship of necessity also stands as a limitation. For the certainty of the conclusion is possible only because its truth is already “contained within” the premises. Deductive reasoning accordingly does not take us beyond what we by implication already know.

(ii)

Inductive reasoning is very different. Induction involves rational processes whereby we infer conclusions that go beyond what is by logical implication contained within the premises. The conclusions of inductive arguments assert new claims of knowledge that are not already present in the premises. The limitation in inductive reasoning is one of risk of error. Since the truth of the conclusion is not “contained within” the premises, it is not proven to be true necessarily. The truth of the conclusion in inductive reasoning thus is always clothed in an element of doubt. For when our inference goes beyond what is present already in the premises, we do not entail the necessary truth of the conclusion, but only its truth to a greater or lesser degree of probability.
Evaluation: Finally, deductive and inductive arguments differ in terms of evaluative descriptors. The evaluative concepts of validity and soundness apply to deductive arguments, but not inductive.

(i)

A deductive argument is valid when its formal structure is such that its premises, if true, provide conclusive grounds for the truth of the conclusion. When a deductive argument has both valid form and true premises, it is said to be a sound argument.

(ii)

Inductive arguments cannot appropriately be evaluated as valid or invalid; nor can they be said to be sound or unsound. This is because the concepts of validity and soundness are attached to arguments whose form permits the drawing of a necessarily true conclusion, a degree of inferential strength unattainable by inductive reasoning. Inductive arguments lead to conclusions that are true to greater or lesser degrees of probability. They are better or worse, given the degree or strength of support the premises provide for the conclusion. A persuasively strong inductive argument with true premises is sometimes called a cogent argument.

Inductive reasoning

Reasoning by analogy

Arguments by analogy are inductive arguments which assert that since some percentage of one or more things (the sample) possesses a property, it can be inferred that some similar thing or things (the target) is more likely than not to have that property as well. The target of an argument by analogy is usually, though not always, an individual thing. It can be helpful to think of reasoning by analogy as reasoning by comparison, or as Aristotle put it, reasoning by “example”.¹³ Reasoning by analogy (or example) involves comparing two things (sample and target) and then inferring, based on similarities and resemblances, that what is known to be true about the members of the sample is probably true as to the target. The logical structure of an argument by analogy can be understood as taking the following form:

(1) One or more things (sample S) is known to have property P.
(2) Sample S resembles or is relevantly similar to some other thing (target T).
(3) Therefore, it is probable that target T also has property P.

In assessing the strength of an argument by analogy, several criteria are relevant:

Size of the sample: In general, the larger the sample population, the stronger the argument for inferring that the target probably has the property too.
Percentage of the sample that has the property: The greater the percentage of the sample population that is known to have the property, the stronger the argument. If 100% of the members of the sample are known to have the property, the inference that can be drawn about the likelihood of the target possessing the property is stronger than if, say, only 75% of the sample have the property.
Similarities or resemblances: The greater the number of similarities, likenesses, and resemblances between the target and the members of the sample, and the fewer the number of dissimilarities or differences, the stronger the argument.
Relevance of the similarities or dissimilarities: In most situations where comparisons are drawn, some similarities and dissimilarities will be more important than others. The importance of a similarity or dissimilarity, a resemblance or difference, is a product of how relevant or material it is toward establishing the truth of the analogical argument’s conclusion.
Diversity within the sample: With regard to a characteristic or feature that as far as is known the target may or may not have, the greater the diversity within the sample, the stronger the argument.

While reasoning by analogy is commonplace in law (as in daily life), it is critical to employ this form of reasoning with care, for “analysis by analogy is problematic and the issues are never exactly the same”.¹⁴ The comparison called for in analogical reasoning requires thoughtful attention to the specifics and nuances of resemblance and difference that hold between the sample and target things. Given that not only issues but facts and circumstances are never precisely the same, it is essential that judicial officers exercise caution in drawing inferences on the basis of analogy.

Fallacies in reasoning by analogy

There are no formal fallacies associated with reasoning by analogy. Reasoning by analogy is fallacious when the content or material of the argument leads to inferences that are “strained”, “false”, “weak”, “overbroad”, or “questionable”. That is, reasoning by analogy is unreliable (fallacious) if the analogy or comparison drawn between the sample and target populations seems on balance, as a matter of fact or evidence, unreasonable or otherwise unconvincing. An analogy is “strained” when the similarities and resemblances between the sample and target lack relevance or appear too distant. An analogy is “false” when the sample and target are truly more dissimilar than similar. An analogy is “weak” when there is some minimal level of resemblance between the sample and target, but it is not enough to support the logical inference proposed. An analogy is “overbroad” when there is some degree of similarity and resemblance between the sample and target, but the analogy is being pushed too far. Finally, drawing an inference by analogy is “questionable”, even when the sample and target are relevantly similar, if the nature of their resemblance does not provide a reasonable basis for the conclusion the argument aims to establish, or if the argument appears to gloss over relevant differences.

References to these fallacies associated with reasoning by analogy are quite common in judicial decision-making. Courts often reject arguments by analogy that are proposed by litigants, and not uncommonly the rejection is couched in the terms mentioned. For example, the US federal district court in Ralston v Capper¹⁵ refused to draw an analogy between federal antitrust law and the Racketeer Influenced and Corrupt Organizations Act 1970 (RICO). The court reasoned that the proposed argument appeared “to be based on a strained analogy to antitrust law, … [even though] analogies to limitations on standing in the antitrust context are entirely inappropriate here”.¹⁶ Though the court rejected the analogy as “strained”, it could equally well have called it a “false” analogy, as the following passage from the opinion shows that the court reasoned that the two statutory schemes were, in relevant part, more dissimilar than similar:¹⁷

The antitrust laws are designed to promote competition in the marketplace

...

RICO has the opposite purpose. It is precisely designed to ruin those individuals and enterprises it is aimed at. It is not designed to increase their efficiency or protect them from insolvency. Thus, the rationale behind the antitrust standing concerns have no applicability here.” [Emphasis in original.]

Innumerable judgments have rejected proffered arguments by analogy on the basis of their setting forth a false analogy.¹⁸ Likewise, judicial opinions not uncommonly find analogical arguments unconvincing (and hence fallacious) because they attempt to draw an inference as to how a target thing has a certain property based on a weak, overbroad, or otherwise questionable analogy between the target and the sample population.¹⁹

Inductive generalisation

Arguments by inductive generalisation infer general conclusions from what is known about a number of particular instances. A generalised inductive inference asserts that since some percentage of a subgroup (the sample) drawn from a class of things (the target) is known to possess a property, it is more likely than not that the entire target class possesses that property to the same extent. The target of an argument by inductive generalisation is always an entire class, and the sample of the generalisation is drawn from that target population. The basic logical structure of an argument by inductive generalisation is as follows:

(1) All (or some percentage of) similar things (sample S) are known to have property P.
(2) Sample S is a representative subgroup of the general class or category target T.
(3) Therefore, it is probable that all (or a given percentage) of target T has property P.

As with arguments by analogy, a number of criteria determine the strength of an argument by inductive generalisation:

Size of the sample relative to the size of the target: In general, the greater the size of the sample population relative to the known or believed size of the target population, the stronger the generalisation.
Percentage of the sample that has the property: The greater the percentage of the sample that is known to have the property, the stronger the claim as to what can be known about the distribution of the property across the entire population of the target class.
Representativeness of the sample: The more representative the sample is believed to be across the entire target population, the stronger the generalisation. A sample is representative of a general target population to the extent it possesses all relevant features of the target and to possess them to the same degree or proportion as the general target population, and does not possess any idiosyncratic features.

Fallacies in reasoning by inductive generalisation

Again, as with arguments by analogy, there are no formal fallacies associated with reasoning by inductive generalisation. There are, however, three named fallacies commonly identified with reasoning in the pattern of a generalised inductive inference:

Fallacy of hasty generalisation: The fallacy of hasty generalisation is committed when a generalisation rests on an inadequate number of instances — that is, the sample is too small or not representative of the entire target population. Since the strength of an inductive generalisation depends primarily on the number of representative instances, it is fallacious to move too quickly (or hastily) to a generalised conclusion.
Fallacy of anecdotal evidence: The fallacy of anecdotal evidence is somewhat the opposite of the fallacy of hasty generalisation. This fallacy occurs when a small number of disconfirming instances is treated as a sufficient reason to reject a generalisation for which there is otherwise a sufficiently large and representative sample.
Accident fallacy: The accident fallacy is very different than the fallacies of hasty generalisation and anecdotal evidence. Those fallacies are committed in the process of drawing a generalised inference. The fallacy of accident, by contrast, takes place in the context of applying to an individual case a generalisation that has already been drawn. The accident fallacy occurs when a generalised proposition (or general rule) is applied in a too rigid or careless manner. In law, the fallacy is committed when a judicial officer or lawyer moves too quickly from a general rule to a particular case, without giving due consideration to whether the case presents special (“accidental”) circumstances which place it outside the general rule.

Deductive reasoning

The most common forms of deductive argument found in legal reasoning are those known as “syllogisms”. The term comes from Aristotle: “A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so”.²⁰ Structurally, a syllogism is any deductive argument that strives to draw a necessary inference on the basis of three propositions or statements: two premises and a conclusion. The four most common deductive syllogisms are categorical syllogisms, hypothetical syllogisms, disjunctive syllogisms and conjunctive syllogisms.

Categorical syllogisms

A categorical syllogism is a deductive argument wherein all three of the argument’s statements are “categorical propositions”. Categorical propositions are statements that assert or deny relationships. Every categorical proposition has two “terms” — that is, two things, classes, or categories about which something is said in the proposition. The two terms are called the subject term and the predicate term. The nature of a categorical proposition is to assert or deny that a relationship exists between the subject term of the proposition and the predicate term. For example, the claim, “All kangaroos are marsupials”, is a categorical proposition asserting that each and every member of the category or class represented by the subject term “kangaroos” falls within the predicate class, “marsupials”. The statement, “Aristotle is not a bandicoot”, is also a categorical proposition, though of a different kind. This statement denies that a relationship exists between the particular thing referenced by the subject term (“Aristotle”) and the entire membership of the predicate class (“bandicoots”).

There are four ways that categorical propositions relate classes or categories, one to another. These are often referred to as the four standard forms of categorical propositions. Each standard-form categorical proposition has a name: universal affirmative, universal negative, particular affirmative, and particular negative. By convention, each also goes by a letter, respectively, A, E, I, O. The nature of the claim made by each standard-form categorical proposition also can be represented by a formal logical statement using the letters S and P as place-holders for the proposition’s subject and predicate terms. The claims made by each form of categorical proposition are — universal affirmative: All S is P; universal negative: No S is P; particular affirmative: Some S is P; particular negative: Some S is not P. The four standard forms can be summarised as follows:

[A] Universal affirmative categorical proposition — All S is P: This form of categorical proposition asserts a relationship of containment, such that each and every member of the first-stated class (the subject class) is said to be a member of (included or contained within) the second class (the predicate class).
[E] Universal negative categorical proposition — No S is P: This form of categorical proposition states that no relationship exists between the memberships of the two classes — that is, that no member of the subject class is also a member of the predicate class.
[I] Particular affirmative categorical proposition — Some S is P: This form of categorical proposition expresses a relationship of partial containment, in that some (at least one) but perhaps not every member of the subject class are said also to be members of (included or contained within) the predicate class.
[O] Particular negative categorical proposition — Some S is Not P: This form of categorical proposition asserts a relationship of partial non-containment, such that some (at least one) but perhaps not every member of the subject class are said not to be members of (included or contained within) the predicate class.

Categorical syllogisms: standard-form

The basic requirements for an argument to be a categorical syllogism with the possibility of being valid in form are the following:

both of the argument’s premises and its conclusion must be categorical propositions
collectively, those three categorical propositions must contain exactly three different terms (that is, three different things, classes, or categories about which something is asserted), and
each of the three terms must occur twice in the argument (that is, be present in two different propositions).

Deductive arguments that satisfy these three requirements and are arranged in a certain order are said to be standard-form categorical syllogisms.

Of the three categorical propositions in a standard-form categorical syllogism, one is designated the conclusion, the other two are premises. The identity of each proposition as a premise or conclusion is determined by the terms it contains. The three terms are known as the major term, the minor term, and the middle term. Their identities are determined by their positions within the categorical syllogism, as follows:

Major term: the term that occurs as the predicate of the conclusion.

Minor term: the term that occurs as the subject of the conclusion.

Middle term: the term that does not occur in the conclusion, but appears in both premises.

Every categorical syllogism states in its conclusion that a relationship exists or does not exist between its minor term and its major term. The two premises assert that each of those terms, minor term and major term, stand in a certain relationship to a common third term, the middle term. While it does not figure in the conclusion, the middle term provides the critical link that makes reasoning by categorical syllogism possible.

When in standard form, a categorical syllogism presents what is called its major premise first, followed by its so-called minor premise, and then the conclusion. The determining feature that makes one premise the major premise is that it contains the major term (that is, the predicate term of the conclusion). The minor premise is the premise that contains the minor term (the subject term of the conclusion). A standard-form categorical syllogism is thus stated as follows:

Major premise: contains major term and middle term

Minor premise: contains minor term and middle term

Conclusion: contains minor term and major term as, respectively, its subject term and its predicate term.

The classic example of a categorical syllogism is found in the claim, “Since Socrates is human and all humans are mortal, Socrates is mortal”. This argument can be stated as a standard-form categorical syllogism in the following way:

Major premise: All humans are mortal.

Minor premise: Socrates is a human.

Conclusion: Therefore, Socrates is mortal.

This form of categorical syllogism represents a very common form of argument in law and judicial decision-making. Consider the following passage from Marshall CJ in the US Supreme Court’s decision in United States v Bevans:²¹

[T]he jurisdiction of a state is co-extensive with its territory; co-extensive with its legislative power.

The place described [Boston Harbor] is unquestionably within the original territory of Massachusetts. It is then within the jurisdiction of Massachusetts.

This passage precisely mirrors the Socrates argument. Chief Justice Marshall’s reasoning can be stated in the form of a standard-form categorical syllogism:

Major premise: All places within the territory of a State are places within the jurisdiction of the State.

Minor premise: Boston Harbor is a place within the territory of the State of Massachusetts.

Conclusion: Therefore, Boston Harbor is a place within the jurisdiction of the State of Massachusetts.

As an argument identical in form to the Socrates argument, the Bevans argument from Marshall CJ carries the same logical force in terms of validity. This is because the validity of a categorical syllogism is entirely a product of the argument’s form — ie, its formal structure as determined by the types of categorical propositions it contains and the positioning of its terms. A valid categorical syllogism is thus valid solely by virtue of its form. Content, subject matter, and the truth or falsehood of its propositions have no bearing on the argument’s validity. Since validity is entirely a matter of formal structure, categorical syllogisms that take the same form are the same in terms of validity, regardless of content. If we know that a certain form of categorical syllogism is valid (for example, the Socrates argument), then another argument in that same form (Bevans) is valid too. This holds even if one or more of the categorical propositions in the argument are false. Consider this argument:

Major premise: All night parrots are dead.

Minor premise: A certain bird photographed (much alive) and captured on video in early July 2013 in western Queensland was a night parrot.

Conclusion: Therefore, that certain bird photographed (much alive) and captured on video in early July 2013 in western Queensland was dead.

This argument is valid. But it is not sound. The logical form of the argument matches exactly the form of the Socrates and Bevans arguments. All three arguments begin with a universal affirmative categorical proposition followed by two particular affirmative categorical propositions follow (AII sequence of categorical propositions). The terms in the arguments also occupy the same positions. While the three arguments follow the same form (which happens to be valid), the night parrot argument is obviously troublesome. Its trouble lies in falsehood; either its major premise or minor premise is not true. And the conclusion is nonsensical. The lack of truth, however, does not affect the validity of the argument. It is valid, but due to the fact that its major premise is false, the argument is unsound.

Determining the validity of categorical syllogisms

Every categorical syllogism in standard form can be tested for validity by enquiring whether it violates one or more rules which must all be satisfied for a categorical syllogism to be valid. If a form of categorical syllogism fails to satisfy any one (or more) of the rules, that form is invalid; and every argument that takes that form is invalid, regardless of the truth of its content. Each rule has associated with it a particular formal fallacy. The five standard rules of validity, along with their associated fallacies, are set out below:

Rule 1: Three terms rule Every valid categorical syllogism contains precisely three terms, each of which is used in the same sense throughout the argument.

Fallacy: Fallacy of four terms or fallacy of equivocation
Rule 2: Middle term distribution rule In every valid categorical syllogism, the middle term is distributed in at least one premise.

Fallacy: Fallacy of the undistributed middle term
Rule 3: Conclusion distribution rule In every valid categorical syllogism, any term distributed in the conclusion is also distributed in the premise where it appears.

Fallacy: Fallacy of the illicit process of the major term or minor term
Rule 4: Negative premise rule No valid categorical syllogism has two negative premises.

Fallacy: Fallacy of exclusive premises
Rule 5: Negative conclusion rule Every valid categorical syllogism with one negative premise has a negative conclusion.

Fallacy: Fallacy of an affirmative conclusion from a negative premise

With these rules in hand it is possible to confirm the validity or prove the invalidity of any categorical syllogism. The form represented by the Socrates/Bevans/night parrot arguments is valid for it satisfies all the rules. It is, as a matter of fact, the most common form of categorical syllogism used in law and ordinary life. Yet just one slight modification from that argument form yields an invalid argument. In the familiar valid form, the middle term (the term that appears in each premise) is positioned as the subject term in the major premise and the predicate term in the minor premise. If instead of that placement, the middle term serves as the predicate term in each premise, the argument is invalid. Consider:

(1) All Hulme Supercars are orange.
(2) Betty’s car is orange.
(3) Therefore, Betty’s car is a Hulme Supercar.

The fallacy this form of categorical syllogism commits is that of the undistributed middle term. This is the most vexing fallacy in reasoning by way of categorical syllogisms. It vexes because it can be difficult to detect and is committed in arguments that are extremely close in formal structure to the most common form of categorical syllogism.

Another invalid categorical syllogism that is close in form to the Socrates/Bevans/night parrot form results from beginning an argument with a particular affirmative major premise instead of the universal affirmative categorical proposition found in the major premise of that most familiar form. This would be to argue like:

(1) Some controversial historical figures from the 19th century were scientists.
(2) Ned Kelly is a controversial historical figure from the 19th century.
(3) Therefore, Ned Kelly was a scientist.

Again, the error of reasoning here is the fallacy of the undistributed middle term. For a categorical syllogism to be valid, the middle term must be distributed in at least one of the premises. Each term in a categorical proposition is either distributed or not. For a term to be distributed means that what is said about it in a categorical proposition involves a claim of knowing something to be true about each and every individual in the entire class or category to which the term refers. Thus, the universal affirmative statement, “All kangaroos are marsupials”, asserts a claim of knowing that each and every member of the category represented by the subject term “kangaroos” falls within the predicate class “marsupials”. The subject term “kangaroos” is thus distributed. The statement does not, however, imply knowing anything to be true about every member of the class “marsupials”; hence, that predicate term is not distributed. A universal affirmative categorical proposition accordingly distributes its subject term but not its predicate term. By contrast, in the particular affirmative categorical proposition form (for example, “Ned Kelly was a scientist”), neither subject nor predicate term is distributed.

Failure to distribute the middle term renders a categorical syllogism invalid regardless of the argument’s content. Were Charles Darwin substituted for Ned Kelly in the argument above, it would read:

(1) Some controversial historical figures from the 19th century were scientists.
(2) Charles Darwin is a controversial historical figure from the 19th century.
(3) Therefore, Charles Darwin was a scientist.

All three propositions in this syllogism are true. Still the argument remains invalid. The fallacy remains the undistributed middle, as it will for every argument that takes this form, no matter the content. For the middle term (here “controversial historical figures from the 19th century”) must be distributed for a categorical syllogism to be valid. This is because the middle term is the argument’s yeoman. While the purpose in arguing by way of a categorical syllogism is to draw a necessary inference about how the minor term relates to the major term, it is the middle term that does the inferential work. The two premises assert relationships between the major and minor terms and the middle term. That middle term is the class or category that they share in common. If the middle term is not distributed in at least one premise, it cannot do its work of bringing the minor and major terms together by necessary inference.

Unfortunately, categorical syllogisms that commit the fallacy of the undistributed middle term are all too common in legal reasoning. Many cases discuss the fallacy. One is the US Court of Customs and Patent Appeals’ judgment in Atlantic Aluminum & Metal Distributors, Inc v United States.²² This case concerned a dispute over the appropriate classification of an importer’s merchandise for the purpose of assessing import duties under the federal Tariff Act of 1930. The merchandise consisted of aluminum tubes. The importer sought to have the tubes classified with bars and rods, which would significantly lower the import duty from the assessment resulting from the classification used by the government. The principal evidence submitted by the importer were definitions from various dictionaries meant to establish the common meaning of the terms “bars” and “rods”. Finding the definitions inconclusive, the court reasoned:²³

These definitions establish that a bar or a rod is “long in proportion to its breadth and thickness”. The evidence establishes that the imported tubes are also “long in proportion to [their] breadth[s] and thickness[es]”. From these premises the importer asks us to find that tubes are bars and rods. This constitutes an invalid syllogism. The undistributed middle term prevents reliance upon the premises to support the importer’s conclusion. If we were to agree with this argument, we would then be required logically to hold that every item having length would be a rod or bar, since every item having length is, by definition, long in proportion to its breadth and thickness.

Essentially, the argument the court here rejects is the following:

(1) Some items long in proportion to breadth and thickness are bars/rods.
(2) The importer’s aluminum tubes are long in proportion to breadth and thickness.
(3) Therefore, the importer’s aluminum tubes are bars/rods.

Just as the court rules, this argument commits the fallacy of the undistributed middle term. The explanation Smith J gives for rejecting the argument nicely illustrates how the fallacy is here implicated.

Another noteworthy judicial discussion of the fallacy of the undistributed middle is found in the judgment of the NSW Court of Appeal in Bishop v Electricity Commission of NSW.²⁴ The plaintiff in Bishop suffered from substantial tinnitus allegedly caused by two decades’ exposure to industrial noise while employed by the defendant. The evidence showed that in addition to his time in the defendant’s employ, the plaintiff had been exposed to industrial noise in previous workplaces. Further, the plaintiff also had a history of exposure to noise through his hobbies of rifle shooting and pistol shooting. The trial judge found the evidence insufficient to establish that the plaintiff’s tinnitus could be causally attributed to his employment with the defendant. In dismissing the appeal, Handley JA reasoned:²⁵

In my judgment [plaintiff’s] submission should not be accepted. The evidence earlier referred to indicates that tinnitus has other causes, apart from exposure to industrial noise. One common cause is the exposure to noise made by firearms, but some persons suffer from tinnitus without having any history of exposure to industrial noise, or the noise made by firearms. In these circumstances, the fact that a significant proportion of persons suffering from industrial deafness also suffer from tinnitus does not permit the Court to draw the conclusion that in this, or any case, the inference is available that proved tinnitus must have been, more probably than not, caused by exposure to industrial noise.

There is, of course, a well-established logical fallacy in that proposition known as the undistributed middle.

Handley JA’s argument can be formally stated as:

(1) Some tinnitus is caused by exposure to industrial noise.
(2) Bishop’s injury is tinnitus.
(3) Therefore, Bishop’s injury is caused by exposure to industrial noise.

This argument precisely matches the form of the Ned Kelly argument. All three propositions (major premise, minor premise, conclusion) in both arguments are particular affirmative categorical propositions. That type of categorical proposition does not distribute either its subject or predicate term. The middle term accordingly is left undistributed. The excerpt here from the judgment of Handley JA admirably describes the logical problem that attends trying to draw an inference without distributing the middle term.

Hypothetical syllogisms

There are three valid types of hypothetical syllogisms: the pure hypothetical syllogism and two forms of “mixed” hypothetical syllogisms: modus ponens and modus tollens. The distinguishing feature of hypothetical syllogisms is that they rely on “hypothetical propositions” — that is, conditional or “if/then” statements.

Using the letters A and C as placeholders for any two simple propositions, it is possible to represent the basic form of a hypothetical proposition as:

If A is true, then C is true.

In the hypothetical proposition, the assertion that follows “if” is called the antecedent. The assertion that follows “then” is the consequent. So every hypothetical proposition states that:

If antecedent A is true, then consequent C is true.

Pure hypothetical syllogism: A pure hypothetical syllogism is a deductive argument containing hypothetical propositions exclusively. Every valid pure hypothetical syllogism takes the following form:

(1) If A is true, then C is true.
(2) If C is true, then E is true.
(3) Therefore, if A is true, then E is true.
Modus ponens: The deductive argument form known as modus ponens is one of two valid forms of “mixed” hypothetical syllogism. A mixed hypothetical syllogism is a deductive argument wherein one premise (the “conditional premise”) takes the form of a hypothetical proposition, while the other premise and the conclusion are simple or categorical propositions. Arguments that take the form of modus ponens claim:

(1) If A is true, then C is true.
(2) A is true.
(3) Therefore, C is true.
Modus tollens: The other valid form of mixed hypothetical syllogism is known as modus tollens. As a mixed hypothetical syllogism, modus tollens, like modus ponens, is an argument that contains one conditional premise (that is, one hypothetical proposition), while the other premise and the conclusion take the form of simple or categorical propositions. Arguments in the form of modus tollens assert:

(1) If A is true, then C is true.
(2) C is not true.
(3) Therefore, A is not true.

Fallacies in reasoning by hypothetical syllogism

There are three fallacies that are committed all too frequently when reasoning by way of hypothetical syllogisms:

Fallacy of the illicit conditional: The fallacy of the illicit conditional is associated with the pure hypothetical syllogism form. This fallacy occurs whenever an argument contains three hypothetical propositions but takes a form different from the valid form set out above. As noted, a valid pure hypothetical syllogism contains three propositions, A, C, and E, each of which appears twice in the argument. Those propositions must be positioned in the argument precisely as stated. If they are positioned differently the argument is invalid. This can be by adding a fourth proposition, by positioning the three propositions differently, or by negating one or more of the propositions the second time it occurs in the argument. If any of these errors occur, we have the fallacy of the illicit conditional.
Fallacy of affirming the consequent: The fallacy of affirming the consequent is a mixed hypothetical syllogism fallacy. It begins with a standard-form conditional proposition — If antecedent A is true, then consequent C is true. The second premise then affirms the truth of the consequent, leading to an attempt to establish the truth of the antecedent. That is, an argument that commits the fallacy of affirming the consequent reads:

(1) If A is true, then C is true.
(2) C is true.
(3) Therefore, A is true.

Note that this fallacious form of mixed hypothetical syllogism contains only affirmative propositions. In that respect, the fallacy of affirming the consequent resembles modus ponens. Essentially it modifies modus ponens by inverting the propositions asserted in the minor premise and the conclusion. While modus ponens affirms the truth of the antecedent in the second premise so as to necessarily prove the truth of the consequent in the conclusion, the fallacy of affirming the consequent inverts the ordering of those propositions.
Fallacy of denying the antecedent: The final hypothetical syllogism fallacy, that of denying the antecedent, is another mixed hypothetical syllogism fallacy. Like the fallacy of affirming the consequent, the fallacy of denying the antecedent begins with a conditional proposition — If antecedent A is true, then consequent C is true. Then in this fallacious form, the argument, in its second premise, denies the truth of the antecedent in an effort to prove, in the conclusion, that the consequent cannot be true. Accordingly:

(1) If A is true, then C is true.
(2) A is not true.
(3) Therefore, C is not true.

Given that the fallacy of denying the antecedent asserts negative propositions in its second premise and conclusion, this fallacious form of mixed hypothetical syllogism quite closely resembles modus tollens. It essentially modifies modus tollens by inverting the propositions asserted in the minor premise and the conclusion. While modus tollens denies the truth of the consequent in the second premise in order to necessarily deny the truth of the antecedent in the conclusion, the fallacy of denying the antecedent reorders those propositions, producing an invalid syllogistic form.

The judgment of the US Court of Appeals for the Second Circuit in Crouse-Hinds Co v InterNorth Inc,²⁶ provides an excellent study of hypothetical syllogisms in the law. InterNorth, desiring to complete a hostile takeover of Crouse-Hinds, filed suit to block a proposed merger between Crouse-Hinds and another company. At trial, InterNorth claimed that the Crouse-Hinds directors, who would remain in control after the merger, were pursuing it out of self-interest and bad faith. InterNorth succeeded in temporarily enjoining the merger by fashioning a hypothetical syllogism on the basis of an earlier Second Circuit judgment. In Treadway Companies v Care Corp,²⁷ the Second Circuit had declined a request to block a merger on the basis of self-interest or bad faith on the part of the directors. Under the facts in Treadway, the directors were not going to remain in control after the merger. The reasoning of the Second Circuit in Treadway thus took the form of modus ponens:

(1) If the directors of a company are not going to remain in control after a merger, then perpetuating their control cannot be their motive in pursuing the merger.
(2) The Treadway directors were not to remain in control after the merger.
(3) Therefore, perpetuating their control could not be the Treadway directors’ motive in pursuing the merger.

Before the trial court in Crouse-Hinds, InterNorth successfully argued, following Treadway:

(1) If the directors of a company are not going to remain in control after a merger, then perpetuating their control cannot be their motive in pursuing the merger.
(2) The Crouse-Hinds directors were to remain in control after the merger.
(3) Therefore, perpetuating their control must be the Crouse-Hinds directors’ motive in pursuing the merger.

Though the starting-point of this argument is the same as Treadway’s, the Second Circuit correctly observed that the syllogism was very different. Instead of modus ponens, the form of the InterNorth argument was that of the fallacy of denying the antecedent. Reversing the trial court that had accepted the fallacious inference crafted by InterNorth, the Second Circuit in Crouse-Hinds astutely ruled that, “This inference has no basis in either law or logic”.²⁸

Disjunctive syllogisms

Disjunctive syllogisms are deductive arguments wherein one premise takes the form of a disjunctive proposition, while the other premise and the conclusion are simple propositions that either deny or affirm part of the disjunctive proposition. Disjunctive propositions are “or” or “either/or” statements. They are compound propositions in that every disjunctive proposition, or disjunction, contains two component propositions called “disjuncts”. One disjunct comes before the “or”; the other appears after it.

Two disjunctive syllogism “moods”

It is often said there are two forms or “moods” that disjunctive syllogisms can take. The two moods differ from one another in two important respects:

Exclusivity of the disjuncts: The first mood does not assume that the disjuncts are mutually exclusive; the second mood requires that the disjuncts be fully exclusive of one another — that is, that it not be possible for both disjuncts to be true.
Conclusions they draw: The first mood denies the truth of one disjunct in its second premise and then affirms, in its conclusion, the truth of the other; the second mood affirms the truth of one disjunct in the second premise and then concludes that the other disjunct must be false. Only the first mood is, in a pure logical sense, a disjunctive syllogism. The second mood presumes, in its disjunctive premise, a proposition that is more complex than a simple disjunctive proposition. Nevertheless, arguments in the second mood do occur in certain situations in legal reasoning. When they do, they are typically presented as simple disjunctive syllogisms.

The two moods can be stated symbolically as follows:

Mood which by denying affirms:

(1) A is true or B is true.
(2) A is not true.
(3) Therefore, B is true.

Mood which by affirming denies:

(1) A is true or B is true.
(2) A is true.
(3) Therefore, B is not true.

While the second mood represents a fairly common argument form, it must be used with care. It is a valid argument form only when the assumption holds that the disjuncts, A and B, are mutually exclusive. The California Court of Appeal addressed this point well and expertly compared the logical validity of the two disjunctive syllogism moods in the case Danzig v Superior Court.²⁹ The court was asked to consider, in a class action suit, whether unnamed class members are, under the applicable State statutory scheme, “parties” to whom interrogatories may be propounded. An earlier California Supreme Court judgment had held that, under the same statutory scheme, unnamed members of a class are “persons for whose immediate benefit an action or proceeding is prosecuted”.³⁰ The petitioners in Danzig argued that in ruling that unnamed class members are “persons”, the Supreme Court had impliedly held that they were not “parties”. Justice Feinberg for the Court of Appeal in Danzig rebuffed this argument as unsound:³¹

The argument suffers from a logical fallacy. When a proposition is in the form of two alternatives, if one alternative is false, then the other alternative must be true. But, if one of the alternatives is true, nothing can be said about the truth or falsity of the other alternative except in the situation when the two alternatives are mutually exclusive.

In Southern California Edison, the Supreme Court holding that unnamed members of a class … were persons for whose benefit the action was being prosecuted tells us nothing as to whether unnamed members of a class in a class action are “parties” within the meaning of [the applicable] section … unless a “party” and “a person …” are mutually exclusive concepts. Since it appears obvious that the two concepts are not mutually exclusive, we conclude that Southern California Edison is not authority for the resolution of the issue at bar.

Fallacies associated with disjunctive syllogisms

There are three fallacies associated with reasoning by way of a disjunctive syllogism:

Fallacy of non-exclusivity: The fallacy of non-exclusivity applies only to the second disjunctive syllogism mood — the mood which by affirming denies. The logic behind this fallacy is that if the disjuncts in a disjunctive proposition are not contradictory or mutually exclusive, then it is possible for both disjuncts to be true. Hence, to affirm one disjunct in a non-exclusive disjunctive proposition provides no basis for denying the truth of the other. Arguments which employ the second disjunctive syllogism mood when it is possible for both their disjuncts to be true commit this fallacy of non-exclusivity. This is the fallacy committed by the petitioners in Danzig.
Fallacy of missing disjuncts: While the fallacy of non-exclusivity can be committed only when an argument takes the second disjunctive syllogism mood, there are two other fallacies associated with disjunctive syllogisms that can occur in either mood. Both of these fallacies go to the truth of the disjunctive proposition, not to the form or structure of the disjunctive syllogism. The first, the fallacy of missing disjuncts, goes to the incompleteness of a disjunctive proposition. This fallacy is committed whenever a disjunctive proposition asserts the truth of one disjunct taken from a pair or set of disjuncts when in fact other disjuncts not enumerated are possible.
Fallacy of false disjunction: The other disjunctive syllogism fallacy that can arise in either mood is the fallacy of false disjunction. This fallacy is committed whenever an argument rests on a disjunctive proposition that sets in opposition two disjuncts that are not in truth alternatives to one another.

Conjunctive syllogisms

Conjunctive syllogisms are deductive arguments wherein one premise is stated in the form of the negation of a conjunctive proposition. Conjunctive propositions are compound propositions that pull together, usually with the word “and”, two or more component propositions known as “conjuncts”. In a simple two-part conjunctive proposition, one conjunct comes before the “and”, while the other appears after it (for example, “The auto dealership sells BMWs and it sells Holdens”; “The plaintiff filed the complaint and the defendant counterclaimed”).

In a conjunctive syllogism, one premise (the conjunctive premise) negates the truth of a conjunctive proposition — that is, it denies the possibility that both conjuncts could be true. The other premise then affirms the truth of one of the conjunctive premise’s conjuncts, while the conclusion denies the truth of the other conjunct. That is, a valid conjunctive syllogism takes the logical form:

Premise 1: The negation of a conjunctive proposition. (the conjunctive premise)

Premise 2: A simple or categorical proposition affirming the truth of one of the conjunctive premise’s two conjuncts.

Conclusion: A simple or categorical proposition denying that the conjunctive premise’s other conjunct could be true.

Symbolically, the standard claim made by a valid conjunctive syllogism can be expressed as follows:

(1) A and B are not both true.
(2) A is true.
(3) Therefore, B is not true.

Note that the conjunctive syllogism form can be used interchangeably with the second disjunctive syllogism mood. Consider the argument:

(1) Ernest Hemingway could not have been born both in Idaho and in Illinois.
(2) Hemingway was born in Illinois.
(3) Therefore, Hemingway was not born in Idaho.

As stated, this argument is a conjunctive syllogism. The same reasoning can be presented as a disjunctive syllogism in the second mood if the first premise is changed to read: “Ernest Hemingway was born either in Idaho or in Illinois”. The resulting disjunctive syllogism would be valid since the disjuncts are mutually exclusive.

Conclusion

The language of logic used herein to describe the basic categories of inductive and deductive reasoning is not everyday language in the law. However, the patterns of reasoning found in the forms of argument presented are the everyday patterns of legal reasoning. For the domain of law, and most significantly within that domain, the practice of judicial decision-making is a realm governed by practical reasoning and deliberative judgment. As a practical matter, humans tend to deliberate, reason, and reflect according to a relatively small set of logical argument forms.

Law, to be sure, concerns more than logic. Yet the abundance of factors that conduce to good lawyering and fair judging disclose that the life of the law, while not logic alone, is a complex manifold of activities that use and depend upon reason in a mosaic of specialised ways. The precision of semantic detail required of solicitors in the drafting of legal documents — contracts, trusts, wills, etc — is a rational precision. The care demanded of barristers in planning, strategising, and deciding how to present their cases is a rational care. The skill in oral and written argumentation necessitated by appellate practice is, quite evidently, a rational skill. The talent commanded of judicial officers to craft understandable findings of fact and conclusions of law is a rational talent. The aptitude the law demands of appellate judges to separate, dispassionately and without bias, the kernel of an argument from the emotive and rhetorical chaff of adversarial presentation, so as to render judgments justified under law is fundamentally a rational aptitude.

While many other factors — self-interest, public policy, science, psychology, moral values, ideals of justice, etc — permeate the deliberations and decision-making of lawyers and judges, all such considerations are intertwined inextricably with reason and logic. Barristers may appeal to the sentiments and psychology of jurors, but only to the extent they reasonably think they can influence the jury to draw rational inferences favorable to their client. Self-interest commonly is the primary if not the only motive for each party in the drafting of a contract, yet the prudential recognition, grounded in practical reason, that to insist on onerous provisions would likely undermine the whole process of contractual negotiation has the tendency to restrain everyone’s self-interest. Though adjudicative practice may well call for judgments of value and policy in choosing, interpreting, and applying legal principles, such judgments do not stand free of the constraints of reason. For fundamentally, as stated by one appellate court: “every legal analysis should begin at the point of reason, continue along a path of logic and arrive at a fundamentally fair result”.³²

¹Revised version of paper presented at the Logic and Legal Reasoning in Judicial Decision-Making Workshop, Judicial Commission of NSW, 12–13 September 2013, Sydney. Published in (2014) 11 TJR 429, updated 2021.

²Professor, Department of Philosophy, Virginia Tech.

³Nuutinen v Finland (Application No 32842/96) (European Court of Human Rights, 27 June 2000) (Zupancic J dissenting).

⁴O Holmes, The common law, Little, Brown and Company, Boston, 1881, p 1.

⁵See, for example, O Holmes, “The path of the law” (1897) 10(8) Harvard Law Review 457 at 465.

⁶See B Cardozo, The nature of the judicial process, Yale University Press, New Haven, 1921, p 31.

⁷For example, J Dewey, “Logical method and law” (1924) 10(1) Cornell Law Quarterly 17.

⁸See J Stone, The province and function of law: law as logic, justice, and social control: a study in jurisprudence, Stevens and Sons, London, 1947.

⁹For example, H Hart, The concept of law, Oxford University Press, Oxford, 1961, pp 132; “Positivism and the separation of law and morals” in H Hart, Essays in jurisprudence and philosophy, Clarendon Press, Oxford, 1983, pp 63, first published in (1958) 71(4) Harvard Law Review 593.

¹⁰E Patterson, Jurisprudence: men and ideas of the law, The Foundation Press, Brooklyn, 1953, p 21.

¹¹W Ross (ed), The works of Aristotle, Vol XI, “Rhetoric”, W Rhys Roberts trans, Oxford University Press, Oxford, 1924, Book 1, at [1356b].

¹²F Dürrenmatt, The physicists, J Kirkup trans, Grove Press, New York, 1964, p 82.

¹³See Aristotle, Nicomachean ethics, M Ostwald trans, The Bobbs-Merrill Company Inc, Indianapolis, 1962, Book 6; The works of Aristotle, Vol XI, “Rhetoric”, above n 11.

¹⁴Cantwell v Sinclair [2011] NSWSC 1244 at [115] (Rothman J).

¹⁵569 F Supp 1575 (1983).

¹⁶ibid at 1580.

¹⁷ibid.

¹⁸For example, John Harris & Associates (Aust) Pty Ltd v Commissioner of Stamp Duties [2001] 1 Qd R 254 at [17] (“Neither of these is a true analogy”); Power v Hamond [2006] VSCA 25 at [32] (Ormiston JA) (refusing “a false analogy which cannot bear close examination”); Conyers v State 115 Md App 114 at 122 (1997) (“false analogy”).

¹⁹See, for example, Hope v Brisbane City Council [2013] QCA 198 at [18] (Jackson J) (“It serves no great purpose to draw broad analogies.”); Schwennesen v Minister for Environment and Resource Management [2010] QCA 340 at [23] (Fraser JA) (“no relevant analogy”); Crusader Resources NL v Santos Ltd (1991) 58 SASR 74 at 99 (Olsson J) (analogy rejected as “neither appropriate nor accurate”); Heck v Humphrey 512 US 477 at 496 (1994) (Souter J concurring) (“weak analogy”).

²⁰W Ross (ed), The works of Aristotle, “Prior analytics”, A Jenkinson trans, Oxford University Press, London, 2006, Book 1, Ch I, at [24b18–20].

²¹16 US 336 (1818) at 386–387 (Marshall CJ).

²²47 CCPA 88 (Customs and Patent Appeals 1960).

²³ibid at 90 (Smith J).

²⁴[1996] NSWCA 50 (Sheller and Powell JJA agreeing).

²⁵ibid.

²⁶634 F 2d 690 (1980).

²⁷638 2 Fd 357 (1980).

²⁸634 F 2d 690 at 702 (1980).

²⁹87 Cal App 3d 604 (1978).

³⁰Southern California Edison Co v Supreme Court 7 Cal 3d 832 (1972).

³¹87 Cal App 3d 604 at 609 (1978).

³²Sunrise Lumber v Johnson, Appeal No 165 (Fort Peck Tribal Court of Appeals, 30 June 1999) (Sullivan CJ).

Basic categories of argumentation in legal reasoning1