Modus ponens
One valid argument form is known as modus ponens, not to be mistaken with modus tollens, which is another valid argument form that has a like-sounding name and structure. Modus ponens (sometimes abbreviated as MP) says that if one thing is true, then another will be. It then states that the first is true. The conclusion is that the second thing is true.[3] It is shown below in logical form.
If A, then B
A
Therefore B
Before being put into logical form the above statement could have been something like below.
If Kelly does not finish his homework, he will not go to class
Kelly did not finish his homework
Therefore, Kelly will not go to class
The first two statements are the premises while the third is the conclusion derived from them.
Modus tollens
Another form of argument is known as modus tollens (commonly abbreviated MT). In this form, you start with the same first premise as with modus ponens. However, the second part of the premise is denied, leading to the conclusion that the first part of the premise should be denied as well. It is shown below in logical form.
If A, then B
Not B
Therefore not A.[3]
When modus tollens is used with actual content, it looks like below.
If the Saints win the Super Bowl, there will be a party in New Orleans that night
There was no party in New Orleans that night
Therefore, the Saints did not win the Super Bowl
Hypothetical syllogism
Much like modus ponens and modus tollens, hypothetical syllogism (sometimes abbreviated as HS) contains two premises and a conclusion. It is, however, slightly more complicated than the first two. In short, it states that if one thing happens, another will as well. If that second thing happens, a third will follow it. Therefore, if the first thing happens, it is inevitable that the third will too.[3] It is shown below in logical form.
If A, then B
If B, then C
Therefore if A, then C
When put into words it looks like below.
If it rains today, I will wear my rain jacket
If I wear my rain jacket, I will keep dry
Therefore if it rains today, I will keep dry
Disjunctive syllogism
Disjunctive syllogism (sometimes abbreviated DS) has one of the same characteristics as modus tollens in that it contains a premise, then in a second premise it denies a statement, leading to the conclusion. In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true.[3] It is shown below in logical form.
Either A or B
Not A
Therefore B
When used A and B are replaced with real life examples it looks like below.
Either you will see Joe in class today or he will oversleep
You did not see Joe in class today
Therefore Joe overslept
Disjunctive syllogism takes two options and narrows it down to one.
A proposition may be universal or particular, and it may be affirmative or negative. Traditionally, the four kinds of propositions are:
A categorical syllogism consists of three parts:
Each part is a categorical proposition, and each categorical proposition contains two categorical terms.[13] In Aristotle, each of the premises is in the form "All A are B," "Some A are B", "No A are B" or "Some A are not B", where "A" is one term and "B" is another:
More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion). For example:
Major premise: All humans are mortal.
Minor premise: All Greeks are humans.
Conclusion: All Greeks are mortal.
Each of the three distinct terms represents a category. From the example above, humans, mortal, and Greeks: mortal is the major term, and Greeks the minor term. The premises also have one term in common with each other, which is known as the middle term; in this example, humans. Both of the premises are universal, as is the conclusion.
Major premise: All mortals die.
Minor premise: All men are mortals.
Conclusion: All men die.
Here, the major term is die, the minor term is men, and the middle term is mortals. Again, both premises are universal, hence so is the conclusion.
All men are mortal. (MaP)
All Greeks are men. (SaM)
∴ All Greeks are mortal. (SaP)
Similar: Cesare (EAE-2)
No reptile has fur. (MeP)
All snakes are reptiles. (SaM)
∴ No snake has fur. (SeP)
Similar: Datisi (AII-3)
All rabbits have fur. (MaP)
Some pets are rabbits. (SiM)
∴ Some pets have fur. (SiP)
All squares are rectangles. (MaP)
All squares are rhombuses. (MaS)
∴ Some rhombuses are rectangles. (SiP)
The best attorneys often use syllogisms to the same effect. To illustrate, I looked at briefs from prominent practitioners in the U.S. Supreme Court in 2019 and 2020. For example, Kannon Shanmugam of Paul, Weiss, used it in a petition for certiorari review in C.H. Robinson Worldwide, Inc. v. Miller, 20-1425 (with citations removed to aid readability):
What is more, the court of appeals badly misconstrued this Court's decision in American Trucking Associations, Inc. v. City of Los Angeles. The court's attenuated chain of reasoning went like this: In American Trucking Associations, the Court stated that the FAAAA's preemption provision “draws a rough line between a government's exercise of regulatory authority and its own contract-based participation in a market.” The FAAAA's preemption provision includes common-law claims. Thus, because Congress also used the term “regulatory authority” in the safety exception, it must also include common-law claims.
He then used that syllogistic framework to attack that reasoning:
That syllogism is multiply flawed. As a preliminary matter, the Court in American Trucking Associations was not interpreting the safety exception-indeed, its only mention of the safety exception was to deem it “not relevant here.” If anything, any hints from American Trucking Associations cut the other way. The governmental action at issue there was a core exercise of the “regulatory authority of a State”: the “Board of Harbor Commissioners” (an administrative agency) enforced a “municipal ordinance” (a positive-law enactment), the violation of which was “a violation of criminal law” (enforced by state or local officials). It is little wonder that the Court described the governmental action there as “regulatory authority.”
Two former members of my office—Tyler Green and Tera Peterson—used it to good effect in an amicus brief supporting Arizona in McKinney v. Arizona, 589 U.S. ____ (2020):
McKinney's argument can be succinctly stated as this syllogism:
The minor premise in McKinney’s syllogism is invalid. So his conclusion is invalid too. The Arizona Supreme Court did not reopen his case—or transform his final sentence into a non-final one—by correcting a non-Ring error. Concluding otherwise would gut Teague’s finality framework, which protects the States’ criminal judgments from unwarranted federal intrusion. It would make those judgments perpetually subject to reopening: Every conditional habeas grant would force States to relitigate convictions under every new procedural rule decided since the original conviction became final.
Finally, Jeff Fisher of Stanford University included this in his winning brief in Ramos v. Louisiana, 590 U.S. ___ (2020) (again, with citations removed):
For decades, this Court has addressed questions like the one here by asking whether the Fourteenth Amendment's Due Process Clause “incorporates” the relevant protection of the Bill of Rights. Applying that test, a simple syllogism establishes that the Due Process Clause incorporates the Sixth Amendment's unanimity requirement against the states. First, the Court held long ago that the Jury Trial Clause applies to the states. The Clause is “fundamental to the American scheme of justice.” Second, “if a Bill of Rights protection is incorporated, there is no daylight between the federal and state conduct it prohibits or requires.” This Court first crystallized this concept in Malloy v. Hogan. . . . The Court reiterated this concept in McDonald. . . . Just last Term, this Court reaffirmed this rule without a dissenting vote. . . . .This reasoning controls here.
The first type of enthymeme is a truncated syllogism, or a syllogism with an unstated premise.[2]
Here is an example of an enthymeme derived from a syllogism through truncation (shortening) of the syllogism:
The complete formal syllogism would be the classic:
All humans are mortal. (major premise – unstated)
Socrates is human. (minor premise – stated)
Therefore, Socrates is mortal. (conclusion – stated)
While syllogisms lay out all of their premises and conclusion explicitly, these kinds of enthymemes keep at least one of the premises or the conclusion unstated.
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The structure of appellate briefs themselves have been compared to syllogisms,[1] but the most helpful place I have found to use them most often is in questions presented. The goal is to have three sentences: one on the law, one with relevant facts, and then a question suggesting the result in light of those law and facts.
Not every question needs the first sentence on the law--it may be implied (making your syllogism an enthymeme) if you know that your audience is familiar with the law. Here’s an example from a drug dealing case:[2]
As “the person who supplies marijuana for the town,” was defendant entrapped when she approached confidential informants and asked them to front $100 for her drug run?”
I would have made the law explicit here: A person is entrapped if law enforcement improperly appeal to a person’s emotions to convince them to do something illegal that they are not otherwise inclined to do. But yeah, the court didn’t think that she was entrapped either.
Another enthymeme example from my office.[3] This was a much tougher case for the State because the defense position had a lot of surface appeal. The defense framed the question as whether the defendant should get a new trial “because the majority of the involved trial (i.e., court reporter notes of the second day of trial and trial exhibits) had been lost or destroyed?” But by adding some key record facts, the attorney (later a member of our court of appeals) was able to turn the tide in the State’s favor:
Did defendant’s absconding for seven years between verdict and sentencing, during which time defense counsel died, the trial reporter’s notes were lost, and the child victim grew up, so prejudice the judicial process that his appeal must be dismissed?
The defendant did not get a new trial.
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To elucidate the difference between hard cases and easy cases, and the concomitant limitations of deductive logic in legal analysis, it is appropriate to again make use the legal syllogism, but the examples that follow utilize the hypothetical rather than the categorical form of logical proposition.75
All rules of law may be stated in the following hypothetical form: If certain facts are true, then a certain legal conclusion follows. For example, if a person purposefully and without justification or excuse causes the death of another, then the person is guilty of homocide.76 An intruder who deliberately shoots and kills a sleeping homeowner in the course of a burglary is clearly guilty of murder; this is an easy case. But what of the case of a woman who has suffered years of serious physical abuse at the hands of her husband, a man who has repeatedly threatened her life;77 is this woman guilty of homocide if she shoots and kills him as he lay sleeping?78 Was her act justified? This is
a hard case because the law of self-defense generally requires that the defendant reasonably believed that her actions were necessary to defend herself against the aggressor‟s imminent use of unlawful force.79 In one case, the North Carolina Court of Appeals ruled that the defendant-wife was in imminent danger because the decedent- husband‟s nap was “but a momentary hiatus in a continuous reign of terror,”80 while the state Supreme Court overruled and held that the wife was not in “imminent” danger.81
But is the imminence of the danger to be determined by what the reasonable person would believe, or by reference to the reasonable belief of a person in the defendant‟s mental state? The meaning of the term “imminent” is ambiguous as applied to the facts of this case, because the imminence of the danger may be measured by an objective or a subjective standard.82 Furthermore, it may be difficult to tell the difference between the objective and the subjective standards:
The distinction between the objective and subjective tests can be elusive. A court nominally applying the objective test may allow the jury to consider so many of the defendant‟s unique circumstances that the hypothetical “reasonable person” assumes most of the fears and weaknesses of the defendant. The jury may thus come close to evaluating the necessity of self-defensive action as the defendant saw it.83
Some will argue that the defendant is guilty84 and some will argue that she is not,85 because the meaning of the word “imminent” in the rule defining self-defense is unclear in the context of a “sleeping husband / battered wife” murder case. This is a problem of ambiguity, and it is a hard case because arguments spring to mind for two different interpretations of the rule.86
To illustrate another type of hard case we return to our earlier example of gestational surrogacy. The relevant rule of law may be stated in hypothetical form as follows: If a woman gives birth to a child, then she is its lawful mother. This rule is not ambiguous in the context of gestational surrogacy; all the words of the fact portion of the rule have but one meaning as applied to this case. But we know intuitively that this is not an easy case, even though the rule of law is unambiguous. The diffic
The foregoing examples illustrate that a case may be difficult because the applicable rule of law is ambiguous, or because the validity of the rule has been challenged.89 Hard cases involve either a question of ambiguity or a question of validity. But how is a court to resolve a case where the meaning or the validity of the existing rule is challenged?90 It is here, in the resolution of hard cases, that the essential difference between law and science becomes apparent. To resolve questions of ambiguity or validity lawyers and judges create legal arguments.
There are five types of legal argument. Legal arguments may be based upon text, intent, precedent, tradition, or policy analysis.91
ulty arises because in this context the rule itself seems to be an incorrect or unfair statement of the law.87 This type of case is hard because the validity of the rule is in question, even though its meaning is clear.88
The five types of legal argument represent different conceptions of what law is. Law may be considered to be legal text itself,92 or it may be considered to be what the text meant to the persons who enacted it into law.93 Law may be considered to be the holdings or opinions of courts saying what the law is,94 and may also be thought of as the traditional ways in which members of the community have conducted themselves.95 Finally, law may be conceived as the expression of the underlying values and interests that the law is meant to serve.96 In this sense, the five types of legal argument each arise from a different source of law.
The five types of legal argument comprise a list of the arguments that lawyers may legitimately invoke to say what the law is. This is a descriptive model of how lawyers behave. 97 This taxonomy of legal argument performs a legitimating function; it delineates the parameters of valid legal argument.98 As such the kinds of argument function as rules of recognition.99
The five types of legal argument also represent the rules of evidence that govern determinations of questions of law. Each category of legal argument is an information set, a collection of evidence that tends to prove what the law is.100
Finally, each type of legal argument represents a different ordering in the values that are served by a system of laws.101 Textual interpretation promotes objectivity. Intent reflects the popular will. Precedent promotes stability. Tradition promotes societal coherence. And policy arguments – consequentialist arguments – enable to law to achieve its purposes. It is common for these values to conflict in particular cases.102 That there are multiple legitimate types of legal argument is a principal reason that hard cases exist; it is why informed people may in good faith legitimately differ as to what the law is.
The forms of legal argument may thus be characterized as arising from different sources of law, as rules of recognition, as collections of evidence of what the law is, or as the separate embodiment of the various values served by a system of laws. And although each kind of argument springs from a different source of law; although each kind of argument requires the court to consider different evidence in determining what the law is; although each kind of argument serves different values; and although each kind of argument, in hard cases, may yield a different answer to legal questions, all five methods of legal analysis share one fundamental point in common. Regardless of how a rule of law was created, it is always the case that it arose because someone, at some point in time, made a value choice. The fundamental nature of law is that it is intentional. A person, or group of persons, chose to elevate one interest over another, and this choice is recognized as our law by a court that selects a method of analysis that accepts that value choice as binding.
Syllogism 1
Issue: Does the Supreme Court have jurisdiction over this case?
Fact: This is a case involving the Supreme Court's exercise of original jurisdiction to issue a writ of mandamus to the Secretary of State.
Law: The Supreme Court lacks original jurisdiction to issue a writ of mandamus to the Secretary of State.
Holding: The Supreme Court lacks jurisdiction over this case.
Syllogism 2
Issue: Does the Supreme Court have original jurisdiction to issue a writ of mandamus to the Secretary of State?
Fact: Section 13 of the Judiciary Act is not valid.127
Law: The Supreme Court may exercise jurisdiction over to issue a writ of mandamus to the Secretary of State only if Section 13 of the Judiciary Act is valid.128
Holding: The Supreme Court lacks original jurisdiction to issue a writ of mandamus to the Secretary of State.129
Syllogism 3
Issue: Is Section 13 of the Judiciary Act valid?
Fact: Section 13 of the Judiciary Act is in conflict with the Constitution.130 Law: Statutes that are in conflict with the Constitution are not valid.131 Holding: Section 13 of the Judiciary Act is not valid.132
Syllogism 4
Issue: Is Section 13 of the Judiciary Act in conflict with the Constitution?
Fact: Section 13 of the Judiciary Act provides that the Supreme Court has original jurisdiction to issue writs of mandamus to officers of the United States,133 while Article III Section 2 of the Constitution does not authorize Congress to grant the Supreme Court original jurisdiction to issue writs of
and Marshall‟s interpretation of Art. III, Sec. 2 necessarily implies that the constitution does not confer jurisdiction over the case on the court. mandamus to officers of the United States.134
Law: If one law permits what another law forbids, the laws are in conflict.135 Holding: Section 13 of the Judiciary Act of the Constitution is in conflict with the
Constitution.136
Syllogism 5
Issue: Does Article III, Section 2, Clause 2 of the Constitution authorize Congress to grant the Supreme Court original jurisdiction to issue writs of mandamus to officers of the United States?
Fact: If Article III, Section 2, Clause 1 of the Constitution is interpreted as allowing Congress to grant the Supreme Court original jurisdiction to issue writs of mandamus to officers of the United States, then Clause 2 would be rendered meaningless.137
Law: The Constitution may not be interpreted in such a way as to render any portion of it meaningless.138
Holding: Article III, Section 2, Clause 2 of the Constitution does not authorize Congress to grant the Supreme Court original jurisdiction
Syllogism 6
Issue: Are statutes that are in conflict with the Constitution valid?
Law: The constitution is to be interpreted according to the intent of the framers.140
Fact: The framers intended for any statute in conflict with the constitution to be invalid.141
Holding: Statutes that are in conflict with the Constitution are not valid.142
The individual syllogisms that make up the reasoning of a court are connected in that the "holding" of the court in one syllogism in the chain of reasoning supplies a "fact" (minor premise) or a "law" (major premise) for other syllogisms in the chain. In the example above, the holding of syllogism 4 is the minor premise of syllogism 3, and the holding of syllogism 6 is the major premise of syllogism 3.
The court's reasoning proceeds from its root premises to the ultimate result, which is dictated by the last syllogism in the court's chain of reasoning. In this case, the court's holding in syllogism 1 that the Supreme Court lacked jurisdiction required them to dismiss Marbury's petition for writ of mandamus.143
Use and Limits of Syllogistic Reasoning in Briefing Cases, Wilson R. Huhn, 2002