The Logic of the 14th Amendment

Back in the day when I was teaching logic to undergraduates, I found that students often got confused about the meaning of “if … then …” sentences. I had to point out time and again that a conditional sentence does not assert the truth of its antecedent (the “if” part), or its consequent (the “then” part). To assert the truth of the consequent, a rule called modus ponens is needed, which says that “p and if p then q logically imply q.” This rule allows us to validly detach the consequent of a conditional, which is why the rule is also called the Rule of Detachment.

With that in mind, let’s try to identify the logical form of the first sentence of Section 1 of the 14th Amendment to our Constitution. Here is the language:

1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.

I wish I’d used this example in class as an illustration of conditional language that is not apparent as such at first sight. Moreover, 1 is in universal conditional form, as indicated by the universal quantifier “all” prefixing its content. The following (tedious but correct) formulation brings this out:

1*. For any person x, if x was born in the United States or x became naturalized in the United States and x is subject to the jurisdiction of the United States, then x is a citizen of the United States and x is a citizen of the State wherein x resides.

What can be correctly inferred from 1*? At most we can instantiate it, for which we need a rule of first-order logic called, naturally enough, Universal Instantiation (UI). Applying UI to 1* retains its conditional form and lets us focus on a specific instance:

1**. If a is a person born in the United States or a became naturalized in the United States and a is subject to the jurisdiction of the United States, then a is a citizen of the United States and a is a citizen of the State wherein a resides.

Anyone who tries to justify “anchor baby” statutes by appealing to 1** is confused about how conditionals work or else is trying to pull a fast one – which Saul Alinsky says is okay. To get anywhere logically, we need modus ponens:

(i) a is a person born in the United States or a became naturalized in the United States and a is subject to the jurisdiction of the United States.

(ii) If a is a person born in the United States or a became naturalized in the United States and a is subject to the jurisdiction of the United States, then a is a citizen of the United States and a is a citizen of the State wherein a resides.

(iii) Therefore, a is a citizen of the United States and a is a citizen of the State wherein a resides.

This is a logically valid argument. Premise (ii) comes from the 14th Amendment, so it is true by assumption. We can grant that premise (i) is true for some arbitrarily selected person, so the argument is also sound.

Now, notice that premise (i) is of the form “(p or q) and r” meaning that the “r” part, “subject to the jurisdiction of the United States,” must hold for the argument to go through. In other words, no matter what “anchor baby” proponents claim,

(i*) a is a person born in the United States or a became naturalized in the United States together with (ii) does not logically imply (iii). Claiming otherwise is a misapplication of modus ponens, or just plain deceptive sophistry – which Saul Alinsky says is okay.

Perhaps liberals who are not trying to be deceptive – which rules out a lot of Democrats running this fall – can get the argument to work by revising (ii):

(ii*)  If a is a person born in the United States or a became naturalized in the United States, then a is a citizen of the United States and a is a citizen of the State wherein a resides.

“Anchor baby” proponents have indeed appealed to (ii*) and statutes have been based on it; and it’s true that (i)* and (ii*) together logically imply (iii).

However, (ii*) is false. By omitting a crucial condition, “subject to the jurisdiction of the United States,” (ii*) ends up having a false consequent no matter how true its antecedent might be. Conditionals with true antecedents and false consequents are false. Therefore, the argument from (i*) and (ii*) to (iii) is unsound.

So, one argument “anchor baby” proponents use is invalid and the other is unsound.

Now what?

By issuing an executive order, President Trump invites needless controversy. He should leave the matter to the Supreme Court, whose logical acumen was significantly enhanced when Judge Kavanaugh was confirmed. Constitutionality can be decided in this case on the purely logical grounds I‘ve indicated.

Image credit: Pixabay

Arnold Cusmariu holds a Ph.D. in philosophy from Brown University and is a frequent contributor to American Thinker.  His publications are available online at www.academia.edu, including “A Methodology for Teaching Logic-Based Skills to Mathematics Students.”

Back in the day when I was teaching logic to undergraduates, I found that students often got confused about the meaning of “if … then …” sentences. I had to point out time and again that a conditional sentence does not assert the truth of its antecedent (the “if” part), or its consequent (the “then” part). To assert the truth of the consequent, a rule called modus ponens is needed, which says that “p and if p then q logically imply q.” This rule allows us to validly detach the consequent of a conditional, which is why the rule is also called the Rule of Detachment.

With that in mind, let’s try to identify the logical form of the first sentence of Section 1 of the 14th Amendment to our Constitution. Here is the language:

1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.

I wish I’d used this example in class as an illustration of conditional language that is not apparent as such at first sight. Moreover, 1 is in universal conditional form, as indicated by the universal quantifier “all” prefixing its content. The following (tedious but correct) formulation brings this out:

1*. For any person x, if x was born in the United States or x became naturalized in the United States and x is subject to the jurisdiction of the United States, then x is a citizen of the United States and x is a citizen of the State wherein x resides.

What can be correctly inferred from 1*? At most we can instantiate it, for which we need a rule of first-order logic called, naturally enough, Universal Instantiation (UI). Applying UI to 1* retains its conditional form and lets us focus on a specific instance:

1**. If a is a person born in the United States or a became naturalized in the United States and a is subject to the jurisdiction of the United States, then a is a citizen of the United States and a is a citizen of the State wherein a resides.

Anyone who tries to justify “anchor baby” statutes by appealing to 1** is confused about how conditionals work or else is trying to pull a fast one – which Saul Alinsky says is okay. To get anywhere logically, we need modus ponens:

(i) a is a person born in the United States or a became naturalized in the United States and a is subject to the jurisdiction of the United States.

(ii) If a is a person born in the United States or a became naturalized in the United States and a is subject to the jurisdiction of the United States, then a is a citizen of the United States and a is a citizen of the State wherein a resides.

(iii) Therefore, a is a citizen of the United States and a is a citizen of the State wherein a resides.

This is a logically valid argument. Premise (ii) comes from the 14th Amendment, so it is true by assumption. We can grant that premise (i) is true for some arbitrarily selected person, so the argument is also sound.

Now, notice that premise (i) is of the form “(p or q) and r” meaning that the “r” part, “subject to the jurisdiction of the United States,” must hold for the argument to go through. In other words, no matter what “anchor baby” proponents claim,

(i*) a is a person born in the United States or a became naturalized in the United States together with (ii) does not logically imply (iii). Claiming otherwise is a misapplication of modus ponens, or just plain deceptive sophistry – which Saul Alinsky says is okay.

Perhaps liberals who are not trying to be deceptive – which rules out a lot of Democrats running this fall – can get the argument to work by revising (ii):

(ii*)  If a is a person born in the United States or a became naturalized in the United States, then a is a citizen of the United States and a is a citizen of the State wherein a resides.

“Anchor baby” proponents have indeed appealed to (ii*) and statutes have been based on it; and it’s true that (i)* and (ii*) together logically imply (iii).

However, (ii*) is false. By omitting a crucial condition, “subject to the jurisdiction of the United States,” (ii*) ends up having a false consequent no matter how true its antecedent might be. Conditionals with true antecedents and false consequents are false. Therefore, the argument from (i*) and (ii*) to (iii) is unsound.

So, one argument “anchor baby” proponents use is invalid and the other is unsound.

Now what?

By issuing an executive order, President Trump invites needless controversy. He should leave the matter to the Supreme Court, whose logical acumen was significantly enhanced when Judge Kavanaugh was confirmed. Constitutionality can be decided in this case on the purely logical grounds I‘ve indicated.

Image credit: Pixabay

Arnold Cusmariu holds a Ph.D. in philosophy from Brown University and is a frequent contributor to American Thinker.  His publications are available online at www.academia.edu, including “A Methodology for Teaching Logic-Based Skills to Mathematics Students.”