Logical Analysis of Supreme Court Arguments

Gamble v US, 1996 (Double Jeopardy)

  • Terance Gamble, a felon, was found in possession of a handgun. He was convicted under Alabama’s possession-of-firearm-by-a felon statute and given a one-year sentence. He was then prosecuted under the federal possession-of-firearm-by-a felon statute and received a 46-month sentence on top of the one-year sentence.
  • The Supreme Court ruled that Gamble’s two convictions did not violate the Double Jeopardy Clause of the Fifth Amendment, that no one shall be “twice put in jeopardy of life or limb” for the same offense.

Alito’s Argument

  • Writing for the Court, Justice Alito argued as follows:
    • Offenses that violate laws of different sovereigns are different offenses.
    • Alabama’s law against a felon possessing a firearm and the federal law against a felon possessing a firearm are laws of different sovereigns, Alabama and the United States.
    • Therefore, Gamble’s two convictions were for different offenses.
    • So, Gamble’s two convictions did not violate the Double Jeopardy Clause.
  • The first premise of the argument is the Dual-Sovereignty Principle:
    • Offenses that violate laws of different sovereigns are different offenses.
  • Alito claimed that the Dual-Sovereignty Principle follows from the Double Jeopardy Clause and therefore from the Constitution. Thus he says:
    • “Although the dual-sovereignty rule is often dubbed an “exception” to the double jeopardy right, it is not an exception at all. On the contrary, it follows from the text that defines that right in the first place.”
    • “We see no reason to abandon the sovereign-specific reading of the phrase “same offence,” from which the dual-sovereignty rule immediately follows.”
  • The core of Alito’s opinion is his argument for the Dual-Sovereignty Principle:
    • “As originally understood, an ‘offence’ is defined by a law, and each law is defined by a sovereign. Thus, where there are two sovereigns, there are two laws and two ‘offences.’”
  • That is:
    • An offense is a violation of a law.  
    • A law is the law of a sovereign. 
    • Therefore, if laws are the laws of different sovereigns, then the laws are different laws and their offenses are different offenses.
  • Alito’s argument can be reconstructed as the following deductive argument:
    • 1. Laws of different sovereigns are different laws.
    • 2. Offenses that violate different laws are different offenses.
    • 3. Therefore offenses that violate the laws of different sovereigns are different offenses.
  • The argument is valid, that is, the conclusion (line 3) follows from the premises (lines 1 and 2) per the rules of deductive logic, in particular, what’s known as Predicate Logic with Identity.
  • Being valid, Alito’s argument establishes the Principle of Dual Sovereignty only if both premises are true. But the second premise succumbs to the following counterexample:
    • A person is guilty of Grand Auto Theft if they take possession of a vehicle without the owner’s consent and with the intent of keeping it permanently.
    • A person is guilty of Joy Riding if they take possession of a vehicle without the owner’s consent.
    • Jones steals a Ferrari with the intention of keeping it and therefore violates both statutes.
    • According to Blockburger v United States:
      • An act that violates two statutory provisions constitutes two offenses if and only each provision requires a proof of fact that the other does not require.
    • It’s not the case that Joy Riding requires a proof of fact that Grand Theft Auto does not require.
    • So, Jones’ theft of the Ferrari is a single offense.
    • It’s therefore false that offenses that violate different laws are different offenses.
  • Thus Alito’s argument fails to establish the Principle of Dual Sovereignty. Alito therefore fails to show that the Principle of Dual Sovereignty follows from the Double Jeopardy Clause of the Fifth Amendment and from the Constitution.

Thomas’ Argument

  • In his concurrence Justice Thomas sets forth a different argument that state and federal prosecutions for the same offense don’t violate the Double Jeopardy clause:
    • The people who ratified the Fifth Amendment did not understand it to prohibit prosecution by a State and the Federal Government for the same offense.
    • Therefore the Fifth Amendment doesn’t prohibit prosecution by a State and the Federal Government for the same offense.
  • But the form of argument is invalid. Here’s what’s called a Refutation by Logical Analogy:
    • Suppose the Constitution included a Contagious Provision that said:
      • No person with a contagious disease shall enter the United States.
    • Assume that the ratifiers mistakenly believed that tuberculosis was not contagious.
    • The following is a logical analog of Thomas’ argument:
      • The ratifiers did not understand the Contagious Provision to prohibit people with tuberculosis from entering the United States.
      • Therefore the Contagious Provision does not prohibit people with tuberculosis from entering the United States.
  • The problem is that a law has a life and logic of its own.  A law that says anyone who satisfies condition C shall be X applies to anyone who satisfies C, no matter what people believed when the law was passed.

Proof that Alito’s Core Argument is Valid

Formalized Argument
  • Let Lμν mean that μ is a law of sovereign ν.
  • Let Oμν mean that μ violates ν (i.e. μ is an offense against statute ν)
  • Alito’s argument can be formalized as follows:
    • Premise 1: Laws of different sovereigns are different laws.
      • ∀x∀u∀y∀w(Lxu & Lyw & u ≠ w x≠y)
        • That is, for any x, u, y and w, if x is a law of sovereign u and y is a law of sovereign w and u and w are distinct, then x and y are distinct)
    • Premise 2: Offenses that violate different laws are different offenses.
      • ∀p∀x∀q∀y(Opx & ∃u(Lxu) & Oqy & ∃w(Lyw) &  x≠y p≠q)
        • That is, for any p, x, q and y, if p violates x and x is a law of some sovereign and q violates y and y is a law of some sovereign and x and y are distinct, then p and q are distinct.
    • Conclusion: Offenses that violate the laws of different sovereigns are different offenses.
      • ∀p∀x∀u∀q∀y∀w(Opx & Lxu & Oqy & Lyw &  u≠w p≠q)
        • That is, for any p, x, u, q, y and w, if p violates x and x is a law of sovereign u and q violates y and y is a law of sovereign w and u and w are distinct, then p and q are distinct
Derivation of Conclusion from the Premises
  1. ∀x∀u∀y∀w(Lxu & Lyw & u ≠ w x≠y)
    • Assumption of Premise 1
  2. ∀p∀x∀q∀y(Opx & ∃u(Lxu) & Oqy & ∃w(Lyw) &  x≠y p≠q)
    • Assumption of Premise 2
  3. Opx & Lxu & Oqy & Lyw &  u≠w
    • Assumption for Conditional Proof
  4. Lxu & Lyw & u ≠ w → x≠y
    • Line 1 Universal Specification
  5. Opx & Lxu & Oqy & Lyw & x≠y
    • Lines 3 and 4 Tautological Inference
  6. Opx & ∃u(Lxu) & Oqy & ∃w(Lyw) &  x≠y
    • Line 5 Existential Generalization
  7. Opx & ∃u(Lxu) & Oqy & ∃w(Lyw) &  x≠y p≠q
    • Line 2  Universal Specification
  8. p≠q
    • Lines 6 and 7 Modus Ponens
  9. Opx & Lxu & Oqy & Lyw &  u≠w → p≠q
    • Lines 3 and 8 Conditional Proof
  10. ∀p∀x∀u∀q∀y∀w(Opx & Lxu & Oqy & Lyw &  u≠w p≠q)
    • Line 9 Universal Generalization
  1. Gamble v US, 1996 (Double Jeopardy)
    1. Alito’s Argument
    2. Thomas’ Argument
    3. Proof that Alito’s Core Argument is Valid
      1. Formalized Argument
      2. Derivation of Conclusion from the Premises