12The tests
The links
Text 01
- Every link is valid. Valid is not sound.
- Each conclusion follows from its premises, and fails without any one of them.
- Income measured in purchasing power AU4 · weak support drags down AL1, AL2 and the binary’s first route.
- Surplusage needs AU9 and AU10, both ruled out; the clause’s words and the canon’s own definition give the opposite AN4 · it follows.
The logic itself has no holes. The trouble is a starting assumption, that income means buying power, and the evidence gives it only weak support.
What the grades meannine grades, from the firmest to the weakest
- statedThe source says it in its own words, and the study quotes them.
- it followsLogic alone gets there from what is stated, and a computer solver checks the step.
- strong supportThe evidence for it far outweighs the evidence against it.
- moderate supportMore of the evidence points for it than against it, but real evidence points the other way.
- one readingThe words allow it but do not require it; another reading fits them as well.
- left openThe evidence does not settle it either way.
- weak supportSome evidence points for it, but more points against it.
- not shownIt is claimed, but the record does not establish it.
- ruled outThe words or the logic exclude it.
A chain is only as good as its weakest link: a conclusion never gets a better grade than the weakest step it needs.
Read in full1,471 words · the study as written
Each link below is one step of argument. It lists the premises it needs, each with its grade and its notation, the definitions it enters, and the conclusion it draws. A solver (Z3) checks two things: that the conclusion follows from the premises, and that it fails when any one premise is dropped, so every premise listed is needed. The conclusion then takes the grade of its weakest needed premise, as the method’s rule requires. The notation is first-order logic: ¬ is not, ∧ is and, ∨ is or, → is only if, ↔ is exactly when, ∀ is for every, and ∃ is for some.
AL1 · The nominal part is not income
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. A4 | The words “incomes” and “gain” mean an accession to wealth. | Inc(p) ↔ Acc(p) | weak support |
| 2. AU4 | An accession to wealth is counted in real terms, in command over goods. | Acc(p) ↔ Real(p) | weak support |
Definitions entered: By definition the inflation part p of a gain is no real increase: it commands no more goods. (¬Real(p)) It is an increase in dollars: the rise in prices, counted in dollars. (Dollar(p))
Conclusion: The inflation part p of the gain is not income within the Sixteenth Amendment. (¬Inc(p))
The solver: it follows, and dropping any one of A4, AU4 makes it fail.
AC1 · The inflation part of the gain is not income. Grade: weak support. Valid from A4 and AU4 (the solver); graded no higher than AU4.
Where the link is weakest: AU4, weak support. Income is “The return in money”; the dollar is “the standard unit of value”; the Constitution states value in dollars; and the first decade under the Amendment taxed dollar gains through a doubling of prices.
AL2 · Taxing it exceeds the power: deficiency zero
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. AC1 | The inflation part is not income (AL1). | ¬Inc(p) | weak support |
| 2. AU5 | In the case taxed the whole gain g is the inflation part. | Inc(g) ↔ Inc(p) | stated |
| 3. AU7 | An unapportioned tax on a gain from property is valid only if the gain is income. | Valid(t) → Inc(g) | one reading |
| 4. A3 | Section 1001 imposes the tax t on the gain, without apportionment. | Imp(t) | stated |
Conclusion: A tax is imposed beyond Congress’s power: on a purely nominal gain the deficiency is zero. (Imp(t) ∧ ¬Valid(t))
The solver: it follows, and dropping any one of AC1, AU5, AU7, A3 makes it fail.
AC2 · Deficiency zero on a purely nominal gain. Grade: weak support. Valid from AC1, AU5, AU7 and A3; graded no higher than AC1.
Where the link is weakest: AC1, weak support, carried from AL1.
AL3 · The government made the increase it taxes
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. A1 | The government regulates the dollar’s value, in exercise of Clause 5. | Reg ∧ C5 | one reading |
| 2. A2 | That regulation produces the nominal increase in the property’s dollar price. | Reg → Cause | moderate support |
| 3. AU2 | The actor is the Executive. | Exec | left open |
Conclusion: The nominal increase is the product of an executive exercise of the Clause 5 power. (Cause ∧ C5 ∧ Exec)
The solver: it follows, and dropping any one of A1, A2, AU2 makes it fail.
AC3 · The increase is the product of an executive exercise of Clause 5. Grade: left open. Valid from A1, A2 and AU2; graded no higher than AU2, whether the Federal Reserve is the Executive, which the Court has left open.
Where the link is weakest: AU2, left open. The Federal Reserve “operates at a deliberate remove from the ordinary political process”, outside plenary Presidential control.
AL4 · Surplusage
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. AU9 | The extra revenue is raised by the monetary action m, not by the tax law b. | Raises(m) ∧ ¬Raises(b) | ruled out |
| 2. AU10 | A clause is surplusage when any revenue escapes it. | Surplus ↔ ∃x (Raises(x) ∧ ¬Gov(x)) | ruled out |
| 3. W-orig | The clause governs Bills: its subject is “All Bills for raising Revenue”. | ∀x (Gov(x) ↔ Bill(x)) | stated |
| 4. F-orig | The tax law b is a Bill for raising Revenue that began in the House (H.R. 8300); the monetary action m is not a Bill. | Bill(b) ∧ ForRev(b) ∧ House(b) ∧ ¬Bill(m) | stated |
Conclusion: The Origination Clause is rendered surplusage (in AU10’s sense). (Surplus)
The solver: it follows, and dropping any one of AU9, AU10, W-orig, F-orig makes it fail.
AC4 · The Origination Clause is rendered surplusage. Grade: ruled out. Not shown by AL4, which needs AU9 and AU10, both excluded; and refuted by AN4, whose premises are the clause’s words, the Bills’ origin and the canon’s own definition of surplusage.
Where the link is weakest: AU9, ruled out. Revenue is “The annual produce of taxes”; the Bill that levies the tax raises what it yields.
AN4 · The clause keeps its effect
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. N4c | A clause is surplusage only if it is “without effect”: if it governs no Bill it names. | Surplus ↔ ¬∃x (Bill(x) ∧ ForRev(x) ∧ Gov(x)) | stated |
| 2. W-orig | The clause governs Bills. | ∀x (Gov(x) ↔ Bill(x)) | stated |
| 3. F-orig | The tax law b is a Bill for raising Revenue that began in the House. | Bill(b) ∧ ForRev(b) ∧ House(b) | stated |
Conclusion: The Origination Clause is not surplusage: it has effect over every Bill for raising Revenue. (¬Surplus)
The solver: it follows, and dropping any one of N4c, W-orig, F-orig makes it fail.
AC4n · The Origination Clause keeps its full effect. Grade: it follows. Valid from N4c, W-orig and F-orig, each stated: it follows.
AL5 · Unauthorized
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. AC3 | The increase is the product of an executive exercise of Clause 5 (AL3). | ExecC5 | left open |
| 2. AU11 | A power Congress delegates, exercised by another body, is a bypass of the House. | ExecC5 → Bypass | weak support |
| 3. A8 | No clause authorizes the Executive to exercise the money power in its own right. | ¬ClauseExec | stated |
Definitions entered: The practice is authorized if a clause authorizes the Executive, or a statute does that is not a bypass of the House. (Auth ↔ ClauseExec ∨ (Statute ∧ ¬Bypass))
Conclusion: The practice that produced the increase is unauthorized. (ExecC5 ∧ ¬Auth)
The solver: it follows, and dropping any one of AC3, AU11, A8 makes it fail.
AC5 · The bypass is unauthorized. Grade: weak support. Valid from A8, AC3 and AU11; graded no higher than AU11.
Where the link is weakest: AU11, weak support. “If Congress shall lay down by legislative act an intelligible principle to which the person or body authorized … is directed to conform, such legislative action is not a forbidden delegation of legislative power.”
AL6 · The binary
Route 1.
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. A4 | The word “incomes” means an accession to wealth. | Inc(p) ↔ Acc(p) | weak support |
| 2. AU4 | An accession is counted in real terms. | Acc(p) ↔ Real(p) | weak support |
| 3. AU5 | The whole gain is the inflation part. | Inc(g) ↔ Inc(p) | stated |
| 4. AU7 | The tax is valid only if the gain is income. | Valid(t) → Inc(g) | one reading |
Route 2.
| Premise | Notation | Grade | |
|---|---|---|---|
| 1. AU12 | Inflation is itself an extraction by the government. | Extraction | weak support |
Definitions entered: By definition the inflation part is no real increase, and it is a dollar increase. (¬Real(p) ∧ Dollar(p)) The gain is taxable when the tax on it is within the power. (Taxable ↔ Valid(t))
Conclusion: Either the nominal gain is not taxable (enforce), or it is taxable and inflation is an extraction (double extraction): the binary. (¬Taxable ∨ (Taxable ∧ Extraction))
The solver: route 1: it follows; dropping any one of A4, AU4, AU5, AU7 makes it fail; route 2: it follows; dropping AU12 makes it fail.
Grade: weak support. Route 1, from A4, AU4, AU5 and AU7; route 2, from AU12: either the words as ratified are enforced (O-enforce) or the Constitution permits double extraction (O-double). Whether no third construction survives is CH-A.
Where the link is weakest: AU4, weak support. Income is “The return in money”; the dollar is “the standard unit of value”; the Constitution states value in dollars; and the first decade under the Amendment taxed dollar gains through a doubling of prices.
What text 01’s links show
Every link is valid: each conclusion follows from its premises, and each premise is needed. The grades fall where the premises do. The measure of income, AU4, has weak support, and it carries AL1, AL2 and the binary’s first route down with it. Surplusage needs AU9 and AU10, both ruled out, and AN4 derives the opposite from the clause’s words, the Bills’ origin and the canon’s own definition. Whether the Federal Reserve is the Executive is left open (AU2), and a delegated power is a bypass of the House only on weak support (AU11). The binary stands at weak support by either route.