Academic journal article ETC.: A Review of General Semantics

House Seats

Academic journal article ETC.: A Review of General Semantics

House Seats

Article excerpt

You can run into mathsemantic difficulties almost anywhere. Even so, it may come as a surprise to find that you need read only five sentences of the Constitution of the United States to reach an enduring mathsemantic problem left us by the founding fathers.

Representatives and direct taxes shall be apportioned among the several States which may be included within this Union, according to their respective numbers, which shall be determined by adding to the whole number of free persons, including those bound to service for a term of years, and excluding Indians not taxed, three-fifths of all other persons. (1) (emphasis added)

Gary Evans of Seattle (2), who has joined our small band as Mathsemantic Monitor #16, reminded me of this problem by asking me to review his proposed solution to one part of it. He's now working on my suggestions for simplifying his proposal. Perhaps this will lead to a later mathsemantic-monitor piece featuring a solution of that part, conceivably even to a national brouhaha. Meanwhile the overall problem itself and some earlier solutions merit attention here.

A Mathsemantic Problem

The founding fathers of our country certainly took a bold and laudable step in establishing equal representation relative to population. Nevertheless, the words "Representatives ... shall be apportioned among the several States ... according to their respective numbers" also established a mathsemantic problem, because (a) their interpretation lies on the boundary of math and ordinary language and (b) they permit many interpretations.

We can break the problem into two main parts, namely, counting and apportionment. The part for which Gary believes he's found a better solution is the apportionment of seats once the counts are settled. But let's consider first the less tractable part, getting the counts.

The Constitution continues after its fifth sentence quoted above with a sixth that mandates a decennial census.

The actual enumeration shall be made within three years after the first meeting of the Congress of the United States, and within every subsequent term of ten years, in such manner as they shall by law direct. (1)


Before getting into more current problems with the census, the Mathsemantic Monitor wishes to take up the infamous "three-fifths of all other persons" matter. We can only with difficulty today feel what a useful compromise this must have seemed in 1787 when it resolved both the allocation of House Seats and tax burden by state. So abhorrent do we find slavery that we can hardly imagine how a "government ... half slave and half free" managed to function for eight decades in the first place. Lincoln got it right in saying "I believe this government cannot endure permanently." (3) In 1865 the Thirteenth Amendment outlawed slavery and then the Fourteenth Amendment (1868) restated the allocation formula:

Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State excluding Indians not taxed. (1)

An unintended and ironic consequence of the brutal Civil War that led to this change was that the vanquished southern states gained seats in the House of Representatives at the expense of the victorious northern states. Former slaves, concentrated of course in the South, now counted more heavily in the "respective numbers" of those states (at "one" each rather than at "three-fifths"), thus entitling those states to proportionally greater representation. In the fall of 1865 the Chicago Tribune estimated that the abolition of slavery had given former slave states sixteen additional seats (at a time when the House had 243 seats). (4)

The Mathsemantic Monitor notes that the exclusion of former slaves from polling booths that soon followed gave each southern voter even more voice in national affairs than a voter from other states. …

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