Negation. Today's took two taps. The grain ran true.
STRATUM I — THE QUARRY FACE
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Today is the day of logic.
Cleave once. Cleave well.
Mark the line of fracture.
The arrow points down because the work points down.
STRATUM II — THE OPERATOR LEDGER
The operators, laid out for the day.
Conjunction. The easy cut. Both edges true, both edges held.
Disjunction. One edge will hold. Either is enough.
Implication. The slab leans. The corner follows the corner.
Biconditional. Twin cleaves. The block answers itself.
Exclusive. One face, never both faces, must come up clean.
Sheffer stroke. The single-cut. From it, every other follows.
Peirce arrow. Neither edge. The slab refuses both.
Assertion. Mark it down. The inference holds for the record.
STRATUM III — THE INFERENCE WALK
A proof, descended.
- i.
All quarries are dust.
- ii.
This place, here under the chisel, is a quarry.
- iii.
Therefore, this place is dust, in time.
- iv.
All dust is borne on the wind off the gulf.
- v.
This place's dust will be borne on the wind off the gulf.
- vi.
If the wind comes off the gulf at four, the slab dries faster than the chisel can score it.
- vii.
Wait until five. The wind cools. The slab takes the line.
- viii.
Therefore: cut at five. Mark it down. The inference holds.
STRATUM IV — THE COMBINATORIAL WHEEL
STRATUM V — THE FREGE PAGE
For every quarry, some marble that is sound.
marginalia
Hover a junction. Each cut has its name.
STRATUM VI — THE DICTATION
End-of-shift, dictated to the clerk.
The morning began grey. The cart came up at four with the second slab from the third bench — Pentelic, two arshini by one, faintly veined to the south corner.
I set my hand on it. The stone was cold. A good cold. The kind that takes a chisel without arguing.
The first cut took on the second tap. Premise: the slab is sound. The mallet rang. The grain ran with us. I marked the corner with the foreman's tally and we set it on the trestle.
By eight the sun had cleared the ridge. Premise the second: the wind off the gulf will rise at four o'clock and dust every working surface. We shut the shed door against it. The shed groaned. The boy from the lower bench came up with cold tea.
The inference is this. If the slab is sound, and if the dust is held off until the score is complete, then the line of fracture obeys the score. We knew this before we cut. We knew it again after.
At ten, second cut. The chisel went in clean. I drew the line of fracture with the heel of my hand and the slab gave on the third tap. Conjunction held. Both edges true.
At noon we ate bread and cheese. The wheel of connectives turned in my head, slow as the shed shadow. I thought of Frege. I thought of his page of strokes and arrows, drawn as if he too had been a foreman, in a colder country, with paper instead of stone.
At two, the long cut. The third axiom of the day: the long cut takes a long patience. We worked at it through the heat. The slab dried where the wind found a gap. We wet it down. The grain held.
At four, as predicted, the wind. We did not work the line then. We swept the shop. We ground the chisel. We waited.
At five the wind cooled. We took the line. The slab gave a single sound, like a struck bell at distance, and the cleave came true.
End of the day. The slab cooled. The inference held. Tomorrow we cut another.
STRATUM VII — THE CALCULATOR
end of the working day. ⊢ logic. ∎