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35. Note on the Boolian Algebra

Peirce, Charles S. Indiana University Press PDF


W R I T I N G S OF C H A R L E S S. P E I R C E , 1879-1884

Note on the Boolian Algebra

MS 401: Fall 1881-Spring 1882

Let the variables, x, y, z, etc. denote propositions. Let two constant numbers v and f be chosen arbitrarily, and let the equality of any variable to v signify that the proposition it denotes is true, while its equality to f signifies falsity.

Then since every proposition is either true or false, every variable must satisfy the equation


In some states of things one factor, in others the other may vanish.

If the proposition y is true in every state of things in which the proposition x is true, the equation is satisfied, that

(x - f )(y - v) = 0

for otherwise x might be true and y false in the same state of things.

The equations of the two syllogistic premises If X, then Y' and 'If

Y, then Z', are

(x - f )(y - v) = 0

(y - f )(z - v) - 0

Multiplying the first by (z — v) and the second by (x — f) and subtracting one from the other, and dividing by (v — f) we get

(x f)(x-cv) which signifies If X, then Z', which is the syllogistic conclusion.

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Believing in Architecture: Berlin since

Iain Bamforth Carcanet Press Ltd. PDF

Believing in Architecture

B  

Rubble Berlin. People keep mislaying things in Berlin, even the city itself. While every European city offers the historian a biography

(the history of Europe is, in large part, the history of its cities),

Berlin, since , has acquired an archaeology, too. Some of its layers are made of compressed nightmare, deposits of sordid misery and not just the eerie atmospheres of the ‘weird tales’ that made E.T.A. Hoffmann famous in the days when Berlin was a most respectably enlightened regional capital. A couple of weeks ago I stood with my son flying a kite on the top of a large sandy hill in the Grünewald area, between Berlin and Potsdam. The hill is called Teufelsberg. The only incline for miles, it offers a superb vantage point across the city from Spandau and Reinickendorf in the north to Tempelhof and Kopenick in the south. In winter it becomes a ski resort. But Devil’s Mountain is no ordinary hill: pipes, bricks, tiles and other detritus can be seen poking out from beneath its sand and scrub. This -metre-high heap is the derelict body of prewar Berlin; this is the city carted away brick by brick at war’s end by the famous ‘rubble women’.

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Retracing Nelson Mandela through the Lineage of Black Political Thought

IU Press Journals Indiana University Press ePub

from Walter Rubusana to Steve Biko

Xolela Mangcu

Out of timber so crooked as that from which man is made nothing entirely straight can be carved.


Reclaiming the Vision

SOUTH AFRICAS TRANSITION to democracy still inspires the imagination of people all over the world, especially those in search of what too often seems like an elusive peace. Even when he lies sick in hospital Nelson Mandela remains the iconic embodiment of that historical transformation, and will remain so for decades to come. South Africans invoke his memory to protest the depredations of his successors, from Thabo Mbeki’s dalliance with HIV/AIDS denialists to the halo of corruption around Jacob Zuma’s head. Compounding the country’s challenges are unacceptably high levels of unemployment, poverty, and inequality and a failing school system. To overcome these challenges and return to the high road of Nelson Mandela and his generation, the country needs much more than technocratic policy solutions. It needs a self-awareness that can only come from a new public narrative that puts present and future generations back on Mandela’s path. The path itself was never straightforward but winding—and winding with too many proverbial forks in the road. The debates were oftentimes clamorous, but they also became the basis for political creativity against daunting odds.

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Chapter Twenty-Two

Scott Russell Sanders Indiana University Press ePub

Whatever was groaning apparently did not feel much need of breathing. Phoenix calculated it was likelier to be a machine than a beast, for what beast could bellow so mournfully without pausing to inhale? Still, in the wilds you could never be sure. Mutants cropped up all the time. Who knew what roomy lungs some of them might have? Maybe he should put on his antlers and go frighten the thing into silence. Nothing like a fierce pair of horns to stiffen the old backbone.

“It’s getting louder,” he observed, twisting round to glance at Teeg. Her haggard look unsettled him. What if it was a beast? “Maybe we should pull over?”

“It’s probably just a drone they put in to scare people off the river.”

“What people?”

“Anybody. Us, for example.”

“Well,” he admitted, “I think it’s done a pretty good job on me.” His playfulness did not erase the pinched look from her face.

According to the map that lay crumpled over his knees, they were passing through the suburbs of Portland now. But there was nothing remarkable on the shore, except some queer mounds of brush and saplings. Did they cover the ruins of buildings? Where the first bridge was supposed to be, crumbling cement piers thrust up from the river. Grass and brush had rooted on the crowns, where electric shuttles used to run. How odd, to have lived in a city that was open to the sky, with plants actually growing in the yards.

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9 Polygyny, Divorce, Widowhood, and Death of a Woman

Vladimir Nalivkin Indiana University Press ePub

RELIGION ALLOWS a Muslim man to have no more than four wives at the same time. The number of wives he can have over time, according to Sharia, is unlimited. For instance, if he already has four wives but for some reason wants to marry a fifth one, he must first divorce one of his current wives, and then religion does not prevent him from replacing her with a new one. A woman who becomes a widow or divorces her husband can also remarry an unlimited number of times.

The eldest, senior wife is considered the mistress of the house; she is responsible for the overall supervision and management of the household economy and the performance of the work she decides to do; the rest of the work must be performed by the younger wives on her order. The latter call her byovyo (bibi, elder sister, aunt, mistress) and must treat her with the respect they would show an older close relative. (We will see below that in most cases these rules are not followed.) If the first wife dies or is divorced, her position is usually taken not by the next one in line but by the one that the husband loves most.

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