NECESSARY AND SUFFICIENT CONDITIONS
Another way of expressing statement (1) is in terms of necessary conditions:
(1) Your insurance company will PAY up for CDs stolen from your car only if you LOCKED the car door.
could be re-expressed as
(6) That you LOCKED your car door is a necessary condition for your insurance company to PAY up for CDs stolen from your car.
That is, “P only if L” is equivalent to “L is a necessary condition for P.” This tells us that necessary conditions are consequents.
The conditions we have been used to—those expressed in the (/-clause—are antecedents. We call these sufficient conditions, since it is sufficient for the antecedent to be true in order for the consequent to follow. Here’s an example:
(7) The fact that our existence has duration is sufficient to demonstrate the existence of God.—Descartes, Principles of Philosophy, I, 21
Re-expressed:
(8) If our existence has DURATION, the existence of GOD can be demonstrated. Symbolized: D → G
Thus sufficient conditions are antecedents.
(b) Only if the statesmen have behind them the will to peace of a decisive MAJORITY in their own countries can they ATTAIN their great end.—Albert Einstein, Ideas and Opinions
(c) This drug is LEGAL in the United States only when the user is STRADDLING a state line.—Steve Martin, Pure Drivel
(d) The SETTLEMENT of the West could only take place if the Indian barrier were REMOVED—Winston Churchill, A History of The English-Speaking Peoples, vol. 4, 1958
(e) Having taken INTRODUCTORY logic is a necessary condition for ENROLLING in the Intermediate Logic course in Philosophy.
(f) A thing is TRUE only if it can be PROVED.—Umberto Eco, Foucaulfs Pendulum, p.
206(g) The fact that our existence has DURATION is sufficient to demonstrate the EXISTENCE of God.—Rene Descartes, Principles of Philosophy [D := our existence has DURATION, E := we can demonstrate the EXISTENCE of God]
(h) It is only when the intellect decides PREMATURELY... that it FALLS prey to error and uncertainty.—Emst Cassirer, The Philosophy of the Enlightenment
(i) Should the Dolphins WIN their division and DEFEAT the Western Champion, the American Conference title game will be held in MIAMI Jan. 2 only if the RUNNER-UP team beats Cleveland.—Sports pages
(j) The only way the BILLS and the CHARGERS can get to the playoffs is if JACKSONVILLE loses.—TV sportscaster
(k) The mere presence of a SUBSTANCE is not sufficient for PERCEPTION.— Leibniz, 3rd paper to Clarke, 11 [S := A SUBSTANCE is merely present, P := there is PERCEPTION]
(l) Only if we succeed in ABOLISHING military service altogether will it be possible to EDUCATE the youth in a spirit of reconciliation, joy in life, and love toward all living creatures.—Albert Einstein, Ideas and Opinions
2. Which of the following statements is naturally construed as a conditional statement? (no need to symbolize):
(a) Often a hen who has merely laid an egg cackles as if she had laid an asteroid.— Mark Twain
(b) The sick do not ask if the hand that smoothes their pillow is pure... —Oscar Wilde
(c)Should Senator Ervin run again, he would be a formidable opponent.—Newspaper
(d) I never encountered any proposition so doubtful that I could not draw from it some quite certain conclusion, if only the conclusion that it contained nothing certain.—Rene Descartes, Philosophical Writings I, 125
(e) And if Hitler can identify that point in the hollow center of the earth, which is also the exact center of the sky, he will be Master of the World, whose king he is by right of race.—Umberto Eco, Foucaulfs Pendulum, p. 514
3. In 1999 Spanish researchers claimed to have found evidence for a black hole circulating around another star in the constellation Scorpius.
They found an abundance of the elements oxygen, magnesium, silicon, and sulfur in the spectrum of the visible star. “The only way you can produce an abundance of these elements is through several billions of degrees,” said Rafael Rebolo, co-author of the study and researcher at the Institute of Astrophysics in the Canary Islands. “The only way to reach these temperatures is when a star goes to a supernova situation.” The argument is completed by noting that the invisible star has a mass of about 40 times the mass of our sun, and if a star had this mass and went supernova, then (according to current theory) a black hole would result.—Boston Globe, Thursday, September 9, 1999Using the following key, (a) symbolize the argument and (b) prove its validity:
Key: A := an ABUNDANCE of the elements oxygen, magnesium, silicon, and sulphur has been produced; T:= the TEMPERATURE was several billion degrees. S := the invisible STAR went supernova; M := the invisible star has a MASS of about 40 times the mass of our sun; B := the invisible star is a BLACK HOLE.
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