From the observation that each member of a group could possess a chara

Question

From the observation that each member of a group could possess a characteristic, it is fallacious to conclude immediately that it is possible for all the group’s members to possess the characteristic. An example in which the fallacy is obvious: arguing that because each of the players entering a tennis tournament has a possibility of winning it, there is therefore a possibility that all will win the tournament.

Which one of the following commits the fallacy described above?

(A) You can fool some of the people all of the time and all of the people some of the time, but you cannot fool all of the people all of the time.

(B) Each of the candidates for mayor appears at first glance to possess the necessary qualifications. It would therefore be a mistake to rule out any of them without more careful examination.

(C) Each of the many nominees could be appointed to any one of the three openings on the committee. Therefore it is possible for all of the nominees to be appointed to the openings on the committee.

(D) If a fair coin is tossed five times, then on each toss the chance of heads being the result is half. Therefore the chance of heads being the result on all five tosses is also half.

(E) It is estimated that ten million planets capable of supporting life exist in our galaxy. Thus to rule out the possibility of life on worlds other than Earth, ten million planetary explorations would be needed.

stne · Answer

Let's rephrase: Just because EACH member of a group COULD posses a characteristic, it is WRONG to conclude that ALL members of the group COULD posses the characteristic. In a Lawn tennis tournament just because EACH member COULD win does not mean that ALL will win.

(A) No characteristic is being attributed to each member here, and then to ALL members. NOT a similar fallacy.  INCORRECT.

(B) First part says that each member posses a certain characteristic,but second part DOES NOT attribute that characteristic to All individuals. INCORRECT.

(C) EACH member could be appointed to any  ONE   of three openings , therefore all the members could be appointed to all the openings. Exactly as our Fallacy:  CORRECT.

(D)No characteristic is being attributed to each member here, and then to ALL members. NOT a similar fallacy.  INCORRECT.

(E) No characteristic is being attributed to each member here, and then to ALL members. NOT a similar fallacy.  INCORRECT.

Ans. C

Hope it's clear.

gautamK0206 · Answer

The logic here is that, if there's a possibility of a characteristic existing in few of the members, then that doesn't necessarily translates to all the members having the same characteristics. Now that same translates to chances/opportunities as well. As stated in the example, that, all the participating players have the calibre and chances of winning, but only one of the wins the tournament. Similarly, on the same logical flaw, if there are three open positions, and all the nominees are equally qualified, then all the members could be appointed to all the openings.
Therefore, the correct answer: C

Sajjad1994 · Answer

Explanation

We need to find the answer that makes this same mistake as done in the argument above.

(A)  This is about fooling people at different times, not a  “same time”  composition fallacy. No fallacy of possibility distribution across a group simultaneously.

(B)  It means ach candidate appears qualified so we shouldn’t rule out any without examination. That’s not claiming all can be chosen simultaneously. No composition fallacy.

(C)   “Each nominee could be appointed to any one of the three openings”  meaning any nominee could fill any slot. Then concludes  “it is possible for all nominees to be appointed to the openings.”  But if there are many nominees and only three openings, then not all nominees can be appointed at once. This again commits the fallacy:  “each could possibly get a spot”  it fallaciously infers  “all could possibly be appointed simultaneously,”  ignoring the limited openings. Keep this one.

(D)  This confuses probabilities, each toss has 1/2 chances of heads, so chance of all 5 heads is (1/2)^5, not 1/2.

(E)  This argues that to rule out life elsewhere, we’d need to explore all planets. That’s about evidence and possibility of life, not the  “all members could have X at once”  fallacy.

Answer: C

From the observation that each member of a group could possess a chara

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From the observation that each member of a group could possess a chara

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