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'Giving charity to young healthy beggars is wrong. Thus, charity is a wrong policy.' Is this a fallacy of converse accident or of composition?

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This is the fallacy of converse accident.

We have a set C of people to whom we can give charity. The set B of young healthy beggars is a subset of C: B ⊂ C. Now, the argument goes as follows:

  • ∀ b:B, givingIsWrong(b)      — for all b in B, giving to b is wrong
  • B ⊂ C                                  — all B's are C's
  • ∴ ∀ c:C, givingIsWrong(c)   — therefore, for all c in C, giving to c is wrong

In other words: Because some property (giving is wrong) holds for all elements of a subset (B), it must hold for all elements of the superset (C). This is a case of faulty generalisation:

A faulty generalization is a conclusion about all or many instances of a phenomenon that has been reached on the basis of just one or just a few instances of that phenomenon. It is an example of jumping to conclusions.

The fallacy of composition occurs in a context of "whole" and "parts of the whole". In this case, "young healthy beggars", i.e. B, is a part of "people to whom we can give charity", C. In this case, the argument would go like this:

  • givingIsWrong(B)     — giving to the set B is wrong
  • B ⊂ C                       — all B's are C's
  • ∴ givingIsWrong(C)  — therefore, giving to the set C is wrong

The argument would have been committing the fallacy of composition if it would have discussed giving charity to the whole group, i.e., if we were discussing giving charity to all young healthy beggars together. This is not the case: we're talking about giving to young healthy beggars as individuals.

For example: "This fragment of metal cannot be fractured with a hammer, therefore the machine of which it is a part cannot be fractured with a hammer."

Don't worry, it is common to confuse the two.

[The fallacy of composition] is often confused with the fallacy of hasty generalization, in which an unwarranted inference is made from a statement about a sample to a statement about the population from which it is drawn.

(Last two quotes from Wikipedia)

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