The Language of Argument

2 7 8

cHaP Te r 1 3 ■ F a l l a c i e s o f V a g u e n e s s

Heaps

The existence of borderline cases is essential to various styles of reasoning

that have been identified and used since ancient times. One such argument

was called the argument from the heap or the sorites argument (from the Greek

word “soros,” which means “heap”). The classic example was intended to

show that it is impossible to produce a heap of sand by adding one grain at

a time. As a variation on this, we will show that no one can become rich. The

argument can be formulated as a long series like this:

(1) Someone with only one cent is not rich.

(2) If someone with only one cent is not rich, then someone with only

two cents is not rich.

∴(3) Someone with only two cents is not rich. (from 1-2)

(4) If someone with only two cents is not rich, then someone with only

three cents is not rich.

∴(5) Someone with only three cents is not rich. (from 3-4)

(6) If someone with only three cents is not rich, then someone with

only four cents is not rich.

∴(7) Someone with only four cents is not rich. (from 5-6)

[and so on, until:]

∴(199,999,999,999) Someone with only 100,000,000,000 cents is not rich.

The problem, of course, is that someone with 100,000,000,000 cents is rich.

If someone denies this, we can keep on going. Or we can just sum up the

whole argument like this:

(1*) Someone with only one cent is not rich.

(2*) For any number, n, if someone with only n cents is not rich, then

someone with n 1 1 cents is not rich.

∴(3*) Someone with any number of cents is not rich.

Premise (2*) is, of course, just a generalization of premises (2), (4), (6), and

so on.

5. Mark is not doing too well (after his operation).


6. Shaq’s a big fellow.


7. Dan’s grades are low.


8. Walter can’t see well.


9. The earthquake was a disaster.


10. The news was wonderful.

97364_ch13_ptg01_273-290.indd 278 15/11/13 11:01 AM

some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,

affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.