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According to Gensler (2017):

An instance of a letter is distributed in a wff if it occurs just after “all” or anywhere after “no” or “not.” (p. 0008)

He then defines the star test as follows:

Star premise letters that are distributed and conclusion letters that aren’t distributed. Then the syllogism is valid if and only if every capital letter is starred exactly once and there is exactly one star on the right-hand side. (p. 0009)

Now, in the 2.2a Exercise, the third problem is as follows:

no Y* is E*

all G* is Y

∴ no Y is E

(p. 0011)

I have made distributed letters bold and starred where appropriate (or so I think; it is late). According to the "Answers to Selected Problems" (Gensler, 2017):

This isn’t a syllogism, because “Y” occurs three times and “G” occurs only once. (p. 0378)

This seems obvious. However, every capital letter is starred exactly once and there is exactly one star on the right-hand side. What am I missing?

Reference:

Gensler, H. J. (2017). Introduction to Logic (3rd ed.) [ProQuest Ebook Central version]. Retrieved from Ebookcentral.proquest.com

michaelgill1969
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1 Answers1

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See H.Gensler, Introduction to Logic, 2nd ed.,2017, page 9 :

More precisely, a syllogism is a vertical sequence of one or more wffs in which each letter occurs twice and the letters “form a chain” (each wff has at least one letter in common with the wff just below it, if there is one, and the first wff has at least one letter in common with the last wff).

Thus, the issue is that the argument is not a syllogism. But it is a valid argument : there are lots of valid arguments that are not in "syllogistic form"; consider e.g. :

"if $P$, then $Q$; therefore if not $Q$, then not $P$."

Mauro ALLEGRANZA
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