I have the following syllogism:

Should all goods come from virtue, no evil man possesses the good.
Some evil men possess the good.
Therefore, some goods do not come from virtue.

I understand that it denies the consequent but it denies it with a particular. If someone can confirm with me whether it is valid or invalid and either provide a reference where it says one cannot have a particular in a hypothetical syllogism, or a reference that states that one can have particulars in a hypothetical syllogism. A reference including other syllogisms that have particulars and states their validity can help as well.

  • 1
    There appears to be some equivocation in the use of "good" in your three terms. Normally, "the good" is considered an absolute non-quantifiable when written that way. But then in your first premise, you speak of "all goods". Do you mean to mean the same thing by good in both uses?
    – virmaior
    Oct 9 '15 at 1:56

Firstly, we have to sharpen up a little by assuming that an evil man is understood to be one who has no virtue, otherwise the argument cannot go through at all. After that, as you say, the argument is denying the consequent, which is to say it has the form "If P then Q; not Q; therefore not P". All we need to ensure that the argument correctly instantiates this form is that the second premise is contradictory to the consequent of the first. The fact that the second premise is a particular does not matter in this respect, because "some evil men possess the good" is clearly contradictory to "no evil man possesses the good". So the argument is valid.

  • Thanks! Do you by any chance know of any references that refer to particulars in conditional/hypothetical syllogisms? Oct 9 '15 at 2:30
  • From the way you are speaking about particulars, it sounds like you are studying Aristotelean term logic. I've not studied that in a long time, so I don't have references. In my view (and that of most modern logicians) Frege's predicate logic has rendered Aristotelean logic outdated. But maybe I can help you with a simple example: 1. If all dogs have four legs then there are no three-legged dogs. 2. My dog Fido has three legs. Therefore 3. It is not the case that all dogs have four legs. Clearly this argument is valid, but it uses a particular to deny the consequent.
    – Bumble
    Oct 9 '15 at 2:38

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