Awkward Logical Incongruities

How one cannot avoid Buzzfeed these days is shown me that even in my complete disinterest in that website and my obliviousness to its various references in other people's use of it as a comedic prop on occasion, I am still unable to avoid its popping up with something that might be "of interest" from time to time.  The case of the logic test on the Secret Service Special Agent exam is a case in point. The Buzzfeed version was so horrible that it can be safely ignored (as with much from that site).

In a United States Secret Service application exam instructions section, there is a description of the logical notions which are to be used in the test, and an accurate and good one at that, albeit one that is very basic and uninvolved beyond what is necessary to test the basic thinking capabilities of those who take the test.

“Some” statements: These statements refer to part of a group by using terms such as “some,” “most,” “a few,” or another term which indicates a portion of a group. Such statements about a portion of a group imply nothing about the remaining portion of the group. You should not jump to a conclusion that you might make in typical conversational speech.

Example Statement:
Many Secret Service Special Agents are not from Alaska.

Invalid conclusion:
A few Secret Service Special Agents are from Alaska.

Valid conclusion:
A few Secret Service Special Agents may or may not be from Alaska.

Then in one of the example questions the problem comes up, the right answer to which is not presented as the right answer by the exam, but is discounted in direct contradiction to the instructions given at above.

Passage 6:

No part-time employees are Secret Service Special Agents.
All part-time employees report to a field office location.
Some full-time employees are Secret Service Special Agents.
Christopher reports to the Maryland field office.
Brian is a Secret Service Special Agent.

Indicate whether the statement is True, False, or if there is Insufficient Information to draw a conclusion.

1. Christopher is a part-time employee.

a)True
b)False
c)Insufficient Information to Decide


2. Brian is a full-time employee.

a)True
b)False
c)Insufficient Information to Decide


3. All full-time Secret Service employees are Special Agents.

a)True
b)False
c)Insufficient Information to Decide

Then proceed the explanations, which we would expect to square with the introductory instructions, to include the one I listed here on "some" statements.

Passage 6 Explanations:

1. You cannot tell from the facts presented whether the first conclusion is true or false. The facts state that all part-time employees report to a field office location and that Christopher reports to the Maryland field office location. However, the facts do not indicate that only part-time employees report to the Maryland field office or that no full-time employees report to field office locations. Therefore, it cannot be assumed that Christopher is a part-time employee from the facts presented. You would fill in the bubble that corresponds to "C" on your answer sheet for INSUFFICIENT INFORMATION TO DECIDE.

2. The second conclusion is TRUE. We know that all Secret Service Special Agents are full-time employees. Brian is a Secret Service Special Agent. Therefore, Brian must be a full-time employee. You would fill in the bubble that corresponds to "A" on your answer sheet for TRUE.

3. The third conclusion is FALSE.  We know that all Secret Service Special Agents are full-time employees. We also know that some full-time Secret Service employees are Special Agents. Therefore, some Secret Service full-time employees must hold titles other than Special Agent. You would fill in the bubble that corresponds to "B" on your answer sheet for FALSE.

Number three is not accurate. As it says in the instructions, we have no information about all of a set of entities based on information about only some members of that set. Therefore, since all we know of the problem is to be drawn from the supplied premises, we can demonstrate that anything is true of false validly only from those premises. But none of those premises for this problem set indicate only general things that cannot be used for this deduction, or specific things that cannot be used for this deduction, to reach the answer "false".

No part-time employees are Secret Service Special Agents. 
(No S are P| S=part timers, P=SSSAs)
This indicates only that there does not exist any agents who are both part-time employees and SSSAs. Therefore we can be sure that if someone is a Secret Service Special Agent, he is not a part-time employee. Therefore, assuming there are only part-time and full-time employees in the USSS, it follows that if someone is a SSSA, then he or she is a full-time employee. This does not show that all full-time employees are SSSA, of course. That would be to affirm the consequent, a logical fallacy. But it is also not possible to reach the "false" answer to the same statement, since that would be to deny the antecedent. So this premise of itself cannot help at all the matter of the supposed answer.


All part-time employees report to a field office location.
(All S are P| S=part-timers,  P=reporters to some field office(s))
This is totally irrelevant to the issue.


Some full-time employees are Secret Service Special Agents.
(Some S are P| S=full-timers, P=SSSAs)
This is relevant, but only as far as it goes. It affirms that if there are full-time employees at all, then it is false that "none of them" are SSSAs. That leaves room for it to be either true or false that all of them are SSSAs. This is a simple and consistent extension of the discussion of "some" statements at outset. Many people like to think it is otherwise, and I can recall the strange ecstasy on the face of one sophomore-level logic professor as he suggested that it is actually the case that this is true only if one assumes that there exists some of the subject in the first place.  But strangely enough, he went on to suggest that "not All S are P" will indicate that at least some of the subject exists which are, and some of the subject exists which are not in the predicate.  

I still cannot understand why he insisted on this, when that is just the colloquialism of human language use creeping into logic, whereas logic aims to be free of such influences to the maximum degree possible, or at least to admit of their influence and detail a justification for it.  Some unicorns are telepathic doesn't establish the existence of either the subject or the predicate, and that should be the end of that.  Likewise, to suggest that this might imply that unicorns exist or that some of them are not telepathic, is no better off.  It is not the case that things which we know exist in general become things we know exist in particular.  We may know of "such things" as full-time employees of the Secret Service, and we may know that if they do exist then at least some of them are SSSAs, but again this would neither mean any FT employees existed per se, nor that any of them are not SSSAs. 
 
So far, none of the premises enable the conclusion that it is false that "all full-time employees are SSSAs". We can understand from the wider world beyond the confines of the test that there are plenty of full-time employees in the USSS who are not SSSAs, and our intuition about this would be correct in most possible worlds. But what if, unlikely as it may be, that there were suddenly no active full-time employees who were not SSSAs (for whatever reason). Then while one might know of one or two full-time employees, and know that they are SSSAs (which fulfills the premise stating that at least some FT employees are SSSAs), there is no way from that to know the truth, that in fact all of the FT employees that remain from whatever reduced their number, are SSSAs. 

So there is not enough information to decide (for us in this scenario), but it is in fact true that "all full-time employees are SSSAs".  I will refrain from any amusing scenarios, such as the President dismantling the entire bureaucracy of the institution and assuming direct control of the remaining personnel, so that all of those who are still full time are only the most trusted and necessary "skeleton crew" of SSSAs.  It could happen.  What else would you do if such an institution were corrupted by rackets on a scale which have usurped even the government as a whole and which operates under better legal protections than the law itself can properly afford, and are therefore literally above the law?  What if not behead the damned thing and keep only the best meat.

 
Christopher reports to the Maryland field office.
 
Brian is a Secret Service Special Agent.

Neither of these help decide the conclusion in question, since whether Christopher is part-time or full-time (neither can be determined from this statement), his reporting to the Maryland field office will not contradict that he is an SSSA. So it may still be not-false, that is "true" that all full-time employees are SSSAs, but indeterminable one way or the other from this particular piece of information. And if Brian is a SSSA, then that simply confirms without proving the possibility that all full-time employees of the USSS, including Brian, are SSSAs.

Just a consideration of consistency. Either the instructions are true and faithful to what can be logically known without recourse to conventional and colloquial forms of expression, or the proper answer to the question is "insufficient information to decide".

But if one wanted to consider the full scope of the matter in a wider frame, one can simply examine the basic syllogistic logic of Aristotle and how it evolved into the modern forms of deductive reasoning systems we have today.