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In one of the Abbot & Costello show episode, the following dialogue occurs:

Abbot: Is it not true that you are a  servant of the public?
Officer: Yes, I am servant of the public.
Abbot: I happen to be one of the public.
Officer: Yes, you are one of the public.
Abbot: Then you are nothing but a public servant.
Officer: Yes I am a public servant.
Abbot: Give me a glass of water.
Officer: Yes.

If I try to simplify this dialogue to a syllogism, I get this:

Officer is a public servant
Abbot is one of the public
Therefore officer is the servant of Abbot

And further:

A is B of C
D is C
Therefore A is B of D

It has a figure of:

  M-P
  S-M
◇S-P
(M: middle term, P: major term, S:minor term)
And by order
Affirmative Universal    A
Affirmative Particular   I
Affirmative Particular   I

This is a valid argument by its mood and figure. Both premises seem to be true, thus giving a sound argument.

I feel like there is something of with the conclusion which is creating the comedy, but I cannot find a formal fallacy, so I think there may be an informal fallacy.

First, is my analysis correct? If not, where is my mistake? If I am correct, what is the informal fallacy here?

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    What is the question? Commented May 14, 2022 at 22:48
  • @MarkAndrews I've asked the question at the end but let me recite it here: First, is my analysis correct? If not, where is my fault? Latter, if I am correct, what is the informal fallacy here?
    – Csopso
    Commented May 14, 2022 at 22:51
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    This is just a fallacy of division (an informal fallacy). en.wikipedia.org/wiki/Fallacy_of_division Abbot claims that what is true of "the public" as a whole (that the officer serves it) must also be true of Abbot who is part of the public. But what is true of the whole is not necessarily true of every part of the whole. Just say no to Aristotelian logic; first order logic is better. Aristotelian logic only persists being taught out of tradition, not because it is any good compared to modern logic.
    – causative
    Commented May 15, 2022 at 2:23
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    Isn't it just that this is over-literal, since "public servant" is a specialized phrase in English that has a different meaning (and different characteristic duties/responsibilities) than "servant" in the personal sense?
    – Hypnosifl
    Commented May 15, 2022 at 3:31
  • @Hypnosifl can we say that it has an Eymological Fallacy?
    – Csopso
    Commented May 15, 2022 at 12:41

4 Answers 4

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I think you are not correct in the characterization of the minor premise: “Abbot is one of the public”. “Public” or “public servant” is the middle term. Thus this syllogism is AAA in the second figure: P thus M, S thus M; therefore S thus P.

AAA-2 is invalid for its failure to have a distributed middle term. In practical terms, an undistributed middle term means that there is nothing linking the two premises. So while each premise alone might be true, nothing follows when they are placed together.

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  • I didn't understand how minor premise and conclusion is Affirmative Universal. They seem like Particular. Abbot is only in a from the entire group which makes it particular.
    – Csopso
    Commented May 15, 2022 at 10:59
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    “Abbot “ is informal shorthand for “All people identical to Abbot”. “Officer” is “All people identical to this officer”. If the minor premise were particular, it would be, “some people identical to Abbot”. True, it could be “Some members of the public are Abbot”, and the major premise could be rephrased in the same way. However, this rephrasing would not alter the position of the middle term. The end result is IIA in the second figure. IIA-2 is invalid for the same reason: an undistributed middle term. Commented May 15, 2022 at 18:01
  • Also, valid syllogisms are just not as funny as the invalid ones. Q.E.D.! Commented May 15, 2022 at 18:04
  • In the conclusion we say "Officer is the servant of Abbott" as the "officer" is the major term doesn't it suppose to be P thus S?
    – Csopso
    Commented May 16, 2022 at 21:10
  • I tried to apply reductio ad absurdum and the inconsistent triad to test its validty. When I wrote it down it seems valid. I can clearly see the undistributed middle fallacy but I don't understand how I get "valid" with other methods? For example reductio ad absurdum: (O:officer, A:Abbott, P:public/public servant)OP!=0,AP!=0 thus OA!=0 ------ now lets take contradictory of the conclusion and couple it with the minor premise: OP!=0, OA=0 thus AP=0 and we see that the new conclusion is the contradictory of the main minor premise thus the argument is valid.
    – Csopso
    Commented May 16, 2022 at 21:42
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There is a category error here.

The fallacy is the idea that a member of the public can stand for "the public" and thus command service from a public servant.

That is, a member of a set is not the set and does not inherit properties of the set. A member of a set, and the set, are different categories.

To borrow a motivational example from computer program design: If B is a type of A, then it is not true to say that collection-of-B is a type of collection-of-A. So, even if B and C are both types-of A, and you can substitute a C for a B, you can't substitute a collection-of-B for a collection-of-C. And you need to watch out for the error of trying to park a nuclear powered aircraft carrier in the spot reserved for electric scooters. Even though you could use either the aircraft carrier or the scooter if all you needed was "a vehicle."

"The public" is a set. In general, it is an abstraction referring to a group of people with shifting membership. As people are born, achieve age of majority, move to or from different countries, and eventually die, the group is changing over time. It is the idea of the people living in a polity. It does not refer to any specific individual.

If the term "the public" does not refer to something very close to this, then the idea of "public servant" does not make sense in the situation. For example, in a totalitarian dictatorship, a "public servant" would not be a sensible title.

A "public servant" is, in theory at least, a servant to the abstraction "the public." For example, in some polities, such persons swear an oath "to the constitution" or "to the crown" or to some other symbol of the community or country.

A "public servant" is thus not a servant to any individual in "the public" since a member of a set is not the same as the set. A member of a set is not of the same category as the set.

Indeed, in political matters, the set of "the public" may easily be in conflict with a single individual. (Whether that conflict is moral or ethical or desirable could lead to a huge collection of interesting philosophical discusssions.) This is a significant portion of the reason that there are such things as public servants, in order to enforce the decisions of "the public" (arrived at by whatever means currently in exsistence, again leading to huge philosophical discussions).

A police officer is a primary example. Through some means, laws have been enacted. (Keep those swaths of philosophical disucssion in mind. The laws may or may not be moral, ethical, desirable, etc.) These laws are presumed to be the will of "the public." Being a "public servant" means the police officer must follow those laws, not what any one member of the public says.

So:

The police officer is a public servant.
Abbot is a member of the public.
The police officer is not a servant to Abbot, because Abbot is a member of the public, but he is not "the public."

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To summarize a little there are several fallacious ideas in place here.

The most obvious one is that the "pars pro toto" approach doesn't work in that Abbot is a part of the public but he's not the public itself.

And the other problem are fallacies of equivocation about the terms "servant", and that wasn't mentioned so far, also on the term "service".

Because the public servant is indeed expected to serve the public, including members of the public, like Abbot. It's just that in context, "servant"≠"Butler", but "a person providing a service" and "service"≠"any service", but "a very particular service".

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Just so it's said, comedy often bends the rules of logic, but it doesn't necessarily break them. Fallacies (formally) refer to particular mistakes in the transference of characteristics between categories and their members. Not every logical error is properly called a fallacy, though obviously the term is applied loosely and broadly outside of the field of logic.

This case, however, seems to invoke the Four Terms Fallacy, where the term 'servant' is used in different senses at different places in the dialog. Logical syllogisms are restricted to three terms: a category, a member of the category, and a characteristic being transferred. IN the beginning, 'servant' (as "public servant") refers to a person of public authority who serves the needs of the community. At then end, 'servant' is used in the sense of a menial who serves the interests of individuals. This effectively creates four terms in the syllogism used, breaking the validity of the logic. The humor lies in the fact that someone would try such an audaciously stupid trick in the first place.

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