Some Are/Some Are Not

Alias: Unwarranted Contrast

Type: Fallacy of Quantificational Logic

Some S are P.
Therefore, some S are not P.
Some S are not P.
Therefore, some S are P.

Venn Diagram:

This diagram is for the first form above. A diagram for the second form is obtained by taking circle P to represent non-P. The diagram shows this form of argument to be non-validating, because the area with a question mark may be empty, so far as the premiss indicates.

Venn diagram


Some politicians are crooks.
Therefore, some politicians are not crooks.


To understand the nature of this fallacy, one needs to know the difference between logical implication and conversational implicature:

  1. Implication: This is a relation between propositions, that is, the meanings of statements.
  2. Implicature: This is a relation between the fact that someone makes a statement and a proposition.

For example, suppose that I state that today is Sunday and it's raining. This statement logically implies that it's raining. In contrast, the fact that I made the statement implicates that I believe that it's raining. The statement taken by itself implies nothing about what I believe; rather, it is the fact that I made the statement which implicates that I believe it.

Why does the fact that I made the statement implicate that I believe it? All conversational implicature is based on certain rules (or "maxims", as the philosopher Paul Grice called them) which govern cooperative communication. One of these rules is that you should state only what you believe (which Grice called a maxim of "Quality"). Thus, from the fact that I state something, you can conclude that I believe it. Of course, I might be lying, but conversational implicature is based upon the presumption that people are trying to cooperate, and thus are obeying the rules.

How does this relate to the Fallacy of Some Are/Some Are Not? There is another rule of conversation (called by Grice a maxim of "Quantity") that one should make statements as logically strong as is consistent with telling the truth (Quality). So, while a statement of the form "Some S are P" does not logically imply "Some S are not P", the fact that someone makes the former statement conversationally implicates the latter. In other words, if one knows that all S are P one should say so, and the fact that one says only that some are implicates that one does not believe that all are. This latter fact, together with the assumption that you know what you're talking about (Quality, again), implicates that not all S are P.

Thus, the theory of conversational implicature explains how it is possible to mislead—if not actually lie—while still speaking the literal truth; by means of what we call "half-truths", we can implicate falsehoods with our statements. If we know that all S are P, then the statement that some are is a half-truth. Half-truths are wholly true, since truth and falsity do not come in degrees, but they are misleading because they violate norms of efficient communication. Hence, the legal oath to tell the truth (Quality), the whole truth (Quantity), and nothing but the truth (Quality, again).

So, what is the Fallacy of Some Are/Some Are Not? It is the mistake of confusing logical implication and conversational implicature by thinking that "some are" statements logically imply "some are not" statements, when the former statements only conversationally implicate the latter.