Modal Scope Fallacy
If you know something then you cannot be mistaken. But if you cannot be mistaken, then you are certain. Thus, certainty is a necessary condition of knowledge. If you're uncertain, then you don't really know, but the only things that you can be truly certain of are logic and mathematics. Therefore, there is no knowledge of anything outside of logic and math.
If a man is a bachelor then he cannot be married, but if he cannot be married then he must be a priest. Therefore, all bachelors are priests.
Modalities, like other logical concepts such as negation, have scope, that is, they logically influence a part of any sentence in which they occur. Moreover, in English grammar the scope of modalities is often ambiguous. Compare the following sentences with their modal terms highlighted:
- "If George is President, then he must be older than 35."
- "If God exists, then he necessarily exists."
Though these two propositions have different subject matter, they seem to have the same form: both appear to be conditional propositions, and the modal words―"must" and "necessarily"―in them are embedded in their consequents. However, on the most plausible interpretations, the modalities differ in scope. Here are the most plausible readings of the examples:
- "It must be the case that if George is President then he is older than 35."
In this example, "must" has broad scope over the whole conditional proposition. That is, the proposition says that it is a necessary truth that if George is President then, based upon a constitutional rule, he is older than 35. If the "must" had narrow scope, then it would say that if George is president then he is necessarily older than 35. But this is false, since no one is necessarily older than 35; that one is a certain age is a contingent fact, not a necessary one.
- "If God exists, then it is necessary that he exists."
In this example, "necessary" has narrow scope, that is, its scope is restricted to the proposition's consequent, rather than the whole proposition. The proposition claims that if God does in fact exist, then His existence is a necessary one. This is a special claim about God which is not true of other things; for instance, it is thankfully not the case that if Osama bin Laden exists then he necessarily exists. If the scope of the modality were broad, then the proposition would say that it is necessarily the case that if God exists then He exists. While this is true, it is true of everything including Osama bin Laden.
In these two examples it is clear what the scope of the modality is, but in other sentences it is not clear whether the modality has a broad or narrow scope. The modal scope fallacy occurs when this amphiboly is exploited.
Simplified a little, the example argument is the following:
- If you know something, then you cannot be mistaken about it.
- If you cannot be mistaken, then you are certain.
- Therefore, if you know something, then you are certain about it.
The scope ambiguity is found in the first premiss, where the alethic modality "cannot" may have two scopes:
- Narrow Scope: If you know something, then it is impossible for you to be mistaken about it.
- Wide Scope: It is impossible to both know something and be mistaken about it.
The modality in the first premiss must have narrow scope in order for the argument to be valid, but the modality must have wide scope in order for the premiss to be obviously true. The wide scope reading is uncontroversially true: it is impossible to know a falsehood. However, the narrow scope reading is at least controversial, and probably false: knowledge does not require the impossibility of error, merely its lack.
Norman Swartz, "'The' Modal Fallacy". "The modal fallacy", as Swartz refers to it, is the modal scope fallacy. There are other fallacies involving modalities, but this is probably the most common one. Swartz provides many examples of the fallacy using different types of modalities. The article is moderately technical, and uses some logical symbolism without explanation.
- Raymond Bradley & Norman Swartz, Possible Worlds: An Introduction to Logic and Its Philosophy (Hackett, 1979), pp. 330-332.
- Torkel Franzén, "Eternal Questions: Free Will and Divine Omniscience". Logician Franzén complains about fallacy lists and the fact that the modal scope fallacy is usually missing from such lists, and gives an example of the fallacy encountered in debates on the web. Franzén goes on to complain about what I call "fallacy abuse"―for instance, the tendencies to think that every bad argument is an instance of some named fallacy, or to hastily denounce debate opponents' arguments as fallacious before understanding them. Some of these errors are the result of what Pope denounced as "a little learning", which can only be remedied by more learning, a lack that this entry may help to fill.