# Fallacy of Modal Logic

Taxonomy: Logical Fallacy > Formal Fallacy > Fallacy of Modal Logic

Subfallacy: Modal Scope Fallacy

### Exposition1:

Modal logic is the branch of logic which studies logical relations involving modalities. Modalities are ways2 in which a statement, or "proposition", can be true or false. The most commonly studied modalities are necessity and possibility, which are modalities because some propositions are necessarily true or false and others are possibly so. Types of modality include:

• Alethic Modalities: These include possibility and necessity, which were already mentioned, as well as impossibility and contingency. Some propositions are impossible, that is, necessarily false, whereas others are contingent, meaning that they are both possibly true and possibly false.
• Temporal Modalities: Historical and future truth or falsity. Some propositions were true or false in the past, some true or false now, and others will be so in the future.
• Deontic Modalities: Obligation and permissibility. Some propositions ought to be true or false, while others are permissibly so.
• Epistemic Modalities: Knowledge and belief. Some propositions are known to be true or false, and others are believed to be so.

Modalities are propositional functions―that is, they are functions that produce a proposition when applied to a proposition―like negation in propositional logic3, but unlike negation in that they are not truth-functional. That is, you cannot determine the truth-value―whether it is true or false―of a modal proposition based solely upon the truth-value of the proposition it contains. For instance, from the fact that a certain proposition is true it does not follow that it is necessarily true, nor that it isn't. Some true propositions are necessarily so, but others are not.

Modal fallacies are formal fallacies in which modality plays a role in the fallaciousness of a type of argument. Modal Fallacy is the most general fallacy involving modalities, but most actual fallacious arguments involving modalities will commit the subfallacy, above.

### Exposure:

Since modalities are frequent topics in philosophy―alethic modalities in metaphysics, epistemic ones in epistemology, and deontic ones in ethics―modal fallacies are quite frequent in philosophical and pseudo-philosophical argumentation. So, while students of philosophy should, of course, study logic and fallacies in general, they should pay particular attention to modal fallacies.

Notes:

1. For introductions to modal logic, see the following:
• James Garson, "Modal Logic", Stanford Encyclopedia of Philosophy. A clear but technical survey of the field that assumes comfort with standard nonmodal logic.
• G. E. Hughes & M. J. Cresswell, A New Introduction to Modal Logic (Routledge, 1996). The standard introduction, which may be too much for novices.
2. Or "modes", hence "modality" and "modal".
3. See the entry for Propositional Fallacy for more on propositional logic.