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formal fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic s ...
of the modal fallacy is a special type of fallacy that occurs in
modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...
. It is the fallacy of placing a proposition in the wrong modal scope, most commonly confusing the scope of what is ''necessarily'' true. A statement is considered necessarily true if and only if it is impossible for the statement to be untrue and that there is no situation that would cause the statement to be false. Some philosophers further argue that a necessarily true statement must be true in all
possible worlds Possible Worlds may refer to: * Possible worlds, concept in philosophy * ''Possible Worlds'' (play), 1990 play by John Mighton ** ''Possible Worlds'' (film), 2000 film by Robert Lepage, based on the play * Possible Worlds (studio) * ''Possible Wo ...
. In modal logic, a proposition P can be necessarily true or false (denoted \Box P and \Box\lnot P, respectively), meaning that it is logically necessary that it is true or false; or it could be possibly true or false (denoted \diamond P and \diamond\lnot P), meaning that it is true or false, but it is not logically necessary that it is so: its truth or falseness is ''
contingent Contingency or Contingent may refer to: * Contingency (philosophy), in philosophy and logic * Contingency plan, in planning * Contingency table, in statistics * Contingency theory, in organizational theory * Contingency theory (biology) in evolu ...
''. The modal fallacy occurs when there is a confusion of the distinction between the two.


Description

In modal logic, there is an important distinction between what is logically necessary to be true and what is true but not logically necessary to be so. One common form is replacing p \rightarrow q with p \rightarrow \Box q. In the first statement, q is true given p but is not logically necessary to be so. A common example in everyday life might be the following: #
Mickey Mouse Mickey Mouse is an animated cartoon character co-created in 1928 by Walt Disney and Ub Iwerks. The longtime mascot of The Walt Disney Company, Mickey is an anthropomorphic mouse who typically wears red shorts, large yellow shoes, and whi ...
is the President of the United States. # The President is at least 35 years old. # Thus, Mickey Mouse is necessarily 35 years or older. Why is this false? The conclusion is false, since, even though Mickey Mouse is over 35 years old, there is no logical necessity for him to be. Even though it is certainly true in this world, a possible world can exist in which Mickey Mouse is not yet 35 years old. If instead of adding a stipulation of necessity, the argument just concluded that Mickey Mouse is 35 or older, it would be valid. Norman Swartz gave the following example of how the modal fallacy can lead one to conclude that the future is already set, regardless of one's decisions; this is based on the "sea battle" example used by Aristotle to discuss the
problem of future contingents Future contingent propositions (or simply, future contingents) are statements about states of affairs in the future that are '' contingent:'' neither necessarily true nor necessarily false. The problem of future contingents seems to have been fi ...
in his ''
On Interpretation ''De Interpretatione'' or ''On Interpretation'' (Greek: Περὶ Ἑρμηνείας, ''Peri Hermeneias'') is the second text from Aristotle's ''Organon'' and is among the earliest surviving philosophical works in the Western tradition to deal ...
:''
Two admirals, A and B, are preparing their navies for a sea battle tomorrow. The battle will be fought until one side is victorious. But the 'laws' of the excluded middle (no third truth-value) and of non-contradiction (not both truth-values), mandate that one of the propositions, 'A wins' and 'B wins', is true (always has been and ever will be) and the other is false (always has been and ever will be). Suppose 'A wins' is today true. Then whatever A does (or fails to do) today will make no difference; similarly, whatever B does (or fails to do) today will make no difference: the outcome is already settled. Or again, suppose 'A wins' is today false. Then no matter what A does today (or fails to do), it will make no difference; similarly, no matter what B does (or fails to do), it will make no difference: the outcome is already settled. Thus, if propositions bear their truth-values timelessly (or unchangingly and eternally), then planning, or as Aristotle put it 'taking care', is illusory in its efficacy. The future will be what it will be, irrespective of our planning, intentions, etc.
Suppose that the statement "A wins" is given by A and "B wins" is given by B. It is true here that only one of the statements "A wins" or "B wins" must be true. In other words, only one of \diamond A or \diamond B is true. In logic syntax, this is equivalent to A \lor B (either A or B is true) \lnot\diamond (A \land B) (it is not possible that A and B are both true at the same time) The fallacy here occurs because one assumes that \diamond A and \diamond B implies \Box A and \Box B. Thus, one believes that, since one of both events is logically necessarily true, no action by either can change the outcome. Swartz also argued that the
argument from free will The argument from free will, also called the paradox of free will or theological fatalism, contends that omniscience and free will are incompatible and that any conception of God that incorporates both properties is therefore inconceivable. See ...
suffers from the modal fallacy.{{Cite web, url=http://www.iep.utm.edu/foreknow, title=Foreknowledge and Free Will, last=Swartz, first=Norman, website=Internet Encyclopedia of Philosophy, access-date=26 August 2017


References

Modal logic Non-classical logic Philosophical logic Formal fallacies