The existential fallacy, or
existential instantiation
In predicate logic, existential instantiation (also called existential elimination)Moore and Parker is a rule of inference which says that, given a formula of the form (\exists x) \phi(x), one may infer \phi(c) for a new constant symbol ''c''. Th ...
, is a
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 syst ...
. In the existential fallacy, one presupposes that a class has members when one is not supposed to do so; i.e., when one should not assume
existential import
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
...
. Not to be confused with the '
Affirming the consequent
Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dar ...
', which states "A causes B; B, therefore A".
One example would be: "''Every unicorn has a horn on its forehead''". It does not imply that there are any unicorns at all in the world, and thus it cannot be assumed that, if the statement were true, somewhere there is a unicorn in the world (with a horn on its forehead). The statement, if assumed true, implies only that if there were any unicorns, each would definitely have a horn on its forehead.
Overview
An existential fallacy is committed in a medieval
categorical syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...
because it has two universal premises and a particular conclusion with no assumption that at least one member of the class exists, an assumption which is not established by the premises.
In modern logic, the presupposition that a class has members is seen as unacceptable. In 1905,
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
wrote an essay entitled "The Existential Import of Proposition", in which he called this Boolean approach "
Peano
Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The sta ...
's interpretation".
The fallacy does not occur in
enthymeme
An enthymeme ( el, ἐνθύμημα, ''enthýmēma'') is a form of rational appeal, or deductive argument. It is also known as a rhetorical syllogism and is used in oratorical practice. While the syllogism is used in dialectic, or the art of log ...
s, where hidden premises required to make the syllogism valid assume the existence of at least one member of the class.
Examples
* All trespassers will be prosecuted.
* Therefore, some of those prosecuted will have trespassed.
This is a fallacy because the first statement does not require the existence of any actual trespassers (stating only what would happen if some do exist), and therefore does not prove the existence of any. Note that this is a fallacy whether or not anyone has trespassed.
See also
*
Affirming the consequent
Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dar ...
*
Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order formula \forall x P(x) expresses that everything i ...
*
Vacuous truth
In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied. For example, the statement "she d ...
References
External links
Fallacy files: existential fallacyFOLDOC: existential fallacy
Syllogistic fallacies
Quantificational fallacies
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