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4.6 4. The Existential Fallacy from the Aristotelian and Boolean…
4.6
4. The Existential Fallacy from the Aristotelian and Boolean Standpoints
The existential fallacy from the Boolean standpoint occurs when an argument has a form that is invalid from the Boolean standpoint but valid from the Aristotelian standpoint if the premise or premises have existential import. Remember that a universal statement has existential import, from the Aristotelian standpoint, only if the subject term denotes something that actually exists.
The existential fallacy from the Aristotelian standpoint occurs when an argument has a conditionally valid argument form, but the subject terms of the premise or premises do not denote something that actually exists. Any argument that commits the existential fallacy from the Aristotelian standpoint also commits the existential fallacy from the Boolean standpoint. However, an argument that commits the existential fallacy from the Boolean standpoint may or may not commit the existential fallacy from the Aristotelian standpoint.
Indicate whether each of the following immediate inferences commits the existential fallacy from the Boolean standpoint and/or from the Aristotelian standpoint.
Immediate Inference 1
No mermaids are mammals with legs.
Therefore, some mermaids are not mammals with legs.
Immediate Inference 1 commit the existential fallacy from the Boolean standpoint.
Immediate Inference 1 commit the existential fallacy from the Aristotelian standpoint.
Immediate Inference 2
It is false that no bigfoot creatures are Sasquatches .
Therefore, some bigfoot creatures are Sasquatches.
Immediate Inference 2 commit the existential fallacy from the Boolean standpoint.
Immediate Inference 2 commit the existential fallacy from the Aristotelian standpoint.
Immediate Inference 3
No baseball teams are football teams.
Therefore, some baseball teams are not football teams.
Immediate Inference 3 commit the existential fallacy from the Boolean standpoint.
Immediate Inference 3 commit the existential fallacy from the Aristotelian standpoint.
Immediate Inference 4
It is false that some military airplanes are commuter airplanes.
Therefore, it is false that all military airplanes are commuter airplanes.
Immediate Inference 4 commit the existential fallacy from the Boolean standpoint.
Immediate Inference 4 commit the existential fallacy from the Aristotelian standpoint.
Immediate Inference 5
It is false that some magical birds are not phoenixes.
Therefore, some magical birds are phoenixes.
Immediate Inference 5 commit the existential fallacy from the Boolean standpoint.
Immediate Inference 5 commit the existential fallacy from the Aristotelian standpoint.
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8. True/False Review and Chapter Summary
Use your knowledge of Venn diagrams for categorical propositions and immediate inferences, from the Aristotelian and the Boolean standpoints, to determine which of the following statements are true. Check all that apply.
An argument with an unconditionally valid form but whose premise has a subject term that does not denote something that really exists, commits the existential fallacy from both the Boolean and the Aristotelian standpoints.
To test an immediate inference for validity, first test it with the Venn diagram method from the Aristotelian standpoint and then from the Boolean standpoint.
The following immediate inference is invalid from the Aristotelian standpoint: No werewolves are Tasmanian devils. Therefore, it is false that some werewolves are Tasmanian devils.
Venn diagrams, from the Aristotelian standpoint, can be used to prove the inferences in the traditional square of opposition.
If an argument commits the existential fallacy from the Aristotelian standpoint, then it also commits the existential fallacy from the Boolean standpoint.
The following argument form is a conditionally valid argument form: It is false that some S are not P. Therefore, it is false that no S are P.
Any argument that is valid from the Boolean standpoint is also valid from the Aristotelian standpoint.
The following argument form is conditionally valid: It is false that some S are not P. Therefore, all S are P.
The following immediate inference commits the existential fallacy from the Aristotelian standpoint: All Sugar Plum Fairies are citizens of the Land of Sweets. Therefore, some Sugar Plum Fairies are citizens of the Land of Sweets.
An uncircled X on a Venn diagram, from the Aristotelian standpoint, represents the existence claim of a particular (I or O) proposition.
An argument with an unconditionally valid form is valid only from the Aristotelian standpoint.
All arguments that are valid from the Aristotelian standpoint are also valid from the Boolean standpoint.
To test the validity of an immediate inference using Venn diagrams, test it from the Boolean standpoint before testing it from the Aristotelian standpoint.
The Aristotelian standpoint and the Boolean standpoint differ in their interpretations of particular (I and O) propositions.
An argument with a conditionally valid form but with a premise whose subject term does not denote anything actual is invalid from the Aristotelian standpoint.
