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Philosophy 103: Introduction to Logic
Syllogistic Fallacies: Existential Fallacy

Abstract:  The Existential Fallacy is illustrated and explained.

I. The final fallacy of the syllogistic fallacies is illustrated in the following argument:
"Since no rigid levers are flexible things, Some rigid levers are not elastic bars because all elastic bars are flexible things."
A. When set up in standard form and order the syllogism looks like this:
All [elastic bars] are [flexible things].
No [rigid levers] are [flexible things].
Some [rigid levers] are not [elastic bars].
1. The Venn Diagram for this argument raises some interesting issues. How would you evaluate the following argument? Is it valid?

Diagram of AEO-2 Syllogism

2. According to our interpretation of the symbols used in Venn diagrams, we would have to have an "X" in the SMP area, but there is no "X" there. The blank space indicates no information is known about that area.
3. If we had independent information concerning the existence of rigid levers, we would know that at least one rigid lever existed, and this one would have to be in the SMP area of the diagram.
4. However, if we are evaluating the argument as given and we do not assume anything else, we cannot validly get to the conclusion from these premisses.
B. On the Boolean interpretation of categorical syllogisms, we cannot assume the existence of individuals mentioned in universal statements. If our language, if we want to assert that individuals exist, we must say so by adding a particular statement.
1. On this convention, the word "some" when used in a particular statement is taken to imply at least one of the individuals exists.
2. In sum, then, universal statements do not imply that the classes exist, whereas particular statements do imply that the classes exist.
3. We take this interpretation in our logic here so that arguments can be presented concerning subjects about ideal or nonexistent objects such as frictionless planes, ideal gasses, and black bodies.
II. Rule (Boolean Interpretation): No valid standard form categorical syllogism with a particular premiss can have both premisses universal.
A. Reason: If the rule were not followed, then we would go from premisses which have no existential import to a conclusion that does have existential import. The problem of existential import can be illustrated by Venn Diagrams.
B. The Existential Fallacy occurs whenever a standard form syllogism has two universal premisses and a particular conclusion.
C. See if you can determine merely by inspection if the following syllogisms are valid or invalid.
D. Note: If your logic presupposes existence, you cannot simply discard this rule, since the remaining rules would not be complete.

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