| I. The final fallacy of the syllogistic fallacies is illustrated in the following argument: |
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"Since no rigid levers are
flexible things, Some rigid levers are not elastic bars because all elastic bars are
flexible things." |
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A. When set up in standard form and order the
syllogism looks like this: |
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All [elastic bars] are
[flexible things].
No [rigid levers] are [flexible things].
Some [rigid levers] are not [elastic bars]. |
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1. The Venn Diagram for this argument raises
some interesting issues. How would you evaluate the following argument? Is it valid? |
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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. |
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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. |
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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. |
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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. |
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1. On this convention, the word "some"
when used in a particular statement is taken to imply at least one of the individuals
exists. |
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2. In sum, then, universal statements do not
imply that the classes exist, whereas particular statements do imply that the classes
exist. |
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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. |
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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. |
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B. The Existential Fallacy
occurs whenever a standard form syllogism has two universal premisses and a particular
conclusion. |
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C. See if you can determine merely by inspection
if the following syllogisms are valid or invalid. |
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AAI-3 |
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EEO-4 |
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EAO-1 |
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EAI-3 |
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AE0-1 |
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AEA-2 |
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E00-2 |
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AOI-3 |
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OEO-4 |
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OOO-1 |
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D. Note: If your logic presupposes
existence, you cannot simply discard this rule, since the remaining rules would not be
complete. |
