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Syllogism
Any deductive argument in which a conclusion is inferred from 2 premises

Categorical Syllogism
Adeductive argument of 3 propositions that together contain 3 terms, each of which occurs in 2 of the constituent propositions

Standard Form Categorical Syllogism
 A categorical Syllogism in which the premises and conclusions are all starndard form categoricalpropositions (A,E,I,O)
 They are arranged with the major premise first, minor premise second, and the conclusion last

Major term/Major premise
 The term that occurs as the predicate of the conclusion.
 The major premise is the premise that contains the major term.
**The predicate term of the conclusion**

Minor term/Minor premise
 term the occurs as the subject of the conclusion.
 The minor premise is the premise that contains the minor term
**Subject term of the conclusion**

Middle Term
The term that occurs in both premises, but never in the conclusion.

Identify the major, minor, and middle terms and premises of the following proposition
No heroes are cowards.
Some soldiers are cowards.
Therefore some soldiers are not heroes.
 Major term Heroes
 Minor term Soldiers
 Middle term Cowards
 Major premise No heroes are cowards
 Minor premise Some soldiers are cowards

Mood of a syllogism
One of the 64 three letter characterizations of categorical syllogisms determined by the forms of the standard form propositions it contains
In the given example, the major premise was an E, the minor premise an I, and the conclusion an O. EIO mood.

Figure
the logical shape of a syllogism, determined by the position of the middle term in its premises; there are 4 possible figures

Syllogisms can have 4 possible different figures;
 1. The middle term may be the subject term of the major premise and the predicate term of the minor premise
 2. The middle term may be the predicate term of both premises
 3. The middle term may be the subject term of both premises
 4. The middle term may be the predicate term of the major premise and the subject term of the minor premise

MP
SM
SP
First figure

PM
SM
SP
Second figure

MP
MS
SP
Third figure

PM
MS
SP
Fourth figure

If the middle term is in the subject place in both premises then the figure is
third figure

If the middle term is in the predicate position in both of the premises then the figure is
PM
SM
SP
second figure

Therefore;
conclusion indicator




In consequence
conclusion




For this reason
Conclusion


For these reasons
Conclusion

It follows that
conclusion

I conclude that
conclusion

Which shows that
conclusion

Which means that
Conclusion

Which entails that
Conclusion

Which implies that
Conclusion

Which allows us to infer that
Conclusion

Which points to the conclusion that
Conclusion










The reason is that
premise

For the reason that
premise

May be inferred from
premise

May be derived from
premise

May be deduced from
premise

In view of the fact that
premise

If the X lands on the line;
then it is invalid

Rules in diagraming Venn Diagrams
 1. Always diagram universal first
 2. If in diagraming particular (I,O) you have more than one region that you think the X should go, put the X on the line between the two regions

Fallacy of Four Terms
A formal mistake in which a categorical syllogism contains more than three terms

Syllogistic Rules and Fallacies
 1. Avoid 4 terms
 2. Distribute the middle term in atleast 1 premise
 3. Any term distributed in the con. must be distributed in the premises
 4. Avoid 2 negative premises
 5. If either premise is negative the con. must be negative
 6. From 2 universal premises noparticular con. me be drawn

Fallacies that stem from the syllogistic rules
 1. Four terms
 2. Undistributed middle
 3. Illicit Major/Minor
 4. Exclusive premises
 5. Drawing an affirmitive conclusion
 6. Existential fallacy

What is the fallacy?
Some M are P
Some S are not M
Some S are not P
Illicit major

What is the fallacy?
Some M are not P
All M are S
No S are P
Illicit minor

What is the fallacy?
No P are M
Some S are not P
Some S are not P
 The fallacy of exclusive premises
 two negative premises

What is the fallacy?
All P are M
All M are S
Some S are P
Existential fallacy

What is the Fallacy?
Some P are not M
All S are M
All S are P
Fallacy of drawing an affirmative conclusion

