Categorical Syllogisms Definition
Three categorical propositions Three terms: each used twice Two Premises One Conclusion All Men are Mortal Socrates is a man/ All people identical with Socrates are Men Socrates is mortal/ All people identical with Socrates are people who are mortal Symbolized
All M are P All S are M All S are P Terms
Major Term: Predicate of the conclusion Symbolized by “P” Minor Term: Subject of the conclusion Symbolized by “S” Premises
Standard Form Major Premise listed first Minor Premise listed second
Example
All M are P Major Premise
All S are M Minor Premise All S are P Standard Form
Same terms Same Sense (no equivocation) Major premise first Minor premise second Mood
Three letter phrase which corresponds to the 3 proposition types in the syllogism Example:
All Great Danes are dogs
No cats are dogs
Therefore: No Cats are Great Danes Mood AEE ( Figure: 2 Unconditionally Valid) Figure 1
M are P S are M S are P Left Right Figure 2
P are M S are M S are P Left Right
Figure 3
M are P M are S S are P Left Right Figure 4
P are M M are S S are P Left Right
Venn Diagrams
Marks/ Shading for premises only Universals shaded first Particulars:
That one thing exists
That it belongs or is excluded from some class Venn Diagrams Continued
Shade areas completely “x” goes in unshaded region “x” on the line when there is insufficient information Not on the intersection of two lines Boolean/ Aristotelian: does the subject denote existent things? Examples EAE- 2 (Valid)
M No P are M All S are M No S are P
S P Example AEE- 4 (Valid)
M All P are M No M are S No S are P
S P AOO- 2 (Valid)
All P are M M Some S are not M Some S are not P
X
S P AOO- 1 Invalid
All M are P M M Some S are not M Some S are not P
X
S P OIO-1 (Invalid)
Some M are not P M Some S are M X Some S are not P X
S P Rules Method Rules and Fallacies
Rules:
The Middle term must be distributed in at least one premise
If not: undistributed middle
If a term is distributed in the conclusion then it must be distributed in the premise in which occurs
If not: illicit Major/ Minor Rules and Fallacies Continued
If there is a negative premise then there must be a negative conclusion There can not be more than 2 negative propositions in the argument Existential Fallacy