Symbolic Logic
Book V
Syllogisms
Book V – Syllogisms
• Introduction
• Problems in Syllogisms
– Determining Conclusions
– Evaluating Conclusions
Introduction
• Syllogism:
– A trio of Biliteral Propositions
– All six terms are Species of the same Genus
– Every two of them contain between them a pair
of codivisional Classes
– The three Propositions are so related that, if the
first two are true, the third must be true
Introduction
• Syllogism:
– The first two Propositions are Premises
– The third Proposition is the Conclusion
– The Pair of Codivisional Terms in the Premises
are “Eliminands”
– The other two Pairs are “Retinends”
Introduction
• An example:
Statement
Type
Eliminand
Retinend
No X-things
are M-things
Premise
M
X
No Y-things
are M’-things
Premise
M’
Y
No X-things
are Y-things
Conclusion
X,Y
Introduction
• An example:
Statement
Type
Eliminand
Retinend
All cats
understand
French.
Premise
Cats
Creatures
understanding
French
Some chickens
are cats.
Premise
Cats
Chickens
Some chickens
understand
French.
Conclusion
Chickens,
Creatures
understanding
French
Problems in Syllogisms:
Determining a Conclusion
•
The Rules:
1.
2.
3.
4.
5.
6.
Determine the Univ
Construct a Dictionary (label your variables)
Translate the Premises into abstract form
Represent them on a Triliteral Diagram
Determine a Biliteral Conclusion
Translate the Conclusion into concrete form
Problems in Syllogisms:
Determining a Conclusion
• No son of mine is
dishonest.
• People always treat
an honest man with
respect.
• Conclusion?
Problems in Syllogisms:
Determining a Conclusion
1. Determine a Univ and rewrite the
Premises (if necessary)
• No son of mine is • Univ = “men”
dishonest.
• No sons of mine are
• People always treat
dishonest men.
an honest man with • All honest men are
respect.
men treated with
• Conclusion?
respect.
Problems in Syllogisms:
Determining a Conclusion
2. Construct a Dictionary
• No sons of mine are
dishonest men.
• All honest men are
men treated with
respect.
• Conclusion?
• M = honest (the
common term)
• X = sons of mine
• Y = treated with
respect
Problems in Syllogisms:
Determining a Conclusion
3. Translate the Premises into abstract form
• No sons of mine are
dishonest men.
• All honest men are
men treated with
respect.
• Conclusion?
• No X are M’
• All M are Y
Problems in Syllogisms:
Determining a Conclusion
4. Represent the Premises on the Triliteral
diagram
• No X are M’
• All M are Y
• Conclusion?
Problems in Syllogisms:
Determining a Conclusion
5. Determine a Biliteral Conclusion
Conclusion: No X are Y’
Problems in Syllogisms:
Determining a Conclusion
6. Translate the Conclusion into concrete
form
• P: No X are M’
• P: All M are Y
• C: No X are Y’
• No son of mine is
dishonest.
• People always treat an
honest man with
respect.
• No son of mine ever
fails to be treated with
respect.
Problems in Syllogisms:
Determining a Conclusion
• All girls get good
grades.
• Lazy students fail.
• Conclusion?
Problems in Syllogisms:
Determining a Conclusion
1. Determine a Univ and rewrite the
Premises (if necessary)
• All girls get good
grades.
• Lazy students fail.
• Conclusion?
• Univ = “students”
• All female students
are students who get
good grades.
• All lazy students are
students who fail.
Problems in Syllogisms:
Determining a Conclusion
2. Construct a Dictionary
• All female students
are students who get
good grades.
• All lazy students are
students who fail.
• Conclusion?
• M = pass (good
grades) (the
common term)
• X = female students
• Y = lazy students
Problems in Syllogisms:
Determining a Conclusion
3. Translate the Premises into abstract form
• All female students • All X are M
are students who get
good grades.
• All Y are M’
• All lazy students are
students who fail.
• Conclusion?
Problems in Syllogisms:
Determining a Conclusion
4. Represent the Premises on the Triliteral
diagram (“No” statements first!)
• P: All X are M
• P: All Y are M’
• Conclusion?
Problems in Syllogisms:
Determining a Conclusion
5. Determine a Biliteral Conclusion
Conclusion (2): All X are Y’, All Y are X’
Problems in Syllogisms:
Determining a Conclusion
6. Translate the Conclusion into concrete
form
• P: All X are M
• P: All Y are M’
• C: All X are Y’, All
Y are X’
• All girls get good
grades.
• Lazy students fail.
• All girls are
hardworking, all lazy
students are boys.
Problems in Syllogisms:
Evaluating a Conclusion
•
The Rules:
1. Follow the rules for determining a Conclusion
from your given Premises.
2. If there is no Conclusion, say so.
3. If there is a Conclusion, compare it with the
proposed Conclusion.
Problems in Syllogisms:
Evaluating a Conclusion
• P: All soldiers are
strong.
• P: All soldiers are
brave.
• C: Some strong men
are brave.
Problems in Syllogisms:
Evaluating a Conclusion
1. Follow the rules for determining a
Conclusion
• P: All soldiers are • Univ = “men”
strong.
• M = soldiers, X =
• P: All soldiers are
strong, Y = brave
brave.
• C: Some strong men
are brave.
Problems in Syllogisms:
Determining a Conclusion
1. Follow the rules for determining a
Conclusion
• P: All soldiers are
• All M are X
strong.
• All M are Y
• P: All soldiers are
brave.
• C: Some strong men
are brave.
Conclusion: Some X are Y
Problems in Syllogisms:
Determining a Conclusion
2. Compare the deduced Conclusion with
the proposed Conclusion
Conclusion: Some X are Y
• C: Some strong men
are brave.
Some strong men are brave.
They match!
Problems in Syllogisms:
Evaluating a Conclusion
• P: I enjoy country
music.
• P: When I enjoy
something, I wish to
expose other people to
it.
• C: I wish to expose
other people to some
country music.
Problems in Syllogisms:
Evaluating a Conclusion
1. Follow the rules for determining a
Conclusion
• P: I enjoy country music.
• P: When I enjoy
something, I wish to
expose other people to it.
• C: I wish to expose other
people to some country
music.
• Univ = “things”
• M = enjoy, X =
country music, Y =
expose other people
Problems in Syllogisms:
Determining a Conclusion
1. Follow the rules for determining a
Conclusion
• P: I enjoy country music.
• All X are M
• P: When I enjoy
• All M are Y
something, I wish to
expose other people to it.
• C: I wish to expose other
people to some country
music.
Conclusion: All X are Y
Problems in Syllogisms:
Determining a Conclusion
2. Compare the deduced Conclusion with
the proposed Conclusion
Conclusion: All Y are X
• C: I wish to expose
other people to
I wish to expose people to all
country music.
some country
music.
The proposed Conclusion is incomplete.
That’s All, Folks!
• Your assignment for
next week:
– Complete the
worksheet
– Have a great weekend!