Identify the Hypothetical Syllogisms
If a man is a conservation biologist, then he seeks to preserve endangered animal species. Noah sought to preserve endangered animal species. Thus, Noah was a conservation biologist.
AC- Affirming the Consequent
A statement that affirms an outcome based on a condition.
Hypothetical
Identify and translate into categorical form:
Rome conquered Carthage's empire.
All Rome was a Carthage empire conquerer.
SINGULAR
Translate:
Fred is an elder.
All Fred is an elder.
Every mistake is a doorway to learning, so mistakes should never be ignored.
(No doors to learning are things to ignore.)
All mistakes are doors to learning.
Therefore, no mistakes are things to ignore.
If war is ever lawful, then peace is sometimes sinful. A just war is lawful. Sometimes, therefore, peace is sinful.
MP- Modus ponens
An argument that uses only hypothetical statements.
Pure Hypothetical
Identify and translate into categorical form:
If a number is odd then it is not a multiple of two.
No odd numbers are multiples of two.
HYPOTHETICAL
Translate:
Bats are not blind.
No bats are blind creatures.
Jesus could be tempted and die, because He was a man.
(All men are tempted mortals.)
All Jesus was a man.
Therefore, all Jesus was a temptable mortal.
If you want to run track net year, then you should rendering the summer. Jon doesn't want to run track next year, so he should not run this summer.
DA- Denying the Antecedent
An argument that uses both hypothetical and categorical statements.
Mixed Hypothetical
Identify and translate into categorical form:
Blood is thicker than water.
All blood is thicker-than-water fluid.
INDEFINATE
Translate:
Only the saved go to heaven.
All heaven goers are saved people.
Sometimes getting good grades is a pleasant thing, since all honest success is pleasant.
All honest success is a pleasure.
(Some good grades are honest successes.)
Therefore, some good grades are a pleasure.
or All good grades are honest successes.
If a whale were a fish, then it would have gills. Whales do not have gills. Consequently, whales are not fish.
MT- Modus Tollens
The result of the condition in a syllogism (the part after the word, "then").
Consequent
Identify and translate into categorical form:
I am not a crook.
No I am a crook.
SINGULAR
Translate:
Jamie passes whenever she studies.
All times she studies are times Jamie passes.
All certainties will occur. Hence, every impossibility is uncertain.
(All things that occur are possibilities.)
All certainties are things that occur.
Therefore, all certainties are possibilities.
"If you are willing, you can make me clean." "I am willing," Jesus said, "Be clean."
MP- Modus Ponens
The condition of a hypothetical statement (the part after the the word, "if").
Antecedent
Identify and translate into categorical form:
Students will graduate this spring.
Some students will be spring graduates.
INDEFINATE
Translate:
Whoever finds wisdom finds life.
All wisdom finders are life finders.
An argument in which a statement is unstated and assumed. A syllogism with one assumed statement.
Enthymeme