Assignment 3
Part A
1a. No diamonds are emeralds, diamonds is the subject and emeralds is the predicate, the terms are distributed because no S is P (E type proposition); it is a negative statement because of the quality of the subject. The quantity of the subject class is a particular proposition because no diamonds are emeralds.
1b. At least one person is a nerd, person is the subject and nerd is the predicate, the terms are distributed because one S exists so that S is a P (I type proposition); it is an affirmative statement because of the quantity of the subject. The quality of the subject class is a particular proposition because one person is a nerd.
Part B
1a. some college students are intelligent, what can be inferred from this statement based on the Aristotelian interpretation is ‘some college students’ because they spend all day trying to increase their knowledge, it is without question that there are college students who are more intelligent than others which is completely true.
1b. some college students are not intelligent, the inference is ‘some college students’ because there are some that are not intelligent, but there are some that are not intelligent in every subject which is completely true.
1c. no college students are intelligent, the inference is ‘no college students’ because no college student gets into college without having some intelligence and this is an existential fallacy because the logic does not exist. To say that no college student is intelligent would infer that college students are not mentally prepared to take college courses let alone understand college level material.
2.
1a. no college students cheat on exams, what I would infer about the truth value of this conclusion is that it is false because there are college students who do cheat on exams even though they are told not to. The inference of this is that ‘college students cheat on exams’ is not based on how many, it is deductive reasoning based on all college students which is false.
1b. some college students do not cheat on exams, what I would infer about the truth value of this conclusion is that it is true because there are college students who do cheat on exams to keep from studying long hours and to make sure their A+ is assured. The inference of this is that some college students do not cheat on exams because they want to earn their A+.
1c. all college students cheat on exams, what I would infer about the truth value of this conclusion is that it is an existential fallacy. While there are students who do cheat on exams, that does not mean that all students cheat on exams which they do not. The inference of this is that some college students are willing to cheat on exams to pass if it means that they will not be caught.
Part C
No saints are reprobates – Conversion – no reprobates are saints which is a true statement because no reprobates are saints so no S are P.
No saints are reprobates – Contrapositive – All non-saints are non-reprobates, so all non P are non S.
Some bombs are not grenades – Conversion – some grenades are not bombs, some P are S.
Some bombs are not grenades – Obversion – no bombs are non-grenades, all S are non P
Some bombs are not grenades – Contrapositive – all non-bombs are non-grenades, all non P are non S.
All forgeries are copies – Conversion – all copies are forgeries, all S are P.
All forgeries are copies – Obversion – no forgeries are copies, all S are non P
All forgeries are copies – Contrapositive – all non-forgeries are non-copies, all non S are non P
Some theologians are non-believers – Conversion – some non-believers are theologian, some S are P
Some theologians are non-believers – Obversion – no theologians are non-believers, all S are non P
Some theologians are non-believers – Contrapositive – all non-theologians are non-believers, all non S are non P
All scientists are non-magicians – Conversion – all non-magicians are scientists, all P are S.
All scientists are non-magicians – Obversion – no scientists are non-magicians, all S are non P
All scientists are non-magicians – Contrapositive – all non-scientists are non-magicians, all non S are non P.
Part D
1.
Some great scientists are famous. No TV stars are greatest scientists. So, some TV stars are not famous. The major term is famous, the minor term is great scientists and the middle term is TV stars. Some S are non P. The mood and figure is AIO-3.
All of the greatest human achievements are accomplishments that have come at a great price. Some accomplishments that have come at a great price are not brilliant discoveries. We may conclude that some of the greatest human achievements are not brilliant discoveries. The major term is greatest human achievements, the middle term is accomplishments and the minor term is brilliant discoveries. All P are S. The mood and figure is IAI-3
2.
a. Only Greeks are Athenians. At least one human is not an Athenian. Therefore, all humans are not Greeks. Only Greeks are Athenians – this does not imply that all Greeks are not Athenian. At least one human is not an Athenian – this does not imply that one human is not an Athenian. Therefore, all humans are not Greeks. The validity of the syllogism is that non Greeks are Athenian and all Greeks are not human. Some S are P. The mood and figure is AII-3
b. No human being is omniscient. Something is both divine and human. So, at least one divine being is not omniscient. No human being is omniscient – does not imply that human beings are omniscient. Something is both divine and human – does not imply the existence of what is divine and human. At least one divine being is not omniscient – does not imply the existence of any omniscient divine being. The validity of the syllogism is that human beings are not divine or omniscient. No S are P. The mood and figure is AEE-2
c. Only metaphorical statements are similarity statements. And every statement is a similarity statement. Accordingly, a thing is a statement only if it is metaphorical. Only metaphorical statements are similarity statements – does not imply the existence of similarity statements. And every statement is a similarity statement – does not imply the existence of statement. Accordingly, a thing is a statement only if it is metaphorical – does not imply the existence of a statement. Only metaphorical statements are similarity statements – does not imply the existence of a metaphorical statements. The validity of the syllogism is that metaphorical statements are not similarity statements. No P are S. The mood and figure is OAO-4.
d. Only persons who have inner conflicts are unhappy. At least one successful comedian is unhappy. We may conclude that some successful comedians are persons who have inner conflicts. Only persons who have inner conflicts are unhappy – does not imply the existence of inner conflicts. At least one successful comedian is unhappy – does not imply the existence of an unhappy comedian. We may conclude that some successful comedians are person who have inner conflicts – does not imply the existence of successful comedians with inner conflicts. The invalidity of the syllogism is that only persons who are comedians are unhappy and have inner conflicts. No S are P. The mood and figure is AIE-3
Part E
EEE-4, invalid. E-S, E-M, E-P, this form is invalid because there is nothing supporting the argument such as no magicians are humans, it would be invalid because there are magicians that are humans.
AAA-2, valid. A-P, A-S, A-M. This form is valid because there is a supporting subject in the form of A such as Jim is fluent in Spanish, Jim’s classmates are fluent in Spanish so the people in Jim’s Spanish class is fluent in Spanish.
AOO-2, valid. A-S, O-P, O-M, This form is valid because there is a supporting subject in the form of A such as Caina loves grapes, Caina loves grapes because they are purple so Caina loves grapes because they are purple and because she loves the color purple.
OOO-2, invalid, O-M, O-S, O-P. This form is invalid because there is no supporting subject in the form of O such as some gold bars are more yellow than other, the gold bars that are more yellow than others are brighter in the light. The gold bars that are brighter in the light are more yellow.
Part F
Babies are illogical
Nobody is despised that can manage a crocodile
Illogical persons is despised
All S are P, in accordance with the Venn diagram, babies are illogical so it would be EAE. Anyone who can manage a crocodile is not despised, so it would be AAI-1, Illogical persons is despised, in accordance with the Venn diagram, illogical persons are only despised so AEE-2.
2. Scientists study what interests them for only a fool would ignore what interests him. This statement is missing a premise, there is no logic supporting what the scientists are studying. The missing statement is scientists study what interests them for the benefit of mankind and only a fool would ignore what interests him.
3. The Aristotelian standpoint is different from the Boolean standpoint because the former standpoint is meant to signify existence such as if high school has children between the ages of 14-18, all high school students are between those ages. Another example is all children are whiners, it signifies the existence of children being whiners. The Boolean standpoint signifies that something does not exist or does not have existence. For example, no man is an enemy of the state, it does not signify the existence of a man or an enemy of the state. Another example is no man is human which does not signify that any man on earth is human or is a species of human.
