Moscow State Institute of International Relations
(MGIMO-University)

B.A. in Government and International Affairs
School of Government and International Affairs

Alexander Shishkin Department of Philosophy

Logic

Tasks and Questions of Quiz 3
(covering themes 6, 8 and 9)

Compiled by Nikolai Biryukov

2022/23 School Year

 

1. Definitions of logical terms (from presentations 6, 8, and 9, viz. “Categorical Syllogism”, “Hypothetical and Disjunctive Syllogisms”, and “Enthymemes and Polysyllogisms”).

Define

o   categorical syllogism

o   complex disjunctive hypothetical

o   constructive disjunctive hypothetical

o   destructive disjunctive hypothetical

o   dilemma (in syllogistic)

o   disjunctive hypothetical

o   disjunctive syllogism

o   enthymeme

o   epicheirema

o   hypothetical syllogism

o   logical biconditional

o   mixed disjunctive syllogism

o   mixed hypothetical syllogism

o   modus ponendo tollens

o   modus ponens

o   modus tollendo ponens

o   modus tollens

o   polysyllogism

o   progressive (Goclenian) sorites

o   progressive polysyllogism

o   pure (wholly) hypothetical syllogism

o   pure disjunctive syllogism

o   regressive (Aristotelian) sorites

o   regressive polysyllogism

o   simple disjunctive hypothetical

o   sorites

o   the extreme terms

o   the fallacy of exclusive premises

o   the fallacy of four terms

o   the fallacy of illicit affirmative

o   the fallacy of illicit major

o   the fallacy of illicit minor

o   the fallacy of illicit negative

o   the fallacy of the converse

o   the fallacy of the inverse

o   the fallacy of undistributed middle

o   the figure of categorical syllogism

o   the first figure of categorical syllogism

o   the fourth figure of categorical syllogism

o   the major premise

o   the major term

o   the middle term

o   the minor premise

o   the minor term

o   the mood of categorical syllogism

o   the second figure of categorical syllogism

o   the third figure of categorical syllogism

o   trilemma (in syllogistic)

 

2. Paralogisms in Categorical Syllogistic.

Explain why the following inference is not valid. Point out the violated rule(s) of categorical syllogism and of the relevant figure of categorical syllogism.

All bishops are high-ranking Churchmen.
Some chessmen are bishops.
Therefore, some chessmen are high-ranking Churchmen.

All Greeks are humans.
Some humans are not poets.
Therefore, some poets are not Greeks.

All Greeks are humans.
Some humans are poets.
Therefore, some poets are Greeks.

All lions are predators.
All tigers are not lions.
Therefore, all tigers are not predators.

All lions are predators.
All tigers are predators.
Therefore, all tigers are lions.

All mammoths are extinct.
Dinosaurs are not mammoths.
Therefore, dinosaurs are not extinct.

All mice are cheese-eaters.
All cats are mice-eaters.
Therefore, all cats are cheese-eaters.

All numbers divisible by 4 are even.
Some numbers divisible by 4 are not divisible by 3.
Therefore, some numbers not divisible by 3 are not even.

All numbers divisible by 4 are even.
6 is an even number.
Therefore, 6 is divisible by 4.

All numbers divisible by 4 are even.
6 is not divisible by 4.
Therefore, 6 is not an even number.

All students study logic.
John is not a student.
Therefore, John does not study logic.

All students study logic.
John studies logic.
Therefore, John is a student.

Some Asians are Arabs.
Some Arabs are not poets.
Therefore, some poets are not Asians.

Some Asians are not Arabs.
Some Arabs are poets.
Therefore, some poets are not Asians.

Some Asians are not Arabs.
Some Arabs are poets.
Therefore, some poets are Asians.

Some numbers divisible by 3 are divisible by 4.
All numbers divisible by 4 are not odd.
Therefore, some odd numbers are not divisible by 3.

Some numbers divisible by 3 are divisible by 4.
All numbers divisible by 4 are not odd.
Therefore, all odd numbers are divisible by 3.

Some numbers divisible by 3 are divisible by 4.
All numbers divisible by 4 are even.
Therefore, all even numbers are not divisible by 3.

Some numbers divisible by 3 are not divisible by 4.
All numbers divisible by 4 are even.
Therefore, some even numbers are divisible by 3.

Some numbers divisible by 3 are not even.
Some numbers divisible by 3 are divisible by 4.
Therefore, some numbers divisible by 4 are not even.

Some numbers divisible by 4 are divisible by 3.
6 is divisible by 3.
Therefore, 6 is divisible by 4.

Some numbers divisible by 4 are divisible by 3.
6 is not divisible by 4.
Therefore, 6 is not divisible by 3.

Some numbers divisible by 4 are not divisible by 3.
6 is divisible by 3.
Therefore, 6 is not divisible by 4.

Some numbers not divisible by 3 are even.
Some numbers divisible by 3 are divisible by 4.
Therefore, some numbers divisible by 4 are not even.

Some poets are Asians.
Some Asians are Japanese.
Therefore, some Japanese are poets.

Some students study logic.
John does not study logic.
Therefore, John is not a student.

Some students study logic.
John is a student.
Therefore, John studies logic.

Some students study logic.
John studies logic.
Therefore, John is a student.

 

3. Rules of categorical syllogism and of the four figures of categorical syllogism.

o   Explain why a categorical syllogism may not have more than three terms.

o   Explain why a categorical syllogism must have three terms, neither more nor fewer.

o   Explain why at least one of the premises of a categorical syllogism must be affirmative.

o   Explain why at least one of the premises of a categorical syllogism must be universal.

o   Explain why both premises of a categorical syllogism may not be particular.

o   Explain why both premises of a categorical syllogism of the second figure may not be affirmative.

o   Explain why no conclusion may be drawn from two affirmative premises of a categorical syllogism of the second figure.

o   Explain why no conclusion may be drawn from two negative premises of a categorical syllogism.

o   Explain why no conclusion may be drawn from two particular premises of a categorical syllogism.

o   Explain why no conclusion may be drawn if the major premise of categorical syllogism of the first figure is particular.

o   Explain why no conclusion may be drawn if the major premise of categorical syllogism of the second figure is particular.

o   Explain why no conclusion may be drawn if the middle term is undistributed in both premises of a categorical syllogism

o   Explain why no conclusion may be drawn if the minor premise of categorical syllogism of the first figure is negative.

o   Explain why no conclusion may be drawn if the minor premise of categorical syllogism of the third figure is negative.

o   Explain why one of the premises of a categorical syllogism of the second figure must be negative.

o   Explain why only terms distributed in the premises of a categorical syllogism may be distributed in its conclusion.

o   Explain why premises a categorical syllogism may not be both negative.

o   Explain why terms undistributed in the premises of a categorical syllogism may not be distributed in its conclusion.

o   Explain why the conclusion of a categorical syllogism may not be affirmative, if one of the premises is negative.

o   Explain why the conclusion of a categorical syllogism may not be universal, if one of the premises is particular.

o   Explain why the conclusion of a categorical syllogism must be negative, if one of the premises is negative.

o   Explain why the conclusion of a categorical syllogism must be particular, if one of the premises is particular.

o   Explain why the conclusion of categorical syllogism of the second figure may not be affirmative.

o   Explain why the conclusion of categorical syllogism of the second figure must be negative.

o   Explain why the conclusion of categorical syllogism of the third figure may not be universal.

o   Explain why the conclusion of categorical syllogism of the third figure must be particular.

o   Explain why the major premise of a categorical syllogism of the first figure must be universal.

o   Explain why the major premise of a categorical syllogism of the first figure may not be particular.

o   Explain why the major premise of a categorical syllogism of the second figure must be universal.

o   Explain why the major premise of a categorical syllogism of the second figure may not be particular.

o   Explain why the major premise of categorical syllogism of the fourth figure must be negative, if the minor premise is not universal.

o   Explain why the major premise of categorical syllogism of the fourth figure may not be affirmative, if the minor premise is not universal.

o   Explain why the major premise of categorical syllogism of the fourth figure must be negative, if the minor premise is particular.

o   Explain why the major premise of categorical syllogism of the fourth figure may not be affirmative, if the minor premise is particular.

o   Explain why the major premise of categorical syllogism of the fourth figure must be universal, if one of the premises is negative.

o   Explain why the major premise of categorical syllogism of the fourth figure may not be particular, if one of the premises is negative.

o   Explain why the middle term must be distributed in, at least, one of the premises of a categorical syllogism.

o   Explain why the minor premise of a categorical syllogism of the first figure must be affirmative.

o   Explain why the minor premise of a categorical syllogism of the first figure may not be negative.

o   Explain why the minor premise of a categorical syllogism of the third figure must be affirmative.

o   Explain why the minor premise of a categorical syllogism of the third figure may not be negative.

o   Explain why the minor premise of categorical syllogism of the fourth figure must be universal if the major premise is affirmative.

o   Explain why the minor premise of categorical syllogism of the fourth figure may not be particular if the major premise is affirmative.

o   Explain why the minor premise of categorical syllogism of the fourth figure must be universal if the major premise is not negative.

o   Explain why the minor premise of categorical syllogism of the fourth figure may not be particular if the major premise is is not negative.