#### Mohamed Selim -- m.selim@innopolis.university #### Albert Akmukhametov -- a.akmukhametov@innopolis.university #### Khush Patel -- k.patel@innopolis.university #### Slava Koshman -- v.koshman@innopolis.university #### Egor Dmitriev -- e.dmitriev@innopolis.university ## Task A Answer the following open questions to the best of your possibility ~~(approx. ½ page A4 for each question)~~ 1. What is a categorical proposition? And What is a class? - ***In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks.*** - ***Classical logic makes great use of the principle of putting things into categories, or classes. Categorical propositions tell you things about these categories.*** 2. How many categorical propositions are out there and what are their characteristics in terms of inclusion/exclusion, universality/particularity, affirmative/negative? Explain the details, you can use a table - ***There are four types of categorical proposition, each of which is given a vowel letter A, E, I and O. A way of remembering these is: Affirmative universal, nEgative universal, affIrmative particular and nOgative particular. To be more correct, A and I letters came from the Latin affirmo, and E and O from the Latin nego.*** | Form | Type | Quality | Quantity | Distribution of X | Distribution of Y | |-----------------|------|-------------|------------|-------------------|-------------------| | All X is Y | A | Affirmative | Universal | Distributed | Undistributed | | No X is Y | E | Negative | Universal | Distributed | Distributed | | Some X is Y | I | Affirmative | Particular | Undistributed | Undistributed | | Some X is not Y | O | Negative | Particular | Undistributed | Distributed | 3. Define quantity, quality and distribution and show whether the four categorical propositions you listed above have those features. Make a table, don’t just copy the slides. ### Opposites - ***There are several types of opposition used in categorical propositions. These can be traditionally placed in the Square of Opposition.*** - Contraries cannot both be true, but both can be false. - Subcontraries cannot both be false, but both can be true. - Subaltern pairs can both be true or both be false. - Contradictories cannot both be true and cannot both be false. ### Converse - ***The converse of a categorical proposition is categorical proposition where the predicate and subject of the original proposition are exchanged. Note that the quantity does not move with the subject or predicate.*** - No dogs are cats --> No cats are dogs - Some dogs are friendly creatures --> Some friendly creatures are dogs - All dogs are animals --> All animals are dogs - ***The converse of any true E or I proposition is also true (making it a useful test). A and O converses are seldom true.*** ### Obverse - ***The obverse of a categorical proposition has predicate term replaced with its complement and quality of the proposition reverse.*** - All dogs are animals --> No dogs are not animals - No dogs are not dangerous --> All dogs are dangerous - ***The obverse of all types of true categorical proposition are also true.*** ### Contrapositive - ***The contrapositive of a categorical proposition is formed by taking the complement of both subject and predicate and then reversing them.*** - All dogs are animals --> All non-animals are not dogs - Some dogs are friendly --> Some non-friendly creatures are not dogs - ***The contrapositive of any true A or O proposition is also true (making it a useful test). Contrapositives of E and I propositions are seldom true.*** ## Task B Which terms are distributed and which are undistributed, explain why 1. All senators are citizens Senators are distributed. Type A proposition. 3. No athletes are vegetarians Both athletes are vegetarians are distributed. Type E proposition. 3. Some soldiers are cowards None of them are distributed. Type I proposition. 4. Some horses are not thoroughbreds Thoroughbreds are distributed. Typr O proposition. ## Task C Individuate quality, quantity and whether subject and predicate terms are distributed 1. Some presidential candidates will be sadly disappointed people. a. Quality -- affirmative b. Quantity -- particular c. Subject -- undistributed d. Predicate -- undistributed 2. No leader of the feminist movement is a major business executive a. Negative b. Universal c. Distributed d. Distributed 3. All new labor-saving devices are major threats to the trade union movement. a. Affirmative b. Universal c. Distributed d. Undistributed ## Task D Identify subject and predicate terms in, and name the form of, each of the following propositions: 1. Some historians are extremely gifted writers whose works read like first-rate novels. Subject: some historians Predicate: are extremely gifted writers 2. Some members of families that are rich and famous are not persons of either wealth or distinction. Subject: some members of rich & famous families Predicate: are not persons of wealth nor distinction 3. No people who have not themselves done creative work in the arts are responsible critics on whose judgment we can rely. Subject: People who have done creative art work Predicate: are responsible critics that we can rely on their judgment ## Task E Which terms are distributed? 1. He who hesitates is lost. He who hesitates 2. Only men play professional football. Professional football players 3. None but citizens may vote. Voters 4. Only students can eat in Seacobeck. Ones who can eat at Seacobeck 5. You can’t run for President if you are not at least 35 years old. Ones who can run for President 6. Whoever runs for President is ambitious. Whoever runs for President 7. Stephen Carter’s novels offer an interesting portrait of the black bourgeoisie. Stephen Carter’s novels 8. Antique dealers can’t run for mayor. Ones who can run for mayor 9. Emoticons annoy everyone. Emoticons, everyone - Emoticons is one of the things that annoys everyone. - Everyone are ones who annoyed by emoticons. 10. A rolling stone gathers no moss. Things that gather moss 11. The skies are not cloudy all day. Cloudy things ## Task F Rewrite these as standard form categorical propositions: 1. Whoever has an allergic reaction has a weakened immune system $\Rightarrow$ All people who have allergic reactions are people who have weakened immune systems. 2. Lunar eclipses don’t occur unless the moon is full. $\Rightarrow$ All times lunar eclipses occur are times the moon is full. 3. From time to time there are concerts at Hurcamp Park. $\Rightarrow$ Some times are times there are concerts at Hurkcamp Park. 4. If a pregnant woman drinks alcohol, she risks giving birth to a deformed child. $\Rightarrow$ All pregnant women who drink alcohol are people who risk giving birth to a deformed child. 5. At the end of “The Daily Show,” John Stewart always checks in with his good friend Stephen Colbert. $\Rightarrow$ All times that the Daily Show ends are times that Jon Stewart checks in with his good friend Stephen Colbert. 6. Guests on “The Colbert Report” don’t always seem to be clear on the satirical nature of the show. $\Rightarrow$ Some guests on “The Colbert Report” are not people who seem to be clear on the satirical nature of the show. 7. Snow days are great. $\Rightarrow$ All snow days are great days. 8. It’s wrong to depart from the syllabus. $\Rightarrow$ All departures from syllabi are wrongs. 9. Not all the exercises make a lot of sense. $\Rightarrow$ Some exercises are not exercises that make a lot of sense. 10. The exercises that make sense are easiest to do. $\Rightarrow$ All exercises that make sense are exercises that are easiest to do.