1. Subject Terms and Predicate Terms A categorical proposition (or categorical statement) is a proposition that relates two classes or categories. The two classes are denoted by the subject term and the predicate term. The subject term is the term (i.e., noun or noun phrase) that appears in the subject position of a categorical proposition. The predicate term is the term (i.e., noun or noun phrase) that appears in the predicate position of a categorical proposition. The subject of a sentence is the object or objects about which a claim is being made, and the predicate of a sentence is what is being claimed about that subject. Every categorical proposition asserts that all or part of the class referred to by the subject term is either included in or excluded from the class denoted by the predicate term. Consider the following categorical propositions. For each categorical proposition, identify the subject term and the predicate term. Categorical Proposition: Not all events in life are reasons to celebrate. Subject Term: Predicate Term: Categorical Proposition: Some religious experiences are genuine mysteries. Subject Term: Predicate Term: Categorical Proposition: Hulk Hogan is a professional wrestler. Subject Term: Predicate Term: Categorical Proposition: All cacti are succulents. Subject Term: Predicate Term: Categorical Proposition: No dedicated teachers are people with selfish ambitions. Subject Term: Predicate Term: Categorical Proposition: Subject Term: Some cellular phones are digital music players. Predicate Term: Categorical Proposition: Laptop computers are digital devices. Subject Term: Predicate Term: Categorical Proposition: Stepfathers are not biological parents. Subject Term: Predicate Term: 2. Standard Form A categorical proposition is a standard-form categorical proposition if and only if it is a substitution instance of one of the following four forms: Standard Forms for Categorical Propositions All S are P. No S are P. Some S are P. Some S are not P. Recall that a substitution instance involves the uniform replacement of letters in a form with content words, which in a categorical proposition are terms (i.e., nouns or noun phrases). Since a categorical proposition states that all or part of the class denoted by the subject term is either included in or excluded from the predicate class, these four forms cover all of the possible relationships between two classes or categories. There are, of course, other ways to express categorical propositions in ordinary language, and later you will explore methods for transforming these other categorical expressions into standard-form categorical propositions. Indicate the subject term and predicate term for each given categorical proposition. Also determine whether the statement is a substitution instance of one of the four standard forms just shown or whether it is not a standard-form categorical proposition. (Remember that a standard-form categorical proposition must be an exact substitution instance of one of the preceding forms.) Categorical Proposition: Subject Term: No modern political parties are organizations immune to dissent. Predicate Term: Which of the following statements is true of this categorical proposition? It is not a standard-form categorical proposition. It is a standard-form categorical proposition because it is a substitution instance of this form: No S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: All S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are not P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are P. Categorical Proposition: All reputable biologists are proponents of evolution. Subject Term: Predicate Term: Which of the following statements is true of this categorical proposition? It is a standard-form categorical proposition because it is a substitution instance of this form: No S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: All S are P. It is not a standard-form categorical proposition. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are not P. Categorical Proposition: Some valid arguments are not sound arguments. Subject Term: Predicate Term: Which of the following statements is true of this categorical proposition? It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are not P. It is a standard-form categorical proposition because it is a substitution instance of this form: All S are P. It is not a standard-form categorical proposition. It is a standard-form categorical proposition because it is a substitution instance of this form: No S are P. Categorical Proposition: Bottlenose dolphins are carnivorous marine mammals. Subject Term: Predicate Term: Which of the following statements is true of this categorical proposition? It is a standard-form categorical proposition because it is a substitution instance of this form: All S are P. It is not a standard-form categorical proposition. It is a standard-form categorical proposition because it is a substitution instance of this form: No S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are not P. Categorical Proposition: No diesel electric locomotives are steam locomotives. Subject Term: Predicate Term: Which of the following statements is true of this categorical proposition? It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are not P. It is not a standard-form categorical proposition. It is a standard-form categorical proposition because it is a substitution instance of this form: All S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: No S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are P. Categorical Proposition: Former presidents of the United States are living ghosts of history. Subject Term: Predicate Term: Which of the following statements is true of this categorical proposition? It is a standard-form categorical proposition because it is a substitution instance of this form: All S are P. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are P. It is not a standard-form categorical proposition. It is a standard-form categorical proposition because it is a substitution instance of this form: Some S are not P. It is a standard-form categorical proposition because it is a substitution instance of this form: No S are P. 3. Quantifiers 1 Quantifiers determine how much of the subject class is included in, or excluded from, the predicate class. There are three quantifiers that are used in standard-form categorical propositions: the words "all," "some," and "no." These quantifiers determine how much of the class denoted by the subject term is being included in, or excluded from, the class denoted by the predicate term. The meaning of "all" and the meaning of "no" are self-explanatory, but in logic the word "some" always means at least one. Therefore, the meaning of the proposition that "some S are P" is that there is at least one object in the class denoted by S that is also within the class denoted by P. Each of the following statements is a standard-form categorical proposition. Identify the quantifier used in each categorical proposition. Example A No residents of the state of Ohio are residents of the state of New Jersey. What is the quantifier in this categorical proposition? Are Residents All New Jersey No Some Residents of the state of Ohio Example B All people who are afraid of doctors are folks who do not enjoy getting physicals. What is the quantifier in this categorical proposition? Some Getting physicals All Are Do not People who No Example C Some mountains in Yosemite National Park are mountains with summits over 13,000 feet in elevation. What is the quantifier in this categorical proposition? In Yosemite National Park No Summits Are Mountains All Some Example D No criminal activities are things that an upstanding citizen would engage in. What is the quantifier in this categorical proposition? Are No All Activities Some Upstanding citizen Criminal Example E All laptop computers are portable electronic devices. What is the quantifier in this categorical proposition? Laptop computers No All Portable electronic devices Are Are not Some Example F Some textbooks are logic books. What is the quantifier in this categorical proposition? Are No Logic Books All Some Textbooks Example G Some orange vegetables are not carrots. What is the quantifier in this categorical proposition? Carrots Orange vegetables Are Are not Some All No Example H All actions that are virtuous are morally laudable deeds. What is the quantifier in this categorical proposition? No Laudable deeds All Some Morally Are Actions that are virtuous Example I No standard-form categorical propositions are sentences without quantifiers. What is the quantifier in this categorical proposition? Quantifiers Propositions All Standard-form Categorical No Some Example J No subatomic particles are things that are visible to the naked eye. What is the quantifier in this categorical proposition? Things that are visible to the naked eye Some Subatomic No Particles All Are 4. Quantifiers 2 Although the meanings of the quantifiers "all" and "no" are fairly intuitive, the word "some" has a specific meaning in logic. The quantifier "some" in logic always means at least one. It is important to remember that categorical propositions relate two sets or classes of objects. Therefore, the words "all" and "no" specify a reference to the entire class being denoted, and the word "some" specifies at least one member of the denoted class. You should form the habit of thinking of categorical propositions in terms of the relationship between two sets, two classes, or two groups of objects that may or may not overlap to various degrees. Consider the following standard-form categorical propositions. Indicate the meaning of these categorical propositions in terms of members of the classes (sets) denoted by the subject term and the predicate term. Categorical Proposition Some ladybugs are red insects. All giant redwoods are conifers. No humans are extraterrestrials. Some geniuses are not well-rounded individuals. Meaning from the class of ladybugs red insects. the class of from the class of giant redwoods class of conifers the from the class of humans extraterrestrials. the class of from the class of geniuses well-rounded individuals. the class of 5. Copulas In a standard-form categorical proposition, the copula is the word "are" or the words "are not." The copula relates the subject term to the predicate term. You should note that the grammatical predicate of a categorical proposition includes both the copula and the predicate term, but the predicate term itself does not include the copula. Identify which copula is used in each of the four standard categorical syllogism forms. Form All S are P. No S are P. Copula Form Copula Some S are P. Some S are not P. For each standard-form categorical proposition, identify the form of which the proposition is a substitution instance. Also identify the copula that relates the subject term to the predicate term. Categorical Proposition Form Copula Some banquet tables are not tables that are lined with white tablecloths. No disreputable cartoon characters are characters that embody moral ideals. All fictional characters from great novels are characters that live on in the imagination. All perplexing dichotomies are things that make you scratch your head. Some positive integers are numbers that are squares of an integer root. All places in the universe are places where the same laws of nature apply. 6. Components of Categorical Propositions - Practice Use your knowledge of the components of categorical propositions to identify the quantifier, subject term, copula, and predicate term for each of the following standard-form categorical propositions. Some modern percussionists are not drummers who prefer steel snare drums. are not = drummers who prefer steel snare drums = modern percussionists = some = All people who know the International Morse Code are qualified telegraphers. people who know the International Morse Code = all = are = qualified telegraphers = No happy marriages are relationships that do not require compromises. happy marriages = are = no = relationships that do not require compromise = All lambs are young sheep who have not been weaned. young sheep who have not been weaned = lambs = are = all = Some fine writing instruments are writing instruments that use water-based ink. fine writing instruments = are = some = writing instruments that use water-based ink = All resort spas are relaxing getaway destinations. all = resort spas = are = relaxing getaway destinations = 7. Components of Categorical Propositions - More Practice Identify the quantifier, subject term, copula, and predicate term from each standard-form categorical proposition shown next. Type each component in the space provided. Categorical Proposition: All chemical batteries are devices that store electrochemical energy. Quantifier: Subject Term: Copula: Predicate Term: Categorical Proposition: Some artificial light sources are not incandescent light bulbs. Quantifier: Subject Term: Copula: Predicate Term: Categorical Proposition: Some traditional academic disciplines are undergraduate university majors. Quantifier: Subject Term: Copula: Predicate Term: Categorical Proposition: No modern slang expressions are eloquent literary devices. Quantifier: Subject Term: Copula: Predicate Term: 8. True/False Review and Chapter Summary Use your knowledge of the components of categorical propositions (including standard forms, quantifiers, copulas, subject terms, and predicate terms) to determine which of the following statements are true. Check all that apply. The copula appears immediately before the predicate term in a standard-form categorical proposition. The subject term appears within the predicate of a categorical proposition. The following form is one of the standard forms for categorical propositions: "No S are not P." A quantifier appears immediately in front of the subject term in a standard-form categorical syllogism. The word "are" is the copula in this standard categorical proposition form: "Some S are P." This categorical proposition is in standard form: "Some former students are not teachers." Reading a standard-form categorical proposition from left to right, you will encounter its components in the following order: quantifier, predicate term, copula, and subject term. A proper name cannot be used as the subject term in a categorical proposition because a proper name does not denote a class. This categorical proposition is in standard form: "Many personal computers are laptop computers." While other texts allow for other forms of the verb "to be" to count as copulas, your text restricts the copula to include only "are" and "are not." Your text allows the following words/phrases to serve as copulas in standard-form categorical propositions: "are," "are not," "will be," "is not," and "will not." A categorical proposition asserts that either all or part of the class denoted by the subject term is included in or excluded from the class denoted by the predicate term. The following form is one of the standard forms for categorical propositions: "S are P." Some categorical propositions are not substitution instances of standard forms. The four components of a standard-form categorical proposition are the quantifier, the subject term, the copula, and the predicate term. 1. Meaning of Categorical Propositions in Class Notation The meaning of categorical propositions in general, and standard-form categorical propositions in particular, can be expressed in class terminology. Class notation expresses the relationships between the members of classes or sets. Answer the following questions about the meanings of the standard categorical proposition forms in terms of classes and their members. Identify the standard categorical proposition form that is best represented by the following statement: "At least one thing is a member of the S class and a member of the P class." Some S are P. Some S are not P. No S are P. All S are P. Identify the standard categorical proposition form that is best represented by the following statement: "At least one member of the S class is not a member of the P class." All S are P. Some S are P. Some S are not P. No S are P. Which of the following best represents the meaning of the form "No S are P" in class notation? Every member of the S class is a member of the P class. At least one member of the S class is not a member of the P class. No member of the S class is a member of the P class. At least one member of the S class is a member of the P class. Which of the following best represents the meaning of the form "All S are P"? The S class is included in the P class. The S class is excluded from the P class. At least one thing is a member of the S class but not a member of the P class. At least one thing is a member of the S class and a member of the P class. 2. Quality The quality of a categorical proposition is determined by whether the proposition affirms or denies class membership in the predicate class. Whereas a categorical proposition has affirmative quality if it affirms class membership, a categorical proposition has negative quality if it denies class membership. The following table shows which standard categorical proposition forms have affirmative quality and which forms have negative quality: Form Quality All S are P. Affirmative No S are P. Negative Some S are P. Affirmative Some S are not P. Negative The forms "All S are P" and "Some S are P" have affirmative quality because they assert that either all or part of the subject class is included in the predicate class. By contrast, the forms "No S are P" and "Some S are not P" have negative quality because they assert that either all or part of the subject class is excluded from the predicate class. Indicate whether each of the following categorical propositions has affirmative or negative quality. Categorical Proposition: Quality: All green apples are objects that reflect green light. This categorical proposition has quality because it membership in the predicate class. Categorical Proposition: Quality: Some carnival rides are not rides that are safe for children shorter than 36 inches. This categorical proposition has quality because it membership in the predicate class. Categorical Proposition: Quality: No rainbow trout hatcheries are places where it is safe to dump hazardous chemicals. This categorical proposition has quality because it membership in the predicate class. Categorical Proposition: Quality: All pieces of fluorescent green paper are things that glow under a black light. This categorical proposition has quality because it membership in the predicate class. Categorical Proposition: Quality: Some forms of dramatic entertainment are great operatic works. This categorical proposition has quality because it membership in the predicate class. Categorical Some community college instructors are tech-savvy individuals. Proposition: Quality: This categorical proposition has quality because it membership in the predicate class. 3. Quantity The quantity of a categorical proposition depends on whether the statement makes a claim about every member or only some members of the class denoted by the subject term. A categorical proposition has universal quantity if it makes a claim about every member of the class denoted by the subject term, whereas a categorical proposition has particular quantity if it makes a claim about only some (which in logic always means "at least one" or "one or more") particular members of the class denoted by the subject term. The following table shows which standard categorical proposition forms are universal statements and which forms are particular statements. Form Quantity All S are P. Universal No S are P. Universal Some S are P. Particular Some S are not P. Particular The forms "All S are P" and "No S are P" have universal quantity (they are universal statements) because they claim that the entire subject class is either included in or excluded from the predicate class. By contrast, the forms "Some S are P" and "Some S are not P" have particular quantity (they are particular statements) because they make a claim that at least one particular member of the subject class is either included in or excluded from the predicate class. Indicate whether each of the following categorical propositions is a universal statement or a particular statement. Categorical Proposition: Quantity: Some fictional superheroes are characters that wear red capes. This categorical proposition is a claim about Categorical Proposition: Quantity: Quantity: of the class denoted by the subject term. Some community college instructors are tech-savvy individuals. This categorical proposition is a claim about Categorical Proposition: statement because it makes a statement because it makes a of the class denoted by the subject term. All pieces of fluorescent green paper are things that glow under a black light. This categorical proposition is a claim about statement because it makes a of the class denoted by the subject term. Categorical Proposition: Some acidic solutions are not chemicals that are hazardous for humans to touch. Quantity: This categorical proposition is a claim about Categorical Proposition: statement because it makes a of the class denoted by the subject term. Some tree-grown nuts are foods that cause allergic reactions. Quantity: This categorical proposition is a claim about Categorical Proposition: statement because it makes a of the class denoted by the subject term. No rainbow trout hatcheries are places where it is safe to dump hazardous chemicals. Quantity: This categorical proposition is a claim about statement because it makes a of the class denoted by the subject term. 4. A, E, I, and O Statements The four types of standard-form categorical propositions are commonly designated by the letters A, E, I, and O. Each letter represents one type of categorical proposition (universal affirmative, universal negative, etc.). These letters originate from letters within the Latin words affirmo ("I affirm") and nego ("I deny"). Though the letters themselves are arbitrary, it is important that you memorize which letter refers to which type of statement. This will be important when you learn to evaluate categorical syllogisms in a later chapter. Therefore, do not neglect to commit the following table to memory. Complete the following table showing the standard categorical proposition forms, their designated letters, whether each type is universal or particular, and whether each type is affirmative or negative. Quantity Quality universal affirmative universal negative particular affirmative particular negative Proposition Letter Indicate whether each of the following categorical propositions is an A proposition, an E proposition, an I proposition, or an O proposition. Categorical Proposition: Type: Some pianos are upright pianos. This categorical proposition is an Categorical Proposition: Type: All notebook computers are portable electronic devices. This categorical proposition is an Categorical Proposition: Type: Type: Type: proposition. Some philosophical disputes are irreconcilable disagreements. This categorical proposition is an Categorical Proposition: proposition. No formal neckties are casual clothing items. This categorical proposition is an Categorical Proposition: proposition. proposition. Some modern languages are not languages descended from ancient Greek. This categorical proposition is an proposition. 5. Distribution of Terms Distribution is an attribute of the terms within a categorical proposition. A term is distributed if the proposition makes an assertion about every member of the class denoted by the term. If the proposition does not make an assertion about every member of the class denoted by the term, then the term is undistributed. All S are P. In an A proposition, the subject term S is distributed, but the predicate term P is undistributed. S is distributed because the proposition asserts that every member of S is a member of P. The proposition makes no claim about every member of P, and so P is undistributed. No S In an E proposition, both the subject term S and the predicate term P are are P. distributed. Since no member of S is a member of P, it also follows that no member of P is a member of S. Since it is possible to know something about every member of both classes (namely, that every member of each class is not in the other class), it follows that both S and P are distributed. Some S are P. In an I proposition, the subject term S and the predicate term P are both undistributed. All that can be known from an I proposition is that there is at least one member of S that is also a member of P. The proposition makes no assertion about every member of either class, and so both S and P are undistributed. Some S are not P. In an O proposition, the subject term S is undistributed because no claim is made about every member of S, but only about at least one particular member of S. But from an O proposition you can know that every member of P is not that specific member of S. So the predicate term P is distributed in an O proposition because the proposition does make an assertion about every member of P. Indicate the letter type for each categorical proposition. Then indicate which, if any, of the terms within the proposition are distributed. Example 1 Some disenchanted lovers are bitter human beings. The categorical proposition in Example 1 is an proposition. Therefore, which of its terms are distributed? Only "bitter human beings" Both "disenchanted lovers" and "bitter human beings" Only "disenchanted lovers" Neither "disenchanted lovers" nor "bitter human beings" Example 2 No puffy white clouds are harbingers of rain. The categorical proposition in Example 2 is an proposition. Therefore, which of its terms are distributed? Both "puffy white clouds" and "harbingers of rain" Only "harbingers of rain" Only "puffy white clouds" Neither "puffy white clouds" nor "harbingers of rain" Example 3 Some decapod crustaceans are not Dungeness crabs. The categorical proposition in Example 3 is an distributed? Only "Dungeness crabs" proposition. Therefore, which of its terms are Neither "decapod crustaceans" nor "Dungeness crabs" Both "decapod crustaceans" and "Dungeness crabs" Only "decapod crustaceans" Example 4 All red wines are fermented grape juices. The categorical proposition in Example 4 is an proposition. Therefore, which of its terms are distributed? Only "red wines" Neither "red wines" nor "fermented grape juices" Both "red wines" and "fermented grape juices" Only "fermented grape juices" Example 5 No princess-cut diamond rings are ugly pieces of jewelry. The categorical proposition in Example 5 is an proposition. Therefore, which of its terms are distributed? Only "ugly pieces of jewelry" Only "princess-cut diamond rings" Neither "princess-cut diamond rings" nor "ugly pieces of jewelry" Both "princess-cut diamond rings" and "ugly pieces of jewelry" Example 6 All people who love gardening are people who enjoy getting their hands dirty. The categorical proposition in Example 6 is an proposition. Therefore, which of its terms are distributed? Both "people who love gardening" and "people who enjoy getting their hands dirty" Only "people who enjoy getting their hands dirty" Neither "people who love gardening" nor "people who enjoy getting their hands dirty" Only "people who love gardening" Example 7 Some cups of coffee are not caffeinated beverages The categorical proposition in Example 7 is an proposition. Therefore, which of its terms are distributed? Neither "cups of coffee" nor "caffeinated beverages" Only "cups of coffee" Both "cups of coffee" and "caffeinated beverages" Only "caffeinated beverages" Example 8 No inherited genetic traits are acquired characteristics. The categorical proposition in Example 8 is an proposition. Therefore, which of its terms are distributed? Only "inherited genetic traits" Neither "inherited genetic traits" nor "acquired characteristics" Only "acquired characteristics" Both "inherited genetic traits" and "acquired characteristics" 6. Practice with Quality, Quantity, and Distribution The four types of categorical propositions are designated with the letters A, E, I, and O. The attributes of categorical propositions include quantity and quality. Distribution is a property of the terms within a categorical proposition. Within a categorical proposition, the subject term is either distributed or undistributed, and the predicate term is either distributed or undistributed. For each categorical proposition, identify the letter designation, quantity, and quality. Also indicate whether the subject and predicate terms are distributed or undistributed. Given Categorical Proposition: Letter name: Quantity Quality: Subject term: Predicate term: All planets in our solar system are heavenly bodies that orbit the sun. Given Categorical Proposition: Some nations that are members of the European Union are not countries that use the euro for currency. Letter name: Quantity Quality: Subject term: Predicate term: Given Categorical Proposition: No Hawaiian vacations are trips to the southern hemisphere. Letter name: Quantity Quality: Subject term: Predicate term: Given Categorical Proposition: All pacemaker installations are minor procedures. Letter name: Quantity Quality: Subject term: Predicate term: Given Categorical Proposition: Letter name: Quantity Some freshwater aquarium plants are not Red Tiger Lotuses. Quality: Subject term: Predicate term: Given Categorical Proposition: Some games of tic-tac-toe are stalemates. Letter name: Quantity Quality: Subject term: Predicate term: 7. Changing Quantity You should learn to convert categorical propositions from one type to another, which is achieved by changing their quantity and/or quality. Learning to perform this task is useful for learning the operations of conversion, obversion, and contraposition in a later section. Change the quantity, but not the quality, of each of the following categorical propositions. Also identify the letter designations for the given proposition's form and for the resulting proposition's form. (Note: You should not assume that the resulting statement will necessarily be true.) Example 1 No fictional starship captains are timid commanders. This categorical proposition is an proposition. If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be? Some fictional starship captains are not timid commanders. Some fictional starship captains are timid commanders. All fictional starship captains are timid commanders. The resulting statement is an proposition. Example 2 Some board games are not games that require dice. This categorical proposition is an proposition. If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be? No board games are games that require dice. All board games are games that require dice. Some board games are games that require dice. The resulting statement is an proposition. Example 3 Some plastic dolls are dolls that walk and talk. This categorical proposition is an proposition. If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be? All plastic dolls are dolls that walk and talk. No plastic dolls are dolls that walk and talk. Some plastic dolls are not dolls that walk and talk. The resulting statement is an proposition. Example 4 Some computer codes are ASCII codes. This categorical proposition is an proposition. If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be? No computer codes are ASCII codes. Some computer codes are not ASCII codes. All computer codes are ASCII codes. The resulting statement is an proposition. Example 5 Some friendly ghosts are not poltergeists. This categorical proposition is an proposition. If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be? Some friendly ghosts are poltergeists. All friendly ghosts are poltergeists. No friendly ghosts are poltergeists. The resulting statement is an proposition. Example 6 All scrapbooking supply stores are stores that sell paper products. This categorical proposition is an proposition. If you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be? No scrapbooking supply stores are stores that sell paper products. Some scrapbooking supply stores are not stores that sell paper products. Some scrapbooking supply stores are stores that sell paper products. The resulting statement is an proposition. 8. Changing Quality You should learn how to convert categorical propositions from one type to another, which is achieved by changing their quantity and/or quality. Understanding how to perform this task is useful for learning the operations of conversion, obversion, and contraposition in a later section. Change the quality, but not the quantity, of each of the following categorical propositions. Also identify the letter designation for the given proposition's form and the letter designation for the resulting proposition's form. (Note: You should not assume that the resulting statement will necessarily be true.) Example 1 Some elected officials are first-rank public servants. This categorical proposition is an proposition. If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be? No elected officials are first-rank public servants. All elected officials are first-rank public servants. Some elected officials are not first-rank public servants. The resulting statement is an proposition. Example 2 Some French philosophers are poststructuralists. This categorical proposition is an proposition. If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be? All French philosophers are poststructuralists. No French philosophers are poststructuralists. Some French philosophers are not poststructuralists. The resulting statement is an proposition. Example 3 All good fairy tales are allegories for the human condition. This categorical proposition is an proposition. If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be? Some good fairy tales are allegories for the human condition. No good fairy tales are allegories for the human condition. Some good fairy tales are not allegories for the human condition. The resulting statement is an proposition. Example 4 No Shakespearean plays are plays by Christopher Marlowe. This categorical proposition is an proposition. If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be? All Shakespearean plays are plays by Christopher Marlowe. Some Shakespearean plays are plays by Christopher Marlowe. Some Shakespearean plays are not plays by Christopher Marlowe. The resulting statement is an proposition. Example 5 Some board games are not games that require dice. This categorical proposition is an proposition. If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be? Some board games are games that require dice. All board games are games that require dice. No board games are games that require dice. The resulting statement is an proposition. Example 6 Some lively fandangos are not square dances. This categorical proposition is an proposition. If you change the quality, but not the quantity, of the given categorical proposition, what will the resulting statement be? Some lively fandangos are square dances. All lively fandangos are square dances. No lively fandangos are square dances. The resulting statement is an proposition. 9. Changing Quantity and Quality You should learn how to convert categorical propositions from one type to another, which is achieved by changing their quantity and/or quality. Understanding how to perform this task is useful for learning the operations of conversion, obversion, and contraposition in a later section. Change both the quantity and the quality of each of the following categorical propositions. Also identify the letter designation for the given proposition's form and the letter designation for the resulting proposition's form. (Note: You should not assume that the resulting statement will necessarily be true.) Example 1 No identical twins are fraternal twins. This categorical proposition is an proposition. If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be? All identical twins are fraternal twins. Some identical twins are not fraternal twins. Some identical twins are fraternal twins. The resulting statement is an proposition. Example 2 Some elected officials are first-rank public servants. This categorical proposition is an proposition. If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be? No elected officials are first-rank public servants. All elected officials are first-rank public servants. Some elected officials are not first-rank public servants. The resulting statement is an proposition. Example 3 Some stoneware goblets are ceremonial containers. This categorical proposition is an proposition. If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be? No stoneware goblets are ceremonial containers. Some stoneware goblets are not ceremonial containers. All stoneware goblets are ceremonial containers. The resulting statement is an proposition. Example 4 Some New World vultures are not California condors. This categorical proposition is an proposition. If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be? All New World vultures are California condors. No New World vultures are California condors. Some New World vultures are California condors. The resulting statement is an proposition. Example 5 All good fairy tales are allegories for the human condition. This categorical proposition is an proposition. If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be? Some good fairy tales are allegories for the human condition. No good fairy tales are allegories for the human condition. Some good fairy tales are not allegories for the human condition. The resulting statement is an proposition. Example 6 No Shakespearean plays are plays by Christopher Marlowe. This categorical proposition is an proposition. If you change both the quantity and the quality of the given categorical proposition, what will the resulting statement be? Some Shakespearean plays are plays by Christopher Marlowe. All Shakespearean plays are plays by Christopher Marlowe. Some Shakespearean plays are not plays by Christopher Marlowe. The resulting statement is an proposition. 10. True/False Review and Chapter Summary Use your knowledge of the attributes of categorical propositions (including quantity, quality, and letter designations) and the properties of terms within categorical propositions (distribution) to determine which of the following statements are true. Check all that apply. Every categorical proposition either has affirmative quality or negative quality. In an A proposition, only the predicate term is distributed. In a type A proposition, the predicate term is undistributed because the proposition makes no assertion about every member of the class denoted by the predicate term. An O proposition has universal quantity and negative quality. Changing both the quantity and the quality of an O proposition will yield an A proposition. Categorical propositions of the form "All S are P" or "Some S are P" have affirmative quality. A categorical proposition has affirmative quality if it denies membership in the predicate class. The proposition "Some S are P" means that at least one member of the S class is a member of the P class. An I proposition has particular quantity and affirmative quality. Changing only the quantity of an A proposition will yield an I proposition. A term in a categorical proposition is distributed if and only if the proposition does not make a claim about the entire class denoted by the term. The proposition "No S are P" means that the P class is included in the S class. A categorical proposition with universal quantity is called a particular statement. A categorical proposition that uses the quantifier "all" or the quantifier "no" has particular quantity. In an O proposition, the subject term is undistributed but the predicate term is distributed.
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