Philosophy C6 Unit - Lecture notes 6 PDF

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Notes from Mrs. Kim's Philosophy class (UGSSD). Covering extensive notes from each textbook/lecture from the unit this summer...

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Chapter 6: Deductive Reasoning- Categorical Logic Learning Objectives: 1. Statements and Classes 2. Translations and Standard Form 3. Diagramming Categorical Statements 4. Assessing Categorical Syllogisms

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Logic is the study of good reasoning or thinking and therefore should be part of every decision and every judgment we make. ● Categorical Logic: A form of logic whose focus is categorical statements, which make assertions about categories, or classes, of things. - The basic unit of concern in categorical logic is the statement component. In categorical logic, we study the relationships not between entire statements but between components known as the subject and predicate of a statement. ● Categorical Statement: A statement or claim that makes a simple assertion about categories, or classes, of things. - —those that make simple assertions about categories, or classes, of things. They say how certain classes of things are, or are not, included in other classes of things. For example: “All cows are vegetarians,” “No gardeners are plumbers,” or “Some businesspeople are cheats.” -

Categorical logic—first formulated by Aristotle over 2000 years ago—is still around. Chief among these reasons are that (1) it is part of everyday reasoning and (2) understanding its rules leads to better, clearer thinking

1. Statements and Classes - The words in categorical statements that name classes, or categories, of things are called terms. Each categorical statement has both a subject term and a predicate term ● Subject Term: The first class, or group, named in a standard-form categorical statement. ● Predicate Term: The second class, or group, named in a standard-form categorical statement. E.g. Claim: “All cats are carnivores” - The subject term here is cats, and the predicate term is carnivores - We can express the form of the statement like this: All S are P.

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This kind of statement—All S are P—is one of four standard forms of categorical statements. Here are all four forms together: 1. All S are P. (All cats are carnivores.) 2. No S are P. (No cats are carnivores.) 3. Some S are P. (Some cats are carnivores.) 4. Some S are not P. (Some cats are not carnivores.) Subject and predicate terms can also consist of noun phrases and pronouns. Noun phrases are used because several words may be needed to specify a class. Sometimes a simple noun like cats won’t do to describe the category we are talking about, but a noun phrase like “cats that live outdoors and hunt mice” will. In standard-form categorical statements, subject and predicate terms can’t be anything but nouns, pronouns, and noun phrases. Only nouns, pronouns, and noun phrases can properly designate classes. So the statement “All cats are carnivores” is in standard form because cats and carnivores are nouns; however, “All cats are carnivorous” is not in standard form, because “carnivorous” is an adjective, not a noun that designates a category.

Categorical statements have four parts and several characteristics expressed in these parts. You already know about two of these parts, the subject term and the predicate term. They are joined together by a third part called the copula, a linking verb—either are or are not. The fourth part is the quantifier, a word that expresses the quantity, or number, of a categorical statement. The acceptable quantifiers are all, no, or some. ● Copula: One of four components of a standard-form categorical statement; a linking verb— either are or are not—that joins the subject term and the predicate term. ● Quantifier: In categorical statements, a word used to indicate the number of things with specified characteristics. The acceptable quantifiers are all, no, or some. - The quantifiers all or no in front of a categorical statement tell us that it’s universal—it applies to every member of a class. - The quantifier at the beginning of a categorical statement says that the statement is particular—it applies to some but not necessarily all members of a class. - Categorical statements can vary not only in quantity but also in the characteristic of quality, being either affirmative or negative

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A categorical statement that affirms that a class is entirely or partly included in another class is said to be affirmative in quality, whereas a categorical statement that denies that a class is entirely or partly included in another class is said to be negative in quality.

Overall: ➢ A: All S are P. (universal affirmative) ➢ E: No S are P. (universal negative) ➢ I: Some S are P. (particular affirmative) ➢ O: Some S are not P. (particular negative)

2. Translations and Standard Form - We translate ordinary statements into standard-form categorical statements so that we can handle them more efficiently. We want to handle them efficiently so that we can more easily evaluate the validity of arguments composed of categorical statements. Translation is necessary to bring out the underlying structure of statements - Must distinguish between subject and predicate term - Sentences with ‘only’, ‘only if’, ‘the only’ can be rearranged to ‘all’ ● Singular Statements: In categorical logic, statements that assert something about a single person or thing, including objects, places, and times. - E.g. DeAnne Smith is a Toronto-based comedian (TO) All persons identical to DeAnne Smith are Toronto-based comedians. - E.g. Calgary is Canada’s finest city. (TO) All places identical to Calgary are places that are Canada’s finest city

3. Diagramming Categorical Statements

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(Shaded is empty) 1. Draw two overlapping circles, each one representing a term in the statement. 2. Label the circles with the letters representing the terms. 3. Shade an area of a circle to show that an area is empty; insert an X to show that at least one member of a class is also a member of another class or that at least one member of a class is outside of another class Venn diagrams can come in handy when you want to know whether two categorical statements are equivalent—that is, whether they say the same thing— because sometimes we can say the same thing—make the identical logical claim—in two different ways. If the diagrams for the statements are identical, then the statements are logically equivalent.

4. Assessing Categorical Syllogisms - Notice that each categorical statement has, as usual, two terms. But there are a total of only three terms in a categorical syllogism, each term being mentioned twice but in different statements. - Example: 1. All elected officials are civil servants. 2. All politicians are elected officials. 3. Therefore, all politicians are civil servants. - In a categorical syllogism, we refer to the predicate term in the conclusion (civil servants, in this case) as the predicate term for the whole argument. The predicate term always also appears in one of the premises (premise 1, in the example above). The subject term in the conclusion is treated as the subject term for the whole argument. The subject term always also occurs in one of the premises (premise 2, in the argument above). The other term, the

one that appears once in each premise but not in the conclusion, is referred to as the middle term: Premise (1) [Middle term] [Predicate term]. Premise (2) [Subject term] [Middle term]. Conclusion (3) Therefore, [Subject term] [Predicate term]. -

We can symbolize this argument form with letters: (1) All M are P. (2) All S are M. (3) Therefore, all S are P. - Here, M stands for the middle term, P for the predicate term, and S for the subject term. - So, summarizing, a categorical syllogism is one that has: 1. Three categorical statements—two premises and a conclusion. 2. Exactly three terms, with each term appearing precisely twice in the argument 3. One of the terms (the middle term) appearing in each premise but not in the conclusion. 4. Another term (the predicate term) appearing as the predicate term in the conclusion and also in one of the premises. 5. Another term (the subject term) appearing as the subject term in the conclusion and also in one of the premises. -

3 Other Facts: 1. A valid categorical syllogism must possess precisely three terms. 2. A valid categorical syllogism cannot have two negative premises. 3. A valid categorical syllogism with at least one negative premise must have a negative conclusion.

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A valid categorical syllogism, like a valid deductive argument of any other sort, is such that if its premises are true, its conclusion must be true. (That is, if the premises are true, the conclusion cannot possibly be false.) Five steps to use Venn Diagrams to check Validity Draw three overlapping circles, each circle representing a term in the syllogism, with the two circles representing the subject and predicate terms placed on the bottom left and bottom right. Label the circles with the letters representing the terms (S, P, and M). Diagram the first premise. (But always diagram universal premises first. When diagramming a particular premise, if it’s unclear where to place an X in a circle section, place it on the dividing line between subsections.) Diagram the other premise.

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5. Check to see if the two circles at the bottom of the diagram represent what is asserted in the conclusion. If it does, the argument is valid; if not, it’s invalid....