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# 4.1 And 4.2 Categorical Propositions

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Course lecture I developed over sections 4.1 and 4.2 of Patrick Hurley\\\'s &quot;A Concise Introduction to Logic&quot;.

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### 4.1 And 4.2 Categorical Propositions

1. 1. 4.1 & 4.2 Categorical Propositions
2. 2. What are categorical propositions? <ul><li>Categorical propositions are statements that relate two different classes of things. </li></ul><ul><ul><li>Examples: </li></ul></ul><ul><ul><ul><li>Horror movies always have obvious endings. </li></ul></ul></ul><ul><ul><ul><ul><li>All horror movies are included in the class of things that have obvious endings. </li></ul></ul></ul></ul><ul><ul><ul><li>Action movies are for movie buffs. </li></ul></ul></ul><ul><ul><ul><ul><li>The whole class of action movies is included in the class of people that are movie buffs. </li></ul></ul></ul></ul><ul><ul><li>Essentially, either all or part of the subject is included in all or part of the predicate. </li></ul></ul><ul><li>Standard form </li></ul><ul><ul><li>A proposition that expresses the relation between subject and predicate with complete clarity. </li></ul></ul>
3. 3. Four types of categorical propositions <ul><li>Categorical propositions are in standard form only if they appear in the following way: </li></ul><ul><ul><li>All S are P. </li></ul></ul><ul><ul><li>No S are P. </li></ul></ul><ul><ul><li>Some S are P. </li></ul></ul><ul><ul><li>Some S are not P. </li></ul></ul><ul><ul><li>All S are not P is not standard form since it can mean two different things: </li></ul></ul><ul><ul><ul><li>It can mean that “No S are P” or that “Some S are not P”. </li></ul></ul></ul><ul><li>Some propositions are not in standard form when they don’t begin with the words “all”, “no”, and “some”. </li></ul><ul><li>Categorical propositions are just specific forms of substitution instances. </li></ul>
4. 4. Breaking down the standard form <ul><li>Normal sentences have a subject and a predicate. </li></ul><ul><ul><li>Example: All bears are brown. </li></ul></ul><ul><li>Standard form categorical propositions break this down further, and have four parts: </li></ul><ul><ul><li>Quantifier </li></ul></ul><ul><ul><ul><li>Specify how much of the subject is included in the predicate. </li></ul></ul></ul><ul><ul><ul><ul><li>All, some, and no. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Some means “at least one”. </li></ul></ul></ul></ul><ul><ul><li>Subject term </li></ul></ul><ul><ul><ul><li>Main subject word, identified without its quantifier. </li></ul></ul></ul><ul><ul><li>Copula </li></ul></ul><ul><ul><ul><li>Word that links the subject term and the predicate term. </li></ul></ul></ul><ul><ul><ul><ul><li>Are and are not. </li></ul></ul></ul></ul><ul><ul><li>Predicate term </li></ul></ul><ul><ul><ul><li>Main predicate word, identified without its copula. </li></ul></ul></ul>
5. 5. Attributes of categorical propositions <ul><li>Quality </li></ul><ul><ul><li>Affirmative or negative, depending on whether it affirms or denies that the subject is included in the predicate. </li></ul></ul><ul><ul><ul><li>All S are P = Affirmative quality </li></ul></ul></ul><ul><ul><ul><li>Some S are P = Affirmative quality </li></ul></ul></ul><ul><ul><ul><li>No S are P = Negative quality </li></ul></ul></ul><ul><ul><ul><li>Some S are not P = Negative quality </li></ul></ul></ul><ul><li>Quantity </li></ul><ul><ul><li>Universal or particular, depending on whether a statement says something about all or some things referenced by the subject. </li></ul></ul><ul><ul><ul><li>All S are P = Universal quantity </li></ul></ul></ul><ul><ul><ul><li>No S are P = Universal quantity </li></ul></ul></ul><ul><ul><ul><li>Some S are P = Particular quantity </li></ul></ul></ul><ul><ul><ul><li>Some S are not P = Particular quantity </li></ul></ul></ul>
6. 6. Rules about quantity and quality <ul><li>A proposition’s quantity can be determined just by looking at the quantifier. </li></ul><ul><ul><li>All and no imply universal, and some implies particular. </li></ul></ul><ul><li>But propositions don’t have a “qualifier”. </li></ul><ul><ul><li>Universal propositions – Determined by the quantifier. </li></ul></ul><ul><ul><li>Particular propositions – Determined by the copula. </li></ul></ul><ul><ul><ul><li>All people are happy. - Affirmative, by looking at the word “all”. </li></ul></ul></ul><ul><ul><ul><li>No people are happy. – Negative. </li></ul></ul></ul><ul><ul><ul><li>Some people are happy. – Affirmative, by looking at “are”. </li></ul></ul></ul><ul><ul><ul><li>Some people are not happy – Negative, by looking it “are not”. </li></ul></ul></ul><ul><li>One thing to remember is that statements imply no more than what they say. </li></ul><ul><ul><li>All S are P – Does not mean that “No S are P”. </li></ul></ul><ul><ul><li>Some S are P – Doesn’t mean that “Some S are not P”. </li></ul></ul>
7. 7. Classifying the four propositions <ul><li>The four kinds of propositions are classified according to the first four vowels in the alphabet. </li></ul><ul><ul><li>A types – All S are P. (Universal affirmative) </li></ul></ul><ul><ul><li>E types – No S are P. (Universal negative) </li></ul></ul><ul><ul><li>I types – Some S are P. (Particular affirmative) </li></ul></ul><ul><ul><li>O types – Some S are not P. (Particular negative) </li></ul></ul>
8. 8. Distribution <ul><li>An attribute of the terms in a proposition (subject and predicate). </li></ul><ul><li>A term is distributed if it makes an assertion about every thing in the class that it refers to. </li></ul><ul><ul><li>All S are P. (S only is distributed) </li></ul></ul><ul><ul><li>No S are P (S and P are both distributed) </li></ul></ul><ul><ul><li>Some S are P (Neither one are distributed) </li></ul></ul><ul><ul><li>Some S are not P (P only is distributed) </li></ul></ul><ul><ul><li>Example: </li></ul></ul><ul><ul><ul><li>All people are happy. (Everyone who is a person falls within the class of being happy). </li></ul></ul></ul><ul><ul><ul><li>Some people are not happy. (The state of being happy is separate from the one person we know who is not happy). </li></ul></ul></ul>
9. 9. Main attributes of categorical propositions P Negative Particular O Some S are not P. Neither Affirmative Particular I Some S are P. S and P Negative Universal E No S are P. S Affirmative Universal A All S are P. Terms distributed Quality Quantity Letter name Proposition