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# Categorical syllogism

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### Categorical syllogism

1. 1. ncjopson080513 Categorical Syllogism A categorical syllogism is a type of argument with two premises—that is, a syllogism—and one conclusion. Each of these three propositions is one of four forms of categorical proposition: A, E, I, and O. In a categorical syllogism there are three terms, two in each premise, and two occurrences of each term in the entire argument, for a total of six occurrences. The S and P which occur in its conclusion—the Subject and Predicate terms— are also called the minor and majorterms, respectively. The major term occurs once in one of the premises, which is therefore called the major premise. The minor term also occurs once in the other premise, which is for this reason called the minorpremise. The third term occurs once in each premise, but not in the conclusion, and is called the middle term. The notion of distribution plays a role in some of the syllogistic fallacies: the terms in a categorical proposition are said to be distributed or undistributed in that proposition, depending upon what type of proposition it is, and whether the term is the subject or predicate term. Specifically, the subject term is distributed in the A and E type propositions, and the predicate term is distributed in the E and O type propositions. The other terms are undistributed. Finally, the A and I type propositions are called "affirmative" propositions, while the E and O type are "negative", for reasons which should be obvious. Now, you should be equipped to understand the following types of syllogistic fallacy. Standard Form Categorical Syllogism The word standard form categorical syllogism refers to the structure and arrangement of propositions in the syllogism. A standard form categorical syllogism is arranged in this order: Major Premise : All Muslims are devoted to Allah Minor Premise : Muhammad is a Muslim Conclusion : Therefore, Muhammad is devoted to Allah Conclusion-indicators are words which imply that what about to follow is a conclusion. Therefore, so, ergo (Latin), thus, hence, accordingly, consequently, in consequence, it implies that, shows that, it proves that, as a result, it means, it follows that, we may infer that, for this reason, we may conclude, and othersare examples of conclusion-indicator. Premise-indicatorson the other hand tell us that what about to follow is a premise. Since, because, as, inasmuch, but, however, follows from, as shown by, as indicated by, and others are examples of premise-indicators. Symbols in Syllogism Terms Symbols Quality Symbols Quantity Symbols Major Term P Affirmative + Universal u Minor Term S Negative - Particular p Middle Term M To illustrate an argument using symbol, we have the following: All poems are uplifting A : Mu + Pp Some songs are poems I : Sp + Mp Therefore, some songs are uplifting I : Mp + Sp No abortionists are pro-life E :Pu + Mu Some pro-life persons are Catholics I : Mp + Sp Therefore, some Catholics are not abortionists I : Sp + Pp Eight Syllogistic Rules 1. There must be only three terms in a syllogism Example: All pitchers are containers Jose in baseball is a pitcher Jose in baseball is a water container
2. 2. ncjopson080513 All fathers have children Pope Francis is a father Pope Francis has children Fallacy committed:Fallacy of Equivocation or Fallacy of Four Terms 2. Neither the major term nor the minor term may be distributed in the conclusion, if it is undistributed in the premises. Example: All Visayans are Malayans No Tagalogs are Visayans No Tagalogs are Visayans No cats are dogs All cats are animals Therefore, no animals are dogs Fallacy committed:Fallacy of Illicit Major or Fallacy of Illicit Minor 3. The middle term must not appear in the conclusion. Example: All Pahiyas Festivals are colorful celebrations All colorful celebrations are human expressions So, all human expressions are colorful celebrations No Filipinos are Indonesians Some Asians are Indonesians Therefore, some Indonesians are not Filipinos Fallacy committed:Fallacy of Misplaced Middle Term 4. The middle term must be distributed at least once in the premises. Example: All Bicolanos are Filipinos All Boholanos are Filipinos Therefore, All Boholanos are Bicolanos All mammals are animals Some animals are not bats Therefore, some bats are not mammals Fallacy committed:Fallacy of Undistributed Middle Term 5. Only an affirmative conclusion can be drawn from two affirmative premises. Example: Every cat is sentient Every cat is an animal No cat is sentient All Lycean students are humans Pedro is a Lycean student Therefore, Pedro is not human. Fallacy committed:Fallacy of Negative Conclusion Drawn from Affirmative Premises 6. No conclusion can be drawn from two negative premises. Example: No cheating is good But corruption is good No conclusion
3. 3. ncjopson080513 Some women are not pregnant But some women are not doctors No conclusion Fallacy committed:Fallacy of Negative Premises 7. The conclusion follows the weaker premise. Examples: All cellular phones are used in communication But some cameras are cellular phones Therefore, all cameras are used in communication No jeans are shirt But clothes are jeans So, some clothes are jeans Fallacy committed: Fallacy of Universal Conclusion Drawn From a Particular Premise, Fallacy of Affirmative Conclusion Drawn From a Negative Premise 8. No conclusion can be drawn from two particular premises. Example: Some animals are dugong Some animals are butanding No conclusion Some philosophers are not mathematicians But some mathematicians are not musicians No conclusion Fallacy committed:Fallacy of Particular Premises INFORMAL FALLACIES Formal fallacies are errors of reasoning by virtue of their forms. Informal fallacies are errors encountered in ordinary discourse and, sometimes described as fallacies of language. Fallacies may be created unintentionally, or they may be created intentionally in order to deceive other people. Sometimes the term “fallacy” is used even more broadly to indicate any false belief or cause of a false belief. Fallacies of Ambiguity (Unclear Meaning) 1. Fallacy of equivocation. Equivocation is the illegitimate switching of the meaning of a term during the reasoning. This is also called fallacy of four terms. Example: God is love, but love is blind, therefore, God is blind. 2. Fallacy of accent. The accent fallacy is a fallacy of ambiguity due to the different ways a word is emphasized or accented. Example: “Woman, without her, man is lost.” 3. Fallacy of amphiboly. This is an error due to taking a grammatically ambiguous phrase in two different ways during the reasoning. Example: Lost : The dog of a lady with a long tail. 4. Fallacy of composition. The composition fallacy occurs when someone mistakenly assumes that a characteristic of some or all the individuals in a group is also a characteristic of the group itself, the group “composed” of those members.