# The following text material and terms defined at the end comprise .docx

15. Nov 2022
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### The following text material and terms defined at the end comprise .docx

• 1. The following text material and terms defined at the end comprise part of what will be asked on the Mid-Term Exam for PHIL 1381. Logic [excerpt from Stan Baronett, Logic, 2E] Logic is the study of reasoning. Logic investigates the level of correctness of the reasoning found in arguments. An argument is a group of statements of which one (the conclusion) is claimed to follow from the others (the premises). A statement is a sentence that is either true or false. Every statement is either true or false; these two possibilities are called “truth values.” Premises are statements that contain information intended to provide support or reasons to believe a conclusion. The conclusion is the statement that is claimed to follow from the premises. In order to help recognize arguments, we rely on premise indicator words and phrases, and conclusion indicator words and phrases. Inference is the term used by logicians to refer to the reasoning process that is expressed by an argument. If a passage expresses a reasoning process—that the conclusion follows from the premises—then we say that it makes an inferential claim. If a passage does not express a reasoning process (explicit or implicit), then it does not make an inferential claim (it is a noninferential passage). One type of noninferential passage is the explanation. An explanation provides reasons for why or how an event occurred. By themselves, explanations are not arguments; however, they can form part of an argument. There are two types of argument: deductive and inductive. A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises
• 2. are true it is impossible for the conclusion to be false. An inductive argument is one in which it is claimed that the premises make the conclusion probable. In other words, it is claimed that, under the assumption that the premises are true, it is improbable for the conclusion to be false. Revealing the logical form of a deductive argument helps with logical analysis and evaluation. When we evaluate deductive arguments, we use the following concepts: valid, invalid, sound, and unsound. A valid argument is one where, assuming the premises are true, it is impossible for the conclusion to be false. In other words, the conclusion follows necessarily from the premises. An invalid argument is one where, assuming the premises are true, it is possible for the conclusion to be false. In other words, a deductive argument in which the conclusion does not follow necessarily from the premises is an invalid argument. When logical analysis shows that a deductive argument is valid, and when truth value analysis of the premises shows that they are all true, then the argument is sound. If a deductive argument is invalid, or if at least one of the premises is false (truth value analysis), then the argument is unsound. A counterexample to astatement is evidence that shows the statement is false, and it concerns truth value analysis. A counterexample to an argument shows the possibility that premises assumed to be true do not make the conclusion necessarily true. A single counterexample to a deductive argument is enough to show that an argument is invalid. When we evaluate inductive arguments, we use the following concepts: strong, weak, cogent, and uncogent. A strong inductive argument is one such that if the premises are assumed to be true, then the conclusion is probably true. In other words, if the premises are assumed to be true, then it is improbable that the conclusion is false. A weak inductive argument is one such that if the premises are assumed to be true, then the conclusion
• 3. is not probably true. An inductive argument is cogent when the argument is strong and the premises are true. An inductive argument is uncogent if either or both of the following conditions hold: the argument is weak, or the argument has at least one false premise. What Logic Studies Logic is the study of reasoning. Its aim is to distinguish correct from incorrect reasoning by establishing the rules or patterns of successful arguments. Typically, we begin a study of logic with a discussion of certain features of language essential to arguments. A. Statements and Arguments A statement is a sentence that is either true or false, that is, a statement has a truth value. Statements are the primary building blocks of an argument. An argument is a collection of two or more statements, one of which is supported by the other or others. The conclusion is the supported sentence, while the premises are the sentences that support the conclusion. The goal of every argument is to establish the conclusion on the basis of the evidence provided by the premise or premises. Thus what distinguishes an argument from other collections of statements is its inferential nature. An argument’s elements reflect a conceptual flow from premises to conclusion. So, “inference” means the reasoning process expressed by an argument. “Statement” is distinguished from “sentence” and “proposition” as follows: 1. A sentence is a set of words complete in itself, as in a statement, question, or exclamation.
• 4. 2. A statement is a sentence that has two possible truth values: true and false. 3. A proposition is the information content or meaning of a statement. B. Recognizing Arguments An argument is distinguished from other collections of statements by its inferential nature. Unlike other passages, an argument involves drawing an inference from one or more statements to another statement. We say that a passage makes an inferential claim when it expresses a reasoning process, i.e., that the conclusion follows from the premises. Drawing an inference is a purely intellectual act. For example, you don’t know what a dibbeltot is, nor do you know what fizzlestrums and poggurets are. Nevertheless, you can draw an inference from the following statements: No dibbeltot is a fizzlestrum. Every fizzlestrum is a pogguret. The inference you draw is “No dibbeltot is a pogguret.” One way to identify the elements of an argument is through indicator words. Conclusion indicators alert you to the appearance of a conclusion, while premise indicators alert you to the appearance of a premise. In each case, indicator words tell you that a conclusion or premise is about to be asserted or has just been asserted. C. Arguments and Explanations
• 5. Distinguishing between arguments and non-arguments can sometimes be tricky. This is especially the case with explanations. Depending on the context, an explanation can be taken for an argument and vice versa. In addition, both arguments and explanations often use the same indicator words. The crucial distinguishing feature of an argument is that the conclusion is at issue. So, even when an explanation involves indicator words, if there is nothing at issue, the passage does not become an argument: “Because you were late meeting me at the restaurant for dinner, I went ahead and placed my order.” Here, an explanation is offered for ordering food. There is no intent to prove anything or settle some sort of issue. D. Truth and Logic Because an argument involves an inferential claim, we say that the truth of the conclusion depends on how good a job the premises do in establishing that truth. In this way, logic is concerned with truth in a rather different way than we determine the truth or falsity of a given statement. Logical analysis involves bearing in mind this distinction. Take another look at the example in B above: No dibbeltot is a fizzlestrum. Every fizzlestrum is a pogguret. Therefore, no dibbeltot is a pogguret. Consider another type of example: Whenever I come home, my dog is so happy to see me that he jumps all over me. So, when I get home later today, my dog will be so happy to see me that he’ll jump all over me. Whether or not each of the statements is true is irrelevant to the
• 6. question of whether or not the premises do a good job of establishing the conclusion. E. Deductive and Inductive Arguments Arguments fall into one of two types: those that rely on experience and those that do not. Each of the two arguments we just saw in D above is an example of, respectively, deductive and inductive argumentation. We do not need experience—what we smell, taste, see, etc.—in order to reason to the conclusion, “No dibbeltot is a pogguret.” In fact, we have no experience of these things. Nevertheless, we can reason successfully to the conclusion by the way the premises’ elements relate to each other. The dog argument is different in that the conclusion is a prediction which relies on past experience. A deductive argument is one in which the conclusion is claimed to follow necessarily from the premises. In other words, the premises are claimed to guarantee the conclusion, or it is impossible for the conclusion to be false if the premises are true. An inductive argument is one in which the conclusion is claimed to follow with a degree of probability. In other words, the premises make it likely for the conclusion to be true, or it is improbable that the conclusion is false if the premises are true. F. Deductive Arguments: Validity and Truth Deductive arguments are either valid or invalid, and sound or unsound. A valid deductive argument is one in which it is impossible for the conclusion to be false, if the premises are true. An invalid argument is one in which it is possible for the conclusion to be false, if the premises are true. A sound argument is valid, and its premises are actually true.
• 7. All invalid arguments are, by definition, unsound. Valid + True Premises = Sound Valid + At Least One False Premise = Unsound Invalid = Unsound A convenient test of validity is the counterexample method. If you can find a counterexample to an argument’s conclusion (while the premises are true), you have shown the conclusion is false. When you extend this method to an argument, you demonstrate the argument is invalid. First, however, be sure that your counterexample matches the original argument’s form. G. Inductive Arguments: Strength and Truth Inductive arguments are evaluated first according to how strong or weak the relation is between the premises and the conclusion. An inductive argument is strong when, assuming the premises are true, it is improbable for the conclusion to be false. An inductive argument is weak when, assuming the premises are true, it is probable for the conclusion to be false. A further evaluation involves the actual truth of the premises. A strong argument is cogent when the premises are true. A strong argument is uncogent when at least one of the premises is false. All weak arguments are uncogent, since strength is a part of the definition of cogency. Strong + True Premises = Cogent Strong + At Least One False Premise = Uncogent Weak = Uncogent