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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 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 evidenc.

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- 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
- 8. Deductive and Inductive Arguments The basic difference between deductive and inductive arguments is experience. When you reason deductively, you reason without relying on experience—without relying on what your five senses tell you. When you reason inductively, you reason according to experience. Here’s an example of reasoning deductively: “All the dibdabs are skeezics. All the skeezics are runnels. Therefore, all the dibdabs are runnels.” You don’t have experience with dibdabs, skeezics, or runnels because they’re made up! You can’t see, taste, smell, touch, or hear them. The way that you are certain the conclusion is true, namely that all the dibdabs are runnels is because your intellect has processed the relations between the groups of things. Here’s an example of reasoning inductively: “My car won’t start. In fact, when I put the key in the ignition, the car won’t turn over. It’s silent. Therefore, my battery is dead.” How can you be so confident that your battery is dead? Aren’t there other potential causes of the car not starting? Yes, but given your previous experience—or similar experiences you’ve heard about—it seems most likely to you that the most likely reason your car won’t start is that there’s a problem with the battery. Notice that, in this case, you reasoned by way of experience. Deductive Arguments: Validity and Truth Valid Argument: When an argument is valid, it’s impossible to make the conclusion false, if the premises are true. Another way to think about validity is in terms of what happens when you accept the premises of a valid argument but deny the conclusion. In that case the denial contradicts what you’ve accepted as true. If I say, “I have candy in my left hand or my
- 9. right hand,” and then I open up my left hand to reveal there’s nothing in it, you’d conclude that the candy is in my right hand. But, suppose I say instead, “I don’t have candy in my right hand.” You’d say, “That’s impossible! You just said you have candy in either your left hand or your right hand but when you opened your left hand, there was no candy. If it’s true to say, ‘I have candy in my left hand or my right hand, but I do not have candy in my left hand,’ you can’t logically deny you have candy in your right hand. It doesn’t make sense to do that!” When we accept the premises of a valid argument, we are committed to the truth of the conclusion. Important words used in logical analysis Argument: A group of statements of which one (the conclusion) is claimed to follow from the others (the premises). Statement: A sentence that is either true or false. Premise: The information intended to provide support for a conclusion. Conclusion: The statement that is claimed to follow from the premises of an argument. Logic: The study of reasoning. Truth value: Every statement is either true or false; these two possibilities are called “truth values.” Proposition: The information content imparted by a statement, or simply put, its meaning. Inference: A term used by logicians to refer to the reasoning process that is expressed by an argument. Conclusion indicators: Words and phrases that indicate that the presence of a conclusion (the statement claimed to follow from
- 10. premises). Premise indicators: Words and phrases that help us recognize arguments by indicating the presence of premises (statements being offered in support of a conclusion). Inferential claim: If a passage expresses a reasoning process— that the conclusion follows from the premises—then we say that it makes an inferential claim. 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. Deductive argument: An argument 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 are true it is impossible for the conclusion to be false. Inductive argument: An argument 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. Valid deductive argument: An argument in which, assuming the premises are true, it is impossible for the conclusion to be false. In other words, the conclusion follows necessarily from the premises. Invalid deductive argument: An argument in which, assuming the premises are true, it is possible for the conclusion to be false. In other words, the conclusion does not follow necessarily from the premises. Sound argument: When logical analysis shows that a deductive argument is valid, and when truth value analysis of the premises
- 11. shows that they are all true, then the argument is sound. Unsound argument: If a deductive argument is invalid, or if at least one of the premises is false (truth value analysis), then the argument is unsound. Counter-example: A counterexample to a statement is evidence that shows the statement is false. 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 the argument is invalid. Strong inductive argument: An argument 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. Weak inductive argument: An argument such that if the premises are assumed to be true, then the conclusion is not probably true. Cogent argument: Strong and the premises are true. Uncogent argument: 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. Constructive Dilemma: A constructive dilemma is a valid deductive argument form of the following pattern: (If A, then B), and/but (if C, then D). A or C. Therefore, B or D
- 12. DataTrident UniversityBUS520: Business Analytics and Decision MakingModule 2: SLP TemplateFILL IN ALL CELLS THAT ARE HIGHLIGHTED IN YELLOWPlease remember to save this file with your last name in the file name. For example: BUS520 Module 2 SLP Template, Doe.docName:Annual Amount Spent on Organic FoodAgeAnnual IncomeNumber of People in HouseholdGender (0 = Male; 1 = Female)7348771096883111598471099815192242311213941129 91381134205116556581141015011515441151005010469341163 30501793375116339601817332117907701230539119071519080 65586035191134858623416185486157921647049621802060005 76220251676071680412085794768407417393476961831816128 73079401080063759005161602477129311080066796186085432 48113140176663886246611264454891675114308288957651973 75892296401330127936145118106489395461114682695937519 54752100846407812291032762115521751041125175984510511 94077837410592531177375610608460782430108616316552571 09038201123241109585516540233783450420028389405072252 34214550537045486775144763348997412800424905811783939 49609413472605327910885457539175089004154716501279167 12630650127127313089351133215713448851880264135711401 43692413970151790825142014411784034142857601510778143 18251120703415098751638934152041216606411547023062916 21555521174255715732930114362316379451761278164108407 51536165851401311544172497511187075174458508450701775 17411632438183779509331351851114091846518646740168036 81891376010709481943515114456241943805016634461973585 01222743197400511347658198650501455466202859519393682 03591411459474206216516628322076792011240612104985013 10142210678511403460211249501783764211961617849532128 51211057862213035511132578214457507105442154422016460 58220178518390272204033114956682208935110903212212234 11205470221498511169738222618511278125229072511745630 22968561128357023022851134033723561750150514023808750 14225292407685011196542425294011475522437655156056524
- 13. 46252098907224520841132274024764850112003624980541960 04325203340157033825281251648673257143119430412581674 17755352586402181002126102031148215926622351106505626 62695112589422675655111600462683804113000342694314117 06570269839601650055270441508600382727952011900512748 4641167236627625050167594327723150 Question 1FILL IN ALL CELLS THAT ARE HIGHLIGHTED IN YELLOWQUESTION 1: Generate a 95% confidence interval for the following two variables by hand: Annual Amount Spent on Organic Food and Age.Average Annual Amount Spent on Organic Food (� ̅)Average Age (� ̅)t-value from the t-table (t)t-value from the t-table (t)standard deviation for this variable (s)standard deviation for this variable (s)number of observations (n)number of observations (n)Margin of ErrorERROR:#DIV/0!Margin of ErrorERROR:#DIV/0!Upper Limit of Confidence IntervalERROR:#DIV/0!Upper Limit of Confidence IntervalERROR:#DIV/0!Lower Limit of Confidence IntervalERROR:#DIV/0!Lower Limit of Confidence IntervalERROR:#DIV/0! Questions 2-3FILL IN ALL CELLS THAT ARE HIGHLIGHTED IN YELLOWQUESTION 2: Generate a 95% confidence interval for the following two variables using the Excel formula =CONFIDENCE.T(): Annual Income and Number of People in the Household. Remember, this formula will just give you the margin of error. You will still need to add it to the mean and subtract it from the mean to get the upper and lower limits of the confidence interval.margin of error from the =CONFIDENCE.T() formulaAverage Annual IncomeUpper Limit of Confidence Interval0Lower Limit of Confidence Interval0margin of error from the =CONFIDENCE.T() formulaAverage Number of PeopleUpper Limit of Confidence Interval0Lower Limit of Confidence Interval0QUESTION 3a: Interpret the confidence intervals for Average Annual Income.QUESTION 3b: Interpret the confidence intervals for Average Number of People Question 4FILL IN ALL CELLS THAT ARE HIGHLIGHTED
- 14. IN YELLOWQUESTION 4: The client insists the average income of his organic food customers is $150,000. Conduct a hypothesis test at the 0.10 level to test his statement. What is your decision?Step 1: State the Null and Alternate HypothesesNull HypothesisAlternate HypothesisStep 2: Determine Alpha (Stated in Question)0.10Step 3: Determine Which Test Statistic Will Be UsedStep 4: Formulate a Decision RuleStep 5: Make a Decision Hint: This will be a 2-tail t-test.