Unit One Logic Basics Page 1 Preface If this is your first semester in college, you may wish to take note of a key difference between college and high school. College courses presume that half to two/thirds of the learning for a given course occurs outside of the classroom. Where one falls in this range depends on how much one already knows, how easily one learns, and other factors. Dining offers an excellent analogy for learning. People tend to dine frequently while consuming reasonable portions. It doesn t seem reasonable to avoid eating for weeks or months and then try to make up for it by storming the buffet. Tummy trouble will likely follow. In the same way, studying should be done frequently, mastering reasonable portions of the material. Thus, we avoid the perilous cram session and the academic upchucking that follows. Education occurs when we learn. A course offers a student the opportunity to learn. The grade that a student earns does not necessarily reflect the degree to which the student has learned. Grades measure the degree to which a student engages in the curriculum. The presumption, sometimes a dubious one, is that engagement translates into learning, so the student becomes educated. Engage in a curriculum successfully over a period of time and you will earn a degree, but will you in fact be educated? Do you know someone who has a college degree and yet doesn t seem well educated? Do you know someone who is well educated with no college degree? Unit One Logic Basics Logic is an organized body of knowledge that evaluates reasoning. The goal of logic is disciplined critical reasoning. Introduction Philosophy A. Philosophy means the love of wisdom B. Wisdom refers to a type of knowledge that enables a person to judge all things in terms of their causes. 1. It s a way of explaining in a meaningful discourse the sum of our experience. 2. The process begins with ordinary experience that we may know with greater certitude and then in careful measured steps moves to extraordinary experience that we know with lesser certitude. C. Philosophy is the art of creating, applying, and evaluating categories. 1. A category is a group in which the members share characteristics. 2. We make categories by making comparisons. D. All thinking is comparative and when the comparisons result in categories, it s philosophy. What categories might we create when considering the items in this picture? You can approach this course as an opportunity to benefit from some of the wisdom of our culture or you can complete the assignments in hopes of securing a grade with a minimal amount of learning. The first option appeals because it brings the enriching experience that learned people enjoy. Perhaps the second option appeals because one seems to be beating the system. A beating occurs, but the victim is not the system; it s the students who beat themselves out of an opportunity for an education. I hope you will make the most of your opportunity and benefit from these tried and true ideas.
Unit One Logic Basics Page 2 Western Philosophy A. Western Philosophy began with the Ionians in the seventh century bce. B. The early philosophers sought the one principle from which all things came, but it wasn t their conclusions, but their method. C. The methodology that begun by Thales said that reality could be understood in accord with two principles. 1. Paired Opposites Up/down, Over/under, In/out, Near/far. 2. We can use what we know to figure out what we don t know. D. Paired opposites create categories. 1. We analyze things by dividing those things (physically or mentally) into categories. 2. We synthesize things by adding those things (physically or mentally) into categories. 3. In either case, we use what we know to figure out what we don t know. Image that you have never seen playing cards before. How would you Thales two principles to figure them out? Ancient Greek Philosophy s Branches A. Philosophy s Branches 1. Metaphysics studies the nature of reality or existence. It deals with questions pertaining to the nature of things and human nature. 2. Axiology studies values including ethics, social philosophy, and aesthetics. 3. Epistemology studies how we learn and know. B. Distinguishing Art and Science 1. Science (knowledge) refers to a systematic set of integrated truths. 2. Art refers to the application of truths in order to obtain a desired outcome. C. Speculative Knowledge is knowledge for its own sake. 1. Metaphysics: study of being; the most abstract. 2. Mathematics: quantification of being; intermediate abstract 3. Natural Philosophy: study of the qualities of a being; immediate and concrete. D. Practical Knowledge is knowledge for the sake of an operation. 1. Arts refer to the operations involved in making things. 2. Ethics refers to the operations involved in living the good life. 3. Politics refers to the operations involved in living in a community. Comparing Philosophy A. Philosophy and Religion are like neighbors. They can get along or fight. Paideia A. The goal of this process was Paideia meaning the process of educating a person into his true, real, and genuine human nature. 1. People would be in balance and harmony with the cosmos. 2. The would be equipped to act morally meaning that they could know good from evil and freely chose to act on that knowledge. B. In so doing, the ideal culture would form. 1. In this culture people would embody the ideal called Arete meaning excellence or virtuous conduct. 2. The end product would be eudemonia or what we call happiness.
B. Philosophy and Science 1. Science applies philosophical-like ideas to material things in hopes of understanding them better. 2. In order to confirm the truth or falsehood of the ideas it must be tested in a way that is direct, observable, and repeatable. Unit One Logic Basics Page 3 Why Study Logic? A. The study of Logic has two benefits. 1. Teaches the patterns applicable in critical reasoning regardless of the subject. 2. Helps the person to become a more nimble and affective critical thinker. B. These arguments share the same valid argument form despite the differing subject matter. 1. No American patriots are disloyal to the Constitution. Some American patriots are war heroes. Some war heroes are not disloyal to the Constitution. 2. No mammals are cold-blooded animals. Some mammals are animals that fly. Some animals that fly are not cold-blooded animals. C. Logic is like calisthenics for the mind.
Unit One Logic Basics Page 4 1.1 Arguments, Premises, & Conclusions Key Concept The argument is the basic unit of logical thought. Key Terms Argument Conclusion Indicators Premise Statement Argument A. An Argument is a group of statements, one or more of which are claimed to infer one of the other statements. 1. Premises refer to the statements that do the inferring. 2. Conclusions are the statements that are inferred. B. There are patterns in the construction of arguments 1. These patterns reliably indicate if the argument is reasonable or not. 2. These patterns occur regardless of the subject matter of the argument. 3. Logic studies these patterns. C. Statement refers to a sentence that has a truthvalue; it s either true or false. 1. Statements are typically declarative sentences or a sentence component that could stand as a declarative sentence. 2. Sentences may not be statements. Question, Proposal, Suggestion Command, Exclamation D. Indicators refer to words that alert us that a statement is either a premise or a conclusion. 1. Premise Indicators include since, because, for, in that, and given that among others. 2. Conclusion Indicators include therefore, thus, we may infer, so, and hence among others. E. Example Premise: Premise: Conclusion: Exercise 1.1 I: 1-10 Exercise 1.1 II: 1-10 All men are mortal. Socrates is a man. Therefore, Socrates is mortal 1.2 Recognizing Arguments Key Concept Not all passages contain arguments. In order to properly evaluate arguments, we must first identify them. Key Terms Truth Claim Expository Passage Explanation Inferential Claim Illustration Criteria for an Argument A. For a passage to be an argument, two criteria must be present in the passage. 1. Truth Claim means that at least one of the statements must claim to present evidence or reasons. 2. Inferential Claim means that there must be a claim that something is inferred or implied. B. Non-Argument Statements 1. A warning is an expression intended to put someone on guard or give notice concerning a dangerous or detrimental situation. 2. A piece of advice is an expression that offers a recommendation about a future decision. 3. An opinion is an expression that states a belief or a point of view concerning something. 4. Loosely Associated Statements refer to a group of statements concerning the same subject. 5. A report refers to a group of statements that convey information. Non-Argument Passages A. Non-Argument Passages 1. An Expository Passage begins with a topic sentence followed by one or more sentences that develop the topic sentence. 2. An Illustration offers examples intended to show what something means or how it is done. B. An Explanation purports to shed light on a thing or event. Every explanation consists of two parts. 1. Explanandum is the statement that describes the thing or event. 2. The Explanans refers to the statements that claim to do the explaining.
Unit One Logic Basics Page 5 1.3 Deduction and Induction Key Concept Deduction begins with a more universal and reasons to a less universal or a particular. Induction begins with particulars and reason toward universals C. Conditional Statements alleges that given something is the case (antecedent), something else logically follows (consequent). 1. Conditional statements are not arguments because they do not state a truth value. If that was the last living Caspian Tiger, then Caspian Tiger is extinct. 2. Conditional statements can be premises or conclusions in an argument. If that was the last living Caspian Tiger, then Caspian Tiger is extinct. That was the last living Caspian Tiger. Therefore, the Caspian Tiger is extinct. 3. Conditional statements express the relationship between necessary and sufficient conditions. a. Item A is to be sufficient condition to cause Item B if whenever A occurs, B occurs. If Fido is a dog, then Fido is an animal. b. Item B is to be a necessary condition to Item A if A cannot occur without B occurring. If Fido is not a dog, then Fido is not a Collie. Exercise 1.2 I: 1-10 Exercise 1.2 II: 1-10 Exercise 1.2 III: Select only one from1-10 Exercise 1.2 VI: 1-10 Key Terms Deductive Argument Inductive Argument Categorical Syllogism Propositional Argument Mathematical Argument Argument/Definition Hypothetical Syllogism Disjunctive Syllogism Hypothetical Outcome Analogy Inductive Generalization Argument/Authority Argument/Sign Argument/ Causal Inference Universal and Particular A. A term is universal if it includes more than one particular. The term dog applies to millions of animals. 1. A term is particular if it applies to one thing. Fido is a dog. 2. Terms can have varying degrees of universality. Dog is a universal. Mammal is more universal than dog because it applies to more particulars. B. The relationship between two universals is expressed with the terms Genus and Species. 1. Genus is the most universal of the pair. 2. Species is the least universal of the pair. Kinds of Argument A. Deductive Argument refers to an inference that goes from the more universal to the less universal or the particular: 1. Deductive conclusions are necessary meaning that if the antecedent is true and the reasoning sound, then the consequent must be true. 2. Deductive arguments are closed means that no new information is expected. 3. Example All birds are feathered animals. All ducks are birds All ducks are feathered animals B. Inductive Argument refers to an inference that goes from the numerous particulars to the universal to the more universal. 1. Inductive conclusions are probable means that if the antecedents are true then the consequent is likely to be true. 2. Inductive arguments are open meaning new information could contradict the conclusion.
Unit One Logic Basics Page 6 3. Example Robins are birds that can fly. Sparrows are birds that can fly. Crows are birds that can fly. Ducks are birds that can fly. All birds are animals that fly Deductive Argument Forms A. Categorical Syllogism refers to an argument consisting of two premises and a conclusion in which three terms appear twice. 1. There are two hundred and sixty-five categorical syllogisms of which fifteen are unconditionally valid. 2. Example: All female mammals are animals that nurse their offspring. All dogs are mammals. Therefore, all female dogs are animals that nurse their offspring. B. Propositional Arguments refer to a branch of symbolic logic dealing with propositions as units and with their combinations and the connectives that relate them C. Other Deductive Patterns 1. Mathematical Arguments refer to arguments that employ numerical computations of some sort. If Maybelle has three apples and two oranges in her bag, then she has five pieces of fruit in her bag. 2. Argument from Definition refers to a deduction based solely on the meaning of words. Sally is a Unicorn, so it follows that she has a single horn. 3. Hypothetical Syllogism refers to an argument in which the premises consist of if-then statements. If we have a snow day, then school will close. If school closes, then the test is postponed. Therefore, If we have a snow day, then the test is postponed. 4. Disjunctive Syllogism refers to an argument using an either-or construction. Either we re snowed in or we go to school. We re not snowed in. Therefore, we go to school. B. Argument from Causal Inference proceeds from knowledge of the cause to a claim about an effect. He put the cola in the fridge yesterday, so it s cold. It may also begin with the knowledge of the effect and work back to the cause. His steak looks like a burnt offering, so he must have cooked it too long. Success based on the ability to account for causes. The more dynamic the realm the less accountability is possible. C. Analogy: Compare what is known to something similar and less known in order to know it better. Putting an injured dog to sleep is like putting an injured cat to sleep. Having an abortion is just like having your gall bladder removed. Success based on the substantial similarity of the cases. Substance means what it is. D. Inductive Generalization: Knowledge is gained from samples to form conclusions about the whole. I have seen lots of teens at the cinema, so a movie that appeals to teens will likely be box office success. This British guy cheated me; the British are all thugs. Success based on whether or not the sample is representative. Samples can predict general trends, but not specific outcomes. E. Other Inductive Patterns 1. Argument from Authority realizes on the veracity of an expert. Dr Episteme, who is a professor of history, says that Abraham Lincoln was the sixteenth president of the United States. 2. Argument from Sign relies on sensible data or a conventional sign to lead to a conclusion. When I saw the smoke billowing from the roof, I concluded there was a fire. We took this exit because the sign on the Interstate said that the Hefty Hog Rib Shack was located off this exit. Exercise 1.3 I: 1-20 Inductive Argument Forms A. Hypothetical Outcome (Prediction) Project possible outcomes and assess probability. If we drive drunk we are more likely to be in a traffic accident. If we have a picnic, a meteorite may hit us. Success based on predictability. The more dynamic the realm the less predictable the outcome.
1.4 Validity, Truth, et al Key Concepts There is a well-settled criterion for evaluating arguments in order to determine if they reliably render a true conclusion. Unit One Logic Basics Page 7 Key Terms Valid Sound Strong Cogent Invalid Unsound Weak Uncogent Theories of Truth A. Truth is the condition of a statement whereby it expresses what is genuine or real. 1. Truth theories answer the question: How do we determine whether or not a statement is true? 2. Each theory has a different criterion for determining if the statement is true and reflects a different facet of the Epistemic Cycle. B. Correspondence theory states that a statement is true if it expresses what appears to be the case. 1. Based on observation 2. Employed in empirical settings 3. Strength: Closest to reality w/out involvement 4. Weakness: Observation error 5. Limit: Access to event 6. Watch the game C. Coherence theory states that a statement is true if it expresses what a knowledgeable source holds to be the case. 1. Based on authority 2. Employed in a research setting 3. Strength: Easy access to knowledge 4. Weakness: Superficial 5. Limit: Problem of new knowledge 6. Read about the game D. Pragmatic theory state that a statement is true if it expresses what experience says is the case. 1. Based on experience 2. Employed in anecdotal setting 3. Strength: Familiar/feels true 4. Weakness: Too subjective 5. Limit: lack of experience 6. Play in the game Certitude A. Certitude: Refers to the level of confidence one can reasonably have as to the truthfulness of the statement. 1. Statements of greater certitude have greater moral force. 2. Statements of lesser certitude have lesser moral force. B. Degrees of Certitude 1. Absolute: No doubt; 100% certain 1+1=2 2. Moral: No reasonable doubt; 90% certain Criminal court conviction 3. Clear and convincing: Evidence, but doubt is reasonable; 75% certain Some civil court judgments 4. Probable: More likely than not; 51% certain. Most Civil court judgment 5. Functional: assumed certain; 10% Articles in the tabloids
Unit One Logic Basics Page 8 Truth and Consensus A. Consensus refers to a widely held view that a statement is in fact true. B. There are two relationships between truth and consensus. 1. The truth-triggered consensus occurs when the truthfulness of a statement seems obvious and so is widely held. Chicago sits at the southwest end of Lake Michigan. 2. The consensus-triggered truth occurs when a widely held view makes the statement function as if it were true. 1. It may be true. There is a world-wide consensus that the American dollar is valuable and so in truth it is valuable. 2. It may be false. Come to find out, the Earth is not the center of the solar system. C. The relationship between truth and consensus is analogous to the relationship of goods to values. 1. Good or goodness refers to an objective quality of a thing or act that means it can actualize potential in whole or in part. The nature of the thing or act determines both what is good for it and what it is good for. I eat nutritious food because it s good for me. 2. A value is anything that anyone holds to be important or worthwhile. I like the taste of Mexican food. 3. Truth is the condition of a statement whereby it expresses what is genuine or real. The American head of state is the President of the United States. 4. Consensus refers to a widely held view that a statement is in fact true. The election determines who American voters think will be the best President from among the candidates. D. Concerning the real and the apparent 1. As we have noted earlier, we want to avoid confusing real goods with apparent goods. 2. We also want to avoid confusing the truth with the apparent truth. Sound Deductive Arguments A. A Valid deductive argument is a deductive argument in which given that the premises are true, the conclusion has to be true. 1. An Invalid deductive argument is an argument in which given the premises are true, the conclusion does not have to be true. 2. There is no middle ground either the deductive argument is valid or not. B. A Sound deductive argument consists of true premises and a valid inference. 1. An unsound deductive argument is unsound because either the argument is invalid or the premises are false. 2. There is middle ground due to the supposition expressed in the statements.
Unit One Logic Basics Page 9 Cogent Inductive Arguments A. A Strong inductive argument is an inductive argument in which given that the premises are true, the conclusion is probably true. 1. A Weak inductive argument is an argument in which given the premises are true, the conclusion does not have to be true. 2. There is middle ground because probability is involved. B. A Cogent inductive argument consists of true premises and a strong inference. 1. An Uncogent inductive argument is uncogent because either is weak or the premises are false. 2. There is middle ground due to the supposition expressed in the statements and the probability inherent in the argument. 1.5 Argument Forms Key Concept The validity of a deductive argument rests in the form of the argument. Any deductive argument that has a valued form is a valid argument regardless of its content. Key Terms Substitution Instance Counterexample Method Argument Form A. Valid arguments have a valid argument form. 1. This may not be immediately apparent because the parts of the argument are implied. Geese are migratory bird, so they fly south for the winter. 2. Rephrasing the argument makes all of the premises explicit. All geese are migratory bird. All Migratory birds fly south for the winter. All geese fly south for the winter. B. The form can then be rendered in a more universal format. All A are B All B are C All A are C C. Any argument that follows this form will be valid. A Substitution Instance is any argument that follows a given form. All dogs are mammals All Mammals are animals All dogs are animals All daisies are flowers All flowers are plants All daisies are plants Exercise 1.4 I: 1-10 Exercise 1.4 II: 1-10 Exercise 1.4 III: 1-10 Exercise Lessons 1.0 1.4 Counterexample Method A. The counterexample method relies on substitution to determine if an argument is invalid. 1. It can prove that an argument is invalid 2. It cannot prove that an argument is valid. B. Steps in the Counterexample Method 1. Take an invalid argument. 2. Extract the form of the argument. 3. Construct a substitute instance that has true premises and a false conclusion. 4. This proves the form invalid. 5. Thin in turn proves the given argument invalid. C. Example Since some employees are not social climbers and all vice-presidents are employees, we may conclude that some vice-presidents are not social climbers. 1. Put into a standard form
Unit One Logic Basics Page 10 Some E are not S All V are E Some V are not S 2. Select a substitute E= Animals S=Mammals V=Dogs 3. Resulting in the following substitution instance Some animals are not mammals All dogs are animals Some dogs are not mammals 4. This argument is invalid because it has all true premises and a false conclusion the definition of invalid. 5. Therefore the original argument is invalid. Restructuring the Argument Some church congregations are not groups that oppose sex education because some church congregations are not organizations that lack a moral compass and some groups that oppose sex education are not organizations that lack a moral compass. A. Sorting 1. Begin by identifying the conclusion. Some church congregations are not groups that oppose sex education. 2. Next, restate the premises with the conclusion. Some church congregations are not organizations that lack a moral compass Some groups that oppose sex education are not organizations that lack a moral compass. Some church congregations are not groups that oppose sex education. 3. Abstract the argument form. Some C are not O Some G are not O Some C are not G 4. Create a substitution with true premises and a false conclusion. Some beagles are not birds Some dogs are not birds Some beagles are not dogs premises; therefore, this argument form is invalid. Exercise 1.5 I: 1-10 Exercise 1.5 II: 1-10 1.6 Diagramming Arguments Key Concept Diagramming arguments offers a way of understanding extended arguments. Diagramming Arguments A. Analyzing extended arguments can prove to be a vexing task. 1. They often include explanations, reports, illustration or other forms. 2. They may include extraneous information that has to be shifted out. B. Diagramming and argument only illustrates the inferential claim. It does not address the truthvalue of the statements. C. Diagramming Basics 1. Number each of the statements in the passage. 2. Determine which statement or statements are the conclusion. 3. Determine the relationship between the various statements and the conclusion(s). D. Basic Patterns 1. One-Step Pattern illustrates the connection between a single premise and a single conclusion. 1. Half of the nation s drinking water, which comes from these aquifers, is being poisoned by chemical wastes dumped into the soil for generations. 2. The contamination of underground aquifers represents a pollution problem of catastrophic proportion. 5. It is impossible for a valid argument form to yield a false conclusion with all true
Unit One Logic Basics Page 11 and selling human organs comes too close to buying and selling life itself. 2. People in desperate financial states may sell their organs. 3. When items are scarce, the price goes up. 4. The buying and selling of human organs should be outlawed. 2. Vertical Pattern illustrates an argument in which prior conclusion becomes a premise for the continuation of the argument. 1. The selling of human organs, such as hearts and kidneys, should be outlawed. 2. Allowing human organs to be sold will inevitably create a situation where only the rich can get them. 3. When scarce things can be bought and sold, the price rises. 4. The law of supply and demand requires it. 4. Conjoined Premises illustrates an argument in which the premises rely on each other for context and cannot stand alone. 1. Most people on welfare are poorly educated, have substance abuse problems, or are mentally ill. 2 These behavior patterns frustrate welfare recipients capacity to get jobs. 3. Getting people off of welfare requires them to modify their lifestyle. 3. Horizontal Pattern illustrates an argument in which two or more independent premises. If one of the premises were excluded, then the others would continue to function. 1. Buying 5. Multiple Conclusions refer to an argument in which a single premise can produce more than a singular conclusion. 1. Dropping out of school and having children outside of marriage are two primary causes of poverty in
America. Therefore, to eliminate poverty 2. we must offer incentives to finish high school and 3. encourage people to get married before having children. Unit One Logic Basics Page 12 Exercise 1.6, I, 1-5 Exercise 1.6, II, 1-5 Exercise Compare and contrast arguments with explanations. Discussion Ichabod the Existentialist says, Hey Maybelle, one guess is as good as another, so why should I pay a doctor to diagnose my skin rash? Help Maybelle respond. Video Example Rugrats Tricycle Thief
Unit One Logic Basics Page 13 1.7 Cause-Effect Key Concept Rational thinking centers on our understanding of cause-effect relationships. Aristotle on Cause Effect A. Every effect is the result of cause. 1. To understand something in context, we must understand its causes. 2. Aristotle said that wisdom is knowledge of causes. B. Any artifact will illustrate causality John Stuart Mill on Cause Effect A. Criteria for Event A to be the cause of Event B the following must be true 1. A must precede B in time 2. A must be sufficient to account for B occurring. A must have the power to make effect B. 3. A must be necessary to B occurring. B could not have happened if A had not happened first. B. Method: These are ways of detecting cause-effect relationships. 1. Agreement: Compare cases where the effect is present in search of a common causal element. All of the poison ivy victims attended the picnic. 2. Difference: Compare cases where the effect is present to proximate cases where it is not present in search of a distinguishing element. Only the people without life vests drowned when the boat sank. 3. Joint: Both agreement and difference. All people who got sick ate at the Greasy Spoon Diner and only the diners who ate the Road Kill Ribs got sick. 4. Variation: Look for parallel patterns of change. When the switch is up, the light is on; when down, the light is off. 5. Residue: What s left when all else is counted. Weigh the truck when it s full, and then weigh the truck when it s empty. The difference is the weight of what was in the truck. Cause Effect, Means & Ends A. Anytime there is a means to an end, a cause effect relationship exists. We think of them as means and ends in the context of the future, and cause effect in the context of the past. B. Means to End 1. Essential Means refers to something that is both sufficient and necessary for a given effect to occur. Learning if one is to become educated. 2. Effective Means refers to something that is sufficient but not necessary for a given effect to occur. Schools can offer a means of educating oneself. C. Cause to Effect 1. Proximate Cause: The closest even that is both sufficient and necessary to the effect occurring. Tuesday, Spike drag raced up the driveway and ran into the garage door. 2. Correlation: An event that is either sufficient or necessary, but not both. The garage door was down. 3. Coincidence: An event that is neither sufficient nor necessary to the effect occurring. It happened on Tuesday. Chapter 10, I: 1-10 Chapter 10, II: 1-5 Exercise Lessons 1.5 1.7