Nigerian Army University, BIU - Logic and Critical Thinking - Lecture Note (PDF)

NIGERIAN ARMY UNIVERSITY, BIU FACULTY OF COMPUTING DEPARTMENT OF COMPUTER SCIENCE BORNO STATE, NIGERIA NAUB_CSC 113 LOGICAL AND CRITICAL THINKING LECTURE NOTE FIRST SEMESTER 3 UNIT COURSE 1...

NIGERIAN ARMY UNIVERSITY, BIU FACULTY OF COMPUTING DEPARTMENT OF COMPUTER SCIENCE BORNO STATE, NIGERIA NAUB_CSC 113 LOGICAL AND CRITICAL THINKING LECTURE NOTE FIRST SEMESTER 3 UNIT COURSE 1 INTRODUCTION Definition of Philosophy The word 'philosophy' is derived from the combination of two ancient Greek words; 'philos', which means 'love', and 'sophia', which means 'wisdom' (philosophia). Literary it means “love of wisdom” Philosophy means the systematic study of the world and our place in it. It entails a critical examination of reality characterized by rational inquiry that aims at the Truth for the sake of attaining wisdom. It is a system of beliefs about reality. It is one's integrated view of the world. It aims at the logical clarification of thoughts. Philosophy is not a body of doctrine but an activity of actualizing reality. It is the foundation of knowledge from which other disciplines we study today is derived. It is the standard by which ideas are integrated and understood The Main Braches of Philosophy There are 4 main traditional branches of philosophy, namely Axiology, epistemology, metaphysics and logic. 1. Axiology: it is from Greek axios, “worthy”; logos, “science” which refers to the philosophical study of values. Various terms have been used in reference to axiology: - Theory of Value, the philosophical study of goodness, or basically, value. The significance of axiology as a field of study lies first in the considerable expansion of the term that has eventually given a wider meaning to the term value and secondly, in the unification that it has provided for the study of a variety of questions- economic, moral, aesthetic, religious, political and even logical values that had often been considered in relative isolation. In Philosophy the study of values is divided into two sets; Ethics and Aesthetics. Ethics is the study of practical reasoning and the normative questions which it gives rise to. Ethics can be defined as the philosophical study of moral values. The study involves systematizing, analyzing, evaluating, applying, defending and recommending concepts of right and wrong behaviour. In general terms, morality has to do with the dos and don’ts as expected of a rational human person. In modern times, Philosophers divide ethical theories into three general subject areas: meta ethics, normative ethics, and applied ethics. Aesthetics. is the study of Art and beauty. It mainly deals with beauty, art, enjoyment, sensory emotional values, perception, and matters of taste and sentiment. It includes what art consists of, as well as the purpose behind it. Major aesthetical questions: Does art consist of music, literature, 2 and painting? Or does it include a good engineering solution, or a beautiful sunset? What is beauty? These are some of the questions aimed at in Aesthetics. It also studies methods of evaluating art and criteria of judgment of art. Is art or beauty in the eye of the beholder? Does anything that appeals to you fit under the umbrella of art? Or does it have a specific nature? Does it accomplish a goal? 2. Epistemology: The term ''epistemology" is derived from the ancient Greek word 'episteme' meaning 'knowledge. The word therefore denotes the philosophical study of knowledge and its justification, and of the family of concepts which are involved in our assessing claims to knowledge or justified belief. As a theory of knowledge, epistemology seeks to establish the process of claiming to know and on what certainty basis are such claims founded. In its broadest sense, epistemology is the study of the method of acquiring and processing knowledge. It answers the question, "How do we know?”, “How do we justify our knowledge claims?" “What are the sources of our knowledge claims?”, “What is the difference between knowledge and beliefs?” etc. Epistemology encompasses the nature of concepts, the constructing of concepts, the validity of the senses, logical reasoning, as well as thoughts, ideas, memories, emotions, and all things mental. It is concerned with how our minds are related to reality, and whether these relationships are valid or invalid. It is concerned with how we know what we do, what justifies us in believing what we do, and what standards of evidence we should use in seeking truths about the world and human experience. 3. Metaphysics: is a branch of philosophy responsible for the study of existence. As a term, metaphysics is derived from two ancient Greek words ‘meta’ which means beyond and ‘physicea’ which refers to material substance or objects of experience. Metaphysics means the study of the essence of being beyond the physical entities. The word metaphysics was coined by Aristotle, a student of Plato when he undertook the task of categorizing the works and writings of his teacher. Aristotle discovered that Plato wrote on many topics some of which dealt with issues of the physical entity while others dealt with abstract concepts that could not be comprehended by senses. Such abstract conceptual topics are what Aristotle classified under the discipline of metaphysics. They included the concepts of being, existence, immortality, God, spiritual beings, time, identity, consciousness, cause, essence, space, constancy etc. Being the foundation of a worldview and essence of beings, it answers the question "What is?" Metaphysics encompasses the conceptual study of everything that exists, as well as the nature of existence itself. It investigates whether the 3 world and existence is real, or merely an illusion. Metaphysics is the study of the fundamental conceptual view of the world around us and it is divided into two wide domains: Ontology which is the study of being and Cosmology- the study of the universe. 4. Logic: is the science which directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness, consistency, and validity in those processes. The aim of logic is to secure clearness in the definition and arrangement of our ideas and other mental images, consistency in our judgments, and validity in our processes of inference. The Greek word logos, meaning "reason", is the origin of the term logic-logike (techen, pragmateia, or episteme, understood), as the name of a science first occurs in the writings of the Stoics. Aristotle, the founder of the science, designates it as "analytic” and the Epicureans use the term canonic. From the time of Cicero, however, the word logic is used almost without exception to designate this science. The names dialectic and analytic are also used simultaneously. Generally, Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning. In its broadest sense, Logic deals with the study of the evidential link between the premises and conclusions. Basic concepts of Logic Logic is the science or study of correct processes of thinking or reasoning. It is derived from the Greek "logos" which has a variety of meanings, ranging from word, discourse, thought, idea, argument, account, reason or principle. It is also defined as the study of the principles and criteria of valid inference and demonstration; or, the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning. In its broadest sense, it is the study of evidential link between premises and conclusions. As a field of study: it is a branch of philosophy that deals with the study of arguments and the principles and methods of right reasoning. As an instrument: it is something, which we can use to formulate our own rational arguments and critically evaluate the soundness of other’ argument. The distinction between correct and incorrect reasoning is the central problem that logic deals with. Despite the fact that there are different definitions of logic – indicating that logicians are not in agreement as to how it should be defined, we can appreciate the focus of logic as having to do with the articulation of the methods distinguishing good reasoning from bad and to present formal criteria for evaluating inferences and arguments as well as techniques and procedures for applying 4 these criteria to concrete cases. The following are some of the basic concepts in logic; Propositions, Argument, inference, premise and conclusion. Critical Thinking Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. This lesson in intended to awaken and equip the mind of the learner with requisite knowledge in critical thinking skills for effective problem solving and decision- making. It covers definitions of critical and thinking, nature and characteristics of critical thinking, uses and importance of critical thinking. Characteristics of Critical and Creative Thinking Wade (1995) identifies 8 (Eight) characteristics of Critical and creative thinking which includes: asking questions defining a problem examining evidence analyzing assumptions and biases avoiding emotional reasoning avoiding oversimplification considering other interpretations and tolerating ambiguity. Logical Ways of Thinking In science & engineering, it is most important to think logically and present a process of thinking for reaching a conclusion clearly. That should be based on formal logic such as propositional logic and predicate logic. Even if a conclusion was come across by insight, its truth must objectively be verified so that the other people are convinced. Therefore, formal logic is the common means of analysis as well as verification necessary for sharing the conclusion. To refresh your memory on formal logic, important concepts and their corresponding English phrases are summarized below. The term sentence below always indicates a declarative sentence that excludes an interrogative sentence (i.e., a question), an imperative sentence (i.e., a command), and an exclamatory sentence. 5 1. Conjunction (AND) denoted ∧ This is a truth-functional connective similar to "and" in English. A connective forming compound propositions which are true only in the case when both of the propositions joined by it are true. Truth Functionality: In order to know the truth value of the proposition which results from applying an operator to propositions, all that need be known is the definition of the operator and the truth value of the propositions used. sentence and sentence | clause and clause o John likes apples and 5 is an odd integer. o John and Mary live in Yola. o Zainab lies down and sleeps. o Zainab lives in Yola and studies at the University of Biu. A conjunction is a compound statement formed by combining two statements using the word and. In symbolic logic, the conjunction of p and q is written p ∧ q. A conjunction is true only if both the statements in it are true. The following truth table gives the truth value of p ∧ q depending on the truth values of p and q. One way of expressing this definition is by way of truth tables. Consider the following examples. i. "John left and Carol arrived" can be symbolized as " J ∧ C " (i. e., (without the quotation marks), so long as we remember that the statement does not mean "Carol arrived after John left" which is a simple proposition). ii. There are four possible states of affairs which might have occurred with respect to John leaving and Carol arriving. These cases can be listed as follows in what is called a truth table. p q p∧q T T T T F F F T F F F F Other ordinary language conjoiners besides "and" include some uses of "but," "although," "however "yet," and "nevertheless." The dot as a truth functional connective doesn't do everything that the "and" does in English. It might be thought of in terms of a "minimum common logical meaning" to conjoined statements. 6  i. I.e., the temporal or causal sequence "Bill tripped and fell" cannot be transposed as "Bill fell and tripped." The clauses cannot be interchanged. ii. Truth functional connectives are more limited than their corresponding English connectives: the whole meaning of the truth functional connective is given in its truth table. iii. So long as we do not expect more from truth-functional connectives, there should be few difficulties in translation. Some characteristics of conjunction (in mathematical jargon) include: i. associative—internal grouping is immaterial I. e.," [(p * q) * r] " is equivalent to " [p * (q * r)] ". ii. communicative—order is immaterial I. e., " p * q " is an equivalent expression to " q * p ". iii. idempotent—reduction of repetition I. e., " p * p " is an equivalent expression to " p ". Which brings us to an overdue additional convention: lower-case letters are variables, the small letters of the English alphabet usually beginning with letters after " p "(toward the end of the alphabet). A variable is not a proposition, but is a "place holder" for any proposition. Think of a variable as a "labeled box" which can be filled with any proposition, so long as we set up a correspondence between the "labeled box" and the variable. E. g., just as "All S is P" is the form of statements like "All men are mortal" and "The whale is a mammal," " p * q " is the form of statements like "John left and Zainab arrived" and " J * Z " (which symbolizes the statement "John left and Zainab arrived." E. g., suppose Alice and Betty are in this room, but Charles is not. The form of the statement corresponding to each person being in the room is [(p * q) * r] and the statement "Alice is in this room and Betty is in this room, and Charles is in this room" can, itself, be symbolized as [(A * B) * C] The truth of the compound expression is analyzed by substituting in the truth values corresponding to the facts of the case, viz., 7  [(T * T) * F] so by the meaning of the " * " the compound statement resolves to being false by the following step-by-step analysis in accordance with the truth table for conjunction: [(T * T) * F] [(T) * F] [T * F] F 2. Disjunction (OR) denoted ∨ either sentence or sentence | sentence or sentence | clause or clause o John majors computer science or 5 is an odd integer. Remark: In formal logic, the word "or" is interpreted as an inclusive OR that allows both to be true. If exactly one of two is true (called an exclusive OR), the phrase "... or... , but not both" is used. o John or Mary lives in Kano. Remark: When a subject includes the word "or", nonnative speakers may be puzzled whether a verb should be singular or plural. Refer to Making Subjects and Verbs Agree regarding rules on this matter. o Mary eats or sleeps. o Mary lives in Yola or studies at the University of Biu. or as it is sometimes called, alternation, is a connective which forms compound propositions which are false only if both statements (disjuncts) are false. The connective "or" in English is quite different from disjunction. "Or" in English has two quite distinctly different senses. 1. The exclusive sense of "or" is "Either A or B (but not both)" as in "You may go to the left or to the right." In Latin, the word is "aut." 2. The inclusive sense of "or" is "Either A or B (or both)." as in "John is at the library or John is studying." In Latin, the word is vel." It is the second sense that we use the "vel" or "wedge" symbol: "V" 8  The truth table definition of the wedge is p Q pVq T T T T F T F T T F F F Consider the statement, "John is at the Library or he is Studying." If, in this example, John is not at the library and John is not studying, then the truth value of the complex statement is false: F v F F 3. Negation (NOT) denoted ¬ Another truth functional operator is negation: the phrase "It is false that …" or "not" inserted in the appropriate place in a statement. The phrase is usually represented by a minus sign " ¬ " or a tilde "~" For example, "It is not the case that Bill is a curious child" can be represented by "~B". be not | adverb not verb | no subject verb o John is not a graduate student. o Zainab does not take a biology course. o No CS student graduates in 3 years. The truth table for negation is as follows: p ~p T F F T Logical Equivalence Logical Equivalence is a term used in formal logic to describe a scenario where two statements or 'propositions' are logically the same. In other words, they imply each other, leading to the same logical conclusion. Essentially, the logical equivalence of two statements 'P' and 'Q' signifies that 'P if and only if Q'. In mathematical notation, it's represented as P⇔Q. E.g. A clear example that illustrates logical equivalence is the relationship between the statements: "If it is raining, then the ground is wet" and 9 "If the ground is not wet, then it is not raining". Here, the truth of one statement confirms the truth of the other which demonstrates logical equivalence. A conditional statement and its contrapositive are logically equivalent. The converse and inverse of a conditional statement are logically equivalent. Be aware that symbolic logic cannot represent the English language perfectly. For example, we may need to change the verb tense to show that one thing occurred before another. Must agree with each other; they must both be true, or they must both be false. Similarly, the converse and the inverse must agree with each other; they must both be true, or they must both be false. Affirmation This is a statement or proposition that is declared to be true. confirmation or ratification of the truth or validity of a prior judgment, decision, etc. Law. a solemn declaration accepted instead of a statement under oath. Affirming the Consequent is the name of an invalid conditional argument form. You can think of it as the invalid version of modus ponens. The form of a modus ponens argument is a mixed hypothetical syllogism, with two premises and a conclusion: 1. If P, then Q. 2. P. 3. Therefore, Q. The first premise is a conditional ("if–then") claim, namely that P implies Q. The second premise is an assertion that P, the antecedent of the conditional claim, is the case. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be the case as well. An example of an argument that fits the form modus ponens: 1. If today is Tuesday, then John will go to work. 2. Today is Tuesday. 3. Therefore, John will go to work. This argument is valid, but this has no bearing on whether any of the statements in the argument are actually true; for modus ponens to be a sound argument, the premises must be true for any true instances of the conclusion. An argument can be valid but nonetheless unsound if one or more premises are false; if an argument is valid and all the premises are true, then the argument is sound. For example, John might be going to work on Wednesday. In this case, the reasoning for John's 10 going to work (because it is Wednesday) is unsound. The argument is only sound on Tuesdays (when John goes to work), but valid on every day of the week. A propositional argument using modus ponens is said to be deductive. Remember, what it means to say that an argument is invalid, is that IF the premises are all true, the conclusion could still be false. In other words, the truth of the premises does not guarantee the truth of the conclusion. Here’s an example: 1. If I have the flu then I’ll have a fever. 2. I have a fever. Therefore, I have the flu. Here we’re affirming that the consequent is true, and from this, inferring that the antecedent is also true. But it’s obvious that the conclusion doesn’t have to be true. Lots of different illnesses can give rise to a fever, so from the fact that you’ve got a fever there’s no guarantee that you’ve got the flu. More formally, if you were asked to justify why this argument is invalid, you’d say that it’s invalid because there exists a possible world in which the premises are all true but the conclusion turns out false, and you could defend this claim by giving a concrete example of such a world. For example, you could describe a world in which I don’t have the flu but my fever is brought on by bronchitis, or by a reaction to a drug that I’m taking. Another example: 1. If there’s no gas in the car then the car won’t run. 2. The car won’t run. Therefore, there’s no gas in the car. This doesn’t follow either. Maybe the battery is dead, maybe the engine is shot. Being out of gas isn’t the only possible explanation for why the car won’t start. Here’s a tougher one. The argument isn’t written in standard form, and the form of the conditional isn’t quite as transparent: “You said you’d give me a call if you got home before 9 PM, and you did call, so you must have gotten home before 9 PM.” Is this inference valid or invalid? It’s not as obvious as the other examples, and partly this is because there’s no natural causal relationship between the antecedent and the consequent that can 11  help us think through the conditional logic. We understand that cars need gas to operate and flus cause fevers, but there’s no natural causal association between getting home before a certain time and making a phone call. To be sure about arguments like these you need to draw upon your knowledge of conditional claims and conditional argument forms. You identify the antecedent and consequent of the conditional claim, rewrite the argument in standard form, and see whether it fits one of the valid or invalid argument forms that you know. Here’s the argument written in standard form, where we’ve been careful to note that the antecedent of the conditional is what comes after the “if”: 1. If you got home before 9 PM, then you’ll give me a call. 2. You gave me a call. Therefore, you got home before 9 PM. Now it’s clearer that the argument has the form of “affirming the consequent”, which we know is invalid. The argument would be valid if the you said that you’d give me a call ONLY IF you got home before 9 PM, but that’s not what’s being said here. If you got home at 9:30 or 10 o’clock and gave me a call, you wouldn’t be contradicting any of the premises. Conditional (aka Implication) denoted → A conditional is a logical compound statement in which a statement 𝑝 called the antecedent, implies a statement p called the consequent. A conditional is written as 𝑝→𝑞 and is translated as "if p then 𝑞 ". if sentence A, then sentence B | sentence A only if sentence B | sentence A implies sentence B when sentence A, sentence B | sentence B if sentence A | sentence B when sentence A | sentence B, provided sentence A Remark: The left-hand side A of a conditional is called a premise and the right-hand side B in a conditional is called a consequence. o If John is a CS student, then he needs to take discrete math courses. o John needs to take discrete math courses if he is a CS student. o Majoring CS implies the minimum 30 credits of CS courses for graduation. o Alice receives a honors degree, provided her GPA is at least 3.5. 12 Example 1 The English statement “If it is raining, then there are clouds is the sky” is a conditional statement. It makes sense because if the antecedent “it is raining” is true, then the consequent “there are clouds in the sky” must also be true. Notice that the statement tells us nothing of what to expect if it is not raining; there might be clouds in the sky, or there might not. If the antecedent is false, then the consequent becomes irrelevant. Example 2 Suppose you order a team jersey online on Tuesday and want to receive it by Friday so you can wear it to Saturday’s game. The website says that if you pay for expedited shipping, you will receive the jersey by Friday. In what situation is the website telling a lie? There are four possible outcomes: 1) You pay for expedited shipping and receive the jersey by Friday 2) You pay for expedited shipping and don’t receive the jersey by Friday 3) You don’t pay for expedited shipping and receive the jersey by Friday 4) You don’t pay for expedited shipping and don’t receive the jersey by Friday Only one of these outcomes proves that the website was lying: the second outcome in which you pay for expedited shipping but don’t receive the jersey by Friday. The first outcome is exactly what was promised, so there’s no problem with that. The third outcome is not a lie because the website never said what would happen if you didn’t pay for expedited shipping; maybe the jersey would arrive by Friday whether you paid for expedited shipping or not. The fourth outcome is not a lie because, again, the website didn’t make any promises about when the jersey would arrive if you didn’t pay for expedited shipping. It may seem strange that the third outcome in the previous example, in which the first part is false but the second part is true, is not a lie. Remember, though, that if the antecedent is false, we cannot make any judgment about the consequent. The website never said that paying for expedited shipping was the only way to receive the jersey by Friday. Example 21 A friend tells you “If you upload that picture to Facebook, you’ll lose your job.” Under what conditions can you say that your friend was wrong? There are four possible outcomes: 1) You upload the picture and lose your job 13 2) You upload the picture and don’t lose your job 3) You don’t upload the picture and lose your job 4) You don’t upload the picture and don’t lose your job There is only one possible case in which you can say your friend was wrong: the second outcome in which you upload the picture but still keep your job. In the last two cases, your friend didn’t say anything about what would happen if you didn’t upload the picture, so you can’t say that their statement was wrong. Even if you didn’t upload the picture and lost your job anyway, your friend never said that you were guaranteed to keep your job if you didn’t upload the picture; you might lose your job for missing a shift or punching your boss instead. In traditional logic, a conditional is considered true as long as there are no cases in which the antecedent is true and the consequent is false. Truth table for the conditional Again, if the antecedent p is false, we cannot prove that the statement is a lie, so the result of the third and fourth rows is true. Example 22 Construct a truth table for the statement (𝑚∧∼𝑝)→𝑟 Solution We start by constructing a truth table with 8 rows to cover all possible scenarios. Next, we can focus on the antecedent, 𝑚∧∼𝑝. 14 Now we can create a column for the conditional. Because it can be confusing to keep track of all the Ts and Fs, why don't we copy the column for r to the right of the column for 𝑚∧∼𝑝? This makes it a lot easier to read the conditional from left to right. 15 When m is true, p is false, and r is false, the fourth row of the table-then the antecedent 𝑚∧∼𝑝 will be true but the consequent false, resulting in an invalid conditional; every other case gives a valid conditional. If you want a real-life situation that could be modeled by (𝑚∧∼𝑝)→𝑟, consider this: let 𝑚 = we order meatballs, p = we order pasta, and r = Rob is happy. The statement (m∧∼p)→r is "if we order meatballs and don't order pasta, then Rob is happy". If m is true (we order meatballs), p is false (we don't order pasta), and r is false (Rob is not happy), then the statement is false, because we satisfied the antecedent but Rob did not satisfy the consequent. For any conditional, there are three related statements, the converse, the inverse, and the contrapositive. Bi-conditionals Bi-conditional statements are if-and-only-if statements. This is when a conditional statement and its converse are true. In other words, the hypothesis implies the conclusion, and the conclusion implies the hypothesis. Write the bi-conditional statement as "hypothesis if and only if conclusion." Two line segments are congruent if and only if they are of equal length. It is a combination of two conditional statements, “if two line segments are congruent then they are of equal length” and “if two line segments are of equal length then they are congruent”. A biconditional is true if and only if both the conditionals are true. Bi-conditionals are represented by the symbol ↔ or ⇔. p↔q means that p→q and q→p. That is, p↔q=(p→q)∧(q→p). Example: Write the two conditional statements associated with the bi-conditional statement below. A rectangle is a square if and only if the adjacent sides are congruent. The associated conditional statements are: a) If the adjacent sides of a rectangle are congruent then it is a square. b) If a rectangle is a square then the adjacent sides are congruent. The biconditional, 𝑝 ↔𝑞, is a two way contract; it is equivalent to the statement (𝑝 →𝑞 ) ∧ (𝑞→𝑝 ). A biconditional statement, 𝑝 ↔𝑞 is true whenever the truth value of the hypothesis matches the truth value of the conclusion, otherwise it is false. 16 The truth table for the biconditional is summarized below. 𝑝 𝑞 𝑝 ↔𝑞 T T T T F F F T F F F T Method of Deduction Using Rules of inference Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning. Logic studies under what conditions an argument is valid. According to the semantic approach, this is the case if there is no possible interpretation of this argument where its premises are true and its conclusion is false. The syntactic approach, by contrast, focuses on rules of inference, that is, schemas of drawing a conclusion from a set of premises based only on their logical form. There are various rules of inference, like the modus ponens and the modus tollens. Invalid deductive arguments, which do not follow a rule of inference, are called formal fallacies. Rules of inference are definitory rules and contrast to strategic rules, which specify what inferences one needs to draw in order to arrive at an intended conclusion. Deductive reasoning contrasts with non-deductive or ampliative reasoning. For ampliative arguments, like inductive or abductive arguments, the premises offer weaker support to their conclusion: they make it more likely but they do not guarantee its truth. They make up for this drawback by being able to provide genuinely new information not already found in the premises, unlike deductive arguments. Deductive inferences, which are inferences arrived at through deduction (deductive reasoning), can guarantee truth because they focus on the structure of arguments. Here is an example: 17  1. Either you can go to the movies tonight, or you can go to the party tomorrow. 2. You cannot go to the movies tonight. 3. So, you can go to the party tomorrow. This argument is good, and you probably knew it was good even without thinking too much about it. The argument uses “or,” which means that at least one of the two statements joined by the “or” must be true. If you find out that one of the two statements joined by “or” is false, you know that the other statement is true by using deduction. Notice that this inference works no matter what the statements are. Take a look at the structure of this form of reasoning: 1. X or Y is true. 2. X is not true. 3. Therefore, Y is true. By replacing the statements with variables, we get to the form of the initial argument above. No matter what statements you replace X and Y with, if those statements are true, then the conclusion must be true as well. This common argument form is called a disjunctive syllogism. Valid Deductive Inferences A good deductive inference is called a valid inference, meaning its structure guarantees the truth of its conclusion given the truth of the premises. Pay attention to this definition. The definition does not say that valid arguments have true conclusions. Validity is a property of the logical forms of arguments, and remember that logic and truth are distinct. The definition states that valid arguments have a form such that if the premises are true, then the conclusion must be true. You can test a deductive inference’s validity by testing whether the premises lead to the conclusion. If it is impossible for the conclusion to be false when the premises are assumed to be true, then the argument is valid. Deductive reasoning can use a number of valid argument structures: Disjunctive Syllogism: 1. X or Y. 2. Not Y. 3. Therefore X. Modus Ponens: 1. If X, then Y. 2. X. 18  3. Therefore Y. Modus Tollens: 1. If X, then Y. 2. Not Y. 3. Therefore, not X. You saw the first form, disjunctive syllogism, in the previous example. The second form, modus ponens, uses a conditional, and if you think about necessary and sufficient conditions already discussed, then the validity of this inference becomes apparent. The conditional in premise 1 expresses that X is sufficient for Y. So if X is true, then Y must be true. And premise 2 states that X is true. So the conclusion (the truth of Y) necessarily follows. You can also use your knowledge of necessary and sufficient conditions to understand the last form, modus tollens. Remember, in a conditional, the consequent is the necessary condition. So Y is necessary for X. But premise 2 states that Y is not true. Because Y must be the case if X is the case, and we are told that Y is false, then we know that X is also false. These three examples are only a few of the numerous possible valid inferences. Invalid Deductive Inferences A bad deductive inference is called an invalid inference. In invalid inferences, their structure does not guarantee the truth of the conclusion—that is to say, even if the premises are true, the conclusion may be false. This does not mean that the conclusion must be false, but that we simply cannot know whether the conclusion is true or false. Here is an example of an invalid inference: 1. If it snows more than three inches, the schools are mandated to close. 2. The schools closed. 3. Therefore, it snowed more than three inches. If the premises of this argument are true (and we assume they are), it may or may not have snowed more than three inches. Schools close for many reasons besides snow. Perhaps the school district experienced a power outage or a hurricane warning was issued for the area. Again, you can use your knowledge of necessary and sufficient conditions to understand why this form is invalid. Premise 2 claims that the necessary condition is the case. But the truth of the necessary condition does not guarantee that the sufficient condition is true. The conditional states that the closing of schools is guaranteed when it has snowed more than 3 inches, not that snow of more than 3 inches is guaranteed if the schools are closed. 19 Invalid deductive inferences can also take general forms. Here are two common invalid inference forms: Affirming the Consequent: 1. If X, then Y. 2. Y. 3. Therefore, X. Denying the Antecedent: 1. If X, then Y. 2. Not X. 3. Therefore, not Y. You saw the first form, affirming the consequent, in the previous example concerning school closures. The fallacy is so called because the truth of the consequent (the necessary condition) is affirmed to infer the truth of the antecedent statement. The second form, denying the antecedent, occurs when the truth of the antecedent statement is denied to infer that the consequent is false. Your knowledge of sufficiency will help you understand why this inference is invalid. The truth of the antecedent (the sufficient condition) is only enough to know the truth of the consequent. But there may be more than one way for the consequent to be true, which means that the falsity of the sufficient condition does not guarantee that the consequent is false. Going back to an earlier example, that a creature is not a dog does not let you infer that it is not a mammal, even though being a dog is sufficient for being a mammal. Watch the video below for further examples of conditional reasoning. See if you can figure out which incorrect selection is structurally identical to affirming the consequent or denying the antecedent. Types of Discourse Discourse is the verbal or written exchange of ideas. Any unit of connected speech or writing that is longer than a sentence and that has a coherent meaning and a clear purpose is referred to as discourse. An example of discourse is when you discuss something with your friends in person or over a chat platform. Discourse can also be when someone expresses their ideas on a particular subject in a formal and orderly way, either verbally or in writing. Discourse has significant importance in human behaviour and the development of human societies. It can refer to any kind of communication. 20 Spoken discourse is how we interact with each other, as we express and discuss our thoughts and feelings. Think about it - isn't conversation a huge part of our daily lives? Conversations can enrich us, especially when they are polite and civil. Civil discourse is a conversation in which all parties are able to equally share their views without being dominated. Individuals engaged in civil discourse aim to enhance understanding and the social good through frank and honest dialogue. Engaging in such conversations helps us live peacefully in society. What is more, written discourse (which can consist of novels, poems, diaries, plays, film scripts etc.) provides records of decades-long shared information. How many times have you read a book that gave you an insight into what people did in the past? And how many times have you watched a film which made you feel less alone because it showed you that someone out there feels the same way you do? What are the four types of discourse? The four types of discourse are description, narration, exposition and argumentation. S/N Types of discourse Purpose for the type of discourse 1 Description Helps the audience visualise the item or subject by relying on the five senses. 2 Narration Aims to tell a story through a narrator, who usually gives an account of an event. 3 Exposition Conveys background information to the audience in a relatively neutral way. 4 Argumentation Aims to persuade and convince the audience of an idea or a statement. 1. Description Description helps the audience visualise the item or subject by relying on the five senses. Its purpose is to depict and explain the topic by the way things look, sound, taste, feel, and smell. Description helps readers visualise characters, settings, and actions with nouns and adjectives. Description also establishes mood and atmosphere (think pathetic fallacy in William Shakespeare's Macbeth (1606). Examples of the descriptive mode of discourse include the descriptive parts of essays and novels. Description is also frequently used in advertisements. 21  2. Narration Narration is the second type of discourse. The aim of narration is to tell a story. A narrator usually gives an account of an event, which usually has a plot. Examples of the narrative mode of discourse are novels, short stories, and plays. Consider this example from Shakespeare's tragedy Romeo and Juliet (1597): hakespeare uses a narrative to set the scene and tell the audience what will occur during the course of the play. Although this introduction to the play gives the ending away, it doesn't spoil the experience for the audience. On the contrary, because the narration emphasises emotion, it creates a strong sense of urgency and sparks interest. Hearing or reading this as an audience, we are eager to find out why and how the 'pair of star-cross'd lovers take their life'. 3. Exposition Exposition is the third type of discourse. Exposition is used to convey background information to the audience in a relatively neutral way. In most cases, it doesn't use emotion and it doesn't aim to persuade. Examples of discourse exposure are definitions and comparative analysis. What is more, exposure serves as an umbrella term for modes such as: Exemplification (illustration): The speaker or writer uses examples to illustrate their point. Michael Jackson is one of the most famous artists in the world. His 1982 album 'Thriller' is actually the best-selling album of all time - it has sold more than 120 million copies worldwide. Cause / Effect: The speaker or writer traces reasons (causes) and outcomes (effects). 4. Argumentation Argumentation is the fourth type of discourse. The aim of argumentation is to persuade and convince the audience of an idea or a statement. To achieve this, argumentation relies heavily on evidence and logic. Lectures, essays and public speeches are all examples of the argumentative mode of discourse. Take a look at this example - an excerpt from Martin Luther King Jr.'s famous speech 'I Have a Dream' (1963): 'I have a dream that one day this nation will rise up and live out the true meaning of its creed: We hold these truths to be self-evident, that all men are created equal. (...). This will be the day when all of God's children will be able to sing with new meaning: My country, 'tis of thee, sweet land of 22 liberty, of thee I sing. Land where my fathers died, land of the pilgrims' pride, from every mountainside, let freedom ring. And if America is to be a great nation, this must become true.'² In his speech, Martin Luther King Jr. successfully argued that African Americans should be treated equally to white Americans. He rationalised and validated his claim. By quoting the United States Declaration of Independence (1776), King argued that the country could not live up to the promises of its founders unless all its citizens lived in it freely and possessed the same rights. Validity and Soundness A deductive argument proves its conclusion ONLY if it is both valid and sound. Validity: An argument is valid when, IF all of it’s premises were true, then the conclusion would also HAVE to be true. In other words, a “valid” argument is one where the conclusion necessarily follows from the premises. It is IMPOSSIBLE for the conclusion to be false if the premises are true. Here’s an example of a valid argument: 1. All philosophy courses are courses that are super exciting. 2. All logic courses are philosophy courses. 3. Therefore, all logic courses are courses that are super exciting. Note #1: IF (1) and (2) WERE true, then (3) would also HAVE to be true. Note #2: Validity says nothing about whether or not any of the premises ARE true. It only says that IF they are true, then the conclusion must follow. So, validity is more about the FORM of an argument, rather than the TRUTH of an argument. So, an argument is valid if it has the proper form. An argument can have the right form, but be totally false, however. For example: 1. Daffy Duck is a duck. 2. All ducks are mammals. 3. Therefore, Daffy Duck is a mammal. The argument just given is valid. But, premise 2 as well as the conclusion are both false. Notice however that, IF the premises WERE true, then the conclusion would also have to be true. This is all that is required for validity. A valid argument need not have true premises or a true conclusion. On the other hand, a sound argument DOES need to have true premises and a true conclusion: Soundness: An argument is sound if it meets these two criteria: (1) It is valid. (2) Its premises are true. In other words, a sound argument has the right form AND it is true. 23 Note #3: A sound argument will always have a true conclusion. This follows every time these 2 criteria for soundness are met. Do you see why this is the case? First, recall that a sound argument is both valid AND has true premises. Now, refer back to the definition of “valid”. For all valid arguments, if their premises are true, then the conclusion MUST also be true. So, all sound arguments have true conclusions. Looking back to our argument about Daffy Duck, we can see that it is valid, but not sound. It is not sound because it does not have all true premises. Namely, “All ducks are mammals” is not true. So, the argument about Daffy Duck is valid, but NOT sound. Here’s an example of an argument that is valid AND sound: 1. All rabbits are mammals. 2. Bugs Bunny is a rabbit. 3. Therefore, Bugs Bunny is a mammal. In this argument, if the premises are true, then the conclusion is necessarily true (so it is valid). AND, as it turns out, the premises ARE true (all rabbits ARE in fact mammals, and Bugs Bunny IS in fact a rabbit)—so the conclusion must also be true (so the argument is sound). One way to summarize these concepts is to represent the logical territory in a "tree- diagram." Arguments _________|___________ Deductive Inductive _____|_____ _____|_____ Valid Invalid correct > > > > incorrect _______|________ Sound Unsound (all statements (at least one are true) premise is false) Argument Both logic and critical thinking centrally involve the analysis and assessment of arguments. “Argument” is a word that has multiple distinct meanings, so it is important to be clear from the start about the sense of the word that is relevant to the study of logic. In one sense of the word, an argument is a heated exchange of differing views as in the following: Sally: Abortion is morally wrong and those who think otherwise are seeking to justify murder! 24  Bob: Abortion is not morally wrong and those who think so are right-wing bigots who are seeking to impose their narrow-minded views on all the rest of us! Sally and Bob are having an argument in this exchange. That is, they are each expressing conflicting views in a heated manner. However, that is not the sense of “argument” with which logic is concerned. Logic concerns a different sense of the word “argument.” An argument, in this sense, is a reason for thinking that a statement, claim or idea is true. For example: Sally: Abortion is morally wrong because it is wrong to take the life of an innocent human being, and a fetus is an innocent human being. In this example Sally has given an argument against the moral permissibility of abortion. That is, she has given us a reason for thinking that abortion is morally wrong. The conclusion of the argument is the first four words, “abortion is morally wrong.” But whereas in the first example Sally was simply asserting that abortion is wrong (and then trying to put down those who support it), in this example she is offering a reason for why abortion is wrong. We can (and should) be more precise about our definition of an argument. But before we can do that, we need to introduce some further terminology that we will use in our definition. As I’ve already noted, the conclusion of Sally’s argument is that abortion is morally wrong. But the reason for thinking the conclusion is true is what we call the premise. So we have two parts of an argument: the premise and the conclusion. Typically, a conclusion will be supported by two or more premises. Both premises and conclusions are statements. A statement is a type of sentence that can be true or false and corresponds to the grammatical category of a “declarative sentence.” For example, the sentence, The Nile is a river in northeastern Africa is a statement. Why? Because it makes sense to inquire whether it is true or false. (In this case, it happens to be true.) But a sentence is still a statement even if it is false. For example, the sentence, The Yangtze is a river in Japan is still a statement; it is just a false statement (the Yangtze River is in China). In contrast, none of the following sentences are statements: Please help yourself to more casserole Don’t tell your mother about the surprise Do you like Vietnamese pho? 25  The reason that none of these sentences are statements is that it doesn’t make sense to ask whether those sentences are true or false (rather, they are requests or commands, and questions, respectively). There are two basic kinds of arguments. Deductive argument: involves the claim that the truth of its premises guarantees the truth of its conclusion; the terms valid and invalid are used to characterize deductive arguments. A deductive argument succeeds when, if you accept the evidence as true (the premises), you must accept the conclusion. Inductive argument: involves the claim that the truth of its premises provides some grounds for its conclusion or makes the conclusion more probable; the terms valid and invalid cannot be applied. How to Construct Logical Arguments Once we get an idea by a logical way of thinking, we need to express the idea and a logical process of deriving it clearly. There are at least two approaches to organizing an argument logically: Top-Down and Bottom-Up. In practice, we often apply both of them so that a global organization (e.g., at levels of sections and chapters) is constructed in a top-down method and local organizations (e.g., at levels of paragraphs and sentences) is constructed in a bottom-up method. A. Top-Down Approach 1. Decide the main theme and choose its appropriate title. 2. Write an outline such as a table of contents. 3. Put a heading to each component (such as a section) in the table of contents. 4. Choose important topic sentences for each component. 5. Repeatedly decompose each component hierarchically so that a component may correspond to a few to several paragraphs. 6. Expand each topic sentence to compose a paragraph. B. Bottom-Up Approach 1. Compose sentences by using the phrases as shown above together with well-defined vocaburary (such as technical terms). 2. Classify the composed sentences into facts, hypotheses, opinions, etc. 26 3. Choose topic sentences that are important. 4. Group sentences for each topic sentence. 5. Form a paragraph consisting of a topic sentence and its supporting sentences. 6. Form a section consisting of paragraphs. 7. Arrange paragraphs in each section. 8. Repeatedly aggregate components at a lower level into a component of a higher level. Technique for Evaluating an argument An argument is a connected series of propositions, some of which are called premises and at least one of which is a conclusion. The premises provide the reasons or evidence that supports the conclusion. From the point of view of the reader, an argument is meant to persuade the reader that, once the premises are accepted as true, the conclusion follows from them. If the reader accepts the premises, then she ought to accept the conclusion. The act of reasoning that connects the premises to the conclusion is called an inference. A good argument supports a rational inference to the conclusion, a bad argument supports no rational inference to the conclusion. Consider the following example: 1. All human beings are mortal. 2. Socrates is a human being. 3. Therefore, Socrates is mortal. This argument asserts that Socrates is mortal. It does so by appealing to the fact that Socrates is a human being, together with the idea that all human beings are mortal. There is clearly a strong connection between the premises and conclusion. Imagine a reader who accepts both premises but denies the conclusion. This person would have to believe that Socrates is a human being and that all human beings are mortal, but still deny that Socrates is mortal. How could such a person maintain that belief? It just doesn’t seem rational to believe the premises but deny the conclusion! Now consider the following argument: 1. I saw a black cat today. 2. My knee is aching. 3. Therefore, it is going to rain. Suppose that it does, in fact, rain and the person who advances this argument believes that it is going to rain. Is that person justified in their belief that it will rain? Not based on the argument 27 presented here! In this argument, there is a very weak connection between the premises and the conclusion. So, even if the conclusion turns out to be true, there is no reason why a reader ought to accept the conclusion given these premises (there may be other reasons for thinking it is going to rain that are not provided here, of course). The point is that these premises do not provide the right sort of evidence to justify the conclusion. Generally, a statement is an ‘argument’ if it: Presents a particular point of view Bases that view on objective evidence If you come across an assertion that is not based on evidence that can reasonably be considered objective, it is just that – an assertion, not an argument. Also, a statement of fact is not an argument, although it might be evidence that could be used in support of an argument. When evaluating an argument, here are some things that you might consider: Who is making the argument? What gives them authority to make the argument? What evidence is given in support of the argument? Has this evidence been tested elsewhere? Could alternative approaches have been used? Does the evidence upon which the argument is based come from a reliable and independent source? How do you know? Who funded the research that produced the evidence? Are there alternative perspectives or counter-arguments? You should evaluate any counter- arguments in just the same way. What are the implications of the argument, for example, for policy or for practice? How to evaluate arguments in a step-by-step manner: 1. Identify the conclusion and the premises. 2. Put the argument in standard form. 3. Decide if the argument is deductive or non-deductive. 4. Determine whether the argument succeeds logically. 5. If the argument succeeds logically, assess whether the premises are true. For premises that are backed-up by sub-arguments, repeat all the steps for the sub-arguments. 6. Make a final judgement: is the argument good or bad? 28 Introduction to Deduction What is deductive reasoning? Deductive reasoning is drawing conclusions based on premises generally assumed to be true. Also called "deductive logic," it uses a logical assumption to reach a logical conclusion. Deductive reasoning is often referred to as "top-down reasoning." If something is assumed to be accurate and another relates to the first assumption, the original truth must also hold true for the second. For example, if a car’s trunk is large and a bike does not fit into it, you may assume the bike must also be large. We know this because we were already provided with the information we believe is accurate—the trunk is large. Based on our deductive reasoning skills, we know that if a bike does not fit in an already large trunk, it must also be large. So long as the two premises are based on accurate information, the outcome of this type of conclusion is often true. Syllogism deductive reasoning One of the most common types of deductive reasoning is syllogism. Syllogism refers to two statements—a major and a minor—joining to form a logical conclusion. The two accurate statements mean that the statement will likely be valid for all additional premises of that category. The reliability of deductive reasoning While deductive reasoning is considered a reliable form of testing, it’s important to recognize it may sometimes lead to a false conclusion. This generally occurs when one of the first assumptive statements is false. It is also possible to come to an accurate conclusion even if one or both of the generalized premises are false. Deductive reasoning examples Here are several examples to help you better understand deductive reasoning: My state requires all lawyers to pass the bar to practice. If I do not pass the bar, I will not be able to represent someone legally. My boss said the person with the highest sales would get a promotion at the end of the year. I generated the highest sales, so I look forward to a promotion. Our most significant sales come from executives who live in our company’s home state. Based on this information, we have decided to allocate more marketing dollars to targeting executives in that state. 29  One of our customers is unhappy with his experience. He does not like how long it takes for a return phone call. Therefore, he will be more satisfied if we provide a quicker response. I must have 40 credits to graduate this spring. Because I only have 38 credits, I will not be graduating this spring. The career counseling center at my college offers students free resume reviews. I am a student, and I plan on having my resume reviewed, so I will not have to pay anything for this service. Each of these statements includes two accurate pieces of information and an assumption based on the first two pieces. As long as the first two pieces of information are correct, the presumption should also be accurate. Deductive reasoning process Deductive thought uses only information assumed to be accurate. It does not include emotions, feelings, or assumptions without evidence because it’s difficult to determine the accuracy of this information. Understanding the process of deductive reasoning can help you apply logic to solve challenges in your work. The process of deductive reasoning includes: 1. Initial assumption. Deductive reasoning begins with an assumption. This assumption is usually a generalized statement that if something is true, it must be true in all cases. 2. Second premise. A second premise is made about the first assumption. The second related statement must also be true if the first statement is true. 3. Testing. Next, the deductive assumption is tested in a variety of scenarios. 4. Conclusion. The information is determined to be valid or invalid based on the test results. When to use deductive reasoning There are many ways you can use deductive reasoning to make decisions in your professional life. Here are a few ways you can use this process to draw conclusions throughout your career: Using deductive reasoning in the workplace Applying existing deductive reasoning skills during decision-making will help you make better- informed choices in the workplace. You may use deductive reasoning when finding and acquiring a job, hiring employees, managing employees, working with customers and making various business or career decisions. Deductive reasoning in the workplace requires the following skills: 30 Problem-solving Many roles require you to use problem-solving skills to overcome challenges and discover reliable resolutions. You can apply the deductive reasoning process to your problem-solving efforts by first identifying an accurate assumption you can use as a foundation for your solution. Deductive reasoning often leads to fewer errors because it reduces the guesswork. Teamwork Many organizations expect employees to work together in teams to achieve results. Teams often have employees with varying work styles, which can hinder collaboration and reduce productivity. Using the process of deductive reasoning, you can identify where the problem lies, draw accurate conclusions, and help team members align. Customer service You can apply deductive reasoning skills to the customer service experience, too. Using this process, you can determine an appropriate solution to a customer’s problem. By identifying what the customer is unhappy with and then connecting it to what you know about their experience, you can adequately address their concern and increase customer satisfaction. Deductive Reasoning and Inductive Reasoning. Deductive Reasoning Inductive Reasoning Theory Theory ↓ ↑ Hypothesis Hypothesis ↓ ↑ Observation Pattern ↓ ↑ Confirmation Observation Specialization Process Generalization Process Example 1.2: Deductive Reasoning 31  All men are mortal. Joe is a man. Therefore Joe is mortal. This is the well-known inference rule called hypothetical syllogism (or simply syllogism). Remark 1.2: A Fallacy in Deductive Reasoning To get a Bachelor's degree, a student must have 120 credits. David has more than 130 credits. Therefore, David has a bachelor's degree. Note that 120 credits are merely a necessary condition for a Bachelor's degree. Having 120 credits does not necessarily imply a Bachelor's degree. Example 1.2: Inductive Reasoning This horse is brown. That horse is brown. Another horse is brown. Therefore, all horses are brown. This example obviously shows that a conclusion drawn by inductive reasoning is not guaranteed to be true. Since the truth of a conclusion drawn by deductive reasoning depends on truth of given hypotheses, we need to apply both deductive reasoning and inductive reasoning for producing a true conclusion in the real world. Review 1.1: Assume that the following hypotheses are all true. Then, deduce a meaningful conclusion from them. a. If today is Tuesday, then I have a test in either Computer Science or Chemistry. b. If my Chemistry professor is sick, then I don’t have a test in Chemistry. c. Today is Tuesday. d. My Chemistry professor is sick. How to Construct a Paragraph A paragraph consists of the following sentences. Topic Sentence (usually at the beginning, but sometimes close to the end), Supporting Sentence(s) presenting details, explanation, analysis, etc. 32  Wrap-Up Sentence(s) To group sentences (or paragraphs) and form a paragraph (or a section, respectively), there are at least two criteria. Cohesion with a topic sentence Deduction process from hypotheses to a conclusion (that is typically a topic sentence) Example 2.1: Assume that we write a user's manual of a rice cooker, where the anticipated readers are users of the rice cooker. Consider the following outline of the manual. Cover Page Disclaimers and Safety Warnings Table of Contents 1. Hardware Configuration 2. Features 3. How to Use 4. Maintenance 5. Error Messages and Diagnosis 6. Specifications Subject Index Then, each section will be decomposed further. For example, the section 6 "Specifications" may consist of the following subsections. 6.1 Physical Dimensions 6.2 Electrical Specifications 6.3 Operational Environments Then, for each section or subsection, list important statements as topic sentences. This will lead to paragraphs. Arrange paragraphs logically and then proceed with composition of supporting sentences for a topic sentence of each paragraph. To design structures of a technical document has similarities with the design of software structures. In addition, software documentation is one of the major tasks in a process of software development. Thus, exercises of technical writing help students to learn how to develop a software system. Review 2.1: Write a paragraph regarding "what is most important to learn a logical way of thinking." 33  Critical Thinking Robert Ennis (1989) defined critical thinking as follows. "Critical thinking is reasonable, reflective thinking that is focused on deciding what to believe or do." Alec Fisher and Michael Scriven (1997) defined it as follows. "Critical thinking is skilled and active interpretation and evaluation of observations and communications, information and argumentation." Three Major Benefits of Critical Thinking in Science & Engineering 1. Ability to Raise Questions → This also leads to creative thinking. 2. Ability to Thoroughly Verify a Claim Objectively → This also leads to reflective thinking. 3. Ability to Think an Issue from Different Viewpoints → This also leads to innovative thinking. California Critical Thinking Skills Test (CCTST) proposes the following five-step problem solving process (IDEAS) by critical thinking. 1. I = Identify the Problem and Set Priorities 2. D = Determine Relevant Information and Deepen Understanding 3. E = Enumerate Options and Anticipate Consequence 4. A = Assess the Situation and Make a Preliminary Decision 5. S = Scrutinize the Process and Self-Correct as Needed This is quite generic so that it can be applied to a wide spectrum of problems. Example 3.1: Assume that you wrote a Java program for computing the power 2k and successfully compiled it without any error. When you get its output 103,520,048 for input k = 30, do you accept the output value without any question? You should start with questioning yourself whether the output is really accurate even if you are an experienced Java programmer and confident with the Java program. Note that 210 = 1024 ≈ 103. With basic knowledge of exponentiation, we can get a ballpark estimate of 230 as follows. 230 = (210)3 ≈ (103)3 = 109 = 1,000,000,000 Thus, it is easy to conclude that the output is erroneous. Remark 3.1: Assume that you conduct a Black Box Testing of the Java program in the above Example 3.1 (for more information about black box testing, refer to Testing Overview and Black-Box Testing Techniques). 34 What kind of a test data set do you use to demonstrate its correctness? How do you generate such a test data set? These are very crucial questions in software engineering. Review 3.1: Consider the 2nd assignment given to students in the episode in the article of Scientific American. What are questions that you raise for creating a recovery plan to protect bald eagles from extinction? Truth Tables: Example 24 Suppose this statement is true: “If I eat this giant cookie, then I will feel sick.” Which of the following statements must also be true? a. If I feel sick, then I ate that giant cookie. b. If I don’t eat this giant cookie, then I won’t feel sick. c. If I don’t feel sick, then I didn’t eat that giant cookie. Solution a. This is the converse, which is not necessarily true. I could feel sick for some other reason, such as drinking sour milk. b. This is the inverse, which is not necessarily true. Again, I could feel sick for some other reason; avoiding the cookie doesn’t guarantee that I won’t feel sick. c. This is the contrapositive, which is true, but we have to think somewhat backwards to explain it. If I ate the cookie, I would feel sick, but since I don’t feel sick, I must not have eaten the cookie. Notice again that the original statement and the contrapositive have the same truth value (both are true), and the converse and the inverse have the same truth value (both are false). Law of Torts A tort is an act or omission, other than a breach of contract, which gives rise to injury or harm to another, and amounts to a civil wrong for which courts impose liability. In other words, a wrong has been committed and the remedy is money damages to the person wronged. There are three types of tort actions; negligence, intentional torts, and strict liability. The elements of each are slightly different. However, the process of litigating each of them is basically the same. Negligence: 35 Negligence is the most common of tort cases. At its core negligence occurs when a tortfeasor, the person responsible for committing a wrong, is careless and therefore responsible for the harm this carelessness caused to another. There are four elements of a negligence case that must be proven for a lawsuit to be successful. All four elements must exist and be proven by a plaintiff. The failure to prove any one of these four elements makes a lawsuit in negligence deficient. The four elements are: Duty Breach Causation Harm A basic negligence lawsuit would require a person owing a duty to another person, then breaching that duty, with that breach being the cause of the harm to the other person. Duty: The first element of negligence is duty, also referred to as duty of care. What is a duty? In its most simplistic terms, it is an obligation to either do or not do something that will harm someone else. Think of duty as an obligation. We all have a duty or an obligation to act reasonably or reasonably refrain from certain actions, in such a way as to not cause injury or harm to another person. For example, as drivers of automobiles on public roads, we all have a duty to follow the rules of the road. It is our obligation as a licensed driver to do so. We understand that rules like speed limits are imposed to protect others. A reasonable person understands that the failure to follow the rules of the road may result in harm to another person. Breach: Once a plaintiff has established and proven that a defendant owned a duty of care to the plaintiff, the second element of negligence a plaintiff must prove is a breach of that duty of care. This is when a person or company has a duty of care to another and fails to live up to that standard of care. A plaintiff must prove that the defendant’s act or omission caused the plaintiff to be exposed to unreasonable risk of injury and/or harm. In other words, the defendant failed to meet their obligation to the plaintiff and therefore put the plaintiff in harm’s way. Causation: The third element of negligence is causation. There are two types of negligent causation, actual cause and proximate cause. Actual cause is sometimes referred to as cause in fact. It means that 36 “but for” the negligent act or omission of the defendant, the plaintiff would not have been harmed. This is known as the “but for” test. For example, driver A is passing through an intersection with a green light. Driver B runs the red light and strikes driver A’s vehicle and injures driver A. Clearly, “but for“ the running of the red light by driver B, driver A’s vehicle would not have been struck by driver B, and drive A would not have been harmed. The second type of negligent causation is proximate cause. Proximate cause requires the natural, direct, and uninterrupted consequence of a negligent act or omission to be the cause of a plaintiff’s injury. Proximate cause also requires foreseeability. It must be foreseeable as to the result, and also as to the plaintiff. If the result is too remote, too far removed, or too unusual from the defendant’s act or omission so as to make them unforeseeable, then the defendant is not the proximate cause of the plaintiff’s harm. For example, driver A is speeding. A squirrel runs in front of driver A’s car so driver A swerves, and because of the high rate of speed of which he is traveling, loses control of his vehicle and hits a mailbox. The mailbox flies so violently up in the air from the impact that it hits an overhead powerline. The force of the mailbox hitting the powerline forces the powerline to break off the utility pole onto the sidewalk where it is still electrified. A pedestrian approaching the scene steps on the powerline and is injured by the live powerline. A jury may find that driver A’s actions are not the proximate cause of the pedestrian’s injuries, because the resulting harm is so remote and so unusual as to render them unforeseeable. Harm: Harm can come in many forms. It can be economic, like medical costs and loss wages. It can be non-economic, like pain and suffering or extreme emotional distress. It can be harm to a person’s body, to a family member, or to property. However, if one is not harmed in some way, the fourth element of negligence is not met and the lawsuit in negligence will not prevail. Harm and causation in some ways are like the chicken and the egg. Which came first? Without harm there is really no causation, just a duty and breach of that duty. However, without causation there is no harm since again, we just have the duty and its breach. Just know this, if there is a duty and breach of that duty, and a subsequent harm or injury, it must be caused by that breach of duty. If there is a harm or injury, then the law allows for compensation to the person harmed or injured in the form of damages. Damages are typically monetary in nature. In other words, we pay someone money when we injure them due to our negligence. There is in most situations no other 37 way to make a person “whole” again. If you lose your leg in an automobile accident caused by someone’s negligence, they cannot get you your leg back. They can however, pay you money to allow you to buy a prosthetic leg, reimburse you for your medical expenditures and loss wages, pay you for future medical expenses, and pay you for all the pain and suffering associated with the injury. These are known as compensatory damages. Negligence: Often in a negligence lawsuit, the defense will raise what are called “affirmative defenses.” This could mean that even if a plaintiff’s claims of negligence are true, the defendant may not be responsible if the affirmative defenses can be proven. Sometimes, there is negligence on the part of both parties involved in a negligence lawsuit. When this happens, the jury will be asked by the defendant to consider the comparative negligence of the plaintiff and reduce the percentage of the plaintiff’s recovery of damages by that percentage. New York is a pure comparative negligence state pursuant to CPLR §1411. Intentional Torts: Intentional torts require an intended act by a wrongdoer against another. Some intentional torts can also be criminal. For example, if a person batters someone and causes them harm, this is also a criminal act and the person can be arrested and sued at the same time. Common intentional torts include: Assault Battery Trespass to Land Conversion Defamation Intentional Infliction of Emotional Distress False Imprisonment Assault: Civil assault is an intentional act by the defendant that causes reasonable apprehension or fear of harmful or offensive contact of the plaintiff. Actual contact is not required. This is a bit different than its counterpart in criminal law where contact is usually required. Assault is an intentional tort to a person. Battery: 38 Battery is an intentional act by the defendant that causes harmful or offensive contact of the plaintiff. The tort of battery often accompanies the tort of assault where it is referred to as assault and battery. Battery is most similar to criminal assault. Battery is an intentional tort to a person. Trespass to Land: Trespass to land requires an intentional act by the defendant which causes the defendant to enter or intrude on the plaintiff’s land. Trespass to land is most similar to criminal trespass. It is an intentional tort to property. Conversion: Conversion is an intentional act by the defendant that causes either the substantial invasion thereof or the outright possession by the defendant of the plaintiff’s personal property without the plaintiff’s consent. Conversion is an intentional tort to property. It is most similar to the criminal statutes of larceny. Defamation: Defamation is the intentional communication (sometimes referred to as publication) by the defendant to a third person of a false statement about the plaintiff that causes harm to the reputation of the plaintiff resulting in damages. The communication can be in writing, which is called libel, or verbally, which is called slander. The communication or publication must be false. It must also cause damage to plaintiff by either lowering the plaintiff’s reputation or exposing the plaintiff to some form of hate, contempt, or ridicule. Defamation is an intentional tort to a person. There is no criminal statute that directly correlates to this tort. Intentional Infliction of Emotional Distress: Intentional infliction of emotional distress is an intentional act by words or actions of extreme or outrageous conduct by the defendant that causes severe emotional distress of the plaintiff. The extreme and outrageous conduct must exceed all bounds of decent behavior. The emotional distress of the plaintiff must also be severe and far outside that which is ordinary. Intentional infliction of emotional distress is an intentional tort to a person. False Imprisonment: False imprisonment is an intentional act by the defendant that causes the confinement of the plaintiff without the plaintiff’s consent. The plaintiff must have no known reasonable means of escape. The confinement can be in the form of fixed barriers like a room or just a corner. False 39 imprisonment is an intentional tort to a person. It often involves store security who detains people suspected of shoplifting. It is most similar to criminal statutes of false imprisonment. Strict Liability: Strict Liability is a very limited theory of tort liability. It has nothing to do with negligence or intent. It applies to situations that are abnormally dangerous. This would include those who work with explosives, fireworks, radioactive materials, or own or control certain dangerous animals. If a person is injured by a defendant while engaged in these activities, liability is imposed regardless of a defendant’s intentions or lack of negligence. The law imposes liability as a matter of public policy. In NYS, strict liability even applies to product liability cases. 40