If two people disagree on whether something is reasonable, who is correct? What is the standard by which we judge a particular line of reasoning to be correct or incorrect? In the Christian worldview, we can answer these questions because we know that God determines the correct way to reason. He is the standard for all truth claims. In this book you will learn about logic and the Christian worldview, the Biblical basis for the laws of logic, if faith is contrary to reason, informal logical fallacies, and more.
The text begins with an introduction to arguments. After some linguistic preliminaries, the text presents a detailed analysis of inductive reasoning and associated fallacies. This order of presentation helps to motivate the use of formal methods in the subsequent sections on deductive logic and fallacies. Lively and straightforward prose assists students in gaining facility with the sometimes challenging concepts of logic.
By combining a sensitive treatment of ordinary language arguments with a simple but rigorous exposition of basic principles of logic, the text develops students' understanding of the relationships between logic and language, and strengthens their skills in critical thinking.
Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. It's appropriate for those in business, education, political or psychology careers. That may sound strange, but if you understand the concept of validity, it is not strange at all. Remember: validity describes the relationship between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true.
George was President of the United States 2. Therefore, George was elected President of the United States from 1 This argument is invalid because it is possible for the premise to be true and yet the conclusion false.
Here is a counterexample to the argument. In other words, it is possible for the premise of the argument to be true and yet the conclusion false. And this means that the argument is invalid. If an argument is invalid it will always be possible to construct a counterexample to show that it is invalid as I have done with the Gerald Ford scenario. A counterexample is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false.
If you can construct a counterexample to an argument, the argument is invalid. To apply the informal test of validity ask yourself whether you can imagine a world in which all the premises are true and yet the conclusion is false.
If you can imagine such a world, then the argument is invalid. If you cannot imagine such a world, then the argument is valid. It will help to better understand the concept of validity by applying the informal test of validity to some sample arguments. Joan jumped out of an airplane without a parachute 2. Therefore, Joan fell to her death from 1 To apply the informal test of validity we have to ask whether it is possible to imagine a scenario in which the premise is true and yet the conclusion is false if so, the argument is invalid.
So, can we imagine a world in which someone jumped out of an airplane without a parachute and yet did not fall to her death? Think about it carefully before reading on.
As we will see, applying the informal test of validity takes some creativity, but it seems clearly possible that Joan could jump out of an airplane without a parachute and not die—she could be perfectly fine, in fact. All we have to imagine is that the airplane was not operating and in fact was on the ground when Joan jumped out of it. If that were the case, it would be a true that Joan jumped out of an airplane without a parachute and yet b false that Joan fell to her death.
Thus, since it is possible to imagine a scenario in which the premise is true and yet the conclusion is false, the argument is invalid. Joan jumped out of an airplane traveling mph at a height of 10, ft without a parachute 2. Joan fell to her death from 1 Is this argument valid? You might think so since you might think that anyone who did such a thing would surely die. But is it possible to not die in the scenario described by the premise?
For example, maybe someone else who was wearing a parachute jumped out of the plane after them, caught them and attached the parachute-less person to them, and then pulled the ripcord and they both landed on the ground safe and sound. Or maybe Joan was performing a stunt and landed in a giant net that had been set up for that purpose.
Or maybe she was just one of those people who, although they did fall to the ground, happened to survive it has happened before. All of these scenarios are consistent with the information in the first premise being true and also consistent with the conclusion being false.
Thus, again, any of these counterexamples show that this argument is invalid. Notice that it is also possible that the scenario described in the premises ends with Joan falling to her death.
And that means that the argument is not valid i. Obama is President of the United States. Kenya is not in the United States. Therefore, Obama was not born in Kenya from In order to apply the informal test of validity, we have to ask whether we can imagine a scenario in which the premises are both true and yet the conclusion is false.
Can you imagine such a scenario? You cannot. The reason is that if you are imagining that it is a true that a person can be President of the United States only if they were born in the United States, b true that Obama is president and c true that Kenya is not in the U. Thus we know that on the assumption of the truth of the premises, the conclusion must be true. And that means the argument is valid. In this example, however, premises 1, 2, and 3 are not only assumed to be true but are actually true.
However, as we have already seen, the validity of an argument does not depend on its premises actually being true. Here is another example of a valid argument to illustrate that point. A person can be President of the United States only if they were born in Kenya 2. Obama is President of the United States 3. Therefore, Obama was born in Kenya from Clearly, the first premise of this argument is false.
And this means that the argument is valid. We cannot imagine a scenario in which the premises of the argument are true and yet the conclusion is false. Rather, validity depends only on the logical relationship between the premises and the conclusion. In the next section we will address this topic.
Exercise 5: Determine whether or not the following arguments are valid by using the informal test of validity. If the argument is invalid, provide a counterexample. Katie is a human being. Therefore, Katie is smarter than a chimpanzee. Bob is a fireman. Therefore, Bob has put out fires. Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.
Monica is a French teacher. Therefore, Monica knows how to teach French. Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie. Craig loves Linda. Linda loves Monique. Therefore, Craig loves Monique. Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God. All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah.
Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals. Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside. Soundness is defined in terms of validity, so since we have already defined validity, we can now rely on it to define soundness. A sound argument is a valid argument that has all true premises. That means that the conclusion of a sound argument will always be true.
But if the premises are actually true, as they are in a sound argument, then since all sound arguments are valid, we know that the conclusion of a sound argument is true. Compare the last two Obama examples from the previous section. While the first argument was sound, the second argument was not sound, although it was valid. The relationship between soundness and validity is easy to specify: all sound arguments are valid arguments, but not all valid arguments are sound arguments.
Although soundness is what any argument should aim for, we will not be talking much about soundness in this book. The reason for this is that the only difference between a valid argument and a sound argument is that a sound argument has all true premises. But how do we determine whether the premises of an argument are actually true? Well, there are lots of ways to do that, including using Google to look up an answer, studying the relevant subjects in school, consulting experts on the relevant topics, and so on.
But none of these activities have anything to do with logic, per se. The relevant disciplines to consult if you want to know whether a particular statement is true is almost never logic! Since this is a logic textbook, however, it is best to leave the question of what is empirically true or false to the relevant disciplines that study those topics.
And that is why the issue of soundness, while crucial for any good argument, is outside the purview of logic. For a deductive argument to fail to do this is for it to fail as a deductive argument.
Tweets is a healthy, normally functioning bird 2. Most healthy, normally functioning birds fly 3. Therefore, Tweets probably flies Given the information provided by the premises, the conclusion does seem to be well supported.
That is, the premises do give us a strong reason for accepting the conclusion. This is true even though we can imagine a scenario in which the premises are true and yet the conclusion is false. For example, suppose that we added the following premise: Tweets is 6 ft tall and can run 30 mph. Were we to add that premise, the conclusion would no longer be supported by the premises, since any bird that is 6 ft tall and can run 30 mph, is not a kind of bird that can fly.
That information leads us to believe that Tweets is an ostrich or emu, which are not kinds of birds that can fly. As this example shows, inductive arguments are defeasible arguments since by adding further information or premises to the argument, we can overturn defeat the verdict that the conclusion is well-supported by the premises.
Inductive arguments whose premises give us a strong, even if defeasible, reason for accepting the conclusion are called, unsurprisingly, strong inductive arguments. In contrast, an inductive argument that does not provide a strong reason for accepting the conclusion are called weak inductive arguments.
Suppose that instead of saying that most birds fly, premise 2 said that all birds fly. Tweets is a healthy, normally function bird. All healthy, normally functioning birds can fly. Therefore, Tweets can fly. This is true even if we add that Tweets is 6 ft tall because then what we have to imagine in applying our informal test of validity is a world in which all birds, including those that are 6 ft tall and can run 30 mph, can fly.
Although inductive arguments are an important class of argument that are commonly used every day in many contexts, logic texts tend not to spend as much time with them since we have no agreed upon standard of evaluating them.
In contrast, there is an agreed upon standard of evaluation of deductive arguments. We have already seen what that is; it is the concept of validity. In chapter 2 we will learn some precise, formal methods of evaluating deductive arguments. There are no such agreed upon formal methods of evaluation for inductive arguments. This is an area of ongoing research in philosophy. In chapter 3 we will revisit inductive arguments and consider some ways to evaluate inductive arguments.
In such a case, we can supply the premise s needed in order so make the argument valid. Making missing premises explicit is a central part of reconstructing arguments in standard form.
We have already dealt in part with this in the section on paraphrasing, but now that we have introduced the concept of validity, we have a useful tool for knowing when to supply missing premises in our reconstruction of an argument. In some cases, the missing premise will be fairly obvious, as in the following: Gary is a convicted sex-offender, so Gary is not allowed to work with children. Gary is a convicted sex-offender 2. Therefore, Gary is not allowed to work with children from 1 However, as stated, the argument is invalid.
Before reading on, see if you can provide a counterexample for this argument. That is, come up with an imaginary scenario in which the premise is true and yet the conclusion is false. Here is just one counterexample there could be many : Gary is a convicted sex-offender but the country in which he lives does not restrict convicted sex-offenders from working with children.
We can and should state that premise explicitly in our reconstruction of the standard form argument.
The obvious one is that no sex- offenders are allowed to work with children, but we could also use a weaker statement like this one: Where Gary lives, no convicted sex-offenders are allowed to work with children. It is weaker because it is not so universal in scope, which means that it is easier for the statement to be made true.
For more on strong and weak statements, see section 1. So here is the argument in standard form: 1. Gary is a convicted sex-offender. Where Gary lives, no convicted sex-offenders are allowed to work with children. Therefore, Gary is not allowed to work with children. As we can see from this example, a missing premise is a premise that the argument needs in order to be as strong as possible. Typically, this means supplying the statement s that are needed to make the argument valid.
But in addition to making the argument valid, we want to make the argument plausible. When it comes to supplying missing premises, this means supplying the most plausible premises needed in order to make the argument either valid for deductive arguments or inductively strong for inductive arguments. Although in the last example figuring out the missing premise was relatively easy to do, it is not always so easy.
Here is an argument whose missing premises are not as easy to determine: Since children who are raised by gay couples often have psychological and emotional problems, the state should discourage gay couples from raising children. Children who are raised by gay couples often have psychological and emotional problems. Therefore, the state should discourage gay couples from raising children. However, as it stands, this argument is invalid because it depends on certain missing premises. The conclusion of this argument is a normative statement— a statement about whether something ought to be true, relative to some standard of evaluation.
Normative statements can be contrasted with descriptive statements, which are simply factual claims about what is true. That is, it is simply a claim about what is in fact the case in Russia today.
An important idea within philosophy, which is often traced back to the Scottish philosopher David Hume , is that statements about what ought to be the case i. This is known within philosophy as the is-ought gap. The problem with the above argument is that it attempts to infer a normative statement from a purely descriptive statement, violating the is-ought gap. We can see the problem by constructing a counterexample.
Suppose that in society x it is true that children raised by gay couples have psychological problems. However, suppose that in that society people do not accept that the state should do what it can to decrease harm to children.
In this case, the conclusion, that the state should discourage gay couples from raising children, does not follow. Thus, we can see that the argument depends on a missing or assumed premise that is not explicitly stated. That missing premise must be a normative statement, in order that we can infer the conclusion, which is also a normative statement. There is an important general lesson here: Many times an argument with a normative conclusion will depend on a normative premise which is not explicitly stated.
The missing normative premise of this particular argument seems to be something like this: The state should always do what it can to decrease harm to children. Thus, we can reconstruct the argument, filling in the missing normative premise like this: 1. The state should always do what it can to decrease harm to children. In order to show this, we just have to imagine a scenario in which both the premises are true and yet the conclusion is false.
Here is one counterexample to the argument there are many. In this case, even if it were true that the state should always do what it can to decrease harm to children, it does not follow that the state should discourage gay couples from raising children. For example, it could be that the reason that children of gay couples have higher rates of psychological problems is that in a society that is not yet accepting of gay couples, children of gay couples will face more teasing, bullying and general lack of acceptance than children of heterosexual couples.
In that case, the state should not necessarily discourage gay couples from raising children. But for the government to discourage black Americans from raising children would have been unjust, since it is likely that if there was a higher incidence of psychological and emotional problems in black Americans, then it was due to unjust and unequal conditions, not to the black parents, per se.
Thus, one way of making the argument at least closer to valid would be to add the following two missing premises: A. The rate of psychological problems in children of gay couples is higher than in children of heterosexual couples. The higher incidence of psychological problems in children of gay couples is not due to any kind of injustice in society, but to the fact that the parents are gay. Their addition makes the argument much stronger, but making them explicit enables us to clearly see what assumptions the argument relies on in order for the argument to be valid.
This is useful since we can now clearly see which premises of the argument we may challenge as false. The important lesson from this example is that supplying the missing premises of an argument is not always a simple matter. In the example above, I have used the principle of charity to supply missing premises.
Mastering this skill is truly an art rather than a science since there is never just one correct way of doing it cf. Exercise 6: Supply the missing premise or premises needed in order to make the following arguments valid.
Try to make the premises as plausible as possible while making the argument valid which is to apply the principle of charity. Ed rides horses. Therefore, Ed is a cowboy. Tom was driving over the speed limit. Therefore, Tom was doing something wrong. If it is raining then the ground is wet. Therefore, the ground must be wet. All elves drink Guinness, which is why Olaf drinks Guinness. Instead, he invited his friend Alexia.
So he must like Alexia more than me. The watch must be broken because every time I have looked at it, the hands have been in the same place. Olaf drank too much Guinness and fell out of his second story apartment window. Therefore, drinking too much Guinness caused Olaf to injure himself. Mark jumped into the air.
Therefore, Mark landed back on the ground. Therefore, as of , the United States was still a racist nation. The temperature of the water is degrees Fahrenheit. Therefore, the water is boiling. Capital punishment sometimes takes innocent lives, such as the lives of individuals who were later found to be not guilty.
Therefore, we should not allow capital punishment. Allowing immigrants to migrate to the U. Therefore, we should not allow immigrants to migrate to the U. Prostitution is a fair economic exchange between two consenting adults. Therefore, prostitution should be allowed. Colleges are more interested in making money off of their football athletes than in educating them.
Therefore, college football ought to be banned. Edward received an F in college Algebra. Therefore, Edward should have studied more. But in practice people do not always give further reasons or argument in support of every statement they make.
Sometimes they use certain rhetorical devices to cut the argument short, or to hint at a further argument without actually stating it. Why would we want to assure our audience? This is one way of assuring our audience: by citing authorities. The rhetorical effect is that by commenting on how sure you are that something is true, you imply, without saying, that there must be very strong reasons for what you believe—assuming that the audience believes you are a reasonable person, of course.
One common way to do this is by implying that every sensible person would agree with the claim. Here are some examples: Everyone with any sense agrees that… Of course, no one will deny that… There is no question that… No one with any sense would deny that… Another common way of doing this is by implying that no sensible person would agree with a claim that we are trying to establish as false: It is no longer held that… No intelligent person would ever maintain that… You would have to live under a rock to think that… Assurances are not necessarily illegitimate, since the person may be right and may in fact have good arguments to back up the claims, but the assurances are not themselves arguments and a critical thinker will always regard them as somewhat suspect.
Next, we will turn to guarding. Guarding involves weakening a claim so that it is easier to make that claim true.
Here is a simple contrast that will make the point. Consider the following claims: A. All U. Presidents were monogamous B. Almost all U. Presidents were monogamous C. Most U. Many U. Presidents were monogamous E. Some U. Presidents were monogamous The weakest of these claims is E, whereas the strongest is A and each claims descending from A-E is increasingly weaker.
President who was monogamous. In contrast, A is much less likely than E to be true because it require every U. President to have been monogamous. One way of thinking about this is that any time A is true, it is also true that B-E is true, but B-E could be true without A being true. That is what it means for a claim to be stronger or weaker. A weak claim is more likely to be true whereas a strong claim is less likely to be true. E is much more likely to be true than A. Likewise, D is somewhat more likely to be true than C, and so on.
So, guarding involves taking a stronger claim and making it weaker so there is less room to object to the claim. Finally, we will consider discounting. Discounting involves acknowledging an objection to the claim or argument that one is making, while dismissing that same objection.
Contrast the following two claims: A. The worker was inefficient, but honest. The worker was honest, but inefficient. By introducing the claim to be dismissed, we are discounting that claim.
Although drilling for oil in Alaska will disrupt some wildlife, it is better than having to depend on foreign oil, which has the tendency to draw us into foreign conflicts that we would otherwise not be involved in. Let there be no doubt: the entity that carried out this attack is a known terrorist organization, whose attacks have a characteristic style—a style that is seen in this attack today.
Privatizing the water utilities in Detroit was an unprecedented move that has garnered a lot of criticism. Nonetheless, it is helping Detroit to recover from bankruptcy. Most pediatricians agree that the single most important factor in childhood obesity is eating sugary, processed foods, which have become all too common in our day and age.
Abraham Lincoln was probably our greatest president since he helped keep together a nation on the brink of splintering into two. No one with any sense would support Obamacare. Even if universal healthcare is expensive, it is still the just thing to do. While our country has made significant strides in overcoming explicit racist policies, the wide disparity of wealth, prestige and influence that characterize white and black Americans shows that we are still implicitly a racist country.
Recent studies have show that there is no direct link between vaccines and autism. Evaluative language can be contrasted with descriptive language. Whereas descriptive language simply describes a state of affairs, without passing judgment positive or negative on that state of affairs, evaluative language is used to pass some sort of judgment, positive or negative, on something. Contrast the following two statements: Bob is tall. Gotte Praveen marked it as to-read Zlan 24, Bobby Withrow added it Mar 29, Jayson Virissimo rated it liked it May 08, Jared rated it it was ok Apr 22, Priya marked it as to-read Mar 19, Tom Mielke marked it as to-read Oct 21, To see what your friends thought of this book, please sign up.
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We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. The purpose of this book is to present the Verilog language together with a wide variety of examples, so that the reader can gain a firm foundation in the design of the digital system using Verilog HDL.
The Verilog projects include the design module, the test bench module, and the outputs obtained from the simulator that illustrate the complete functional operation of the design. Where applicable, a detailed review of the theory of the topic is presented together with the logic design principles—including: state diagrams, Karnaugh maps, equations, and the logic diagram.
Numerous examples and homework problems are included throughout. The examples include logical operations, counters of different moduli, half adders, full adders, a carry lookahead adder, array multipliers, different types of Moore and Mealy machines, and arithmetic logic units ALUs.
Download Logic Design And Verification Using Systemverilog Revised books , SystemVerilog is a Hardware Description Language that enables designers to work at the higher levels of logic design abstractions that match the increased complexity of current day integrated circuit and field-programmable gate array FPGA designs.
The majority of the book assumes a basic background in logic design and software programming concepts. The book starts with a tutorial introduction on hardware description languages and simulation. It proceeds to the register-transfer design topics of combinational and finite state machine FSM design - these mirror the topics of introductory logic design courses. The book covers the design of FSM-datapath designs and their interfaces, including SystemVerilog interfaces.
Then it covers the more advanced topics of writing testbenches including using assertions and functional coverage. A comprehensive index provides easy access to the book's topics. The goal of the book is to introduce the broad spectrum of features in the language in a way that complements introductory and advanced logic design and verification courses, and then provides a basis for further learning. Solutions to problems at the end of chapters, and text copies of the SystemVerilog examples are available from the author as described in the Preface.
The author begins with a brief study of binary and hexadecimal number systems and then looks at the basics of Boolean algebra. The study of logic circuits is divided into two parts, combinational logic, which has no memory, and sequential logic, which does. Numerous examples highlight the principles being presented. The text ends with an introduction to digital logic design using Verilog, a hardware description language.
The chapter on Verilog can be studied along with the other chapters in the text. After the reader has completed combinational logic in Chapters 4 and 5, sections 9. Similarly, the rest of Chapter 9 could be studied after completing sequential logic in Chapters 6 and 7. This short lecture book will be of use to students at any level of electrical or computer engineering and for practicing engineers or scientists in any field looking for a practical and applied introduction to digital logic.
The author's "pragmatic" and applied style gives a unique and helpful "non-idealist, practical, opinionate" introduction to digital systems. The book also covers the logic synthesis, low power, multiple clock domain design concepts and design performance improvement techniques.
This volume can be used as a core or supplementary text in undergraduate courses on logic design and as a text for professional and vocational coursework. In addition, it will be a hands-on professional reference and a self-study aid for hobbyists. A Verilog equivalent of authors Roth and John's previous successful text using VHDL, this practical book presents Verilog constructs side-by-side with hardware, encouraging students to think in terms of desired hardware while writing synthesizable Verilog.
Following a review of the basic concepts of logic design, the authors introduce the basics of Verilog using simple combinational circuit examples, followed by models for simple sequential circuits. Subsequent chapters ask readers to tackle more and more complex designs.
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