LOGIC DUMMIES PDF
Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for the. Rest of Us!, The Dummies Way, Dummies Daily, The. The Certified Wireless Network Professional (CWNP) Program. Hacking Kevin is author of Hacking Hacking Wireless Networ. Logic For Dummies tracks an introductory logic course at the college level. Concrete, real- Logic For Dummies PDF Download Free | Logic For.
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mathematics. Also, in saying that logic is the science of reasoning, we do not mean The definition of 'argument' that is relevant to logic is given as follows. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you're a . INTRODUCTION: LOGIC IS RARE. Crime is common. Logic is rare. SHERLOCK HOLMES in The Adventure of the Copper Beeches. Logic Made Easy is a book.
Press Command-1 to open a new main window displaying the tracks area. Use the audio and MIDI editors for fine editing. You can manipulate the smallest details of your track in the editors. Press E to display the editors. Press T to open the tools menu.
What is Python?
Look in the Edit and Functions menus for commands that will help you achieve your editing needs. Logic Pro X: 3 Sound-Mixing Tips Mixing is the art of balancing tracks and manipulating sound to achieve a cohesive listening experience.
Fundamental rules of audio may apply to mixing, but the subjective tastes of you and your listeners ultimately decide whether a mix is a great experience. Your level meters should never reach 0 dBFS, the digital audio limit. Lowering the levels dB will improve the sound quality and your workflow. Mix at different volume levels. Mix at low volume levels to focus on the balance of the midrange frequencies roughly, between Hz and 8 kHz. One for All and All for One.
Syntactical Maneuvers and Semantic Considerations. Introducing Quantifier Logic. QL Translations.
Zegarelli M. Logic for Dummies
Table of Contents Chapter Proving Arguments with QL. Universal Instantiation UI Existential Generalization EG Existential Instantiation EI Universal Generalization UG Good Relations and Positive Identities.
Planting a Quantity of Trees. Computer Logic. Non-Classical Logic. Paradox and Axiomatic Systems.
Recognizing the problem with set theory Ten Quotes about Logic. Ten Big Names in Logic. Ten Tips for Passing a Logic Exam. For instance, consider these examples of times when you might use logic: And logic is one of the big reasons why humans have lasted so long on a planet filled with lots of other creatures that are bigger, faster, more numerous, and more ferocious.
This book is designed to show you how logic arises naturally in daily life. Once you see that, you can refine certain types of thinking down to their essence. Logic gives you the tools for working with what you already know the premises to get you to the next step the conclusion.
Logic is also great for helping you spot the flaws in arguments — unsoundness, hidden assumptions, or just plain unclear thinking. About This Book Logic has been around a long time — almost 2, years and counting!
So, with so many people past and present thinking and writing about logic, you may find it difficult to know where to begin. But, never fear, I wrote this book with you in mind. In this book, I give you an overview of logic in its many forms and provide you with a solid base of knowledge to build upon.
Logic is one of the few areas of study taught in two different college departments: The reason that logic can fit into two seemingly different categories is historical: Logic was founded by Aristotle and developed by philosophers for centuries. But, about years ago, mathematicians found that logic was an indispensable tool for grounding their work as it became more and more abstract.
One of the most important results of this overlap is formal logic, which takes ideas from philosophical logic and applies them in a mathematical framework.
Formal logic is usually taught in philosophy departments as a purely computational that is, mathematical pursuit. When writing this book, I tried to balance both of these aspects of logic.
Generally speaking, the book begins where logic began — with philosophy — and ends where it has been taken — in mathematics. Conventions Used in This Book To help you navigate through this book, we use the following conventions: No one has that kind of time these days.
How much of this book you read depends on how much logic you already know and how thoroughly you want to get into it. Do, however, feel free to skip anything marked with a Technical Stuff icon. This info, although interesting, is usually pretty techie and very skippable. You can also bypass any sidebars you see. Even though each part builds on the information from earlier parts, the book is still arranged in a modular way.
So, feel free to skip around as you like. For example, when I discuss a new topic that depends on more basic material, I refer you to the chapter where I introduced those basics. Part I: Overview of Logic What is logic? What does it mean to think logically, or for that matter illogically, and how can you tell? Part I answers these questions and more! The chapters in this part discuss the structure of a logical argument, explain what premises and conclusions are, and track the development of logic in its many forms, from the Greeks all the way to the Vulcans.
Part II: Formal logic, also called symbolic logic, uses its own set of symbols to take the place of sentences in a natural language such as English.
You discover sentential logic SL for short and the five logical operators that make up this form. I also show how to translate back and forth between English and SL.
Part III: In this part, you discover the ins and outs of proof writing. You also find out how to write conditional and indirect proofs, and how to attack proofs as efficiently as possible using a variety of proof strategies. You also begin looking at SL from a wider perspective, examining it on the levels of both syntax and semantics.
Introduction You find out how to tell a statement from a string of symbols that just looks like a statement. I also discuss how the logical operators in SL allow you to build sentence functions that have one or more input values and an output value.
From this perspective, you see how versatile SL is for expressing all possible sentence functions with a minimum of logical operators. Part IV: This part serves as your one-stop shopping introduction.
QL encompasses everything from SL, but extends it in several important ways. In this part, I show you how QL allows you to capture more intricacies of a statement in English by breaking it down into smaller parts than would be possible in SL. I also introduce the two quantification operators, which make it possible to express a wider variety of statements. Finally, I show you how to take what you already know about proofs and truth trees and put it to work in QL. Part V: Modern Developments in Logic The power and subtlety of logic becomes apparent as you examine the advances in this field over the last century.
In this part, you see how logic made the 19th century dream of the computer a reality. I discuss how variations of post-classical logic, rooted in seemingly illogical assumptions, can be consistent and useful for describing real-world events. I also show you how paradoxes fundamentally challenged logic at its very core. Paradoxes forced mathematicians to remove all ambiguities from logic by casting it in terms of axiom systems.
Ultimately, paradoxes inspired one mathematician to harness paradox itself as a way to prove that logic has its limitations. Just for fun, this part of the book includes a few top-ten lists on a variety of topics: I use this icon to point out the key ideas that you need to know. Make sure you understand the information in these paragraphs before reading on! This icon highlights helpful hints that show you the easy way to get things done. They show you common errors that you want to avoid.
This icon alerts you to interesting, but unnecessary, trivia that you can read or skip over as you like. Where to Go from Here If you have some background in logic and you already have a handle on the Part I stuff, feel free to jump forward where the action is. This chapter on logical paradoxes has some really cool stuff to take your thinking to warp speed.
Part I Overview of Logic S In this part. In this part, you get a firsthand look at what logic is all about. Chapter 1 gives an overview of how you whether you know it or not use logic all the time to turn the facts that you know into a better understanding of the world. Chapter 2 presents the history of logic, with a look at the many types of logic that have been invented over the centuries. Chapter 3 also focuses on key concepts such as premises and conclusions, and discusses how to test an argument for validity and soundness.
If you doubt this fact, just flip on the evening news. Or really listen to the guy sitting at the next barstool. Or, better yet, spend the weekend with your in-laws.
With so many people thinking and acting illogically, why should you be any different? Well, okay, being illogical on purpose is probably not the best idea. For one thing, how can it possibly be sensible to be illogical? In this chapter, I introduce you to the basics of logic and how it applies to your life. I tell you a few words and ideas that are key to logic.
And, I touch very briefly on the connections between logic and math. Getting a Logical Perspective Whether you know it or not, you already understand a lot about logic.
In fact, you already have a built-in logic detector. How many pancakes does it take to shingle a doghouse? In this section, I start with what you already understand about logic though you may not be aware of it , and build towards a foundation that will help you in your study of logic. Bridging the gap from here to there Most children are innately curious.
They always want to know why everything is the way it is. And for every because they receive, they have one more why. For example, consider these common kid questions: Why does the sun rise in the morning? Why do I have to go to school? Why does the car start when you turn the key? Why do people break the law when they know they could go to jail?
Getting from here to there — from ignorance to understanding — is one of the main reasons logic came into existence. Logic grew out of an innate human need to make sense of the world and, as much as possible, gain some control over it. Understanding cause and effect One way to understand the world is to notice the connection between cause and effect.
As you grow from a child to an adult, you begin to piece together how one event causes another.
Typically, these connections between cause and effect can be placed in an if-statement. For example, consider these if-statements: Chapter 1: If I practice on my own this summer, then in the fall the coach will pick me for the football team.
If I keep asking her out really nicely and with confidence, then eventually she will say yes. Understanding how if-statements work is an important aspect of logic. Breaking down if-statements Every if-statement is made up of the following two smaller statements called sub-statements: The antecedent, which follows the word if, and the consequent, which follows the word then. For example, consider this if-statement: In this statement, the antecedent is the sub-statement It is 5 p.
Stringing if-statements together In many cases, the consequent of one if-statement becomes the antecedent of another. When this happens, you get a string of consequences, which the Greeks called a sorites pronounced sore-it-tease. For example: In this case, you can link these if-statements together to form a new if-statement: Overview of Logic Thickening the plot With more life experience, you may find that the connections between cause and effect become more and more sophisticated: If I practice on my own this summer but not so hard that I blow my knees out, then in the fall the coach will pick me for the football team only if he has a position open, but if I do not practice, then the coach will not pick me.
Everything and more As you begin to understand the world, you begin to make more general statements about it. All horses are friendly. All boys are silly. Every teacher at that school is out to get me. Words like all and every allow you to categorize things into sets groups of objects and subsets groups within groups.
Some of my teachers are nice. There is at least one girl in school who likes me. No one in the chess club can beat me. There is no such thing as a Martian. Words like some, there is, and there exists show an overlapping of sets called an intersection.
A few logical words As you can see, certain words show up a lot as you begin to make logical connections. Some of these common words are: Figure out what we know to be true. Spend some time thinking about it. Find the best course of action. In logical terms, this three-step process involves building a logical argument. An argument contains a set of premises at the beginning and a conclusion at the end.
In many cases, the premises and the conclusion will be linked by a series of intermediate steps. Generating premises The premises are the facts of the matter: The statements that you know or strongly believe to be true.
In many situations, writing down a set of premises is a great first step to problem solving. Everyone is very excited about the project, but you make some phone calls and piece together your facts, or premises.
The entire project will take at least eight months to complete. So far, you only have a set of premises. In the next section, I show you how to combine the premises together. Bridging the gap with intermediate steps Sometimes an argument is just a set of premises followed by a conclusion. In many cases, however, an argument also includes intermediate steps that show how the premises lead incrementally to that conclusion. Using the school construction example from the previous section, you may want to spell things out like this: But, school begins in September.
The word therefore indicates a conclusion and is the beginning of the final step, which I discuss in the next section. Forming a conclusion The conclusion is the outcome of your argument. In some cases, an argument may not be valid.
If not, the argument is invalid. Understanding enthymemes The school construction example argument may seem valid, but you also may have a few doubts. For example, if another source of funding became available, the construction company may start earlier and perhaps finish by September. Thus, the argument has a hidden premise called an enthymeme pronounced en-thim-eem , as follows: There is no other source of funds for the project.
Logical arguments about real-world situations in contrast to mathematical or scientific arguments almost always have enthymemes. So, the clearer you become about the enthymemes hidden in an argument, the better chance you have of making sure your argument is valid.
Uncovering hidden premises in real-world arguments is more related to rhetoric, which is the study of how to make cogent and convincing arguments.
I touch upon both rhetoric and other details about the structure of logical arguments in Chapter 3. Making Logical Conclusions Simple with the Laws of Thought As a basis for understanding logic, philosopher Bertrand Russell set down three laws of thought.
These laws all have their basis in ideas dating back to Aristotle, who founded classical logic more than 2, years ago. See Chapter 2 for more on the history of logic.
All three laws are really basic and easy to understand. Truth Grows on Trees. Part III: Proofs, Syntax, and Semantics in SL. Chapter 9: What Have You Got to Prove?
Logic Pro X: The Beginner’s Guide
Chapter Equal Opportunities: Putting Equivalence Rules to Work. Big Assumptions with Conditional and Indirect Proofs. Putting It All Together: One for All and All for One. Syntactical Maneuvers and Semantic Considerations.
Part IV: Quantifier Logic QL. Expressing Quantity with Quality: Introducing Quantifier Logic. QL Translations. Proving Arguments with QL. Good Relations and Positive Identities. Planting a Quantity of Trees.
Part V: Modern Developments in Logic.What happens if you start with a different set of axioms? Wiley also publishes its books in a variety of electronic formats. Sporting Propositions: If not, the argument is invalid. Aristotle invents syllogistic logic Before Aristotle — BC , logical argument was applied intuitively where appropriate in math, science, and philosophy.
From this perspective, you see how versatile SL is for expressing all possible sentence functions with a minimum of logical operators. The word therefore indicates a conclusion and is the beginning of the final step, which I discuss in the next section. Formal logic, also called symbolic logic, uses its own set of symbols to take the place of sentences in a natural language such as English.