1.1 What is Logic?
Reasoning is the process of moving from one thought to another. All of us engage in reasoning, but not all reasoning is good or “sound” reasoning. Logic is the study of the general principles of sound reasoning.
Learn what we mean by “reasons” and “conclusions”, observe that good reasoning neither concludes too much nor too little, and think about how studying logic can help us avoid “fallacies” – common mistakes in reasoning.
Table of Contents
- 1.1 What is Logic?
1.1.1 Reasoning
If you saw paw prints in the dirt, what would you conclude?
Reasoning is the process of moving from one thought to another.
You are a thinking thing. “Thinking” is an ongoing process in your mind that almost never stops. You are constantly forming new thoughts based on what you perceive. When you hear a car horn, for instance, you might think thoughts like, “that was a loud noise”, or “a car just honked its horn”, or “somebody is upset”, or “somebody is a rude or dangerous driver”. If you see fresh paw prints in the dirt, you might form thoughts like “a cat made those prints”, or “there is a stray cat around here”, or “the county needs to take care of the stray cat problem around here”, or even “county officials should be voted out of office over the cat issue.” Most people don’t voice all or even most of their thoughts, though some voice more than others, but we are all constantly moving from one thought to another.
When reasoning from one thought to another, the first thought is called a reason and the thought it leads to is called a conclusion. A reason is the basis which is supposed to justify a conclusion. When we voice our thoughts out loud, our reasoning can be corrected: your neighbor might point out that they are dog prints, not cat prints, and you’ve been reasoning from faulty assumptions. When somebody thinks, “the clock says it is 11:00am”, and because of this they conclude “it is time to get out of bed”, the first thought is serving as the reason for their second thought. Similarly, when someone thinks that there is a risk of car theft, and because of this they conclude, “I should lock my car doors”, the reason “there is a risk of car theft” is what leads to their conclusion, “I should lock my car doors.” Understanding someone else’s thinking means understanding not only the conclusions they reach, but the reasons why they reached them.
Words like therefore, so, accordingly, and thus all typically come after a reason and before a conclusion:
“I am hungry, so I will eat.”
Although reasons are not always explicitly marked, words like since, because, for, and given that all typically come after a conclusion and before a reason.
“I will eat, given that I am hungry.”
Notice that in both sentences, “I will eat” is the conclusion, and “I am hungry” is the reason, even though they appear in a different order in each sentence. So, don’t rely on the order of the sentences to decide which is the reason and which is the conclusion.
Not every cause of someone’s conclusion is a reason for that conclusion. For example, someone who is very sleepy may draw certain conclusions because they are not thinking clearly, which they would not draw while they were awake: they might hear a noise at the door, and conclude “a burglar is trying to break in!”, for example. It is the noise at the door, not being sleepy, which is supposed to justify their conclusion. They would say, “I hear a noise at the door, so there must be a burglar”, not “I am sleepy, so there must be a burglar”.
Many things influence our psychology and what we believe, and some of them we are not entirely aware of. Asking for the reasons for someone’s belief isn’t asking for what might have psychologically influenced them, but rather asking how they might justify the belief or explain why it makes sense to hold when talking to other people.
1.1.2 Sound Reasoning
Reasoning is “sound” in the sense that a traveler completes a journey “safe and sound”.
Good and Bad Reasoning
Not all reasoning is good reasoning. Some reasoning makes “leaps” or “jumps”. Suppose that somebody sees one roach crawling across the floor, and they conclude from this, “my home is infested with roaches”. Similarly, suppose that somebody sees that one stock price has gone down today, and they conclude from this “I should sell all my stocks”. Those are cases of bad reasoning, because what they conclude doesn’t follow from their reasons.
On the other hand, people often fail to engage in reasoning when they should. For instance, somebody who is constantly turned down on requests for a date may fail to reason to the conclusion, “this person does not want to date me”, even though they have a good reason to reach that conclusion. Similarly, somebody might fail to reason from their employer’s negative comments at work to the conclusion that they are likely to need to find a new job soon.
Good reasoning seeks the middle ground between the extreme of concluding too much and the extreme of concluding too little.
Sound Reasoning
Good reasoning is called sound reasoning. We call it “sound” in the sense of being solid and healthy, just like a traveler who completes their journey “safe and sound”.
There is no single test to determine in every case when reasoning is sound and when it is not. Many “reasonable” people nonetheless jump to unreasonable conclusions, or fail to draw reasonable conclusions, when dealing with topics that are personally important to them. Being intelligent or highly educated does not guarantee that someone won’t make mistakes in reasoning; simple laziness or carelessness in thinking can influence anyone to reason badly. People are often blind to their own bad reasoning, because an idea makes perfect sense in their own head, or because they’re part of a group of people who make the same mistake, affirm the same error, and amplify the same bad information throughout a group. Two very common reasons that people make mistakes in reasoning come from our human tendency to make sweeping generalizations from limited evidence, and our tendency to think that we know the minds of other people better than we really do.
Because it is so easy to make mistakes, we need general principles of sound reasoning that can help guide our thinking and help us avoid repeating common errors.
Logic
Logic is the study of the general principles of sound reasoning. These principles can help us avoid common mistakes and know when our conclusions stretch too far or conclude too much.
Of course, learning to reason well is not simply a matter of learning a list of rules. Much like learning to play a musical instrument or to play a sport, reasoning well also takes a lot of practice and exercise, and it is best learned by following examples from others who do it well, not merely studying sheet music or a playbook. At the same time, knowing the principles of logic is very helpful for becoming an excellent reasoner and clear thinker.
Following the rules of logic doesn’t guarantee that you will always be right. Two people can both follow the rules of logic and yet still disagree with each other. Logic can’t solve the problem of making sure that you start out with good information. But logic can help you recognize what follows from that information, and what doesn’t follow from it. Following the rules can guarantee that your conclusions will be at least as likely to be true as your reasons were.
1.1.3 How do We Know Logic?
“Aristotle”, by Paolo Veronese
Logic as the Most General Field of Study
Logic is the most general field of study, applicable to everything that is and that could be. More specialized fields of study all rely on the tools of logic, from mathematics to marketing, physics to finance, or biology to sociology. The world, at least insofar as we are capable of studying it, can only be understood within the boundaries imposed by the laws of logic. Because of this, studying logic isn’t something recommended only for philosophy majors, but something which students of all majors can benefit from. The ability to reason carefully and to develop and defend an argument is at the center of logic, and this is the same skill which a lawyer employs in a courtroom, a doctor relies on when weighing a diagnoses, an engineer appeals to when advocating for a specific solution to a problem, a businessperson utilizes when making a sales pitch, or a job applicant uses when composing a cover letter. The principles of sound reasoning are one of the most broadly applicable things one can study.
Logic as an Innate Capacity
Logic is an innate mental capacity which needs to be trained. Some grasp on logic is, arguably, innate in humans and perhaps some other highly intelligent mammals. We all grasp intuitively, for instance, that if something is true, then it isn’t false, or that if there are only two routes to get where we’re going, and one of the routes is blocked, then we have to take the other route. Because of this, studying logic often feels more like stating explicitly things that one already knows rather than learning something new. At the same time, our intuitive grasp of basic logic is not enough to prevent us from regularly falling into logical errors when problems become more complicated. By default, someone who hasn’t been trained in logic is inclined to make certain common mistakes, which we call fallacies. What seems like “common sense” is sometimes wrong, and without training most people are unable to see their own errors. Training in logic consists in making more explicit and specific the rules which govern sound reasoning, and practicing applying them to highly abstract situations. Much like exercising a muscle encourages the muscle to grow, exercising abstract thinking helps you grow in your ability to think abstractly and to handle more complex and more challenging problems.
A Brief History of Logic
Because logic is an innate capacity, much like mathematical ability, different civilizations have developed systems of logic spontaneously and independently from one another. The Nyāya school in ancient India developed a system of logic, for instance, as did the Mohist school in ancient China. Much like systems of mathematics can differ in terms of how they represent mathematical relationships, while managing to represent the same underlying truths, “systems” of logic can differ in terms of the specific rules they use, but the rules all represent the same underlying system of logical truths. The system of logic we will study in this class is the descendant of two systems of logic developed in ancient Greece.
The first system, called propositional logic, was developed by the Stoic school of philosophers, including Euclid of Megara (435 – 365 BCE) and Chrysippus (279-206 BCE). Propositional logic studies relationships between claims or propositions, their truth or falsity, and the relationships between propositions produced by logical connectives “or” (disjunction), “and” (conjunction) and “if-then” (conditionals). We use propositional logic everyday. For instance, if we know that:
Mary is either driving home or staying late at work
and we know that:
Mary is not driving home
then we know that:
Mary is staying late at work
The second system, sometimes known as categorical logic or syllogistic logic, was most notably developed by Aristotle (384-322 BCE) and is sometimes called “Aristotelian Logic”. Syllogistic logic studies relationships between categories of things, and what we can conclude when we know how many members of one category (all / every, some, or none) are members of another category. Categorical logic was studied and developed in the Middle ages by Islamic philosophers like Avicenna, Al-Farabi, and Averroes, and by the Catholic Scholastic philosophers such as Boethius, Peter Abelard, and Francisco Suárez. Categorical logic continues to be used today. For instance, if we know that:
All of our cows are in the barn
and we know that:
Some of our cows are sick
then we know that:
Some animals in the barn are sick
We will study both propositional logic and categorical logic in this class. Since both systems are needed for making valid arguments, we will move back and forth between them regularly, and we will study how to determine which set of rules to use when trying to construct an argument for your view or to show if a particular argument is valid.
Logic has developed over time. Comparatively recently, with the publication of Bertrand Russell and Alfred North Whitehead’s Principia Mathematica (1913), a single system was found to unite both propositional logic and categorical logic. This system of logic lies at the foundation of modern mathematics and computer science. The programming on which your computer or cell phone runs, for instance, is developed from this system of logic. Although we will offer some hints in this class as to why the two systems are closely related, the unity of the two systems is typically studied in upper-division courses in logic, so we will study them separately in this class.
1.1.4 Why Study Logic?
Logic is the basis of modern computing.
Why would someone want to study logic? There are many reasons why everyone ought to take a course in logic when they begin in College, regardless of their major. Three specific applications of logic are identified here: making more intelligent decisions, learning to think like a computer, and working within systems of rules in a business, management, or legal setting.
Making More Intelligent Decisions
Regardless of major, every student has to make decisions. These include personal decisions, like whether to enroll in a particular class or whether to sign a lease on an apartment with somebody else. They also include decisions within their other classes about how to interpret data or whether they have enough evidence to support their claims. Studying logic, while often extremely abstract, trains the mind to make more reasonable decisions in practical cases. Someone who has studied logic can better understand the terms of a lease agreement, for example, or can know when to appeal a health insurance claim. They can better avoid scam artists and sales pitches. Academically, they can recognize when a classmate, or a text studied in class, is drawing a conclusion that isn’t supported by the evidence. They know when they’ve done enough research, and when more research is needed. They can write more persuasively. When a student studies logic early on in college, they’re likely to be more effective and efficient in their other classes, because they know when a conclusion follows, and when it doesn’t. Both in everyday life and in college, studying logic makes someone smarter.
Thinking like a Computer
Thinking like a computer is another skill which studying logic can offer, which has great value in our day and age. Because computer programming is based on logic, understanding how logic works will help you understand how computers process information, and getting practice in seeing how computers process information can help you understand how logic works. As more rote and mundane human tasks are increasingly handed over to computers, it is likely that more humans will be needed in the future who are trained to “think like a computer”, who can serve as human-to-computer translators for other people.
As you have probably experienced, simple computer programs do not process information like people do. When people try to understand one another, we engage in a process of “mind-reading”, trying to figure out what the other person wants us to believe or do on the basis of what they said, or did, or left unsaid or undone. One roommate might subtly communicate to the other, for instance, “I’ve done my fair share of cleaning up, and it’s your turn to do some of it”, by leaving out some unwashed dishes. Simple computer programs do not understand this subtle communication: they require explicit instructions and often need specific words.
You don’t have to study computer programming to begin to understand how computers think. Because logic is the basis of computer programming, you can start to learn to think like a computer by studying logic.
The exercises in this class will often be graded by a computer. As you do the exercises in this class, you will need to try to think like a computer. You will need to use the exact wording and spelling the computer is looking for, or else you will get the question wrong. If you add a word, or subtract a word, or try to give a non-literal answer, you will get the question wrong. This is part of training in logic!
(Note: because punctuation is so easy to mess up, we will avoid using punctuation in “fill in the blank” exercises in this class.)
Logic in a Business, Management, or Legal Setting
Lastly, logic is especially important for those who deal with systems of rules, contracts, or laws. Most businesses have to sign agreements or contracts, adopt internal policies and rules, and must comply with governmental laws and regulations. It is important to be able to correctly interpret and apply rules or agreements in a way that other people will recognize as predictable and fair, rather than arbitrary or biased. Knowing how to do this requires a solid understanding of logic. Rules of logic state clearly what does follow and what does not follow from a specific statement. For example, suppose that one roommate agrees to “take out the trash every weekday”. The agreement does not say that the roommate will not also take out the trash on weekends, or that the roommate will take out the trash only once each weekday, or that the roommate will take out the trash between the reasonable-seeming hours of 6am and 10pm. Those things do not follow from the agreement. On the other hand, it does follow from the agreement that the roommate will take the trash out at least once on Tuesday, since Tuesday is a weekday. Much more serious issues can hinge on the interpretation of agreements or laws, and so logic is an important thing to study for those who want to work in government or business someday. This is why logic is essential preparation for the LSAT and GMAT exams, which determine admission to law school (JD) programs and business school (MBA) programs, since both tests have extensive critical reasoning sections.
Submodule 1.1 Quiz
Key Sources
Watson, Jeffrey (2019). Introduction to Logic. Licensed under: (CC BY-SA).
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