Introduction to Logic Course description A study of the most basic forms of reasoning and their linguistic expressions, this course provides an introduction to the traditional theory of syllogism, contemporary symbolic logic, the nature of scientific reasoning, and the relationship between logic and language.
Logic is the study of formal and informal reasoning. Originally a branch of philosophy, logic has also become a mathematical discipline, a tool of modern linguistics, the core of computer science and an object of study for psychologists and cognitive scientists of every description.
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AnswerWhy should one take a college course on logic?
The courses in logic at Harvard cover all of the major areas of mathematical logic—proof theory, recursion theory, model theory, and set theory—and, in addition, there are courses in closely related areas, such as the philosophy and foundations of mathematics, and theoretical issues in the theory of computation.
What do you learn in a logic class?
Introduction to Logic Course description A study of the most basic forms of reasoning and their linguistic expressions, this course provides an introduction to the traditional theory of syllogism, contemporary symbolic logic, the nature of scientific reasoning, and the relationship between logic and language. Learn More Instructor Eli Hirsch
What are examples of college courses?
This course is an introduction to Logic from a computational perspective. It shows how to encode information in the form of logical sentences; it shows how to reason with information in this form; and it provides an overview of logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.
What are the basic courses of college?
An Online Course on Symbolic Logic Appropriate for secondary school students, college undergraduates, and graduate students. To date, over 650,000 people have enrolled in various offerings of this course. Learners Click here to take the course. Teachers Click here to get teaching materials for the course. Advocates
What is logic course?
Course description A study of the most basic forms of reasoning and their linguistic expressions, this course provides an introduction to the traditional theory of syllogism, contemporary symbolic logic, the nature of scientific reasoning, and the relationship between logic and language.
Should I take a logic class in college?
Logic courses will help you adapt to strict formal reasoning, a key skill on the LSAT. Many students have a hard time adjusting from “common sense” to LSAT formal logic. A logic course can give you an extra semester to learn this new form of thinking. You'll learn some concepts you'll need on the LSAT.Feb 22, 2011
What do you learn in logic class?
Mastery of a subject requires the ability to analyze its concepts, structure, and methods. Logic teaches you to do this by focusing on concepts, judgments, and arguments. The central concepts in any field are given by terms that have definitions.
Is logic a math class?
The courses in logic at Harvard cover all of the major areas of mathematical logic—proof theory, recursion theory, model theory, and set theory—and, in addition, there are courses in closely related areas, such as the philosophy and foundations of mathematics, and theoretical issues in the theory of computation.
Is logic class easy?
Treat Logic Class As A Class If you are already afraid of the subject matter, avoiding it, will only make it harder. Time and patience are required for any course, and your logic course will be no different, even if you're taking it as the "easy" alternative to a math course.Dec 27, 2018
Is logic a college major?
Coursework. Logic & Computation is a Bachelor of Science degree. The curriculum of the major is designed to be flexible and tailored to the individual student's interests. There are three pre-requisite courses that students will take to prepare them in computer science, mathematics and statistics.
Why studying logic is important?
Studying Logic Develops Critical Thinking Skills Finally, it's important to study logic to become an effective communicator. After all, logic is also the backbone necessary for crafting compelling arguments in speech and writing that point others toward truth.Feb 3, 2022
What are the disadvantages of logic?
Limitations of Logic ModelsA logic model only represents reality; it is not reality. Programs are not linear. ... A logic model focuses on expected outcomes. ... A logic model faces the challenge of causal attribution. ... A logic model doesn't address the questions: "Are we doing the right thing?" "Should we do this program?"
What are the reasons for studying logic?
2. Knowing Whether an Argument Is Valid or Invalid Is a Valuable SkillKnowing Whether an Argument Is Valid or Invalid Is a Valuable Skill.Good Logic Is an Effective Tool of Persuasion.Studying Logic Helps You to Spot Fallacies.Logic Is a Foundational Discipline.Clear Thinking Makes One a Better Citizen.
What subject does logic fall under?
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science.
What are the 2 types of logic?
The two main types of reasoning involved in the discipline of Logic are deductive reasoning and inductive reasoning. Deductive reasoning is an inferential process that supports a conclusion with certainty.
Is logic the foundation of math?
Logic is usually said to be a foundation of mathematics because it makes mathematical reasoning formal.Jul 13, 2016
What is the negation of R?
Given a statement R, the statement ∼ R is called the negation of R. If R is a complex statement, then it is often the case that its negation ∼ R can be written in a simpler or more useful form. The process of finding this form is called negating R. In proving theorems it is often necessary to negate certain statements. We now investigate how to do this.
What is a statement in logic?
The study of logic begins with statements. A statement is a sentence or a mathematical expression that is either definitely true or definitely false. You can think of statements as pieces of information that are either correct or incorrect. Thus statements are pieces of information that we might apply logic to in order to produce other pieces of information (which are also statements).
Why is logic important?
There are three very significant reasons. First, the truth tables we studied tell us the exact meanings of the words such as “and,” “or,” “not,” and so on. For instance, whenever we use or read the “If…, then” construction in a mathematical context, logic tells us exactly what is meant. Second, the rules of inference provide a system in which we can produce new information (statements) from known information. Finally, logical rules such as DeMorgan’s laws help us correctly change certain statements into (potentially more useful) statements with the same meaning. Thus logic helps us understand the meanings of statements and it also produces new meaningful statements.
What is the systematic way of thinking that allows us to deduce new information from old information and to parse the
Logic . Logic is a systematic way of thinking that allows us to deduce new information from old information and to parse the meanings of sentences. You use logic informally in everyday life and certainly also in doing mathematics.
Why is logic important in mathematics?
Since a major objective in mathematics is to deduce new information , logic must play a fundamental role. This chapter is intended to give you a sufficient mastery of logic. It is important to realize that logic is a process of deducing information correctly, not just deducing correct information.
Why is it important to distinguish between correct information and correct logic?
This distinction between correct logic and correct information is significant because it is often important to follow the consequences of an incorrect assumption. Ideally, we want both our logic and our information to be correct, but the point is that they are different things.
Is S2 odd or even?
S2 : The number 1 is even or the number 3 is odd. S3 : The number 2 is even or the number 4 is odd. S4 : The number 3 is even or the number 2 is odd. In mathematics, the assertion “ P or Q ” is always understood to mean that one or both of P and Q is true. Thus statements S1, S2, S3 are all true, while S4 is false.
PredictionX: John Snow and the Cholera Epidemic of 1854
An in-depth look at the 1854 London cholera epidemic in Soho and its importance for the field of epidemiology.
PredictionX: Omens, Oracles & Prophecies
An overview of divination systems, ranging from ancient Chinese bone burning to modern astrology.
The Health Effects of Climate Change
Learn how global warming impacts human health, and the ways we can diminish those impacts.
How big is Stanford University?
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto, California, United States.
What is a logic course?
This course is an introduction to Logic from a computational perspective. It shows how to encode information in the form of logical sentences; it shows how to reason with information in this form; and it provides an overview of logic technology and its applications - in ma thematics, science, engineering, business, law, and so forth .
Can you see your course materials in audit mode?
If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option: The course may not offer an audit option.
Can you see lectures in audit mode?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit.
What is the opposite of deductive reasoning?
Another type of logical reasoning is inductive. Inductive reasoning uses specific data to form a larger, generalized conclusion. It is considered the opposite of deductive reasoning. For example: Yesterday, you left for work at 7:15 a.m. and arrived at work on time.
What is formal logic?
Formal logic deals with deductive reasoning and the validity of the inferences produced. For an argument to work, the conclusion must logically follow the premises and the premises must be true. For example:
How does informal logic help in writing?
In writing, informal logic can assist with the formulation of sound arguments. Like an outline, using inductive and deductive reasoning models can help keep writing organized and on point. Once this reasoning is understood, it is fun to apply it to everyday occurrences.
What is the type of logical reasoning?
One type of logical reasoning is deductive . Deductive reasoning uses information from a large set and applies that information to any member of that set. The major premise makes a statement concerning members of a profession. The minor premise identifies a member of that profession.
What is logic in science?
Logic is a tool to develop reasonable conclusions based on a given set of data. Logic is free of emotion and deals very specifically with information in its purest form. There are many subsets in the study of logic including informal logic, formal logic, symbolic logic, and mathematical logic. We will discuss each type of logic ...
What is proof theory?
Proof theory is, quite logically, the study of formal proofs. Sets of propositions can be used to conclude new relationships. Set theory studies 'sets,' which are collections of objects. Model theory studies these sets and other mathematical structures. Recursion theory deals with the definability of sets of numbers.
What is the major premise of the premise?
The major premise makes a statement concerning members of a profession. The minor premise identifies a member of that profession. The conclusion declares that since Lauren is a member of a profession, then she must have the characteristics attributed to the profession as a whole.
What are the three types of deductive reasoning?
Our study of deductive reasoning will consist in the development of three different logical systems: categorical logic, propositional logic, and predicate logic . Categorical logic (a.k.a. syllogistic logic) — which formed the basis of logic for over two thousand years — is the study of arguments whose constituent sentences express certain relations between classes (or categories) of things. Propositional logic (a.k.a. Boolean logic) is the study of arguments that depend on the a number of important sentence-connecting expressions in ordinary language like and, or , and not — expressions whose logic also lies at the foundation of modern computer systems. Predicate logic (a.k.a. first-order logic) extends propositional logic to arguments that depend on the linguistic phenomena of predication (e.g., “Socrates is a philosopher”) and quantification (e.g., “ All prime numbers except 2 are odd”). Predicate logic arose in the 19th century originally to aid in the clarification of mathematical arguments but has since extended its reach considerably into the fields of (notably) philosophy, linguistics, and artificial intelligence. To study these various logical systems, we develop in each case an appropriate formal language — a rigorously defined symbolic system — for representing a relevant class of natural language sentences. We then introduce a variety of mathematical methods for evaluating arguments that are formalized in the relevant formal language, notably, Venn diagrams (for categorical logic), truth tables (for propositional logic), and formal deductive systems (for both propositional and predicate logic).
How to do formal logic?
Learning Outcomes. At the end of the course, students will be able to: 1 Represent information in symbolic forms, notably the formal languages of categorical, propositional, and predicate logic. 2 Interpret and evaluate formalized arguments by means of formal semantic and deductive models, notably, Venn diagrams, truth tables, and formal deductive systems. 3 Calculate complex probabilities on the basis of the eight mathematical axioms of the probability calculus and Bayes’ Theorem. 4 Identify and evaluate assumptions in both inductive and deductive reasoning as they appear in our daily experience. 5 Express an understanding of the fundamental concepts of deductive (categorical, propositional, and predicate) logic and probability theory including: formal language, Boolean operator, truth table, quantification, class , argument, validity, proof, probability , and Bayes’ Theorem .
When did predicate logic start?
Predicate logic arose in the 19th century originally to aid in the clarification of mathematical arguments but has since extended its reach considerably into the fields of (notably) philosophy, linguistics, and artificial intelligence.
What is the medical confirmation note for Fall 2020?
While Student Rule 7, Section 7.3.2.1, indicates a medical confirmation note from the student’s medical provider is preferred, for Fall 2020 only, students may use the Explanatory Statement for Absence from Class form in lieu of a medical confirmation.
How long does it take to make up a missed exam?
NB: Missed exams/quizzes must be made up within one week of the scheduled exam/quiz unless circumstances do not permit it. In such cases, your instructor must be notified as soon as circumstances permit to discuss your situation.
What is a reasonable belief in a discrimination or harassment incident?
The incident is reasonably believed to be discrimination or harassment. The incident is alleged to have been committed by or against a person who, at the time of the incident, was (1) a student enrolled at the University or (2) an employee of the University.
When can students be excused from class?
Students will be excused from attending class on the day of a graded activity or when attendance contributes to a student’s grade, for the reasons stated in Student Rule 7, or other reason deemed appropriate by the instructor.
Treat Logic Class As A Class
If you want to pass your logic class, you'll still need to do the basics: attend class, do your reading, and complete all the homework. If you are already afraid of the subject matter, avoiding it, will only make it harder.
Approach Material As It Is
Remember that logic is supposed to make sense. There are no hidden tricks, and your professor isn't trying to teach you some kind of mysterious language. Once you have figured out how one axiom, law, or derivation works, it will never do anything differently.
Follow The Rules of Logic
Don't over think the problems. Symbolic logic works by following very simple rules. They are also the only rules that can be used. If you know P and P → Q, you may write down Q. If you know ~ Q and P → Q, you may write down ~ P. Think like a robot if that helps. If you don't know a rule for how to do something, try another rule.
Practice and Get Help
Do extra practice exercises. Even if it feels like torture, getting good at logic is like getting good at a game. You have to practice in order to know when each rule is appropriate to use.
What is the mental activity of reasoning?
Reasoning is a special mental activity called inferring, what can also be called making (or performing) inferences. The following is a useful and simple definition of the word ‘infer’.
Is logic a science?
Logic may be defined as the science of reasoning. However, this is not to suggest that logic is an empirical (i.e., experimental or observational) science like physics, biology, or psychology. Rather, logic is a non-empirical science like mathematics. Also, in saying that logic is the science of reasoning, we do not mean that it is concerned with the actual mental (or physical) process employed by a thinking entity when it is reasoning. The investigation of the actual reasoning proc-ess falls more appropriately within the province of psychology, neurophysiology, or cybernetics.
Statements
- The study of logic begins with statements. A statementis a sentence or a mathematical expression that is either definitely true or definitely false. You can think of statements as pieces of information that are either correct or incorrect. Thus statements are pieces of information that we might apply logic to in order to produce other pieces of information (which are also statemen…
And, Or, Not
- The word “and” can be used to combine two statements to form a new statement. Consider for example the following sentence. R1 : The number 2 is even andthe number 3 is odd. We recognize this as a true statement, based on our common-sense understanding of the meaning of the word “and.” Notice that R1is made up of two simpler statements: P : The number 2 is even. Q: The nu…
Conditional Statements
- There is yet another way to combine two statements. Suppose we have in mind a specific integer a. Consider the following statement about a. R: If the integer a is a multiple of 6, then a is divisible by 2. We immediately spot this as a true statement based on our knowledge of integers and the meanings of the words “if” and “then.” If integer a is a multiple of 6, then a is even, so therefore a …
Biconditional Statements
- It is important to understand that P ⇒ Q is not the same as Q ⇒ P. To see why, suppose that a is some integer and consider the statements (a is a multiple of 6) ⇒ (a is divisible by 2), (a is divisible by 2) ⇒ (a is a multiple of 6). The first statement asserts that if a is a multiple of 6 then a is divisible by 2. This is clearly true, for any multiple of 6 is even and therefore divisible by 2. The …
Truth Tables For Statements
- You should now know the truth tables for ∧, ∨, ∼, ⇒ and ⇔. They should be internalizedas well as memorized. You must understand the symbols thoroughly, for we now combine them to form more complex statements. For example, suppose we want to convey that one or the other of P and Qis true but they are not both true. No single symbol expresses this, but we could combine t…
Logical Equivalence
- In contemplating the truth table for P ⇔ Q, you probably noticed that P ⇔ Q is true exactly when P and Q are both true or both false. In other words, P ⇔ Q is true precisely when at least one of the statements P ∧ Q or ∼P ∧ ∼Q is true. This may tempt us to say that P ⇔ Q means the same thing as (P ∧ Q)∨(∼P ∧ ∼Q). To see if this is really so, we can write truth tables for P ⇔ Q and (P ∧ Q) …
Negating Statements
- Given a statement R, the statement ∼R is called the negation of R. If R is a complex statement, then it is often the case that its negation ∼R can be written in a simpler or more useful form. The process of finding this form is called negating R. In proving theorems it is often necessary to negate certain statements. We now investigate how to do this. We have already examined par…
Logical Inference
- Suppose we know that a statement of form P ⇒ Q is true. This tells us that whenever P is true, Q will also be true. By itself, P ⇒ Q being true does not tell us that either P or Q is true (they could both be false, or P could be false and Q true). However if in addition we happen to know that P is true then it must be that Q is true. This is called a logical inference: Given two true statements w…
An Important Note
- It is important to be aware of the reasons that we study logic. There are three very significant reasons. First, the truth tables we studied tell us the exact meanings of the words such as “and,” “or,” “not,” and so on. For instance, whenever we use or read the “If…, then” construction in a mathematical context, logic tells us exactly what is meant. Second, the rules of inference provid…
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