Tư Duy Lô-gic

Tư Duy Lô-gic

LOGICAL THINKING Logical thinking is a key to making sound decisions and solving complex problems. In this lesson, we will examine a few facets of logic in hope of helping you become a better thinker and problem-solver. Today, we will discuss some basic ideas about premises and conclusion, explore methods of logical arguments, analyze data, and use logic in solving puzzles. Human beings have ability of thinking, but they do not always reason correctly. The science of correct reasoning is called logic. An understanding of logic will help you correctly arrange supporting evidence that leads to a conclusion. 1. STATEMENTS The basic components of logic are its statements. Statements in logic must have a clear meaning, either true or false. Statements can not both true and fall at the same time. That means, they must have only one true value, only one false value. IN general, questions, commands, or vague sentences can not be used as statements in logic because they can not be judged to be true or false. Statement Non-statement Today is a holiday Do your homework! I did my homework This statement is true! Pigeons fly It smells like daisies 2. NEGATION OF STATEMENT That is changing a statement to one that has the opposite meaning. If a statement is true, then its negation is false. If a statement is false, then its negation is true. Statement Non-statement Today is a holiday Today is not a holiday I did my homework I did not do my homework Pigeons fly He is not here Be careful with words (“all, every, no, none, some”) when forming negation. Statement Negation All men are mortal Some men are not mortal Some women can swim No women can swim None of the flashlights worked Some of the flashlights worked We can summarize the above as follows: Statement Negation All / every Some … not Some … not All / every                   None / no Some Some None / no EX: Write the negation of the following statements: My car did not start Some of the cars did not start None of the cars start Every car starts Some of the car started 3. CONDIDTIONAL STATEMENTS  It is a statement formed by two individual statements joined by the words: “If … , then …”. In the conditional statement: “If A, then B”, A represents the If-clause, the hypothesis, or antecedent. B represents the Then-clause, the conclusion, or consequent. The same conditional statement can be written in different ways: If A, the B:      If you are a student, then you should study.             A implies B:   Being a student implies that you should study.             A à B:            Being a student à one should study.             All A are B :   All students should study. There are three basic types of conditional statements “A ...> B”:             Converse:                       B ....> A             Inverse :                    Not A ...> Not B             Contrapositive:       Not B ...> Not A These above statements lead to valid arguments. It can be shown that if a statement is true, then its contrapositive statement is also true; if a statement is false, then its contrapositive statement is also false. A conditional statement and its contrapositive are logically equivalent. However, if a statement is true, its converse or inverse may be either true or false. A conditional statement and its converse or inverse are not logically equivalent. EX:      If it is an IBM PC, then it is a computer. Let :    “it is an IBM PC = A”;             “it is a computer = B”             A ...> B :           Conditional statement             Converse:      B ...> A: If it is a computer, then it is an IBM PC (False) Inverse:           Not A ...> Not B: If it is not an IBM, then it is not a computer (False)             Contrapositive: If it is not a computer, then it is not an IBM PC. (True)             If x is an even number, then the last digit of x is 2.             Let:      A = x is an even number.                         B = the last digit of x is 2.                         A à B : the conditional statement. Converse: B ...> A : if the last digit of x is 2, then x is an even number.                                  (True) Inverse: not A ...> not B: if x is not an even number, then the last digit of                                           x is not 2. (True).             Contrapositive: not B ...> not A: If the last digit of x is not 2, then x is not                                                                    an even number. (True)                         4. DEFINITIONS: A definition states the properties of the term being defined, gives us a way of recognizing what is defined ,and provide a way of distinguishing what is being defined from other objects. A definition must: Name the term being defined. Use the words that have already defined or already understood. Be biconditional. The statement of the definition and its converse must both be true. Besides three necessary properties, a good definition should also: Place the term in the smallest or nearest group to which it belongs to. Use the minimum information needed to distinguish the object from other objects. EX: A social insect is a bee. (this definition is not biconditional. The statement is false because a social insect could be an ant.) A treasurer is in charge of finances of an organization. (This is not a good definition because the group to which the treasurer belongs to is not included. The treasurer is not a machine or a report.) Note the kind of statement, and the way of combining them: if a statement is true, its negation is false, and vice versa. if a conditional statement is true, then its contrapositive is also true. A definition must be biconditional. 5. INDUCTION Induction is a process of reasonging in which conclusions are based on experimentation or experience. When using induction, we make a conclusion about a situation after observing results, analyzing experiences, citing authorities, or presenting statistics, we predict future experience by extending patterns seen in present experiences. OBSERVED PATTERNS --------INDUCTION----------> CONCLUSIONS EX: Inductive arguments to persuade your friend to vacation in Hawaii. Here are list of premises: the weather is great in Hawaii. The beaches are fantastic. My friend has a condo, you can rent for only 150 USD a week. the airlines are having a special on fares to Hawaii this month. I went there last month and had a wonderful time. the people there were friendly and treated me kindly. there are lots of nice people vacationing there. You will have a great time and are bound to meet the special person that you are looking for. in a recent travel magazine, 95% of vacationers polled said that they enjoyed their vacation inHawaii. Anna Holiday, worldwide traveler and economist, in her book “Travel to Paradise”, states that a vacation in Hawaii is the best bet for your travel dollar. The above arguments show that vacationing in Hawaii makes good sense.  6. DEDUCTION Deduction is a process of reasoning in which conclusions are based on accepted premises. These premises are usually articles of faith, laws, rules, definitions, assumptions, and commonly accepted facts. The conclusions we reach are either explicitly or implicitly contained in the premises. ACCEPTED PREMISES -------DEDUCTION----> CONCLUSIONS 6.1. Hypothetical syllogism If A, B, and C represent statements, a hypothetical syllogism is constructed from the statements. The first two lines being the premises and the third line being the conclusion. Hypothetical syllogism can be written in three different ways: If A, then B A implies B A à B If B, then C B implies C B à C Therefore If A, then C Therefore A implies C Therefore A à C The argument of this type of reasoning is correct even when one or both the premises are false. Logic deals with the relationship between premises and conclusion, not the truth of premises. 6.2. Affirming the antecedent If A and B represent statements. An argument that affirms the antecedent has the following form.             Major premise: A à B             Minor premise: A             Conclusion: > B    (> = therefore) The major premise is a conditional statement. The minor premise states that the hypothesis of the major premise is true or has occurred. This is called affirming the antecedent. EX:             If I study six hours, I will pass the exam.             I studied for six hours.             Therefore, I wil pass the exam. A classical argument:             All men are mortal.             Socrates is a man.             Therefore, Socrates is mortal. Or the about argument can be written like this:             If one is a man, then, one is mortal.             Socrates is a man.             Therefore, Socrates is mortal. 6.3. Denying the consequent             Major premise:        A à B             Minor premise:        Not B             Conclusion:             Therefore, not A EX:      If John is at the beach, then he wears sun screen on his nose.             John does not have sun screen on his nose.             Therefore, John is not at the beach. Nguồn: sites.google.com/site/dangquangdiem