LOGIC What is logic What is the difference

LOGIC What is logic? What is the difference between logic and reason? What is ‘deductive logic’? What distinguishes ‘truth’ from ‘validity’? What is a syllogism? Why would someone go to all of the trouble to come up with such a complicated system? (Especially if it does not always result in the truth). What is ‘inductive logic’? Is intuition a form of logic?

WHAT IS LOGIC? �Logic is a branch of philosophy that explores the way we reason – how do we come to ‘logical’ conclusions about our surroundings and life? (rhetorical) �It attempts to: ◦ Define ‘correct’ reasoning ◦ Distinguish good arguments from bad ones ◦ Pick out flaws and weaknesses in reasoning ◦ Create rules which enable us to test whether our reasoning is coherent and

LOGIC VS. REASON �Reason is the ability to figure things out in our world. �Logic consists of formal systems developed by philosophers to determine whether or not our reasoning has a solid foundation and is ‘true. ’ �Reason is the ability �Logic systematically tests the ability

DEDUCTIVE LOGIC �Deductive logic is concerned primarily (if not solely) with propositional knowledge – “knowledge that” (as opposed to “knowledge how”). �It is concerned with rules for determining when an argument is valid – it follows a FORMAL set of rules – hence when it does so, it is called FORMAL LOGIC. �It produces knowledge based on reason rather than experience.

LAWS OF LOGIC Let’s take a moment to revisit the three laws of logic that you read about last night. 1. The law of identity: A thing is what it is. For example, a book is a book and a leaf is a leaf. 2. The law of non-contradiction: A statement cannot be both true and false at the same time. For example, if it is true that I always tell the truth, it cannot be true that I am a liar, and if I am dead then I cannot be alive. �

LAWS OF LOGIC The law of the excluded middle: A statement is either true or false (that is, there is no middle ground between true and false). So, for example, it is either true or false that I am alive, and it is either true or false that I am holding a book. � This is not, as you read, universally accepted, and alternatives have been proposed. 3.

LAWS OF LOGIC 3 a. There are many other possibilities other than true and false. If true corresponds to the number ‘one’ and false to ‘zero’ then these other possibilities refer to numbers between zero and one. (Alternately, false corresponds to ‘zero’ and true corresponds to ‘ten’. )

LAWS OF LOGIC 3 b. In addition to ‘true’ and ‘false’ there is one other possibility which is neither true nor false. �What do these “alternate” ideas mean? �Do these alternate possibilities lead to confusion, or do they simply acknowledge the fact that the world is not black and white? �With which one do you most agree:

TRUTH VS. VALIDITY • • • Truth and validity are NOT interchangeable in the world of logic. Truth is a property of statements. Validity is a property of arguments. An argument is valid if the conclusion follows logically from the premises. An argument is invalid if the conclusion does not follow logically from the premises. The validity of an argument is independent of the truth or falsity of the premises it contains.

FORMAL LOGIC �Formal (part of deductive logic) logic is based on what are called syllogisms which consist of the following items: 1. Two premises and one conclusion 2. Three terms, each of which occurs twice 3. Quantifiers, such as “all”, or “some” or “no”, which tell us the quantity that is being referenced.

SYLLOGISMS �Examples: Premise True or False? Premise All dogs are mammals. True or False? Fido is a dog. Conclusion Therefore, Fido is a mammal. True or False? Valid or Invalid? All panthers are pink. Che Guevara is a panther. Therefore Che Guevara is pink. �Are these both valid arguments?

SYLLOGISMS �Decide if the following is valid: All weightlifters drink milk. John, drinks milk. Therefore, John is a weightlifter. How could you change this to make it a valid argument?

SYLLOGISMS �Arguments can be valid not only when the premises and conclusion are false, but also when the premises are false and the conclusion is true. All ostriches are teachers. Mr. Snow is an ostrich. Therefore Mr. Snow is a teacher.

Another way of looking at the validity of syllogisms is to use Venn Diagrams. Consider the following: All As are Bs. Some As are Cs Therefore Some Bs are Cs A B C

Venn Diagrams also illustrate invalid arguments. Consider the following: All As are Bs. All Bs are Cs. Therefore all Cs are As. A B C

If you want some practice using Venn Diagrams, consider the following and try to determine whether each syllogism is valid or invalid. All Italians eat spaghetti. Giovanni Rossi eats spaghetti. Therefore Giovanni Rossi is an Italian. All bobos have dogs. No doctors have dogs. Therefore no bobos are doctors. Some monks are Tibetans. All Tibetans are good at yoga.

ACTIVITY TIME � Get together with a small group to make up valid syllogisms to illustrate each of the following: 1. Two true premises and a true conclusion. 2. One true premise, one false premise, and a true conclusion 3. One true premise, one false premise, and a false conclusion 4. Two false premises and a true conclusion 5. Two false premises and a false conclusion

BENEFITS OF FORMAL LOGIC �Take just a minute to complete the “Importance of Premises” sheet. �Does this tell you the difficulty with things that we deal with every day? Can you turn any of the stuff on this sheet into a syllogism to better determine whether or not the conclusions are valid? �I know you are wondering how valid arguments can be made from false statements. �That is the beauty of logic. It analyzes an argument based on structure rather than content to help avoid the danger of belief bias. �Just because we agree with the conclusion, it doesn’t necessarily make an argument valid.

QUESTIONS ABOUT LOGIC �Formal logic is the study of form in argument, irrespective of the subject matter. �Is it really possible to study the logic of an issue independent of its content, and how beneficial is it to do so? Does the answer to this question depend upon the subject matter under consideration? Does it depend on the area of knowledge to which the subject matter belongs?

QUESTIONS ABOUT LOGIC �What constitutes a good argument? �What is the value of learning to distinguish between valid and invalid arguments? �What are the advantages of discriminating between valid and invalid arguments, good and bad reasons, more or less persuasive reasoning, both for the individual knower and for society?

INDUCTIVE LOGIC �This is the logic used to make generalizations or analogies. �It is based on experience and empirical knowledge from which we make inferences. �The soundness of our conclusions is not based on the structure of our argument, but on the reliability of the empirical evidence we use in our argument.

INDUCTIVE LOGIC Generalizations are based on previous experience – we have been through or seen something time and again, and make an assumption based on experience. � The two main features of this are: 1. It gives good reasons for supporting a conclusion, but it does not guarantee that conclusion. 2. Its conclusion contains information that is not in the argument. �

INDUCTIVE LOGIC �Example: Will you enjoy Mr. Paulk’s class the next time you go? �What are the problems with using induction as a means of drawing conclusions? �Isn’t this what most of scientific discovery is based upon? �How do we cope with such uncertainty?

THREE TESTS FOR SOUNDNESS Sufficient Number: What numerical information would be acceptable as sound evidence for generalization? 2. Varying Circumstances: Is the generalization based on information from everywhere for which it has been generalized? 3. Exceptions: Has a thorough and reliable search for exceptions been made? 1.

INDUCTIVE LOGIC �Analogy – comparison of two things which are similar and infer that they are similar in other ways too. �Examples: 1. Lab testing on animals to develop products for humans 2. Acre: Land a. Distance: Space b. Kinsfolk: Family c. Gallon: Liquid d. Degree: Thermometer e. Year: Birthday

LOGICAL PROBLEMS �Adam, Marco, Florian, Matteo, and Kenji all have favorite subjects but no two have the same favorite. Using the following information determine which subject is the favorite of which student. 1. 2. 3. 4. 5. 6. Adam’s favorite is not math. Marco dislikes math and English. One of the five really hates German. Florian’s favorite is To. K. Matteo hates physics. Kenji’s favorite subject is the one Matteo hates.

USING MATRICIES TO SOLVE LOGIC PROBLEMS Math English German Physics To. K Adam X Y X X X Marco X X Y X X Florian X X Y Matteo Y X X Kenji X X X Y X • Have you ever done a Sudoku puzzle? It is a matrix logic puzzle. You are just eliminating different possibilities until you have all of the boxes filled in.

IS INTUITION LOGIC? �“Intuitive logic is a way of making choices without analysis. It's a seeing and knowing without weighing things in the mind. It has great value. Some people just always do the right thing and everything they touch turns to gold. They know which way turn, how to decide, what are the best choices intuitively. It is also a way of coming to terms with reality, especially things that create conflict. The prideful person with a big ego needs to struggle to solve his own problems, and this drops the soul into the analytical mind, constantly scheming and planning, which is the opposite of intuition. ” From: http: //answers. yahoo. com/question/index? qid=20071028100811 AAsx. Sq. P

IS INTUITION LOGIC? �“Intuition is not considered to be a logical idea. Logic examines the methodology and validity of arguments. Logic searches for actual facts, not speculation. ” �“…the more ‘knowing’ we are, i. e. , the more knowledge we have accumulated, the more intuitive we may be. ” Therefore, ‘intuition’ is based on knowledge from which we can make logical conclusions.

A CURIOUS INCIDENT �In Chapter 67 Christopher examines a Chain of Reason in his murder investigation. What kind(s) of logical reasoning is he using in his chain? �In Chapter 47 Christopher explains how he determines the kind of day that he will have. Explain his method. Is it reasonable? Is it logical? Is it orderly? Is it consistent? �Do people usually use logic when dealing with things like the kind of day they are going to have? �What methods do we use to predict the

MORE LOGIC QUESTIONS �What is the relationship between reason as a way of knowing and logic in its different forms (inductive, deductive, intuitive)? Is it possible and worthwhile to “translate” everyday arguments into formal logical structure, and what might be lost in the translation? �How does the commonsense use of “it’s logical”, meaning “it makes sense to me”, differ from its technical meaning of “it has a valid argument form”?