logic

1. logic THE SCIENCE OF ARGUMENTS

2. The distinction between analytic and synthetic judgments • Any sentence has a Subject and a Predicate. • “All bachelors are unmarried,” • “This chalk is white.” • A sentence is Analytic if, and only if, the predicate concept is “contained in” the subject concept. 

3. synthetic • A judgment is syntheticif, and only if, it is not analytic. • Or, a judgment is synthetic just when the predicate concept is not contained in the subject concept. • For example: • * “All bachelors are tall” • * “The Sun will rise tomorrow” • * “All triangles are blue”

4. The distinction between a priori and a posteriori knowledge • Consider these two statements: • “All bachelors are unmarried men.” • “Some bachelors are happy.” • While we know both to be true, how we know differs.

5. How do we know? • A judgment is known a priori if it can be known independently of experience: • “All bachelors are unmarried men” requires no experience of bachelors. • A judgment is a posteriori if it cannot be known without recourse to experience: • “All bachelors are happy requires experience.”

7. Synthetic or analytic?A priori or a posteriori? • For every two events, if one of them is later than the other, the other is not later than the first one. • Frozen water is ice. • Children play with toys. • Planet earth rotates on its axis. • After today at midnight there is going to be another day (tomorrow).

8. If you dunk a bar of soap in a tub filled with water, the soap will float on the water. • Stones thrown at windows break glasses. • Everything red is colored. • My sister is not the only child. • No surface, if it is red all over, is at the same time green all over. • Everything that is square has a shape. 

9. What is logic? • Logic is the Study of the principles and concepts of good reasoning. • This implies that there is a distinction between good and bad reasoning. • Logicians are not interested in why people reason the way they do. • Logicians are interested in the principles of reasoning.

10. Biology, is the study of life and living organisms. • Life and living organisms are the subject matter of biology. • The subject matter of logic is the study of arguments. • In logic, an argument is reasoning in support of a point. For example: • All humans are mortal. • My logic prof. is human. • Therefore, my logic prof. is mortal.

11. ARGUMENT DEFINITION • An argument is a group of premises (at least one premise) in support of a conclusion. • PREMISE: A premise is a statement capable of being true or false.“Fetch me a bagel!” is not a premise. “Joe is my dog.” is a premise. • CONCLUSION: A conclusion is also a statement capable of being true or false; and it is the main point of the argument.

12. Good argument • A good argument is one that has two characteristics: • It has true premises. • The premises support the conclusion in either of these ways: • Logical necessity. • Inductive strength.

13. DEDUCTION VS. INDUCTION • An argument is a group of statements given in support of a conclusion. • The premises of an argument can support its conclusion either necessarily or probably. • If you are in Brooklyn, you are in the USA. • You are in Brooklyn. • Therefore, you are in the USA. • Given the premises, the conclusion is logically necessary. • If the premises are true it is not merely probable that you are in the USA, but it is necessarily so.

14. An argument is DEDUCTIVE. when the premises are intended to support the conclusion necessarily. • In other words, if the premises are true, then it would be impossible for the conclusion to be false. • An argument in which the premises succeed in supporting the conclusion is called deductivelyVALID. • An argument in which the premises DO NOT succeed in supporting the conclusion is called deductivelyINVALID.

15. Arguments are not always intended to support the conclusion necessarily. Consider this argument: • As far as I remember, it always has snowed in January in New York. • This year in January it has snowed in New York. • Therefore, it will snow (it is very likely) next January in New York. • Here the premises are not meant to support the conclusion necessarily. The premises offer strong reasons as to why snowing will occur next January. • In this case, even if the premises are true, the conclusion does not follow necessarily. • Can we say that the conclusion does not follow at all? No! The conclusion follows probably. This kind of argument is called inductive.

16. DEDUCTIVELY VALID • If I am eating I have food. • I am eating. • Therefore I have food. • Given premises 1 and 2, the conclusion, 3, is necessary. If you deny (3) you contradict yourself.

17. All bachelors are unmarried men. Joe is a bachelor. Therefore, Joe is an unmarried man. • If it rains my car is wet. • It rains. • Therefore my car is wet. If you are in France, then you must be in Europe. You are in France. Therefore, you are in Europe.

18. Note that an argument can be deductively VALID, even if it contains one or more false premises. • An argument is valid if, assuming that the premises are true, then the conclusion must be true. • When an argument is deductively valid (its conclusion follows necessarily from the premises) but one or more premises is false, we call it UNSOUND. • If you live in Brooklyn you are in South America. • You live in Brooklyn. • Therefore, you are in South America.

19. The moon is made of peanut butter. • Peanut butter can be eaten. • Therefore, you can eat the moon. • Notice that the conclusion to these arguments is necessary: GIVEN THE PREMISES, the conclusion follows from the premises necessarily—not probably. So, these are deductively valid arguments. But they are unsound because soundness requires true premises.

20. SOUND = DEDUCTIVE + VALID + TRUE PREMISES • When an argument is deductively valid (the conclusion follows necessarily from the premises) and the premises are true, we call it a Sound argument: • All humans are mortal. • Nancy is human. • Therefore, Nancy is mortal. • All physical objects occupy space. • My book is a physical object. • Therefore, my book occupies space.

21. what is an INVALID argument? One whose conclusion does not follow at all. • If it rains my car is wet. • My car is wet. • It follows that it rains. • If you are eating you have food. • You have food. • Therefore, you are eating. • All bachelors are males. • Mark is a male. • So, Mark is a bachelor. To be president of the US one must be 35 or older. Trump is older than 35. Therefore, Trump is the president of US.

22. INDUCTION • The conclusion to an inductive argument is never necessary. • If tell you that in my pocket I have a triangle, knowing that all triangles have three sides, you deduce that the triangle in my pocket has three sides. • Imagine each one of us has a triangle in his or her pocket; most of them are red. • Now based on this information, you could never know with absolute certainty that all are red. • So an argument is inductive just if given the premises, the conclusion follows probably.

23. Inductive arguments have the following characteristics: • The premises and the conclusion are all empirical propositions (observations/experiences). • The conclusion is not claimed to follow by logical necessity, but probably. • The premises do not imply the conclusion. (The conclusion does not follow by logical necessity). • The conclusion is inferred from the premises based on the assumption that the regularities described in the premises will persist. • Terms such as probably, in all likelihood, and most likely are often used in inductive arguments.

24. There are 3 kinds of inductive arguments: • Inductive Generalizations. • Arguments from Analogy. • Causal Arguments.

25. 1. INDUCTIVE GENERALIZATION • To move from a sample to a general conclusion about a population. • An argument of this type involves a certain number of observations of an object or event. • I may observe that a desk is brown. • The desk is my sample. • The population is what I decide: All the desks at CUNY, All the desks in North America, All the desks in NYC, etc. • For example: • This desk is brown. • That desk is brown. • Therefore, all desks are brown.

26. Assuming that the premises are true, it is possible that the conclusion is true. • This desk is brown. • That desk is brown. • Therefore, all desks are brown. • Notice that the structure of the above argument is not deductive: It moves from particular to general. • A deductive argument, for example, would move from general to particular: • All desks are brown. • I have a desk. • Therefore, my desk is brown.

27. Can inductive arguments be good? Yes! If… • The premises of an inductive argument give strong support for he conclusion. • The sample: how representative is the sample? • Is the number of observations enough to establish the conclusion? • Is the characteristic(s) observed about the samples shared by the population? • I may need 10 defective iPhones X devices to declare all iPhone X devices are bad. But you may need fewer. • Size of Population: How big is the population with respect to the samples matters?

28. Consider the following: • 40% of all CUNY teachers we interviewed are underpaid. • So, it is likely that all CUNY teachers are underpaid. • I’ve seen things fall to the ground when dropped. • So, upon release, all objects will fall to the ground.

29. ARGUMENTS FROM ANALOGY • Using an analogy between two or more things (also people, events, etc.) in order to support a conclusion about one of them. • An analogy is a comparison between two objects, people, events, etc. • Analogies are used to explain or claim that two distinct things are similar in some respect. • For example: • Capitalists are like vampires. • Like the Earth, Europa has an atmosphere containing oxygen. • Marriage is like jail! • You are like a saint!

30. Earth has an atmosphere that contains oxygen. • Planets that have an atmosphere that contains oxygen might have life. • Europa’s atmosphere contains oxygen. • Therefore, there might be life on Europa. • This book is boring. • That book has the same author and same plot. • Therefore, that book must also be boring.

31. Evaluating analogical arguments • Analogical arguments rely on analogies between two things. But any two objects are bound to be similar in some respect: • A Bird is very different from a car, but they are similar in that they can both move. • A society is very different from a family, but they both have individuals with specific roles. • So when we give arguments by analogy or we evaluate them, we must understand in what respect two things are similar. • We have to determine whether the two things in question are indeed similar in such a way that their similarity supports the conclusion. 

32. evaluate inductive argument by analogy • Truth: Are the two things being compared similar in the way assumed? • Relevance: Even if two things are similar, are those aspects in which they are similar relevant to the conclusion? • Number: If we discover many shared properties between two things, and they are all relevant to the conclusion, then the analogical argument is strong. Suppose we find out that this book is not only similar to that book in terms of author. • Diversity: Are the shared properties of the same kind or of different kind?   • Dis-analogy: Even if two objects X and Y are similar in lots of relevant respects, we should also consider whether there are dissimilarities between X and Y.

33. CAUSAL ARGUMENT • Causal Arguments contain causal statements as either a premise or the conclusion. • Causal statements (typically) state that an event A is the cause of another event B • Or that B is caused by A.

34. What Causes What?not always clear • A study reported that people who leave school before the age of 16 are 5 times more likely than university graduates to die from heart attack. What is really the cause? Poor education? The fact that they leave school? • Increased stress causes increased risk of heart attack. • Drinking alcohol during pregnancy cause birth defects. • Smoking causes cancer. • Eating heavy food causes stomachache. • Jogging cause my side pain. • The conflict over slavery caused the Civil War.

35. TYPES OF CAUSAL ARGUMENTS • Causal Prediction: An argument consisting of a causal generalization, an example of an effect, and concluding that a specific effect occurs. • Given a causal statement, we can predict what will happen: • Reduction in swelling causes relief of pain. (Causal generalization statement) • The swelling in my arm is diminishing. (Example) • Therefore, relief of pain will occur. (Prediction)

36. Causal Explanation: An argument consisting of a causal generalization, an example of an effect, and concluding that an example of a specific cause explains the occurrence of the effect. • Given a causal statement, we can explain how two events are related. • Exercising a lot makes you fit. (Causal generalization statement) • You are very fit. (Example) • Therefore, you exercise a lot. (Explanation)

37. Causal Prescription: An argument consisting of a causal generalization and concluding with a prescription for producing or preventing a certain effect. • This is an argument asserting how something is to be achieved. Given a causal statement, we know that if we want to achieve a certain result we need to bring about the cause. • Exercising makes you fit. (Causal generalization statement) • Therefore, if fitness desired, exercise a lot. (Prescription)

38. Causal Conclusion: An argument consisting of a premise in support of a causal statement. • This type of argument provides evidence for concluding that one event causes another. • Whenever I turn the knob right the volume increases. (Premise) • Therefore, turning the knob right causes the volume to increase. (Causal statement)

39. Logical Fallacies • Logical Fallacy are instances of bad or poor reasoning. The conclusion of any argument that contains a logical fallacy make an argument invalid or weak. • A formal fallacy is an error in logic that can be seen clearly. For example: • If Taylor is president of the US, then Taylor must be 35 years of age or older. • Taylor is 35 years of age. • Therefore, Taylor is president of the United States.

40. On the other hand, informal fallacies occur for reasons other than structural, and thus require examination of the argument’s content. Here are some of the most obvious examples: • Appeal to Authority • Fallacious appeal to authority is when you back up your reasoning by the assertion(s) of someone who is not relevantly qualified or is biased. • According to my classmate, philosophy is stupid. So I don’t waste my time on it! • Professor Alvaro is one of the most important philosophers of this century. I have that on the authority of his mother!

41. Appeal to the People • If you suggest too strongly that someone’s claim or argument is correct simply because it’s what most or everyone believes, you commit this fallacy. • Eating meat is morally permissible. Look how many people eat meat. • People have believed in God for millennia. I don’t see how so many people could be wrong. Therefore, God exists.

42. Appeal to Ignorance • This is an argument in which it is claimed that the conclusion is true (or false) because there is no evidence of the contrary. • There is no conclusive evidence that God exists. Therefore he doesn’t exist. • Scientists have not proven that drinking alcohol is unhealthful. Therefore it must be healthful.

43. Ad Hominem • You must give objective reasons for your views. Sometimes people get frustrated and attack another person. Often, people attack their opponents rather than their arguments. There are 3 common variations of ad hominem: abusive, circumstantial, and “you too!” • My doctor told me I should lose some weight. But why should I listen to him? He’s fat! • Professor Alvaro told us about the theory of evolution. But he’s a Godless atheist! Therefore, professor the theory cannot be true.

44. Slippery Slope • Suppose someone claims that a first step will probably lead to a second step that in turn will probably lead to another step and so on until a final step ends in trouble. If the likelihood of the trouble occurring is exaggerated, the slippery slope fallacy is present. • We should oppose same sex marriage because if we allow it then eventually people would demand to marry animals.

45. Equivocation • This fallacy occurs when the conclusion of an argument rests upon the equivocal use of a key word or phrase, typically used in two different senses. • They told me that the body needs amino acids. But acids corrode your stomach. So I am not eating amino acids. • Humans are animals. Animals eat other animals and it’s not immoral. Therefore, humans eating animals are not immoral.

46. Begging the Question • A form of circular reasoning in which a conclusion is derived from premises that presuppose the conclusion. • I can beat anybody. Why? Because nobody can beat me. • Africa is the largest continent because it has the largest area of any continent. • Left-handed people are better painters because right-handed people can’t paint as well. • Objects that are less dense than water will float because such objects won’t sink in. • Erica: “How do you know that the Book of God is divinely inspired?” Pedro: “Because it says it right in the third chapter that ‘all scripture is given by divine inspiration of God’.” • Happiness is the highest good for a human being, since all other values are inferior to it. • Of course smoking causes cancer. The smoke from cigarettes is a carcinogen.

47. Straw Man • Your reasoning contains the straw man fallacy whenever you misinterpret the position of your opponent and then proceed to attack the easily refuted position (the straw man) believing you have undermined the opponent’s actual position. • The theory of evolution says that man comes from monkeys. But how come monkeys don’t give birth to human babies? The theory of evolution is absurd!

48. The Red Herring • This is a fallacy in which attention is deliberately moved away from the issue under discussion. • A: “Eating animals is immoral.” • B: “But what about children starving in the world. That’s a real problem. So eating animals is not immoral”

49. The end.questions?