THE SCIENCE OF REASONING Logic is the Study

THE SCIENCE OF REASONING

§ Logic is the Study of the principles and concepts of good reasoning. § Yes, there is such a thing as bad reasoning. § Logicians are not interested in why people reason the way they do. § Logicians are interested in the principles of reasoning.

§ 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. § An argument is reasoning in support of a point. For example: 1. US presidents always have been men. 2. Men by nature are competitive and belligerent, women compassionate and caring. 3. But competition and war have led us to many issues—to mention a few examples, to social and economic inequality, the neglect of public schools, and a disastrous health system. 4. If we want to make “America great again”, we should allow a woman to become president. 5. Therefore, in the next elections you should vote for a woman.

§ A group of statements in support of a conclusion. A paper, A Speech, A book, An article, An oral presentation, can be arguments. But to be arguments they require a conclusion. Conclusion: the main point or thesis.

§ A Good argument has 1. True premises. 2. And a conclusion that follows from the premises either necessarily or probably. NECESSARILY and PROBABLY imply 2 different ways to argue.

If the conclusion follows necessarily, the argument is DEDUCTIVE. If it follows probably, it is INDUCTIVE. 1. If you are in Brooklyn, you are in the US. 2. You are in Brooklyn. 3. It follows that… You are in the US How does it follow?

§ DEDUCTIVE means that given the premises, the conclusion either follows necessarily or it doesn’t follow at all—all or nothing! § Given the premises, if the conclusion does follow necessarily, a deductive argument is called is VALID. § Given the premises, if the conclusion does not follow at all, a deductive argument is called INVALID.

For example: 1. If you live in Brooklyn you are in South America. 2. You live in Brooklyn. 3. Therefore, you are in South America. § In this case we call the argument UNSOUND.

1. All physical objects occupy space. 2. My book is a physical object. 3. Therefore, my book occupies space.

1. If you leave your car out on the street and it rains, your car get wet. 2. Your car is wet. 3. It follows that it rained.

1. To be president of the US one must be 35 or older. 2. Trump is older than 35. 3. Therefore, Trump is the president of the US.

§ Often arguments are intended to support the conclusion with a matter of probability: 1. Every time I come to your house, your cat rubs against me. 2. I’m coming to your house later today. 3. Therefore, your cat will rub against me. § Here the premises are not meant to support the conclusion necessarily. § Given the premises, conclusion does not follow necessarily. § Does it not follow at all? No! § So how does it follow? § It follows probably.

§ Given the premises, an argument is called INDUCTIVE just if the conclusion follows probably. There are three kinds of inductive arguments: 1. Inductive Generalizations. 2. Arguments from Analogy. 3. Causal Arguments.

§ To move from a sample to a general conclusion about a population. 1. This desk is brown. 2. That desk is brown. 3. Therefore, all desks are brown.

§ Using an analogy between two or more things (also people, events, etc. ) in order to support a conclusion about one of them. 1. Earth has oxygen. 2. Planets that have oxygen might have life. 3. Europa has oxygen. 4. Therefore, there might be life on Europa. 1. This book is boring. 2. That book has the same author and same plot. 3. Therefore, that book must also be boring.

§ An arguments that contains a causal statement as either a premise or the conclusion. 1. Exercising a lot makes you fit. 2. You are very fit. 3. Therefore, you exercise a lot. 1. Fever is caused by demonic possession. 2. You have fever. 3. Therefore, you are possessed by demons.

DEDUCTIVE INDUCTIVE Conclusion follows necessarily or not at all Conclusion always follows probably VALID: Given the premises, the conclusion follows necessarily. SOUND: A deductively valid argument with all true premises THIS IS A GOOD ARGUMENT INVALID: Given the premises, the conclusion does not follow at all—even if the premises are true. NOT A GOOD ARGUMENT UNSOUND: A deductively valid argument with at least one false premise. NOT A GOOD ARGUMENT UNCOGENT: True premises but weak. Weak means given the premises, the conclusion is not likely to be true. NOT A GOOD ARGUMENT UNCOGENT: False premises but strong. Strong means given the premises, the conclusion is very likely to be true. NOT A GOOD ARGUMENT COGENT: Strong plus all true premises. THIS IS A GOOD ARGUMENT

1. Most bachelors are happy. 2. Mark is a bachelor. 3. So, Mark is happy. 1. Oh no! Eating soap gives you stomach ache, Jennifer. 2. You are eating soap. 3. Your stomach will ache, Jennifer.

1. If I am eating, obviously I have food. 2. And I am eating. 3. Therefore I have food. 1. Whenever I turn the knob right the volume increases. 2. Therefore, turning the knob right causes the volume to increase.

1. If it rains my car is wet. 2. It rains. 3. Therefore my car is wet. 1. All bachelors are males. 2. Joe is a male. 3. Therefore, Joe is a bachelor.

1. All humans are mortal. 2. Nancy is human. 3. Therefore, Nancy is mortal. 1. 40% of all CUNY teachers we interviewed are underpaid. 2. So, all CUNY teachers are underpaid.

1. The moon is made of peanut butter. 2. Peanut butter can be eaten. 3. Therefore, the moon can be eaten. 1. If you are anywhere in France, then you are in Europe. 2. You are in Paris. 3. Paris is in France. 4. Therefore, you are in Europe.

1. All US presidents have been men. 2. Research shows that US citizens are tired of male presidents and are ready for a female president. 3. Consequently, next US president will be a female. 1. Fordham is in Brooklyn. 2. Brooklyn is in NYS. 3. Therefore, Brooklyn was built before Manhattan.

VALID VS INVALID Distinguish valid from invalid arguments and sound from unsound gs. e l 4 e s hav g o egs. d l l l 4 A e v les. a b h a t s e e r l All tab e, all dogs a or Theref

1. All actors are robots. 2. Tom Cruise is an actor. 3. Therefore, Tom Cruise is a robot.

1. People from England speak English. 2. Marc is from England. 3. Therefore, Marc speaks English.

1. The president of the US must be born in the US. 2. Donald Trump was born in the US. 3. Therefore, Donald Trump is the president of the US.

1. All actors are robots. 2. Tom Cruise is a robot. 3. Therefore, Tom Cruise is an actor.

1. British people speak English. 2. Marc speaks English. 3. Therefore, Marc is British.

1. The Pope speaks 13 languages. 2. This man speaks 13 languages. INVA 3. Therefore, this man is the Pope. LID!

1. All female TV hosts are successful TV hosts. 2. Oprah Winfrey is a successful TV host. 3. Therefore, Oprah Winfrey is a female TV host. IN L A V ! ID

§ Premise 1 says that all females who are TV hosts are successful. § So, if you are a female, and you are a TV host, you are successful. § However, premise 1 does not assert that ALL TV hosts are females. This implies that there are successful male TV hosts too. § Now, what does premise 2 assert? It asserts that Oprah Winfrey is a successful TV host. But it does not say anything about her sex. § I know what you’re thinking: “But I know Oprah! She is a female TV host. ” § Granted, but the question is NOT who Oprah in fact is. § Once again, the question is whether the premises imply the conclusion. § It is a matter of relationship between premises and conclusion, and not between reality and conclusion.

1. Students who received an F pass the course. 2. Philippa received an F. 3. Therefore Philippa passed the course. ! D I L A V D N U O S N U BUT

1. If you are playing soccer, you have a soccer ball. 2. You have a soccer ball. 3. Therefore you are playing soccer. D I L A V IN

1. All trees are plants. 2. This is a plant. D I L A V 3. Therefore, this is a tree. N

1. All plants are green. 2. Trees are green. 3. Therefore, trees are plants. IN D I L A V

1. All things with 3 sides are triangles. 2. Some things with 3 angles are triangles. 3. Therefore, some things with 3 angles are things with 3 sides. INVALID

Let’s change terms: Things with 3 sides become ants Triangles become insects Things with 3 angles become things that fly

1. All ants are insects. 2. Some things that fly are insects. 3. Therefore, some things that fly are ants. IN D I L A V

1. All dogs are cats. 2. Fluffy is a dog. 3. Therefore, Fluffy is a cat. VALID BUT UN SOUND

1. Whatever begins to exist has a cause. 2. The universe began to exist. 3. Therefore, the universe has a cause. But is it s o D I L A V und ? ?

ARGUMENT? Research has shown that people who do at least 30 minutes a day of vigorous exercise reduce their risk of heart disease and some forms of cancer. It would be wise for you to begin a daily program of exercise.

PREMISE 1: Research has shown that people who do at least 30 minutes a day of vigorous exercise reduce their risk of heart disease and some forms of cancer. CONCLUSION: It would be wise for you to begin a daily program of exercise.

In 2014, we introduced a new textbook in the Logic course taught at SFC, and we negotiated with the publishers to have a discount for the students. It was agreed with the publisher that the textbook would cost $95, but the book was listed at $130. When students complained about the price, we called the publisher. Eventually, we understood what happened: the textbook was more expensive because the person with whom we had made an agreement on a reduced price had left the company, and the new employee wasn’t aware of the agreement. Therefore, at some point, the agreement was lost, and that’s why we didn’t get the discount.

NOT AN AR GUM ENT !

Paying chief executives hundreds of times more than ordinary employees creates economic inequality, which contributes to political instability, violent crime, and reduced life expectancy. Whatever contributes to political instability, violent crime, and reduced life expectancy is not morally justified. So, there is no moral justification for chief executives being paid hundreds of times more than ordinary employees.

! T EN Y A ! ES M U RG

PREMISE 1: Paying chief executives hundreds of times more than ordinary employees creates economic inequality, PREMISE 2: it contributes to political instability, violent crime, and reduced life expectancy. PREMISE 3: Whatever contributes to political instability, violent crime, and reduced life expectancy is not morally justified. CONCLUSION: So, there is no moral justification for chief executives being paid hundreds of times more than ordinary employees.

Dude, Wendy’s is the best restaurant on the planet! They have the Jr. Bacon Cheeseburger there, and it tastes like a fried slice of Megan Fox’s ass.

YES, IT’S AN ARGUMENT! HOWEVER, DO YOU THINK SOMETHING IS MISSING?

PREMISE 1: At Wendy’s they have the Jr. Bacon Cheeseburger. PREMISE 2: the Jr. Bacon Cheeseburger tastes like a fried slice of Megan Fox’s ass. PREMISE 3: A restaurant that serves a burger that tastes like a fried slice of Megan Fox’s ass must be the best restaurant in the world. CONCLUSION: So, Wendy’s is the best restaurant on the planet!

By the time Marx published the first volume of Capital in 1867, economic and social realities had changed profoundly: the question was no longer whether farmers could feed a growing population or land prices would rise sky high but rather how to understand the dynamics of industrial capitalism, now in full blossom.

NOT AN AR GUM ENT !

We must resist all effort to allow the government to censor entertainment. Freedom of speech and expressions are essential to a democratic form of government. As soon as we allow some censorship, it won't be long before censorship will be used to silence the opinions critical of the government. The next thing we know, we will have no more freedom than the Germans did under Hitler.

YES! ARGUMENT.

PREMISE 1: Freedom of speech and expressions are essential to a democratic form of government. PREMISE 2: As soon as we allow some censorship, it won't be long before censorship will be used to silence the opinions critical of the government. PREMISE 3: The next thing we know, we will have no more freedom than the Germans did under Hitler. CONCLUSION: We must resist all effort to allow the government to censor entertainment.

To install the program, you must first put the CD in the player. Open up the File Manager, click on "Run" and type in "D: Install. " After the program is loaded, you will need to restart the computer to use the program.

NOT AN AR GUM ENT !

Roger Maris' record of 61 homeruns in a single season stood from 1961 until 1998! He should be admitted into the Baseball Hall of Fame.

YES, ARGUMENT! HOWEVER, SOMETHING’S MISSING.

PREMISE 1: Roger Maris' record of 61 homeruns in a single season stood from 1961 until 1998! PREMISE 2: Anyone with that record should be admitted into the Baseball Hall of Fame. CONCLUSION: He should be admitted into the Baseball Hall of Fame.

All of this talk about banning guns makes me sick! Isn't it obvious that if we ban guns, law-abiding citizens will not own them, while only the criminals will have them?

NOT AN AR GUM ENT !

Two teenagers saw the movie, Natural Born Killers and went out on a killing spree. A number of teenagers who have committed violence have spent many hours playing video games filled with murder and violence. We must have some stricter controls on the content of entertainment that is viewed by teenagers.

YES, BUT SOMETHING IS MISSING.

PREMISE 1: Two teenagers saw the movie, Natural Born Killers and went out on a killing spree. PREMISE 2: A number of teenagers who have committed violence have spent many hours playing video games or watching movies filled with murder and violence. PREMISE 3: Playing video games or watching movies filled with violence causes teenagers to commit violence. CONCLUSION: We must have some stricter controls on the content of entertainment that is viewed by teenagers.

I am more concerned with the microcosm than the macrocosm; I am more interested in how a man lives that how a star dies; how a woman makes her way in the world than how a comet streaks across the heavens. If there is a God, He is present as much in the creation of each of us as He was at the creation of the earth. The human condition is the mystery that engages my fascination, not the condition of the cosmos. (Sherwin Nulan, How We Die)

NOT AN AR GUM ENT !

For myself, I like a universe that includes much that is unknown and, at the same time, much that is knowable. A universe in which everything is known would be static and dull, as boring as the heavens of some weak-minded theologians. A universe that is unknowable is no fit place for a thinking being. The ideal universe for us is one very much like the universe we inhabit. And I would guess that this is not really much of a coincidence. (Carl Sagan, “Can We Know the Universe? ” in The Sacred Beetle) YES! IT’S AN ARGUMENT!

For myself, I like a universe that includes much that is unknown and, at the same time, much that is knowable. 1. A universe in which everything is known would be static and dull, as boring as the heavens of some weak-minded theologians. 2. A universe that is unknowable is no fit place for a thinking being. 3. (Therefore) The ideal universe for us is one very much like the universe we inhabit. And I would guess that this is not really much of a coincidence.

§ Every literature major must take a course in Shakespeare. John has taken the Shakespeare course; therefore, he must be a literature major.

§ 1. Every literature major must take a course in Shakespeare. § 2. John has taken the Shakespeare course; § 3. therefore, he must be a literature major.

§ A time-honored policemen adage has it that with homicide, if you haven’t nailed your killer inside a week, your chances of ever doing so divide by half for every subsequent week that passes.

§ A time-honored policemen adage has it that with homicide, if you haven’t nailed your killer inside a week, your chances of ever doing so divide by half for every subsequent week that passes.

§ If the president dies in office, then the first lady becomes the new president. Since Barbara Bush is the first lady, she will take over if President Bush dies in office.

§ 1. If the president dies in office, then the first lady becomes the new president. § 2. Barbara Bush is the first lady, § 3. Therefore, she will take over if President Bush dies in office.

§ A person can’t be a marine and a sailor both. Since Max is a sailor, it must be that he is not a marine.

§ 1. A person can’t be a marine and a sailor both. § 2. Max is a sailor. § 3. Therefore, it must be that he is not a marine.

§ There is freedom in the sense of being able to move as one pleases, freedom in the sense of being able to do and speak as one pleases, and freedom in the sense of being able to think for oneself. This last type makes the others possible. Consequently, it is our most important freedom.

§ 1. There is freedom in the sense of being able to move as one pleases, § 2. There is freedom in the sense of being able to do and speak as one pleases, § 3. and there is freedom in the sense of being able to think for oneself. § 4. This last type makes the others possible. § 5. Consequently, it is our most important freedom.

§ Every chemistry major must take a year of organic chemistry. Max is a chemistry major, so he takes a year of organic chemistry.

§ 1. Every chemistry major must take a year of organic chemistry. § 2. Max is a chemistry major, § 3. So he takes a year of organic chemistry.

§ You shouldn’t buy a foreign car. Patrick and Richard did, and within a year they had to have the transmission replaced.

§ 1. Patrick and Richard bought foreign cars, and within a year they had to have the transmission replaced. § 2. Therefore, you shouldn’t buy a foreign car.

§ Most people who major in the humanities go on to teach humanities. People who teach the humanities are happy because the humanities are always exciting and fun and they are about things of human importance. Work that keeps you focused on being human is hardly work at all. It comes to be a labor of love. Therefore, people who major in the humanities love their work.

§ 1. Most people who major in the humanities go on to teach humanities. § 2. People who teach the humanities are happy because the humanities are always exciting and fun and they are about things of human importance. § 3. Work that keeps you focused on being human is hardly work at all. § 4. It comes to be a labor of love. § 5. Therefore, people who major in the humanities love their work.

§ I heard that most MDs are conservatives. My doctor is an MD. So he is a conservative.

§ 1. I heard that most MDs are conservatives. § 2. My doctor is an MD. § 3. So he is a conservative.

§ When a mild electrical current is applied to a muscle, the muscle contracts. When the current stops, the muscle relaxes. Therefore, the application of a mild current to a muscle is the cause of contraction.

§ 1. When a mild electrical current is applied to a muscle, the muscle contracts. § 2. When the current stops, the muscle relaxes. § 3. Therefore, the application of a mild current to a muscle is the cause of contraction.

§ Some fruits are sweet. Honey is sweet. Therefore it must be a fruit.

§ 1. Some fruits are sweet. § 2. Honey is sweet. § 3. Therefore it must be a fruit.

§ Computers don’t have feelings for the reason that only living things can have feelings. And computers are not living things.

§ 1. Only living things can have feelings. § 2. Computers are not living things. § 3. Therefore, computers don’t have feelings.

§ Logical Fallacy are instances of bad or poor reasoning. Fallacies are FORMAL or INFORMAL: § A formal fallacy is an error that can be seen clearly. For example: 1. If Taylor is the president of the US, she must be 35 or older. 2. She is 35. 3. Therefore, she is the president of the US.

§ Appeal to Authority § Fallacious appeal to authority is when you claim that your conclusion is true on the basis of the assertion(s) of someone who is not relevantly qualified or is biased. § According to Gordon Ramsey, eating meat is morally permissible. § According to Einstein, abortion is always immoral. § Professor Alvaro is one of the most important philosophers of this century. I have that on the authority of his mother!

§ Appeal to the People If you argue that your conclusion is true simply because it’s what most people or all people believe, you commit this fallacy. § Assume you were alive during colonial times when slavery was accepted by the majority of people in the 13 colonies. Jeremiah argues as follows: Slavery is morally permissible. Why? Because virtually everyone considers slavery a moral practice. § People have believed in God for millennia. I don’t see how so many people could be wrong. Therefore, God exists.

§ 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. This results in a fallacy. 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 theory of evolution. But he’s a Godless atheist! Therefore, theory cannot be true. § A: “You don’t exercise at all? ! You should at least a couple of days a week. It is very important. ” B: “Yeah, yeah, of course you say that. You are a personal trainer. So it is not true that exercising is important. ”

§ 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. § We cannot unlock our child from the closet because if we do, she will want to roam the house. If we let her roam the house, she will want to roam the neighborhood. If she roams the neighborhood, she will get picked up by a stranger in a van, who will sell her in a sex slavery ring in some other country. Therefore, we should keep her locked up in the closet.

§ Equivocation § 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 anything that has amino acids. § Sure logic helps you argue better, but do we really need to encourage people to argue? There's enough hostility in this world. § Humans are animals. Animals eat other animals and it’s not immoral. Therefore, humans eating animals are not immoral.

§ Begging the Question § A form of circular reasoning in which a conclusion is derived from premises that presuppose the conclusion. § Africa is the largest continent because it has the largest area of any continent. § Paranormal activity is real because I have experienced what can only be described as paranormal activity. § 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.

§ Straw Man § Your reasoning contains the straw man fallacy whenever you misinterpret the position of your opponent. § 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! § Jordan says that we should stop using animals for scientific research. Pamela replies that she does not believe Jordan doesn’t care about the progress of medicine. § Zoe: What is your view on God? Mike: I don’t believe in any gods. Zoe: Oh, so you think that we are here by accident, and all this design in nature is pure chance, and the universe just created itself? Mike: You got all that from my stating that I don’t believe in any gods?

§ 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” § There is a lot of commotion regarding saving the environment. We cannot make this world an Eden. What will happen if it does become Eden? Adam and Eve got bored there! § "The crime in this city, has, in fact increased lately. However, let's consider that the weather has changed as well. Things change over time. Sometimes they are linked, sometimes they are not, but only time will tell. " § A: “Eating meat is immoral because it causes suffering to innocent animals. ” § B: “Oh yeah, and what about the pain vegetarians cause to plats? What about the fact that harvesting vegetables kills millions of insects and rodents? Then eating meat is not immoral. ”