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.

§ Any sentence has a Subject and a Predicate. § A simple subject-predicate sentence can be either universal: ‘All bachelors are unmarried men’ or particular: ‘My house is small’

§ A sentence is Analytic if, and only if, the predicate concept is “contained in” the subject concept. § For example: § ‘All triangles are three-sided figures’ § SUBJECT: Triangles § PREDICATE: Three-sided figures § Triangles are defined as three-sided figures

§ Another example: § ‘All objects occupy space’ § Objects are defined as things that occupy space § The predicate concept ‘occupying space’ is contained in the subject concept ‘object’ § Philosophers call these statements ‘tautologies’ § Tautologies are empty truths like ‘A = A’ or ‘Plato is either Greek or he is not Greek’ or ‘A rose is a rose’

§ A judgment is synthetic if and only if it is not analytic. (Duh!) § Or, a judgment is synthetic just when the predicate concept is not contained in the subject concept. § For example: § ‘All bachelors are tall’ § SUBJECT: Bachelors § PREDICATE: Tall § Here the predicate concept is not contained in the subject concept § Being tall does not mean being a bachelor and vice versa

§ ‘New York City in the winter is lovely’ ! c i t the Syn ‘The Sun will rise tomorrow’ S ynth etic

§ Consider these two statements: § ‘All bachelors are unmarried’ § ‘Some bachelors are happy’ § While we know both to be true, how we know differs.

§‘All bachelors are unmarried’ §How do you know that all bachelors are unmarried?

§A judgment is a priori if it can be known independently of experience: §If I tell you that I have a triangle in my pocket, you know it has three sides without the need to see it. §True in all possible worlds(? )

§‘Some bachelors are happy’ §How do you know this?

§ Definition of ‘bachelor’ does not include the concept of happiness. § Bachelor: ‘A man who is not and has never been married. ’ (Merriam-Webster) § How do you know? Through experience

Analytic A priori A posteriori Synthetic X X

There are prime numbers larger than Graham’s number 1. Graham's number is bigger than the number of atoms in the observable Universe, which is estimated to be 1082.

The shortest distance between two points is a straight line.

Seven plus five is twelve.

That rat is a rodent

Ice is frozen water

Children play with toys

Planet earth rotates on its axis

All objects have weight

Stones thrown at windows break glasses

A red object is colored

New Orleans is the largest city in Louisiana

Objects released in air fall downward.

Touching fire burns the skin

Hitting a billiard ball with a cue stick makes the ball move onto the table.

The Sun is 92. 96 million miles from Earth

Donald Trump is the President of the United States

Water drowns

§ 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. Eating soap gives you stomach ache. 2. You are eating soap. 3. Your stomach will ache.

1. Most philosophers are single, liberal, and untidy. 2. Robert is a philosopher who is single and is liberal. 3. Therefore Robert is probably untidy. 1. Any complex mechanism, like a watch, is the product of intelligence. 2. The universe, like a watch, is a complex mechanism. 3. Therefore the universe is the product of intelligence.

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.

All dogs have 4 legs. All tables have 4 legs. . s le b ta e r a s g o d ll a , e Therefor

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

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

§ 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. ”