123philosophy.files.wordpress.com file · Web viewAlso, logicians, people who study logic, are not interested in HOW people reason, those are psychologists. Logicians are interested

NYC COLLEGE OF TECHNOLOGY Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro

LOGICLOGIC – DEFINITION, AND MORE

Logic is the Study of the principles and concepts of good reasoning.

This implies that there is a distinction between good and bad reasoning.

Also, logicians, people who study logic, are not interested in HOW people reason, those are psychologists. Logicians are interested in the principles of reasoning.

THE THREE “LAWS OF THOUGHT”

Early Logicians defined logic as the “science of the laws of thought” and that there are three basic laws we must obey to think correctly:

1. The principle of identity: Whatever is, is! (A=A)2. The principle of non-contradiction: Nothing can both be and not be. (– [A and –A]) 3. The principle of excluded middle: Everything must either be or not be. (A or –A)

History of LogicAristotle (384-322 B.C.E.) invented logic. He used letters for terms, he created syllogistic logic, which studies arguments like these

All humans are mortal. = All H are M.

All Greeks are humans. = All G are H.

Therefore All Greeks are mortal. = All G re M.

This argument is valid because of its structure. So any argument with the same structure is valid.

Aristotle studied the logic of possibility and necessity.

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Stoics continued Aristotle’s work and in the Medieval Period many thinkers developed ways to teach Aristotle’s system of logic. During the Enlightenment many philosophers would just agree that nothing significant was invented in logic after Aristotle. Leibniz (1646-1716), however, anticipated modern logic, proposing a concept of symbolic language, but his work was published after George Boole (1815-1864).

In 1879, Gottlob Frege (1848-1925) invented modern logic. He created more ways to express logic through symbols and operators. His project was to show that arithmetic is reducible to logic. Some sets, such as the set of all teacups, or of all cats are not members of themselves. The set of all teacups is not a teacup and the set of all cats is not a cat. Other sets, such as the set of all non-teacups, or the set of all abstract objects are members of themselves because the set of all non-teacups is a non-teacup and the set of all abstract objects is an abstract object. Now, consider the set of all sets that are not members of themselves “R.” If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Frege’s life work was destroyed! This is known as the Russell’s Paradox. Russell and Whitehead developed a system that fixed this problem.

These new developments propelled logic forward to new territories that Aristotle would be impressed. Systems like truth tables were invented. Modern Logic was important in the development of computers. Also the most important aspect of logic is modal logic dealing with necessary and possible.

The distinction between analytic and synthetic judgments, and by that between a priori and a posteriori knowledge.

Analytic and Synthetic Judgments

Any sentence has a Subject and a Predicate.

A simple subject/predicate sentence can be either universal, “all bachelors are unmarried,” or particular, “this chalk is white” is Analytic if and only if the predicate concept is “contained in” the subject concept.

To analyze something is to determine how it is constructed out of its constituent parts. An analysis of a concept is like a definition of the concept. For example, we might discover that something fits the concept bachelor if and only if it is an unmarried male person. In this case we can say that the concept bachelor contains such concept as being unmarried. So a judgment is analytic if analysis of the subject-concept reveals that it contains the predicate-concept.

A judgment is synthetic if 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,” or “the children are playing in the playground,” are synthetic judgments.

A Priori and A Posteriori Knowledge:

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Consider these two statements:

1. All bachelors are unmarried.2. Some bachelors are happy.

While we know both to be true, how we know differs.

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. A judgment is a posteriori if it cannot be known without recourse to experience. If I tell you that the triangle in my pocket is red, there is no possible way for you to know that is the case unless you see it.

Can we have synthetic a priori knowledge?

Immanuel Kant says yes.

Consider, for example, our knowledge that 7+5=12 and that the interior angles of any triangle add up to a straight line. These (and similar) truths of mathematics and geometry are synthetic judgments: the concept “the sum of the interior angles” is not contained in the concept of a triangle. Yet, clearly, such truths are known a priori, since they apply with strict and universal necessity to all of the objects of our experience, without having been derived from that experience itself.

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Analytic Synthetic

A Priori X ?A Posteriori X


Quine

In 1951, Willard Quine argued that the analytic–synthetic distinction is untenable. The argument at bottom is that there are no “analytic” truths, but all truths involve an empirical aspect.

Quine argues:

Analytic propositions – propositions grounded in meanings, independent of matters of fact.

Synthetic propositions – propositions grounded in fact.

The notion of an analytic proposition requires a notion of synonymy, but establishing synonymy inevitably leads to matters of fact – synthetic propositions.

What is knowledge? What is Truth? Religion: many have justified belief in claiming knowledge of the existence of a god.

Others, in a similar way, have sound justification to claim that there isn’t any god. Then to what extent is it possible for a given subject or entity to be known? One view is the objection that there is very little or no knowledge at all—skepticism. Before Galileo, earth was “known” to be at the center of the universe. Today we “know”

better—but do we? What puts us in a better position? If knowledge is linked with truth, what is the best instrument with which to acquire truth? Is it science? Is it religion?

Traditional Theory of knowledge: Many epistemologists hold the Justified True Belief (JTB) account of knowledge: the claim that knowledge can be conceptually analyzed as justified true belief.

A subject S knows that a proposition P is true if and only if:

1. P is true2. S believes that P is true, and3. S is justified in believing that P is true

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Is Justified True Belief (JTB) knowledge? Consider the following scenario:

I. Your roommate is watching TV in the kitchen. You’re in the bathroom preparing for work. You need to know the time and so you get out of the bathroom and see the time as it appears on the lower right corner of the TV set, which reads 2:15 P.M. You’re late for work. You get dressed quickly and zoom out. Now what you don’t know is that your friend was playing a tape. It just so happened that the time in the video precisely coincided with the real time. Now, do you know the time?

1. It is true that the time is 2:15.2. You believe that the time is 2:15, and,3. You are justified in believing that the time is 2:15.

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LOGIC THE SCIENCE OF ARGUMENTS

Different sciences, like biology, mathematics, etc. study their respective subject matters. Logic studies arguments. Arguments are the subject matter of logic.

In logic, an argument is a piece of reasoning used to show or express or prove a point; that point, whatever it may be, is supported by sub-points, which are statements.

For example:

All humans are mortal. My logic prof. is human.

Therefore, my logic prof. is mortal.

This is a classic example of an argument. A point is expressed—namely, that logic prof. is mortal. This is called conclusion. The conclusion is supported by certain statements, All humans are mortal and my logic prof. is human.

ARGUMENT DEFINITION: An argument is a group of premises (at least one premise) in support of a conclusion.

OR

A group of statements, one of which is claimed to follow from the others.

PREMISE DEFINITION: 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.

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CONCLUSION DEFINITION: A conclusion is also a statement capable of being true or false; in addition, it is the main point of the argument, that is, the statement that is claimed to follow from other premises (statements).

HOW TO UNDERSTAND/RECOGNIZE AN ARGUMENT

To understand an argument you must first pick out the conclusion. To pick out the conclusion ask yourself, “What’s the main point? What does the speaker want to persuade me to believe?”

Also you can spot the conclusion as it is often preceded by certain clue words: Therefore, thus, it must be deduced that, so, consequently…

On the other hand, premises often begin with these words: Since, because, for, given that…

ARGUMENT FORM

Arguments are given by people in the form of a speech. We will study textbook examples of arguments to facilitate our discussion.

Also, the arguments I will present will have numbered premises. Conclusions will be differentiated by other premises with a straight line that separates them from premises, like this:

1. All flowers are plants. (Premise 1)2. All Roses are flowers. (Premise 2)_______________________________

3. Therefore, all roses are plants. (Conclusion)

Exercise: Argument form – Determine Arguments, put them in argument form

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SUPPLYING MISSING PARTS – ENTHYMEMES

What’s missing?

An argument missing a premise, or a conclusion, is an enthymeme. Eg:

1. All chemists are scientists. 1. If you wake up late, you’ll miss your train.

2. So Joe is a scientist. OR 2. And as usual, you woke up late.

Exercise: Supply Missing Parts

DIAGRAMMING ARGUMENTS

Another technique to identify arguments is diagramming them. To diagram, read it through and then number each statement.

e.g.: Joe was promoted to VP; therefore, he will move to DC.

Number Like such:

(1) Joe was promoted to VP.(2) He will move to DC.

The above example is called “Single support” because the conclusion is directly supported by the premise.

Now draw an arrow from the statement to the conclusion:

(1)

|

(2) e.g.: If Joe is promoted to VP, he will move to DC. He was promoted; therefore, he will move to DC.

Number Like Such:

(1) If Joe is promoted to VP he will move to DC.(2) He was promoted.(3) Therefore he will move to DC.

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In this case you have a “Joint Support” (if…then)

(1) + (2)

|

(3)

Let’s do it again…

e.g.: Cats make good pets because they are affectionate, they’re clean, they’re entertaining, and they do well in apartments.

(1) Cats make good pets...(2) They’re affectionate,(3) They’re clean,(4) They’re entertaining,(5) They do well in apartments.

This is an example of “Independent Support”

(2)(3)(4)(5)

\ | / / (1)

One More Time…

e.g.: Cats make good pets because they are affectionate, they’re clean, they’re entertaining, and they do well in apartments. So if you want a good pet, you should get a cat.

(1) Cats make good pets...(2) They’re affectionate,(3) They’re clean,(4) They’re entertaining,(5) They do well in apartments.(6) If you want a good pet, you should get a cat.

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This is an example of “Extended Argument”

(2) (3) (4) (5)

|

(1)

|

(6)

Last one and then you do it…

e.g.: Cats make good pets and cats make good anatomical subjects. Therefore, some good pets make good anatomical subjects. Since good anatomical subjects are in high demand in medical schools, it follows that some good pets are in high demand in medical schools.

(1) Cats make good pets,(2) Cats make good anatomical subjects,(3) Therefore some good pets make good anatomical subjects. (4) Since good anatomical subjects are in high demand in medical schools, it follows that(5) Some good pets are in high demand in medical schools.

(1) + (2)

|

(3) + (4)

|

(5)The above argument is also an extended argument: there is an argument within an argument. You see that (1) and (2) support conclusion (3). Then (3) is combined with (4) to support (5)

Exercises: Diagramming arguments

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IN SEARCH FOR A GOOD ARGUMENT

What’s a good argument? Good arguments have

(A) A conclusion that follows from the premises and(B) The premises are true.

What does it mean to follow? 2 ways to follow: deductive validity or inductive strength.

DEDUCTION VS. INDUCTION

We defined an argument as a group of statements (premises) given in support of a conclusion.

We said that the premises of an argument can support its conclusion either necessarily or probably.

1. If you are in Brooklyn, you are in the USA.2. You are in Brooklyn.3. Therefore, you are in the USA.

In the above argument, the conclusion is logically necessary. If the premises are true (and in this case they are) It is not merely probable that you are in the USA, but it is necessarily so.

So, the premises of the above argument support the conclusion by logical necessity. We call this type of argument DEDUCTIVE.

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 a deductively valid argument.

When the conclusion does not follow at all, we call it a deductively INVALID argument.

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But arguments are not always intended to support the conclusion by logical necessity. Consider this argument:

1. As far as I remember, it always has snowed in January in New York.2. This year in January it has snowed in New York.3. Therefore, it will snow (it is very likely) next January in New York.

In the above example, the premises are not meant to support the conclusion by logical necessity. The arguer, by offering the premises, intends to offer strong reasons as to why snowing will occur next January.

So 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 in this case follows probably. This kind of argument is called inductive.

DEDUCTIVELY VALID

1. If I am eating I have food.2. I am eating.3. Therefore I have food.

Given premises 1 and 2, the conclusion, 3, is necessary. If you deny (3) you contradict yourself.

1. If it rains my car is wet.2. It rains.3. Therefore my car is wet.

1. If you are in France, then you must be in Europe.2. You are in France.3. Therefore, you are in Europe.

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1. All bachelors are unmarried men.2. Joe is a bachelor.3. Therefore, Joe is an unmarried man.

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.

1. All animals have teeth.2. Dogs are animals.3. Therefore, dogs have teeth.

1. The moon is made of marshmallow.2. Marshmallow is edible.3. Therefore, you can eat the moon.

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1. If you live in Brooklyn you are in South America.2. You live in Brooklyn.3. Therefore, you are in South America.

1. All unicorns have wings.2. Juju is a unicorn.3. Therefore, Juju has wings.

1. All living things can fly.2. Women are living things.3. Therefore, women can fly.

1. All felines have six legs.2. Tigers are felines.3. Therefore, tigers have six legs.

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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.

SOUND = DEDUCTIVE + VALID + TRUE PREMISESWhen an argument is deductively valid (the conclusion follows necessarily from the premises) and the premises are true, we call it a Sound argument:

1. All humans are mortal.2. Nancy is human.3. Therefore, Nancy is mortal.

1. All US presidents are politicians2. Trump is our current US president.3. Therefore Trump is a politician.

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

1. Citytech is either in China or In Brooklyn.2. Citytech is not in China.3. Therefore, Citytech is in Brooklyn.

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Now, what is an INVALID argument? A deductive argument is INVALID when its conclusion does not follow at all.

DEDUCTIVE + INVALID

1. If it rains my car is wet.2. My car is wet.3. It follows that it rains.

1. Dogs have teeth.2. Dogs are animals.3. So, we must deduce that all animals have teeth.

1. If you are eating you have food.2. You have food. 3. Therefore you are eating!

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1. All bachelors are males2. Joe is a male.3. It follows that Joe is a bachelor.

1. All politicians are liars. 2. All used car salesmen are liars. 3. Therefore all politicians are used car salesmen.

1. All ants are insects.2. All mosquitoes are insects.

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3. Therefore, all ants are mosquitoes.

The above arguments are INVALID because their conclusions are not granted by the premises; or, they neither follow necessarily nor probably—they just don’t follow!

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INDUCTIONOn the other hand, INDUCTIVE arguments have a different nature. The conclusion to an inductive argument is never deduced from the premises, but rather inferred from the premises. Here is what I mean: if I 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; I ask you to take it out and look at its color and it turns out that most of them, or all of them, are red. Now based on this information, you could never know with absolute certainty that the triangle in my pocket is red too. But considering that most or all triangles are red, you may infer that my triangle is red. That is to say, there is a good chance that it is red.

Inductive arguments have the following characteristics:

1. The premises and the conclusion are all empirical propositions (observations/experiences).

2. The conclusion is not claimed to follow by logical necessity, but probably.

3. The premises do not imply the conclusion. (The conclusion does not follow by logical necessity).

4. The conclusion is inferred from the premises based on the assumption that the regularities described in the premises will persist.

5. Terms such as probably, in all likelihood, and most likely are often used in inductive arguments.

There are 3 kinds of inductive arguments:

1. Inductive Generalizations.2. Arguments from Analogy.3. Causal Arguments.

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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 SFC, All the desks in North America, All the desks in NYC, etc.

For example:

1. This desk is brown.2. That desk is brown.3. Therefore, all desks are brown.

Assuming that the premises are true, it is possible that the conclusion is true.

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:

1. All desks are brown.2. I have a desk.3. Therefore, my desk is brown.

Can inductive arguments be good?

Remember what a good argument is?

An argument is good if it satisfies 2 requirements:

1. All true premises.2. The conclusion follows from the premises either:

a. By logical necessity, orb. Very likely.

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A deductively sound argument, obviously, is a good argument: All true premises, conclusion follows by logical necessity.

An inductive argument cannot be valid or sound. It can be weak or strong.

A strong inductive argument is called “cogent.”

Is the above argument good? Is it strong? Is it Cogent?

To determine this we need to consider a few things:

1. 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?

a. I may need 10 defective iPhones X devices to declare all iPhone X devices are bad. But you may need fewer.

2. Context/Interpretation: The likelihood that a conclusion is the case varies depending on the situation: The Love Bridge. At Yale University, an attractive female on a sturdy bridge and on a rickety bridge interviewed male students. The students interviewed in the rickety bridge were more likely to call the interviewer and ask her out.

3. Size of Population: How big is the population with respect to the samples matters?

So is the above argument good?

Well, it is a very weak argument!

Assuming the premises are true, it seems unreasonable to conclude that all desks are brown on the basis of only two observed brown desks.

But we need to have further info: Obviously, if the population (all desks) is three desks, and I observed two desks, then the conclusion is quite possible to be the case.

Consider the following:

1. All the teachers we interviewed at St. Francis College are underpaid.2. Therefore, all teachers at St. Francis College are underpaid.

Is this a good argument?

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What if I add this?

1. All the teachers we interviewed at St. Francis College are underpaid.2. Three-hundred teachers were interviewed.3. Therefore, all teachers at St. Francis College are underpaid.

What if I say this?

1. 40% of all CUNY teachers we interviewed are underpaid.2. Therefore, it is likely that all CUNY teachers are underpaid.

Or…

1. Every swan I’ve seen was white.2. Therefore, all swans are white.

Or…

1. 90 % of Citytech students are females.2. Therefore, the first person I’ll run into in the hallway is a female.

Or…

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1. There are 1000 marbles in a jar.2. I take one and it’s red.3. Therefore they’re all red.

INDUCTIVE STRENGTH: Inductive generalizations can become strong, thus even cogent, if the number of samples observed increases or the number of the population decreases.

1. There are 1000 marbles in a jar.2. I take 980 and they’re red.3. Therefore they’re all red.

Or…

1. There are 50 marbles in a jar.2. I take 20 and they’re red.3. Therefore, they’re all red.

Or…

In certain cases, the sample observations are so numerous that we are tempted to think that the conclusion follows necessarily!

1. I’ve seen things fall to the ground when dropped.2. Therefore, upon release, all objects will fall to the ground.

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2. 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!

Analogies are often used in arguments to argue that because two (or more) things are similar, what is true of one (or a number of them) is also true of the other.

Be careful!Not all analogical arguments inductive arguments!

Consider this:

1. ABC is an isosceles triangle.2. Every isosceles triangle has two equal internal angles.3. ABC has two equal internal angles.

The above example is a deductively valid argument that employs an analogy.

But we are now interested in inductive arguments that use analogies.

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Let’s look at some:

1. Earth has an atmosphere that contains oxygen.2. Planets that have an atmosphere that contains oxygen might have life.3. Therefore, there might be life on Europa.

Wait! Isn’t there something missing? What’s missing?

What is the name for such an argument?

Consider this one:

1. The novel Pass The Salt is very boring.2. The novel Smell My Feet is supposed to have a similar plot to Pass The Salt. 3. So, probably Smell My Feet is also very boring.

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.

How to evaluate the strength of an inductive argument by analogy:

Truth: Are the two things being compared similar in the way assumed?

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o For example, in the argument about the two novels, if they actually have completely different plots, one a romance and the other a horror story, then the argument is obviously unacceptable.

Relevance: Even if two things are similar, are those aspects in which they are similar relevant to the conclusion?

o For example, suppose two books both have green covers. Just because one of them is boring does not mean that the other one is also boring, since the color of a book's cover is completely irrelevant to its contents.

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 novel A is not only similar to another boring novel B with a similar plot. We also know that the same author wrote the two novels. Then it makes it more plausible to conclude that B is likely to be a boring novel.

Diversity: Are the shared properties of the same kind or of different kind? Consider two Italian restaurants A and B, and A is very good. We then find out that restaurant B uses the same olive oil in cooking as A, and buys ingredients of the same quality from the same supplier. Such information increases the probability that B is also good. But the information we have so far is of the same kind, the ingredients.

o If we are further told that A and B use the same brand of pasta, this will increase our confidence in B further still. And if we are told that both restaurants have lots of customers, and that both restaurants have obtained Michelin star awards, then these different aspects of similarities are going to increase our confidence in the conclusion a lot more.

Disanalogy: 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. For example, if we find out that restaurant B now has a new owner who has just hired a team of very bad cooks, we would think that the food is probably not going to be good anymore despite being the same as A in many other ways.

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Let’s practice now: Evaluate the following arguments. Identify the following:

(a) The analogy, what’s compared to what?(b) In what respect the two things being compared are or are not relevantly similar.(c) State whether they are weak or strong arguments.

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 mechanism like a watch is the product of intelligence.2. The universe is a complex mechanism.3. Therefore, the universe is also the product of intelligence.

1. The state is like family.2. You must respect your family.3. Therefore, you must respect the state.

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1. No one is obligated to donate his or her kidney to a person who needs one to live.2. Therefore, no woman should be under the obligation to donate the use of her womb to the

fetus that needs to live.

1. A and B are both spherical, yellow, waxy, small and light.2. A is sweet.3. So, probably B is sweet as well.

Remember: When people give arguments, they rarely list premises and conclusions; also, they don’t necessarily state the conclusion as the last sentence!

Evaluate the following:

(1) We should not blame the media for deteriorating moral standards. Newspapers and TV are like weather reporters who report the facts. We do not blame weather reports for telling us that the weather is bad.

(2) Democracy does not work in a family. Parents should have the ultimate say because they are wiser and their children do not know what is best for themselves. Similarly the best form of government for a society is not a democratic one but one where the leaders are more like parents.

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(3) A unicorn is like a horse. Horses have no magical powers, so unicorns have no magical powers.

(4) Werewolves are like Vampires: they are scary creatures. Vampires feed on human blood. So, werewolves also feed on human blood.

(5) Drug use is a matter of behavior control. It’s like overeating or gambling. It would be ridiculous to declare war on overeating, so it's ridiculous to declare war on drugs.

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3. CAUSAL ARGUMENT Arguments that rely on the concept of causality.

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.

When we deal with causality, we must consider Sufficient VS Necessary Condition.

Necessary Conditions

“X is a necessary condition for Y” means that if X is not there, then Y will not be there. Or without X, you won’t have Y.

However, to say that X is a necessary condition for Y does not mean that X guarantees Y.

Some examples:

(a) Having gasoline in my car is a necessary condition for my car to run. Without gasoline (X) my car (Y) will not run. Of course, having gasoline in the car does not guarantee that my car will run. There are many other conditions needed for my car to run.

(b) Having oxygen in the earth’s atmosphere is a necessary condition for human life. However, having oxygen will not guarantee human life. There are many other conditions needed for human life other than oxygen in the atmosphere.

(c) Being 35 years of age is a necessary condition for becoming the president of the US. Of course, being 35 does not guarantee that a person will become the president of the US. There are many other conditions that lead to a person becoming the president of the US than being 35 years of age.

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Sufficient Conditions

“X is a sufficient condition for Y” means that if we have X, we know that Y must follow. In other words, X guarantees Y.

Consider the following examples:

(a) Earning a total average of 95 in this class is a sufficient condition for earning a final grade of A. If your average is 95 for the course, then it must follow that you will have a final grade of A.

(b) Earning a final grade of C is a sufficient condition for passing the course.

(c) Rain pouring from the sky is a sufficient condition for the ground to be wet.

Please note that in none of these example is the sufficient condition also a necessary condition.

For example, it is not necessary to earn an average of 95 to earn an A in this course. You can earn an average of 94 to earn an A. (That is, we cannot say that if you do not have 95 then you can’t have an A.)

It is not necessary to earn a final grade of C for passing the course. You can earn a C+, a B-, or a B and pass the course.

Similarly, it is not necessary for rain to be pouring from the sky for the ground to be wet. The sprinkler could take care of that as well.

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What Causes What?

It is not always clear what the cause of an event is.

In November 2003, a man resisting arrest died shortly after being beaten into submission by police officers in Ohio. What caused his death? The struggle, Lack of oxygen, damage of brain?

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.

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:

1. Reduction in swelling causes relief of pain. (Causal generalization statement)2. The swelling in my arm is diminishing. (Example)3. Therefore, relief of pain will occur. (Prediction)

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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.

1. Reduction in swelling causes relief of pain. (Causal generalization statement)2. There is relief of pain. (Example)3. Therefore, the swelling in my arm has gone down. (Explanation)

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.

1. Reduction in swelling causes relief of pain. (Causal generalization statement)2. Therefore, if relief of pain is desired, reduce the swelling. (Prescription)

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.

1. Whenever swelling is reduced, pain is relieved. (Premise)2. Therefore, reduction in swelling causes relief of pain. (Causal statement)

Exercises pp. 199, 209.

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Mill’s MethodsJohn Stewart Mill (1806 – 1873) describes 5 methods for identifying causes and effects: METHODS OF AGREEMENT, DIFFERENCE, CONCOMITANT VARIATION, RESIDUE, and the joint method of AGREEMENT AND DIFFERENCE.

1. THE METHOD OF AGREEMENT

This method tells us to look at antecedent circumstances. The cause of an event is that antecedent circumstance common to all cases in which that event occurs.

Explanation: Suppose 5 friends eat at the same restaurant and an hour later 3 of them get sick. The method of agreement suggests that we identify the cause by looking at which food in common was eaten among the three.

If something like this happens, naturally the first question that comes to mind is, what did Amy, Beth, and Clara eat? Or which food was in common?

Denise ate salad, potatoes, apple pie, and tea. DID NOT GET SICK

Amy ate bananas, salad, apple pie, and coffee. GOT SICK

Beth ate bananas, apple pie, cola. GOT SICK

Ellen ate spinach, fries, and cola. DID NOT GET SICK

Clara ate bananas, beans, and coffee. GOT SICK

Following the method of agreement, we focus on those who got sick and see for a common element.

Notice that Amy, Beth, and Clara all got sick and ate bananas. So, it is reasonable to conclude that bananas are at least a causal factor in producing the illness.

You can see that this method is not very reliable. What if nothing is in common?

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2. THE METHOD OF DIFFERENCE

According to this method we can find out the cause of an event by looking at the antecedent event that is present when something occurs and we compare to those events that lack that antecedent event.

Explanation: Suppose you touch the TV antenna and the image gets clear. If you don’t touch the antenna the image is blurry. So by comparison, we infer that touching the antenna is the cause of clear images. Naturally you ask, “What’s the difference?” The answer: The difference is that this time I did not touch the antenna.

If you make soup with the same ingredients many times and one day you add a new or omit an ingredient, you infer that the cause of, say, a bitter taste is the new ingredient or the lack of taste is caused by the removal of, say, oregano. You ask, “What’s the difference?”

Again the restaurant:

Denise ate salad, apple pie, and tea. DID NOT GET SICK

Amy ate bananas, salad, apple pie, and tea. DID NOT GET SICK

Beth ate bananas, apple pie, cola. DID NOT GET SICK

Ellen ate spinach, fries, and coffee. DID NOT GET SICK

Clara ate bananas, beans, and coffee. GOT SICK

Clara is the only one who gets sick. In order to determine what caused Clara to get sick, naturally we want to ask, “What’s the difference?” We need to see which food might be different that Clara ate but not the others.

The difference is that Clara ate beans and is the only one who got sick. So probably, eating beans caused her to be sick.

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3. THE METHOD OF CONCOMITANT VARIATION

Things and people exhibit variation, they change. Often we observe that such variations are in concomitance with variations in other circumstances:

Explanation: If a variation in a certain event E coincide with another variation in phenomenon P, then it is probable that E and P are causally related.

~ The more you exercise the stronger you get.

~ The better you eat the healthier you become.

~ The higher the humidity, the longer it takes for my clothes to dry.

~ The thinner the air the harder it is to run.

4. THE METHOD OF RESIDUE

This method suggest that to know the cause of a certain phenomenon we need to subtract causes that are known from previous induction, and the residue of a certain phenomenon is the effect of the remaining antecedent.

Explanation: Suppose we investigate the increased incidence of AIDS in a community. Suppose we already know that the AIDS virus is transmitted through exchange of body fluids. All the cases observed in the antecedent circumstances were contaminated needles, unsafe sex, and blood transfusions. We have established that contamination is causal in 65% of cases, unsafe sex 25%. So, we infer that the remaining cases, the residue, are caused by blood transfusions.

5. THE JOINT METHOD (AGREEMENT + DIFFERENCE)

Every time I visit your house, your cat is there and I start sneezing. But when you visit me, and your cat is not here, I do not sneeze. So, by combining the methods of agreement and difference, I conclude that I am allergic to your cat.

By agreement I know that whenever your cat is present allergic reaction occurs; this is what’s in common.

By difference, I know that whenever your cat is not present, allergic reaction does not occur; this is the difference.

Exercises: Identify Types of Arguments p. 219

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Logical FallaciesOne type of invalid argument is called a Logical Fallacy. These arguments are instances of bad or poor reasoning. The conclusion of a logical fallacy either does not depend on the truth of the premises at all or the conclusion only follows very weakly from the premises. Fallacies can be formal or informal. A formal fallacy is an error in logic that can be seen in the argument’s form without requiring an understanding of the argument’s content. For example, see if you can spot the logical error in this argument:

E.g. 1:

1. If Taylor is president of the US, then Taylor must be 35 years of age or older.2. Taylor is 35 years of age.________________________________________________________________________3. Therefore, Taylor is president of the United States.

The obvious error here is to assume that Taylor is the president of the US. Many people are 35 years of age or older, but it does not follow that they are presidents of the US. Imagine how many presidents we would have!

The above is an invalid argument.

E.g. 2:

1. People who are allergic to peanuts won’t eat peanuts.2. Mike won’t eat peanuts._______________________________________________3. Therefore, Mike is allergic to peanuts.

The obvious error here is to assume that Mike is allergic to peanuts, which we cannot possibly know, since the premises do not make that explicit. The fact is that there are many people who are not allergic to peanuts but don’t like peanuts, so they won’t eat them.

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On the other hand, informal fallacies occur for reasons other than structural, and thus require examination of the argument’s content.

Here are some 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.

Examples:

~ 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!

~ Bill: “I believe that abortion is morally permissible. Women should have a right to their bodies.Jane: “I disagree completely. Dr. John Spin says that abortion is always immoral, regardless of the situation. He has to be right because he is a respected expert in his field.”Bill: “Never heard of him. Who is he?”Jane: “He’s the guy who won the Nobel Prize in physics for his work on cold fusion.”Bill: “I see. Does he have any expertise in morality?Jane: “I don’t know. But he is a famous physicist, so I believe him.”

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.

Example:

~ 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.

Appeal to Force

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This is an argument based upon a threat to persuade you into accepting a conclusion.

Example:

~ Ladies and gentlemen of the jury, if you do not convict this person, you may be this killer’s next victim.

Appeal to Pity.

This is an appeal to your emotion. One who commits this fallacy wants you to accept a conclusion out of pity.

Example:

~ It is true that this man committed a crime; however, consider this: he never knew his father, his mother died, he has been poor for his whole life…therefore, you should acquit him.

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.

Example:

~ I have examined all the arguments for the existence of God and found them all invalid. Therefore, there is no God.

~ Scientists have not proven that ghosts do not exist. Therefore they exist.

Ad Hominem

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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!”

Examples of abusive:

~ 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 neglected to tell us that he’s a Godless atheist! Therefore, professor Alvaro cannot speak the truth.

~ (Suppose you argue for the moral superiority of suicide for terminally ill patients.) I say to you that I disagree because life is sacred. You respond “You disagree because you are a religious bigot, and religious people are nuts.”

Examples of circumstantial:

~ The auto industry lobbyists have been arguing that tax reform is unnecessary. Just remember that it is in their interest to argue that way because it benefits the auto industry if there is no tax reform!

~ I am not surprised that your mechanic suggests a complete engine overhaul. Do you know how much money he makes from that?

~ I am not surprised you suggested that I join a gym. You are a personal trainer, right? More money for you, huh?

Examples of “you too!”

~ You argue that eating meat is immoral. But you too used to eat meat. So why should I listen to you?

~ A: Smoking causes all sorts of problems, not to mention it causes cancer. So, do not ever start, kid.

B: You should talk! You smoke!

False Cause40


This is committed when the arguer concludes that one event causes another without giving good evidence for their causal connection.

Example:

~ Last night I had an argument with Frank and I wished him dead. This morning they found him dead in his apartment. God, if only I hadn’t thought that! I killed him!

Slippery Slope

Suppose someone claims that a first step (in a chain of causes and effects, or a chain of reasoning) 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.

Example:

~ We should oppose same sex marriage because if we allow it then eventually people would demand to marry animals.

Either/Or/Black-or-White/False Dichotomy

Example:

~ Well, it’s time for a decision. Either you contribute $10 to our environmental fund, or you are on the side of environmental destruction?

~ Either you drove here or you walk. So if you didn’t walk, you must have driven.

~ Either we enforce death penalty or we find convicted murderers back out on the streets. We cannot have murderers out on the streets. Therefore, we must enforce the death penalty.

A VERY IMPORTANT POINT TO REMEMBER: Informal logical fallacies are not exclusive of inductive arguments. The above examples are deductively valid arguments. Being valid, the fallacy is not structural; it is not formal. Rather, it stems from a false premise—the premise that there are only two options. But if there are more than two options, then the fallacy is a false dichotomy.

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If I say to you, “Either you’re alive or you are dead. You are not dead. Therefore, you are alive.” This is not a false dichotomy because there is no other option.

Equivocation

This fallacy occurs when the conclusion of an argument rests upon the equivocal use of a word or phrase, typically used in two different senses.

Example:

~ If God is love and love is blind, and Stevie Wonder is blind. Then Stevie Wonder is God!

~ The doctor told me I need amino acids. But acids corrode your stomach. So I am not eating amino acids.

~ All feathers are light. Whatever is light cannot be dark. Therefore, feathers cannot be dark.

~ Logic is the study of arguments. My parents argue a lot. Therefore, I can learn logic by listening to my parents argue.

Hasty Generalization

This occurs when a generalization is made on the basis of an unrepresentative sample.

Example:

~ Last night I went to a town called Butte Creek and everywhere I went I saw children. So the inhabitants of that town are all children.

Composition

This is due to fallacious reasoning about the relationship between a whole and its parts.

Example:

~ Each member of the orchestra is excellent; therefore the orchestra is excellent.

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~ Drinking this glass of whiskey cannot harm me, so how can drinking harm me?

~ Every brick of that house is relatively light. Therefore, the house must be light.

Division

The fallacy of division is the opposite of that of composition.

Example:

~ The union voted to strike. Therefore, each member voted to strike.

~ Humans are the only animals capable of philosophical thinking. Therefore, every human being is capable of philosophical thinking.

False Analogy

An argument from analogy draws a conclusion about something on the basis of an analogy with some other thing. But sometimes the analogy is not relevant enough or false.

Example:

~ Teaching teenagers to stay away from drinking by getting them drunk is like teaching gun safety by playing Russian roulette.

~ To say humans are immortal is like saying a car can run forever.

~ If complicated mechanisms require a maker, then the universe must have a maker as well.

Begging the Question

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A form of circular reasoning in which a conclusion is derived from premises that presuppose the conclusion.

Example:

~ “Killing a human being is morally wrong. But a fetus is not a human being, so it is not wrong to kill a fetus.”

~ A student argues: “You can’t give me a C. I’m an A student!”

~ Whatever is less dense than water will float, because such objects won’t sink in.

~ The Bible asserts that God exists. The Bible is the truth revealed by God. Therefore, God exists.

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.

Example:

~ 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!

The Red Herring

This is a fallacy in which attention is deliberately moved away from the issue under discussion.

Example:

~ A: “What we do to animals is morally appalling.”

B: “But what about children starving in the world. That’s a real problem. And where would you get your proteins if all went vegan. And what would happen to the economy…”

Inconsistency

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This occurs when one argues from inconsistent premises.

Example:

~ Parents are the sole authority on the education of their children. But the state is to ensure a quality and equal education for all children. That’s why we give teachers the authority to determine educational goals.

~ I’m completely against violence for any reason, and I would punch anybody in the face who is in favor of violence.

~ I love animals, you know. You can call me an animal lover! But let’s order now: “I will take the T-bone steak for main course and veal tartar as an appetizer, please.”

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123philosophy.files.wordpress.com file · Web viewAlso, logicians, people who study logic, are not interested in HOW people reason, those are psychologists. Logicians are interested