NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
L O G I C
LOGIC – 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.
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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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
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)
SUPPLYING MISSING PARTS – ENTHYMEMES
What’s missing?
An argument missing a premise, or a conclusion, is an enthymeme. Eg:
1. If you wake up late, you’ll miss your train.
1. All chemists are scientists.
2. So Joe is a scientist.
OR
2. And as usual, you woke up late.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
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
Arguments can be deductive or inductive. A deductive argument can be valid or invalid; and a
valid argument can be sound or unsound. An inductive argument can be weak or strong.
An argument is called DEDUCTIVE when its conclusion follows NECESSARILY—by logical
necessity. Deductive arguments may be valid or invalid.
DEDUCTIVE + VALID
1. IF IT RAINS, MY CAR IS WET.
2. IT RAINS.
3. MY CAR IS WET.
1. IF I AM EATING, I HAVE FOOD.
2. I AM EATING.
3. I HAVE FOOD.
Given premises 1 and 2, the conclusion, 3, is necessary. If you deny (3) you contradict yourself.
1. PEOPLE FROM FRANCE SPEAK FRENCH.
2. MARK IS FROM FRANCE.
3. MARK SPEAKS FRENCH.
1. TO BE A BACHELOR ONE MUST BE MALE.
2. JOE IS A BACHELOR.
3. THEREFORE, JOE IS A MALE.
1.
2.
3.
4.
A HUMAN FETUS HAS A BRAIN WAVE AFTER 25 WEEKS OF GESTATION.
A HUMAN WITH A BRAIN WAVE IS A PERSON.
KILLING A PERSON IS MORALLY WRONG.
THEREFORE, KILLING A FETUS WITH A BRAIN WAVE IS MORALLY WRONG.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
1. ALL ANIMALS HAVE TEETH.
2. DOGS ARE ANIMALS.
3. SO, DOGS HAVE TEETH.
1. THE MOON IS MADE OF CHEESE.
2. CHEESE CAN BE EATEN.
3. THUS, YOU CAN EAT THE MOON.
Note that an argument may be deductively valid, yet have one or more false premises.
Premise (1) is false because birds, and octopi, shrimp, etc. are not teethed animal. The second
argument has a false premise and false conclusion.
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 RAINS.
1. DOGS HAVE TEETH.
2. DOGS ARE ANIMALS.
3. SO, ALL ANIMALS HAVE TEETH.
1. IF I AM EATING, I HAVE FOOD.
2. I HAVE FOOD.
3. THEREFORE, I AM EATING.
1. A FETUS HAS A BRAIN WAVE AFTER 25 WEEKS OF GESTATION.
2. A CONSCIOUS ADULT HAS A BRAIN WAVE.
3. KILLING A FETUS AFTER 25 WEEKS IS AS WRONG AS KILLING AN ADULT.
1. TO BE A BACHELOR, ONE MUST BE MALE
2. JOE IS MALE.
3. JOE IS A BACHELOR.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
1. ALL POLITICIANS ARE LIARS.
2. ALL USED CARS SALESMEN ARE LIARS.
3. THEREFORE, ALL POLITICIANS ARE USED CARS SALESMEN.
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!
Next, deductive arguments can be sound or unsound.
DEDUCTIVE + VALID + SOUND
1. ALL MEN ARE MORTAL.
2. X IS A MAN.
3. THUS, X IS MORTAL.
1. ALL US PRESIDENTS ARE POLITICIANS
2. OBAMA IS A US PRESIDENT.
3. THEREFORE OBAMA IS A POLITICIAN.
1.
2.
3.
5 IS GREATER THAN 3.
3 IS GREATER THAN 2.
5 IS GREATER THAN 2.
1. ALL PHYSICAL OBJECTS OCCUPY SPACE.
2. MY BOOK IS A PHYSICAL OBJECT.
3. 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.
The foregoing arguments are DEDUCTIVE because their conclusions follow by logical necessity
and not probably. Hence, they are VALID. Furthermore, they are SOUND because their premises
are true.
DEDUCTIVE + VALID + UNSOUND
1. IF THE JAN. HAS 33 DAYS, THE 33Rd IS THE LAST DAY.
1. JAN. HAS 33 DAYS.
2. THUS, THE 33Rd IS THE LAST DAY.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
1. ALL UNICORNS CAN DO MAGIC.
2. JUJU IS A UNICORN.
3. THUS, JUJU CAN DO MAGIC.
1. ALL LIVING THINGS CAN FLY.
2. WOMEN ARE LIVING THINGS.
3. THUS, WOMEN CAN FLY.
1. FELINES HAVE SIX LEGS.
2. TIGERS ARE FELINES.
3. THUS, TIGERS HAVE SIX LEGS.
1. THE MOON IS MADE OF CHEESE.
2. CHEESE CAN BE EATEN.
3. THUS, THE MOON CAN BE EATEN.
1. NY HAS THE ONLY SUBWAY SYSTEM IN THE WORLD.
2. F TRAIN IS ONE OF THE NY SUBWAY TRAINS.
3. THUS, F TRAIN IS THE ONLY SUBWAY TRAIN IN THE WORLD.
1. ALL MUSIC GENRES STARTED IN INDIA.
2. JAZZ IS A MUSIC GENRE.
3. THUS, JAZZ STARTED IN INDIA.
Notice that the conclusion to these arguments is necessary. The premises are related: one leads to
the other; GIVEN THE PREMISES, the conclusion follows from the premises necessarily and not
probably. So, these are deductively valid arguments. But they are unsound because soundness
requires true premises.
INDUCTION
On the other hand, INDUCTIVE arguments work differently. The conclusion to an inductive
argument can be strong or weak, depending on the circumstances, but never 100% true or 100%
false. There are 2 kinds of inductive arguments: Inductive Generalizations and Arguments By
Analogy.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
INDUCTIVE GENERALIZATION

To move from a sample to a general conclusion about a population.
1. THE LAST TEN TIMES I’VE PLAYED POKER, I’VE WON MONEY.
2. I’M PLAYING POKER TONIGHT.
3. I’LL WIN MONEY TONIGHT.
NOTICE THAT EVEN IF I DENY THE CONCLUSION, UNLIKE IN DEDUCTIVE
ARGUMENTS, THE CONCLUSION IS STILL POSSIBLE!
1. THE LAST TEN TIMES I’VE PLAYED POKER, I’VE WON MONEY.
2. I’M PLAYING POKER TONIGHT.
3. I WILL NOT WIN MONEY TONIGHT.
1. 90% OF CITYTECH STUDENTS ARE FEMALES.
2. THEREFORE, IF I WALK OUT IN THE HALLWAY NOW, CHANCES
ARE I’LL RUN INTO A FEMALE STUDENT.
1. OUT OF 1000 FETUSES WITH ECHOGENIC FOCUS, 80% ARE BORN WITH DOWN
SYNDROME.
2. MARY’S FETUS HAS AN ECHOGENIC FOCUS.
3. THEREFORE, MARY’S BABY WILL BE BORN WITH DOWN SYNDROME.
1. THERE ARE 20 CARDS IN THE DECK, AND THAT INCLUDES 13 ACES.
2. I NEED TO DRAW 1 ACE TO WIN.
3. I’LL GET AN ACE ON THE NEXT DRAW.
1. THERE ARE 1000 MARBLES IN THE JAR.
2. THE FIRST MARBLE I TAKE OUT IS RED.
3. THEREFORE, ALL MARBLES IN THE JAR ARE RED.
INDUCTIVE STRENGTH
1. THERE ARE 100 MARBLES IN THE JAR.
2. THE FIRST MARBLE I TAKE OUT IS RED.
3. THEREFORE, ALL MARBLES IN THE JAR ARE RED.
1. THERE ARE 100 MARBLES IN THE JAR.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
2. THE FIRST 89 I TOOK OUT ARE RED.
3. THEREFORE, ALL MARBLES IN THE JAR ARE RED.
1. EVERY TIME I HAVE SEEN A THING BE DROPPED IN THE PAST, IT HAS FALLEN TO THE
GROUND.
2. I AM ABOUT TO DROP THIS PEN.
3. THEREFORE, IT WILL FALL TO THE GROUND.
ARGUMENTS BY ANALOGY

Comparing two or more things in order to support a conclusion about one of them.
1. PROFESSOR ALVARO TEACHES LOGIC, ETHICS, AND INTRO PHIL.
2. INTRO PHIL AND ETHICS WERE BOTH ENTERTAINING.
3. THUS, LOGIC WILL ALSO BE ENTERTAINING.
1. IT HAS SNOWED IN FEBRUARY IN NY FOR THE PAST 5 YEARS.
2. THIS YEAR IS SNOWING AS WELL.
3. THEREFORE, NEXT YEAR IT WILL SNOW IN FEBRUARY.
1. A WATCH, UNLIKE A ROCK, IS A COMPLEX MECHANISM, WHICH WAS MADE BY A
WATCHMAKER.
2. THE WORLD IS, LIKE A WATCH, A COMPLEX MECHANISM (THINK OF THE
COMPLEXITY OF NATURE).
3. THUS, THE WORLD, LIKE A WATCH, HAS A MAKER, TO WIT, GOD.
…AND MORE
All observed people are right-handed; therefore all the people are right-handed. (Inductive
generalization)
All the dogs that have been observed can bark, therefore all the dogs can bark. (Simple induction)
Joe leaves home at 08:30 in the morning and arrives late for work, based on which he concludes that
he will be late for work every time he leaves at 08:30. (Causal inference)
John and Joe are friends. John likes to sing, write and read. Joe likes to sing and write. Therefore
one assumes that Joe also likes to read. (Argument from analogy)
Every time John eats pizza, he gets cramps, and therefore he assumes that he gets cramps because
he eats pizza.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
I am an amazing athlete. So my son too will go on to become an amazing athlete.
Every time you get a call from some unknown number, you find a telemarketer on the other side of
the line. It makes you conclude that if it's an unknown call, it is most likely to be a telemarketer.
A few episodes of a particular sitcom make you laugh, and you conclude that the said sitcom is very
funny.
APPLIED INDUCTION
Look at the patterns below. Can you draw the next figure or next set of dots using inductive
reasoning?
People are naturally inclined to see patterns in nature. But “How do you interpret these patterns?” is
the question. So, one may be tempted to say that logically the next pattern should have 9 dots or 12
if multiply by 2. However, notice that one dot is always placed between and above two dots. Also,
the next figure always has one more dot at the very bottom row
Keeping this in mind, your next figure should look like this:
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
Logical Fallacies
One 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:
1. All men are mortal.
2. X is mortal.
______________________
3. Therefore, X is a man.
The error is that the arguer does not carefully consider that entity X may not be a man. X could be a
cat, which is mortal, but is not a man.
Consider this other:
1. If it rains, then my car gets wet.
2. My car is wet.
______________________
3. Therefore, it rains.
Again, the error here is to jump to the conclusion without carefully considering the premises. That
is to say, my car could be wet for a number of reasons other than that it rained.
On the other hand, informal fallacies occur for reasons other than structural, and thus require
examination of the argument’s content.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
Here are some examples:
Ad Hominem
In ethics, 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.
Example:
My doctor told me I should lose some weight. But why should I listen to him? He’s fat!
This attack may undermine the doctor’s physical aspect, but it does not undermine his reasoning.
That reasoning should stand or fall on the scientific evidence, not on the doc’s age or anything else
about his aspect or personally.
Reductio ad Absurdum
This is a strategy used to reduce an argument to the absurd by taking a premise and show that it has
ridiculous consequences.
Example:
Imagine one argues that nine-day-old embryos are persons. You respond thus: “So you would
baptize all embryos that fail to survive to become fetuses? And you think heaven has millions of
embryos?”
Equivocation
Shifting meaning of a key word in an argument results in the fallacy of equivocation.
1.
2.
3.
4.
God is love.
Love is blind.
Stevie Wonder is blind.
Thus, Stevie Wonder is God.
Appeal to Authority
You appeal to authority if you back up your reasoning by saying that it is supported by what some
authority says on the subject.
Example:
A TV commercial that gives you a testimonial from a famous film star who is against abortion and
that suggests you, too, should be against abortion is using a fallacious appeal to authority. The film
star—maybe—is an authority on how to act, not on the morality of abortion.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
Appeal to Ignorance
The fallacy of “Appeal to Ignorance” occurs when the subject implies that not knowing that a
certain statement is true is taken to be a proof that it is false, or vice versa. The fallacy occurs in
cases where absence of evidence is not good enough evidence of absence. The fallacy uses an
unjustified attempt to shift the burden of proof.
Example:
There is no evidence that frogs feel pain. They exhibit a certain behavior, but since they have no
consciousness they do not feel pain.
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.
Example:
Eating meat is morally permissible. Look how many people eat meat.
Begging the Question
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.”
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?
Circular Reasoning
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.
A: “Why do you believe in Zeus?”
B: “Because it is written in the Holy Scripture.”
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
A: “But why do you believe the Holy Scripture?”
B: “Because it’s the word of Zeus”
False Analogy
The problem is that the items in the analogy are too dissimilar. When reasoning by analogy, the
fallacy occurs when the analogy is irrelevant or very weak or when there is a more relevant
disanalogy.
Example:
The human body is a miniature copy of the universe.
Watchmaker/designer.
Government is like a family.
God is a father.
Reification
Considering an abstract noun to be a term referring to an abstract object, when the meaning of the
noun can be accounted for more mundanely without assuming the object exists.
Example:
“Nature has designed some amazing creatures.”
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 to homosexual marriage because if we allow it then one day people would
demand to marry animals.
Straw Man
Your reasoning contains the straw man fallacy whenever you attribute an easily refuted position to
your opponent, one that the opponent wouldn’t endorse, and then proceed to attack the easily
refuted position (the straw man) believing you have undermined the opponent’s actual position. If
the misrepresentation is on purpose, then the straw man fallacy is caused by lying.
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NYC COLLEGE OF TECHNOLOGY
Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro
Example:
We should oppose the Obamacare because it’s a communist bill that will take away all our
freedoms. Obamacare means that instead of private insurance there will be a death panel that
chooses whether you will live or die. Illegal aliens will get covered.
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!
Unfalsifiability
This error in explanation occurs when the explanation contains a claim that is not falsifiable,
because there is no way to check on the claim. That is, there would be no way to show the claim to
be false if it were false.
Post-hoc ergo propter hoc
This fallacy follows the basic format of: A preceded B, therefore A caused B, and therefore assumes
cause and effect for two events just because they are temporally related (the latin translates to “after
this, therefore because of this”). This is often encountered with health claims: I was sick, a took a
treatment, and now I am better, therefore the treatment made me better. Of course, it’s possible the
illness resolved on its own.
Genetic Fallacy
It is committed whenever an idea is evaluated based upon irrelevant history or of meaning of that
idea.
Argument from age is a common version of the genetic fallacy where the thing in question is very
new or old, so it must be better. Examples include products advertised as "New!" or "Old Fashioned
remedy or medicine.
Another variation is to dismiss or end praise ideas because they did or did not originate from here.
"Not good because it is made in China!” or commercials that claim “Made in the USA!” Or “This
cream is invented by German scientists…”
“Don't you know that the wedding ring originally symbolized ankle chains worn by women to
prevent them from running away from their husbands? So, you should not be a party to such a sexist
practice."
When we use the terms “sunset” and “sunrise” we’re not implying belief in a geocentric cosmology
in which the sun revolves about the Earth and literally “rises” and “sets.”
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