Introduction to Logic

The Nature of Philosophy and Logic
I. What is Philosophy?
The derivation of the word is from the Greek roots:
1. philo—love of, liking of As in the words ...
philology—having a liking for words
2. sophia—wisdom As in the words ...
sophist—one who loves knowledge
sophomore—one who thinks he knows everything
sophisticated—one who is knowledgeable

The Nature of Philosophy and Logic
A suggested definition:
philosophy is the systematic inquiry into
the principles and presupposition (to
suppose beforehand) of any field of inquiry.
 Psychologically, philosophy is an approach,
or a calling to answer, or to ask, or even to
comment upon problems.

The Nature of Philosophy and Logic
The Main Branches of Philosophy are divided as to the nature of
the questions asked in each area. The integrity of these divisions
cannot be rigidly maintained.
A. Axiology: the study of value; the investigation of its nature.
•The definition of axiology is the branch of philosophy that deals
with the nature and types of value such as in ethics and religion.
•Examples:
•Is morality defined by our actions, or by what is in our hearts?
•What values should be taught in character education?
•Studying the ethics of the Christian and Jewish religions is an
example of a study in axiology.

The Nature of Philosophy and Logic
2. Axiology is sub-divided into ...
a. Ethics: the study of values in human behavior; the study
of moral problems which seeks to discover how one
ought to act, not how one does in fact act or how one
thinks one should act.
b. Aesthetics: the study of value in the arts—
 Aesthetics is the branch of philosophy concerned
with the nature and appreciation of art, beauty and good
taste.
 The study of the beauty, sublimity, and principles of taste,
harmony, order, and pattern.
 Examples: Poetry, music, painting, drama, design.
 (How about layouts design?)

The Nature of Philosophy and Logic
B. Epistemology: the study of nature of knowledge
• In particular, the study of the nature, scope (limitations of
knowledge).
•As an example of orders of knowledge, consider the statement,
"The earth is round." This can be successively translated depending
upon context as ...
The earth is spherical.
The earth is an oblate spheroid (i.e., it's flattened at the poles).
But what of the mountains, oceans, and so forth?
Note: Oblate= flattened at the poles.
Spheroid= a sphere-like but not perfectly spherical body.

The Nature of Philosophy and Logic
C. Ontology or Metaphysics: the study of what is "really" real.
Metaphysics deals with the so-called first principles of the natural
order or the ultimate generalizations available to the human
intellect.
1. What kinds of things exist? How do they exist?
a. E.g., ideas have no size, shape, color, etc. Do ideas exist in the
same manner that physical objects exit?
b. What is spirit made of? Or Soul? Or Matter? Or Space? Or a
vacuum?

The Nature of Philosophy and Logic
•To which of these branches of philosophy do you
think logic belongs?
A. Logic: the study of the methods and principles
used in distinguishing correct from incorrect
reasoning.
B. Our knowledge is interrelated by logic.
C. Hence, logic is usually considered a subdivision
of epistemology, although, of course, logic is
used in all areas of philosophy.

The Nature of Philosophy and Logic
I. Logic is the study of the methods and principles used in
distinguishing correct from incorrect reasoning.
1. It prescribes how one ought to reason; it's not concerned
with how one actually does reason.
2. Logic is concerned with laying down the rules for correct
reasoning.
3. Consequently, logic seeks to distinguish good arguments
from poor ones

Logic
Logic is the study of methods, principles, and
techniques used to distinguish correct from bad
reasoning.

Logic (Invalid)
• Some apples are red. Therefore it follows that
President Obama was actually born in the old
Soviet Union, which makes him ineligible to be
President of the United States.

Reasoning
 The action of constructing thoughts into a valid
argument.
 This it what we probably do everyday.
 In decision making process, we are using reasoning.
 we are taking different thoughts and making those
thoughts into reasons (i.e., why should I go with one
option over the other option available, buying a coat
red/brown/black color, which one should I chose? And
why?).
 When we construct an argument, it will be either valid
or invalid
 A valid argument (reasoning that is comprehensive on
the foundation of logic)

Reasoning
 The process of using a rational, systematic series of
steps based on sound procedures and given
statements to arrive at a conclusion.
 A special kind of thinking in which problems are
solved, in which inference takes place., that is, in
which conclusions are drawn from premises.

Reasoning
Inference /Conclusion
 Refers to the process by which one proposition is arrived at
and affirmed on the basis of one or more other propositions
accepted as the starting point of the process.

Propositions/Statement
 A claim/statement that either affirms or denies
something or is either true or false.
 a statement or assertion that expresses a judgment or opinion
 Although its truth or falsity may be unknown.
 If a proposition is true, then we say it has a truth value of
"true”.
 if a proposition is false, its truth value is "false".
 For example, "Grass is green", and "2 + 5 = 5" are propositions.
The first proposition has the truth value of "true" and the
second "false"

Propositions (important)
•Propositions A proposition is a declarative
sentence that is either true or false.
•Examples of propositions:
•The Moon is made of green cheese.
• Trenton is the capital of New Jersey.
•Toronto is the capital of Canada.
•1 + 0 = 1
• 0 + 0 = 2
•Examples that are not propositions.
•What time is it?
•What is your name?

Proposition
• For example
– “There is life on some other planet in our galaxy”

Proposition
• Do you know how to play chess?
– Question assert nothing, therefore it is not
proposition

Proposition
• Proposition is the term we use to refer to
what it is that declarative sentences are
typically used to assert.
• For Example
– It is raining

 Difference between sentence and proposition
• Sentences are always parts of some language, but
propositions are not tied to English or to any given
language. The four sentences
– It is raining. (English)
– Está lloviendo. (Spanish)
– Il pleut. (French)
– Es regnet. (German)
are in different languages, but they have a single
meaning: all four, using different words, may be
uttered to assert the very same proposition.

Proposition/Sentence
• Proposition: A statement; what is typically asserted
using a declarative sentence, and hence always either
true or false—although its truth or falsity may be
unknown.
• “The largest state in the United States was once an
independent republic”
– “once” expressed a true statement or proposition (about
Texas)
– but if asserted today would express a false statement or
proposition (about Alaska)
– The same words assert different propositions at different
times.

Proposition
• Compound Proposition
– containing other propositions within themselves
– For Example
• The Amazon Basin produces roughly 20 percent of the
Earth’s oxygen, creates much of its own rainfall, and
harbors many unknown species.
– In above sentence we have three Proposition
» What it produce
» What it create
» What it harbors

Proposition
• Conjunctive Proposition
– The conjunctive proposition is one which asserts that
two alternatives cannot be true at the same time. (It is
possible for both alternatives to be false.)
– For Example
• “Canada is in North America and New York City is the biggest
city in Canada”.
• From above example it is clear that, if either one of the
individual propositions are False, then the whole thing is
False. And since we know that one is False, indeed the whole
thing is taken as False

Proposition
• Disjunctive Proposition
– It presents two or more alternatives, one of which
is true. Its members are linked by the conjunctions
“either…or”
– For Example
• "Canada is in North America or New York City is the
biggest city in Canada.“
• Now we have one proposition that is True, so the whole
thing is seen as True.

Proposition
• Conditional Proposition
– In this type of proposition one clause asserts
something as true provided that the other clause
is true
• The first clause is “if”
• The second one is “then”
• For Example
– If strong typhoons come, then crops will be destroyed
– If you work hard, you will get an A in this course.

Argument
• Argument: made to address specific problem, by offering a
position and providing reasons for that position.
• Two parts to a basic argument
– One or more premise
– A conclusion
• An argument is one or more statements, called premises,
offered as a reason to believe that a further statement,
called the conclusion, is true, that is, corresponds to reality.
• To tell your audience that you are drawing your conclusion,
introduce your statement using a word or phrase such as
“therefore,” “in conclusion,” “thus,” “consequently,” and so
on.
• To indicate a premise, introduce a statement using words
such as “because,” “since,” “for the reason that,” and so on.
Premise and conclusion indicator words help your audience
follow the “flow” of your reasoning.

Argument
• For Example
– No one was present when life first appeared on
earth. Therefore any statement about life’s origins
should be considered as theory, not fact
– Premise: No one was present when life first
appeared on earth
– Conclusion: Therefore any statement about life’s
origins should be considered as theory, not fact.

Deductive Argument
• A deductive argument starts with a conclusion and then
explains the facts, details and examples.
• Links premises with conclusions
• If all premises are true and clear, that conclusion must also
be true.
• Example 1
• All dog are mammals. All mammals have hearts. All dogs
must have hearts
• All dog are mammals (that’s true). All mammals have hearts
(That’s true). As both premises are true and clean, on the
basis of that the conclusion is also true, All dogs must have
hearts (true).
• Hence, this is a true conclusion on the basis of deductive
argument.

Deductive Argument
• A deductive argument starts with a conclusion
and then explains the facts, details and
examples.
• Links premises with conclusions
• If all premises are true and clear, that conclusion
must also be true.
• Example 2
• All birds can fly. An ostrich is a bird. All ostriches
can fly.
• All birds can fly (not true). An ostrich is a bird
(true). All ostriches can fly (Not true conclusion).

Deductive Argument
• A deductive argument is an argument in which it is
thought that the premises provide a guarantee of the
truth of the conclusion.
• In a deductive argument, the premises are intended to
provide support for the conclusion that is so strong
that, if the premises are true, it would be impossible
for the conclusion to be false.
• For Example
– There are 32 books on the top-shelf of the bookcase, and
12 on the lower shelf of the bookcase. There are no books
anywhere else in my bookcase. Therefore, there are 44
books in the bookcase.

Deductive Argument
• You can tell your audience that your argument
is deductive by introducing your conclusion
with wording such as “therefore it must be
that,” or “it necessarily follows that,” or
“therefore it is certain that,” or “it is
conclusively proven that,” and so on. These
phrases are called “deductive indicators.”

Inductive Argument
• An inductive argument starts with facts and
details and move to a general conclusion.
• Is probabilistic
• Weak, strong
• Can be proved false
• For Example
–We have seen 30 white swans. Therefore,
all swans are white.
–We made a conclusion on the basis of a
sample size of 30. But is it a true
conclusion. Answer is NO, as not all are
swans are white.

Inductive Argument
• An inductive argument starts with facts and
details and move to a general conclusion.
• Is probabilistic
• Can be proved false
• For Example
–Basketball players are tall. John is a
basketball player. John must be tall.
–We actually don’t know John. We never
saw him. Its very probable that John is
short and in the team as he can score
points (Probabilistic)

Inductive Argument
• An inductive argument is an argument in which it is
thought that the premises provide reasons supporting
the probable truth of the conclusion.
• In an inductive argument, the premises are intended
only to be so strong that, if they are true, then it is
unlikely that the conclusion is false.
• For Example
– The members of the Williams family are Susan,
Nathan and Alexander.
Susan wears glasses.
Nathan wears glasses.
Alexander wears glasses.
Therefore, all members of the Williams family wear
glasses.

Inductive Argument
• You tell your audience that your argument is
inductive by introducing your conclusion with
wording such as “therefore it is probably the
case that,” or “it is likely that,” or “therefore it
is reasonable to conclude that,” and so on.
These phrases are called “inductive
indicators.”

Argument
• Ann and Bob are not both home. But Ann is
home. Therefore, it follows that Bob must not
be home.
• Which type of argument is this? (Deductive or
Inductive)
• Deductively valid argument

Argument
• Even when premise and conclusion are united
in one sentence, the conclusion of the
argument may come first.
– “Every law is an evil, for every law is an infraction
of liberty”
– “Smoking is bad for health because it causes lung
cancer”

Argument
• No single proposition can be an argument, because an
argument is made up of a group of propositions.
• Although every argument is a structured cluster of
propositions, not every structured cluster of
propositions is an argument.
• For example
– “In the same world in which more than a billion people live at a level of affluence
never previously known, roughly a billion other people struggle to survive on the
purchasing power equivalent of less than one U.S. dollar per day. Most of the
world’s poorest people are undernourished—lack access to safe drinking water or
even the most basic health services and cannot send their children to school.
According to UNICEF, more than 10 million children die every year—about 30,000
per day—from avoidable, poverty-related causes”.
– So it is cluster of proposition but its not an argument because we have no
conclusions.

Assignment 1
• Identify the premises and conclusions in the
passages (from 5 to 15)
• Chapter 1, Book: Introduction to logic, Page 14

Exercise
Q1
• A well-regulated militia being necessary to the security
of a free state,
the right of the people to keep and bear arms shall not
be infringed.
• Premise: A well-regulated militia is necessary for the
security of a free state
• Conclusion: The right of the people to keep and bear
arms shall not be infringed

Exercise
Q2
• What stops many people from photocopying a book
and giving it to a friend is not integrity but logistics; it’s
easier and inexpensive to buy your friend a paperback
copy.
• Premises:1) it’s easier to buy your friend a paperback
copy.
2) it’s inexpensive to buy your friend a
paperback copy.
• Conclusion: What stops many people from
photocopying a book and giving it to a pal is not
integrity but logistics

Exercise
Q3
• Thomas Aquinas argued that human intelligence
is a gift from God and therefore “to apply human
intelligence to understand the world is not an
affront to God, but is pleasing to him.”
• Premise: human intelligence is a gift from God
• Conclusion: therefore “to apply human
intelligence to understand the world is not an
affront to God, but is pleasing to him.”

Q4
• Sir Edmund Hillary is a hero, not because he was
the first to climb Mount Everest, but because he
never forgot the Sherpas who helped
him achieve this impossible feat. He dedicated his
life to helping build schools and hospitals for
them.
• Premise: He dedicated his life to helping build
schools and hospitals for them.
• Conclusion: Sir Edmund Hillary is a hero

Q5
• Standardized tests have a disparate racial and
ethnic impact; white and Asian students score, on
average, markedly higher than their black and
Hispanic peers. This is true for fourth-grade tests,
college entrance exams, and every other
assessment on the books. If a racial gap is
evidence of discrimination, then all tests
discriminate.
• Now its yours task