1) Logic is the study of valid reasoning and establishing criteria to determine whether reasoning is valid or invalid. Valid reasoning is where conclusions truly follow from previous statements, while invalid reasoning is where conclusions do not follow. 2) Logic examines reasoning in a topic-neutral way, focusing on universal logical principles rather than empirical facts. Logical truths are necessary, in that their validity does not depend on how the world happens to be. 3) The principles of logic tell us what must be true given certain assumptions, but do not guarantee those assumptions are sound. Logic guides implication rather than truth directly.

1. Principles of Logics
Dr. Akhlas Ahmed
IBT, City Campus
Jan 28th
, 2017
Lecture # 2

2. • The etymology of word logic!
• Greek word
• Logos…
• Sometimes translated as sentence,
discourse, reason, rule and ratio.
• These translations are not enough to help us
understand the more specialized meaning of
"logic" as it is used today.

3. • What is logic?
• Logic is the study of the principles of
correct reasoning. (a rough definition)

4. • Logic…a new definition
• Logic is not the psychology of reasoning.
• According to this definition, logic is concerned
with the principles of correct reasoning.
• Studying the correct principles of reasoning is not
the same as studying the psychology of reasoning.
• Logic is the former discipline that tells us how we
ought to reason if we want to reason correctly.
• Whether people actually follow these rules of
correct reasoning is an empirical matter,
something that is not the concern of logic.

5. • Psychology…
• The psychology of reasoning is an empirical
science.
• It tells us about the actual reasoning habits of
people, including their mistakes.
• A psychologist studying reasoning might be
interested in how people's ability to reason varies
with age. But such empirical facts are of no
concern to the logic.

6. • The principles of logic…
• What are these principles of reasoning that
are part of logic?
• There are many such principles, but the
main (not the only) thing that we study in
logic are principles governing the validity of
arguments - whether certain conclusions
follow from some given assumptions.

7. • The principles of logic…
• Look at the arguments…
• Example # 1:
• If Tom is a philosopher, then Tom is
poor.
• Tom is a philosopher.
• Therefore, Tom is poor.
• Your opinion about argument?

8. • The principles of logic…
• Look at the arguments…
• Example # 2:
• If K>10, then K>2.
• K>10.
• Therefore, K>2.
• Your opinion about argument?

9. • The principles of logic…
• Look at the arguments…
• Example # 3:
• If Tarragona is in Europe, then
Tarragona is not in China.
• Tarragona is in Europe.
Therefore, Tarragona is not in China.
• Your opinion about argument?

10. • Findings from the examples…
• In all three examples, these arguments are
obviously good arguments.
• Their conclusions follow from the
assumptions. If the assumptions of the
argument are true, the conclusion of the
argument must also be true.
• A logician will tell us that they are all cases
of a particular form of argument known as
"modus ponens":
• If P, then Q. P. Therefore, Q.

11. • Conclusion…
• Logic is not just concerned with the
validity of arguments.
• Logic also studies consistency, and
logical truths, and properties of
logical systems such as completeness
and soundness.

12. • Rules of reasoning in logic…
• Modus ponens might be used to illustrate two
features about the rules of reasoning in logic.
• First feature is its topic-neutrality. As the four
examples suggest, modus ponens can be used in
reasoning about diverse topics. This is true of all
the principles of reasoning in logic.
• The laws of biology might be true only of living
creatures, and the laws of economics are only
applicable to collections of agents that engage in
financial transactions.
• But the principles of logic are universal principles
which are more general than biology and
economics.

13. • Famous definition of logic…
• According to famous logician Alfred Tarski
(1901-1983)…
• From his famous book ‘Introduction to logic and
to the methodology of deductive sciences, Dover,
page xi.’
• [Logic is] ... the name of a discipline which
analyzes the meaning of the concepts common to
all the sciences, and establishes the general laws
governing the concepts.

14. • Famous definition of logic…
• According to famous logician Gottolob
Frege (1848-1925)…
• From his 1956 paper "The Thought : A
Logical Inquiry" in Mind Vol. 65
• [Logic is] ...To discover truths is the task of
all sciences; it falls to logic to discern the
laws of truth. ... I assign to logic the task of
discovering the laws of truth, not of
assertion or thought.

15. • Concept of Necessity in Logic…
• Logic is different from the empirical sciences like
physics, chemistry or biology.
• Logic truths donot depend on any particular
accidental features of the world.
• The principles of logic are derived using reasoning
only, and their validity doesnot depend on any
contingent features of the world.
• Example, logic tells that any statement of the form
"If P then P." is necessarily true. This is a
principle of the second kind that logician study.
This principle tells us that a statement such as "if it
is raining, then it is raining" must be true. We can
easily see that this is indeed the case, whether or
not it is actually raining. Furthermore, even if the
laws of physics or weather patterns were to
change, this statement will remain true.

16. • Concept of Necessity in Logic…
• The scientific truths are contingent.
• Physics and the other empirical sciences
investigate the way the world actually is
• Physicists might tell us that no signal can travel
faster than the speed of light, but if the laws of
physics have been different, then perhaps this
would not have been true.
• Similarly, biologists might study how dolphins
communicate with each other, but if the course of
evolution had been different, then perhaps
dolphins might not have existed.
• So the theories in the empirical sciences are
contingent in the sense that they could have been
otherwise.

17. • What is logic?
• Logic is the study of valid reasoning.
• That is, logic tries to establish criteria to
decide whether some piece of reasoning is
valid or invalid.
• OK, so then what do we mean by ‘valid
reasoning’?

18. • Reasoning…
• A piece of reasoning consists of a sequence
of statements, some of which are claimed to
follow from previous ones. That is, some are
claimed to be inferred from others.
• Example: “Either the housemaid or the butler
killed Mr. X. However, if the housemaid
would have done it, the alarm would have
gone off, and the alarm did not go off.
Therefore, the butler did it.”

19. • Valid Reasoning…
• While in every piece of reasoning certain
statements are claimed to follow from others, this
may in fact not be the case.
• Example: “If I win the lottery, then I’m happy.
However, I did not win the lottery. Therefore, I am
not happy.”
• A piece of reasoning is valid if the statements that
are claimed to follow from previous ones do
indeed follow from those. Otherwise, the
reasoning is said to be invalid.

20. • Sound Reasoning…
• Not all valid reasoning is good reasoning.
• Example: “If I win the lottery, then I’ll be
poor. So, since I did win the lottery, I am
poor.”
• This piece of reasoning is valid, but not very
good, since it assumed an absurd claim (‘If I
win the lottery, I’ll be poor.’ Huh??)
• Sound reasoning is valid reasoning based on
acceptable assumptions.

21. • Truth and Implication…
• Logic studies the validity of reasoning.
• Logic does not study soundness.
• Therefore, logic alone cannot tell us whether
an argument is good. Hence, logic alone is
not a guide to truth.
• Instead, logic can tell us, assuming certain
things to be true, what else will be true as
well. Thus, logic is a guide to implication.

22. • Arguments, Premises and Conclusion
• In logic, pieces of reasoning are analyzed using
the notion of an argument
• An argument consists of any number of premises,
and one conclusion
• Again, in logic, we are merely interested in
whether the conclusion follows from the premises:
we are not interested in whether those premises
are true or acceptable.

23. Quiz # 2 (28.1.2017)
Q2. How is science different
from logic?

24. Assignment # 2 (28.1.2017)
Q1. Suppose we find out that people
reason better when they are not under
stress. Should this be counted as a
principle of logic?
Q2. How is mathematics different from
logic?