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Section II: Logic: Clear/Critical Thinking

Belief and Critical Thought
• since our beliefs (the claims we accept) constitute our view of the
world and of ourselves, and affect how we act, it is important to
examine more carefully the beliefs we hold.
• This applies both to large scale philosophical issues (Does God exist?
Do I have a soul? Am I free? Does it matter?), and to small scale
mundane issues (Should I buy this car? Should I believe what she
said? How should I dress?).
• Let’s officially define some of the terms we use in the study:
Logic:
• Logic is the study of (i) criteria for distinguishing successful from
unsuccessful argument, (ii) methods for applying those criteria, and
(iii) related properties of statements such as implication, equivalence,
logical truth, consistency, etc.

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Statement:
• A statement is a declarative sentence; a sentence which attempts to
state a fact—as opposed to a question, a command, an exclamation.
Truth Value:
• The truth value of a statement is just its truth or falsehood. At this
point we make the assumption that every statement is either true
(has the truth value true) or false (has the truth value false) but not
both. The truth value of a given statement is fixed whether or not we
know what that truth value is.
• Our assumption regarding truth values—that all statements are either
true or false and not both—is one that may reasonably be
questioned.
• Issues of vagueness, ambiguity, subjectivity, and various sorts of
indeterminacy may lead us to think that some statements are
neither true nor false, or both true and false, or “somewhere in
between”.

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Argument:
• An argument is a (finite) set of statements, some of which—the
premises— are supposed to support, or give reasons for, the
remaining statement—the conclusion.
• When we encounter an argument in the course of reading or during
discussion the premises and conclusion may come in any order.
Consider the following versions of a classic example:
• Socrates is mortal, for all humans are mortal, and Socrates is human
• Given that Socrates is human, Socrates is mortal; since all humans are mortal
• All humans are mortal; Socrates is human; therefore, Socrates is mortal
• Despite the fact that they appear in different order in each one, all
three examples express the same argument.

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Premise Indicators:
• as, since, for, because, given that, for the reason that, inasmuch as
Conclusion Indicators:
• therefore, hence, thus, so, we may infer, consequently, it follows that
• So it is usually a relatively simple task to put arguments into standard
form.
• Of course, if the argument is long and complex, with sub-conclusions
acting as premises for further conclusions, analysis can get messy.
Thinking in Two Directions: Deductive and Inductive Reasoning
• Logic is the method we use to distinguish good thinking from bad
thinking.
• Deductive and Inductive reasonings are the two basic types of criteria
for evaluating arguments.

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(1) Deductive Reasoning is where our conclusion must be true if our

assumptions and reasoning are good.
• Deductive reasoning is an up side down V.

(2) Inductive Reasoning is where our conclusion is probably true if our

reasoning and evidence is good.
• Inductive reasoning is more like the normal V

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• Deductive thinking starts with certain assumptions and then shows what
must be true if those assumptions are true.
• Much of math, particularly geometry, is deductive in nature.
• In inductive reasoning, we gather evidence and then hypothesize possible
or probable conclusions given the evidence we have.
• Most scientific thinking is inductive, where we form hypotheses to try to
explain a set of data.
Thinking Deductively
• If we have ever had a class in geometry, we will no doubt remember having
to prove things like “the measures of the angles of a triangle add up to 180
degrees.”
• These kinds of statements are called theorems. To prove them, we drew on
a number of “givens” that our geometry textbook did not try to prove.
• These were things we were supposed to assume were true, like “two points
make a line” or “parallel lines never meet.”

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• Deductive logic is like math: either we get it right or we get it wrong.

• If the logic is valid and the premises are true, the conclusion must
be true.
• If the logic is invalid, then we say that the conclusion is called “it does
not follow.”
• Mistakes in deductive reasoning are usually mistakes in the way the
argument is set up, “formal” fallacies.
• one more aspect of deductive logic is the tautology, when some claim
is equal to itself.
• For instance, the statement “he is single because he is not married” is
a tautology, because we have simply said the same thing in two
different ways.

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• It can be helpful to recognize a tautology, because sometimes people

think they are saying something that advances an argument when in
fact they are simply saying the same thing in a different way.
Thinking Inductively
• In inductive reasoning, one gathers evidence and hypothesizes
possible or probable conclusions based on that evidence.
• In life, we are constantly observing and drawing conclusions from
what we see.
• The scientific method is a great example of solid, inductive reasoning.
You identify a question and gather relevant evidence in relation to
that question.

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• Then you form hypotheses that you test against the data until a
hypothesis emerges that accounts so well for the data that it merits
being considered a theory.
• Much is made in some Christian circles of the difference between a
theory and a fact.
• For example, you sometimes hear of arguments between scientific
creationists and evolutionists over whether evolution is fact or theory.
• Both should be able to agree, however, that evolution is a scientific
theory.
• Inductive reasoning is about probabilities given the evidence rather
than about certainties.
• Facts are certainties. Theories are about probabilities.

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• In science, if something has been tested enough to be called a

theory, then it is the most probable reading of the evidence at this
time, a reasonable thing to believe for the time being, even though it
is not absolutely certain.
• For instance, I notice that every tree in my yard has leaves. I form a
hypothesis: all trees have leaves.
• I might walk around my neighborhood and test this hypothesis.
Perhaps I come across a dead tree without leaves, so I have to
modify it. All living trees have leaves.
• Continued observation will further modify my hypothesis in more
than one way. All healthy trees have either leaves or needles at
some point during the year.
• After extensive travel, testing, and modification of my hypothesis
against the data of the world, I will at some point upgrade my
hypothesis to a theory.

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• However, I cannot consider it a fact that all healthy trees have, have
had, and will have either leaves or needles at some point during the
year.
• Neither I nor any human is capable of observing all trees on earth.
• Who knows? Maybe one day a tree will arise that has something else.
• Therefore, inductive reasoning by its very nature tends to be open
ended for possible modification on the basis of new evidence.
• Even when one has all the relevant evidence, inductive reasoning
involves interpretation and thus can still be open ended.
Formal and Informal Fallacies:
• Fallacies are logical errors people make when they are reasoning.
• Fallacies of inductive reasoning tend to be informal fallacies in
contrast to formal fallacies, which are more a matter of deductive
reasoning.

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• Formal fallacies have to do with the way an argument is set up, the
structure of an argument.
• Informal fallacies often have to do with false assumptions and the
specific claims of an argument being wrong in some way.
Formal Fallacy:
• Someone might come up to me and say, “I can tell you’re a man
because you have short hair.”
• This person has committed a logical or formal fallacy; the length of a
person’s hair is not logically linked to his or her gender.
• The conclusion was true: I am male. It is this person’s logic that was in
error, even though the conclusion was correct for other reasons.
Informal Fallacy:

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What is a Fallacy?
• A fallacy is an error in reasoning. Incorrect reasoning is always
fallacious.
• Logicians commonly use the term ‘fallacy’ more narrowly, to
designate not any errors in reasoning, but for typical errors- mistakes
in reasoning that exhibit a pattern that can be identified and named.
• In narrower sense, every fallacy is justified through an incorrect
argument.
• Although mainly fallacies concern mistakes in arguments, some
fallacies relate to explanations, definitions, or other instances of
reasoning.
• A Fallacy is also different form of factual mistake.

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Examples of Mistakes
Logical mistake:- Fallacy: Formal & Informal- Errors in reasoning/
argument/explanation are fallacious.
1. Making a contradictory claim, putting forward a question with
unwarranted presuppositions, misinterpreting a statement by putting
wrong emphasis on a word or phrase in it are counted as fallacies.
2. Any other argument form where there is no connection between
premise and conclusion is also called a fallacy.
Factual mistake:- Mistakes done while depicting any fact, figure or
information of any type that can be
1. Total 11 countries are affected by Corona Virus all over the world-
Wrong
2. India is a poor populated nation-Wrong
3. Holy Trinity University is established in 21st century-Wrong

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• Rectification of these above-mentioned errors are factual errors are

possible by correcting the facts based on right information.
Relevance of Fallacy
• Logician’s task is to indicate the pitfalls laid by language in the way of
the thinker.
• Different forms of fallacies can help us
1. Improving our ability to argue well.
2. Developing the analytical skills.
3. Avoiding in committing mistakes repeatedly.
4. Detecting the error.
5. Making/promoting fair/just decision.

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1. Fallacy: Appeal to Force

• forcing someone to hold a certain position does not make that
position true.
• The law usually will reject a confession from a suspect that has been
coerced.
• Force is the stuff of power and politics, but it is not the stuff of logic.
• You cannot change what is logically true by torture or pressure.
2. Fallacy: Appeal to Emotion
• It can’t be wrong, when it feels so right.
• Whatever merit this thought might have in other contexts, it has no
merit in logic.
• Whether or not something is true logically has nothing to do with
feelings or emotions.

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3. Fallacy of Subjectivism
• This fallacy is closely related to the appeal to emotion.
• Something is not true or false logically because of what I want to be
true or false.
• For example, the question, does God exist objectively, apart from
human thinking? has nothing to do with whether I like the idea of
God or whether it works for me.
• It is not a matter of my motivation to believe or disbelieve.
• The question of whether God exists objectively depends on, well,
whether or not God exists objectively.
• When we are talking about this kind of existence, then God exists or
does not exist regardless of my feelings or desires.

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4. Fallacy: Appeal to the Majority

• Something is not logically true or false simply because a majority of
individuals wants it to be true or false.
• In general, truth or falsity in logic is not a matter of vote.
• Whether or not an idea is true or false is a matter of, well, whether
it is true or false.
• Is it raining right now outside in the normal sense of what it means
to rain?
• The answer to this question is not a matter of a vote. Either it is
literally raining or it is not.

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5. Fallacy: Appeal to Improper Authority

• It is a fallacy of bringing other people into arguments.
• In some circumstances it might make sense to put weight on a
person’s claims because of who that person is, that person’s
credibility.
• Take a victim of a crime who is mentally stable, knew his or her
attacker, has no apparent ulterior motives, and observed the person
who attacked.
• This person certainly seems a credible authority on the identity of
the attacker.
• This credibility does not prove guilt absolutely, but it may argue for
truth beyond reasonable doubt.
• Mostly, we rely on the opinions of individuals who are not really
appropriate authorities on an issue.

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• “Everyone’s entitled to their opinion.”

• but it does not mean that everyone’s opinion is equally valuable or
likely to be true.
• Informed opinion is, at least logically, more valuable than an
individual’s whims and fancies.
• In the realm of thinking, opinion is worthless unless it has
reasonable arguments behind it.
• The fallacy of improper authority is a real issue in matters of religion
and politics.
• For example, a person who does not understand or know the science
involved in climate change or evolution is not competent to evaluate
the weight of the evidence with regard to the science surrounding
those subjects.

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• He or she could theoretically have received revelation from God on

these issues, but he or she cannot be an authority on the science.
• Similarly, a person may know something true that God has revealed
to him or her while reading the Scripture, but such individuals cannot
be authorities on the original meaning of the Bible unless they know
the original languages, the historical background, the history of
interpretation, and the process of reading in context (exegesis).
6. Fallacy: Argument against the Person
• It is often effective in debate to attack your opponent rather than
the actual issue you are debating—effective rhetorically but not
logically.
• Politics is rife (common) with this sort of sleight of hand.
• So-and-so is in a picture with this other so-and-so—thus I illogically
transfer what you do not like about the one to the other.
• So-and-so cusses a lot or had an affair, therefore I illogically suggest
so-and-so’s ideas on some unrelated issue must be wrong.

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• So-and-so is a liberal or a conservative or a communist or a fascist or

unpatriotic—death by labeling the person.
• I dismiss this person’s thinking on a particular issue, not by arguing
against this person’s position, but by suggesting he or she belongs to
an untrustworthy group.
• But logically you cannot dismiss the truth of an idea by attacking the
person who holds the idea.
• Whether or not an idea is true or false depends on, well, whether or
not the idea is true or false. It does not depend on the person who
has the idea.

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7. Genetic and Circumstantial Fallacies

• Two related fallacies are the genetic fallacy and the circumstantial
fallacy.
• The genetic fallacy is to say that something must be false because of
the reasons someone came to the idea.
• Here are some examples of the fallacy. Sigmund Freud suggested that
people believe in God because they want a father figure to take care
of them.
• Karl Marx famously called religion the “opiate of the masses.”
• But even if these scenarios proved to be true for many—let’s say that
some people believe in God because they want divine help or to
make life bearable—that motivation would not logically disprove the
existence of God.
• Whether or not God exists depends on, well, whether or not God
exists.

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• The circumstantial fallacy argues against a person’s position by

pointing out the circumstances in which the person is making the
claim.
• “Isn’t it true that the district attorney has cut you a deal if you will
testify?”
• It may be true, but that does not logically lead to the conclusion that
the witness is lying to get a deal.
• For this reason, circumstantial evidence is of varying value in a trial.
• From a practical standpoint, it can be very compelling.
• Let’s say I find my son with cookie crumbs and chocolate smears
around his mouth, a trail of crumbs leading back to a cookie drawer
that is opened, with a box of cookies opened and standing upright in
the drawer.
• I did not actually see my son take or eat the cookie.

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• I am not an eyewitness to the “crime.”

• Nevertheless, it is reasonable to infer that he in fact has just eaten a
cookie from the drawer.
• At the same time, this circumstantial evidence does not logically
prove that he did.
• He could have been framed by one of his clever sisters, without him
even realizing it.
• For that matter, space aliens or a mischievous angel might have set
the whole thing up.
• This scenario gives us a good illustration of the difference between
what is logically necessary and what is possible or even probable.
8. Fallacy: Appeal to Ignorance
• Sometimes someone will argue that because you have not or cannot
prove one thing to be true, the opposite must be true.
• “Prove it. You can’t prove I did it.”

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• Of course the fact that I cannot prove that you did something says nothing
definitive about whether you did it or not.
• Either you did it or you did not, and my ability to tell which does not affect
anything.
• Sometimes people use this fallacy in relation to God’s existence. “You
cannot prove God exists; therefore, God must not exist.” This argument
commits the fallacy of ignorance.
• An individual may certainly think he or she has no reason to believe in God.
But this fact does not in any way serve as a proof that God does not exist.
9. Fallacy: Hasty Generalization
• One of the most frequently committed logical fallacies is that of hasty
generalization.
• You draw an inference when you do not have enough information to do so,
or perhaps you ignore important information that should be considered.
• This fallacious reasoning often accompanies the commission of other
fallacies.

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10. Fallacies of Composition and Division

• The fallacy of composition is when you assume something is true of a
whole group of things because it is true of some of the things within
the group.
• We see this fallacy at work in what sociologists call in-group/out-
group dynamics.
• People tend to pick positive individuals or traits from the groups to
which they belong and then ascribe these particular characteristics to
the whole group.
• “America is a Christian nation, whose people are honest and want to
help the world.” But obviously the United States has its share of sin
and dishonesty.
• Similarly we tend to pick negative traits or examples from other
groups we do not like and paint the whole group with the same
brush.

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• “You have to watch out for such and such a group; they steal or lie or
cheat all the time.” “All Muslims are terrorists.” “Catholics do not
believe in the Bible.”
• This is the stuff of prejudice—and often the fallacy of composition.
• By contrast, the fallacy of division is when you take something that is
true of the whole and then apply it to all of its parts.
• The fact that a team loses a ball game does not mean that every
individual on the team played poorly or worse than those on the
other team.
• The fact that an administration as a whole makes bad decisions does
not mean that everyone in that administration agreed with those
decisions or thought them the best course of action.

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11. Fallacy: After This, Therefore Because of This

• One frequent expression of hasty generalization is the assumption
that because something happened after something else, the first
thing must have caused the second thing.
• In other words, if event Y happens after event X, then event X must
have caused event Y. This isn't necessarily the case.
• For example, let’s say I touch your earlobe, and then immediately
someone across the room gets up and leaves the room.
• It might be tempting to think that the touch had something to do
with the person walking out, but it is not at all a logical certainty.
• We especially have to be careful about this fallacy when looking at
historical events and trying to ascribe praise or blame to some alleged
cause.
• Just because something happens before something else—this does
not prove that the first was the cause of the second.

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12. Fallacy: Correlation

• A related fallacy is when you assume something that correlates or
happens concurrently with something is the cause of that thing.
• Let’s say that one year both the crime rate increases in a particular
city, and, at the same time, a large number of people move away.
• It is of course possible that the rise in crime is causing some people to
leave town.
• But it is also logically possible that the rise in crime correlates with
the people leaving town and that the two events are unrelated.
• One has to be very careful when doing research not to assume a
cause-effect relationship without sufficient evidence.
• Things can happen at the same time without being related causally.

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13. Fallacy of Diversion

• The fallacy of diversion involves changing the subject in the middle of
debate.
• Some of the fallacies we have already mentioned can serve such a
diversion, for example, attacking the person instead of his or her
position.
• One common form of diversion confuses the potential consequences
of a course of action with the validity of the action itself.
• For example, it may very well be that prohibiting certain drugs could
lead to people selling them illegally and a whole host of undesirable
consequences.
• However, such consequences, abuses that others commit, would not
necessarily mean that prohibiting those drugs was inappropriate.

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• Whether or not some course of action is right or wrong is a question

distinct from whether others might take advantage of or do bad
things in light of the situation it creates.
• Another form of diversion is a straw man argument.
• In this fallacy, you create a portrait of your opponent’s position that
looks a little like it but is actually not quite the same as what the
opponent is claiming.
• Most of us would have a hard time beating up your average weight
lifter or wrestler.
• But we could probably vanquish quite easily a version of one stuffed
with straw.
• In the same way, it is easy to dismiss someone else’s argument when
he or she is not in the room and you are misrepresenting that
person’s position.

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14. Fallacy of Equivocation

• The fallacy of diversion involves a change of subject.
• The fallacy of equivocation changes in midargument the sense of the
words you are using.
• Take the quip, can God make a rock so big that he cannot lift it?
• The person who poses this question usually wishes to argue that it
does not make sense to say that God is all powerful.
• But this person has mixed up two distinct concepts associated with
the word can.
• One has to do with power or ability, and the other has to do with
possibility.
• Christians do not normally suggest that it is possible for God to do
everything (e.g., to fail), for “everything” includes things that
contradict each other.

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• Christians believe rather that God has all power or, as some Christian
philosophers put it, that God can do anything that is logically
possible.
• The answer to the question, can God make a rock so big that he
cannot lift it? is thus no, precisely because God is all powerful. God
can (has the power to) lift any rock.
• But he cannot (it is not possible) for him not to be able to lift a rock.
• The question is worded in a way that plays into the fallacy of
equivocation.
15. Fallacy: False Alternative
• Another fallacy is to present an either/or option, when in fact other
alternatives exist.
• Either you love me or you hate me. Either you favor the war or you do
not. Life is rarely this simple.

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• Here are two more examples: if you do not believe every word of the
Bible is true, then you do not believe any of the Bible is true;
• if you believe in evolution, then you do not believe God created the
world.
• These last two statements are examples of fallacious thinking even if
we believe every word of the Bible is true and do not believe in
evolution.
• For example, there are Christians who believe that God created the
world through evolution.
• They may be wrong, but they represent another possibility for which
the either/or sentence above did not allow.
• And if for some strange reason someone believed that Lot’s wife
turned into mustard rather than salt (see Gen. 19:26), that would not
imply that this person did not believe in the resurrection or that we
should love our neighbors.
• This is the fallacy of false alternative.

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• One notable example of the fallacy of false alternative is the slippery

slope fallacy.
• A slippery slope refers to the idea that if you start down a certain
path or line of reasoning, you will not be able to stop before you
reach an undesirable end.
• If we let students dance at our college, then next they will try to get
permission to drink. So let’s not allow dancing to stop the slippery
slope there.
• In real life, slippery slopes can actually have some substance to them.
It is a good idea not to let your teenage son or daughter be alone in
an empty house with his girlfriend or her boyfriend if you don’t want
certain things to happen.
• But logically, it is not an absolute certainty that one thing will lead to
another. Other alternatives exist.

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16. Fallacy: Begging the Question (Circular Reasoning)

• Yet another fallacy is begging the question, which is when you assume
your conclusion in your argument.
• You cannot use the fact that Ken said he never lies to prove that Ken
never lies.
• What if I am a flagrant (blatant) liar? You cannot assume something
you want to prove in order to prove it.
• Circular reasoning can be tricky because we aren’t always aware of
our own assumptions.

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17. Fallacy: Complex Question

• A related fallacy is the complex question, such as in some cases when
a lawyer leads a witness by asking, “When did your anger issues
stop?”
• The attorney here is assuming that the person had anger issues.
• The question thus asks a follow-up question when no one has yet
established the answer to the first question, namely, “Did you have
an anger problem?”
Conclusion
• In a world where so much seems uncertain, the rules of logic remain
clear and indisputable.
• There are coherent and fallacious ways of thinking, arguments that
are valid, and arguments that are invalid.
• We live in an age when opinion sometimes seems to count as much
as expertise and every opinion is considered as valid as any other.

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• In such a context, the rules of logic provide at least one irrefutable

measure by which to evaluate certain claims and arguments.
• If we do not share “ground rules” like these for thinking in common, it
will prove very difficult for us to communicate with each other or to
decide between conflicting positions.
• Deductive reasoning is when you draw a conclusion based on
premises you assume.
• In such reasoning, if your premises are true and your logic is valid,
the conclusion must follow without exception.
• Inductive reasoning starts with a body of evidence and creates
hypotheses to explain the data.
• Along the way, we regularly see all sorts of bad reasoning.
• You might subtly change the subject or attack the person instead of
the argument.

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• You might mistake an exception for the rule or falsely stereotype

everyone in a group.
• Sometimes we try to disguise feelings as arguments when they are
none of the sort.
• We present false alternatives or create fear by invoking a slippery
slope.
• The more we are able to think coherently and avoid fallacious
thinking, the more empowered we will be to sort out truth from
falsehood.

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