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Understanding Logic

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Anoud Abusalim

on 26 April 2015

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Transcript of Understanding Logic

WHAT IS LOGIC?
Logic may be defined as the science of reasoning. However, this is not to suggest that logic is an empirical (i.e., experimental or observational) science like physics, biology, or psychology. Rather, logic is a non-empirical science like mathematics. Also, in saying that logic is the science of reasoning, we do not mean that it is concerned with the actual mental (or physical) process employed by a thinking being when it is reasoning.
Distinguishing correct reasoning from incorrect reasoning is the task of logic.

INFERENCES AND ARGUMENTS
Reasoning is a special mental activity called inferring, what can also be called making (or performing) inferences.
The following is a useful and simple definition of the word ‘infer’.

To infer is to draw conclusions from premises.
Examples of Inferences:
(1) You see smoke and infer that there is a fire.
(2) You count 19 persons in a group that originally had 20, and you infer that someone is missing.
Infer vs Imply
Note carefully the difference between ‘infer’ and ‘imply’, which are sometimes confused.
We
infer
the fire on the basis of the smoke, but we do not
imply
the fire.
On the other hand, the smoke
implies
the fire, but it does not
infer
the fire.
The word ‘
infer
’ is not equivalent to the word ‘
imply
’, nor is it equivalent to ‘insinuate’.

A Special Note before You Go Crazy :)
The reasoning process may be thought of as beginning with input (premises, data, etc.) and producing output (conclusions).
In each specific case of drawing (inferring) a conclusion C from premises P1, P2, P3, ..., the details of the actual mental process

(how the "gears" work) is not the proper concern of logic, but of psychology or neurophysiology. The proper concern of logic is whether the inference of C on the basis of P1, P2, P3, ... is warranted (correct).

Arguments in Logic
Inferences are made on the basis of various sorts of things – data, facts, information, states of affairs.
In order to simplify the investigation of reasoning, Logic correspondingly treats inferences in terms of collections of statements, which are called arguments.
The word ‘argument’ has a number of meanings in ordinary English.
The definition of ‘argument’ that is relevant to logic is given as follows:
An argument is a collection of statements, one of
which is designated as the conclusion, and the
remainder of which are designated as the premises.
Usually, the premises of an argument are intended to
support (justify) the conclusion of the argument.

A Small Detour: Arguments and Statements
The word ‘statement’ is intended to mean
declarative sentence.
In addition to declarative sentences, there are also interrogative, imperative, and exclamatory sentences. The sentences that make up an argument are all declarative sentences; that is, they are all statements.

A statement is a declarative sentence, which is to say a sentence that is capable of being true or false.

Remember that for our logical fallacies class next class.
Statements vs Sentences
The following are examples of statements.
It is raining
I am hungry
2+2 = 4

On the other hand the following are examples of sentences that are not statements.

are you hungry?
shut the door, please
#$%@!!! (replace ‘#$%@!!!’ by your favorite expletive)
How does that Relate to Writing an Essay?
When writing any form of a persuasive essay or prose, you should make sure that:
1- Your sentences are declarative sentences
2- Your conclusions are based on logically connected sentences.
Understanding Logic
Anoud Abusalim
WRI 102
Spring 2015
American University of Sharjah

Examples of Students' Writing
P1:
Saudi Arabia is the only count in the world where it is illegal for women to drive. ( Declarative Sentence).
P2:
But why is it illegal? ( Question)
P3:
Continuous protests and arguments have been going on since the law has been declared on May 2009 when Saudi Arabia banned them to drive ( Factually wrong, but it is a sentence)
P4:
Some argue that women should not drive due to health purposes and traditional obstacles in addition to cultural restrictions. ( Declarative Sentences despite the faulty reasons)
P5:
The question is, what is the solution for this problem?
P6:
Should Saudi women be authorized to drive or should they not?
Inferences and Arguments
(a1) there is smoke (premise)
therefore, there is fire (conclusion)

Here the argument consists of two statements, ‘there is smoke’ and ‘there is fire’.
The term ‘
therefore
’ is not strictly speaking part of the argument; it rather serves to
designate the
conclusion
(‘there is fire’), setting it from the premise (‘there is smoke’). In this argument, there is just one premise.
Inferences and Arguments
In the case of the missing-person inference, the corresponding argument is given as follows.
(a2) there were 20 persons originally (premise)
there are 19 persons currently (premise)
therefore, someone is missing (conclusion)
Here the argument consists of three statements – ‘there were 20 persons originally’,
‘there are 19 persons currently’, and ‘someone is missing’. Once again, ‘therefore’ sets off the conclusion from the premises
How to Build an Argument?
In principle, any collection of statements can be treated as an argument simply
by designating which statement in particular is the conclusion. However, not every collection of statements is intended to be an argument. We accordingly need
criteria by which to distinguish arguments from other collections of statements.
Arguments in Writing
There are no hard and fast rules for telling when a collection of statements is intended to be an argument, but there are a few rules of thumb. Often an argument can be identified as such because its conclusion is marked. We have already seen one conclusion-marker – the word ‘therefore’. Besides ‘therefore’, there are other
words that are commonly used to mark conclusions of arguments, including ‘consequently’, ‘hence’, ‘thus’, ‘so’, and ‘ergo’. Usually, such words indicate that what follows is the conclusion of an argument.

Other times an argument can be identified as such because its premises are marked. Words that are used for this purpose include: ‘for’, ‘because’, and ‘since’.
For example, using the word ‘for’, the smoke-fire argument (a1) earlier can be rephrased as follows.
(a1') there is fire
for there is smoke
Final Notes
Arguments
To state things somewhat differently, when a person (speaking or writing) advances an argument, he(she) expresses a statement he(she) believes to be true (the conclusion), and he(she) cites other statements as a reason for believing that statement
(the premises).
In an argument, the premises are intended to support (justify) the conclusion.
Deduction
Steps:
In the process of deduction, you begin with some statements, called 'premises', that are assumed to be true.
You then determine what else would have to be true if the premises are true.
Famous examples:
You can begin by assuming that God exists, and is good, and then determine what would logically follow from such an assumption. ( God is good).
You can begin by assuming that:
if you think, then you must exist, and work from there.
In mathematics, you can also start will a premise and begin to prove other equations or other premises.
With deduction you can provide absolute proof of your conclusions, given that your premises are correct. The premises themselves, however, remain unproven and unprovable, they must be accepted on face value, or by faith, or for the purpose of exploration.
Induction
Steps:
In the process of induction, you begin with some data.
Then, you determine what general conclusion(s) can logically be derived from those data.
In other words, you determine what theory or theories could explain the data.
Poplar examples ( mostly used in sciences):
You note that the probability of becoming schizophrenic is greatly increased if at least one parent is schizophrenic, and from that you conclude that schizophrenia may be inherited.
That is certainly a reasonable hypothesis given the data.
However, induction does not prove that the theory is correct.
There are often alternative theories that are also supported by the data.
For example, the behavior of the schizophrenic parent may cause the child to be schizophrenic, not the genes.
What is important in induction is that the theory does indeed offer a logical explanation of the data.
To conclude that the parents have no effect on the schizophrenia of the children is not supportable given the data, and would not be a logical conclusion. ( This is vital for your synthesis skills and paper).
Examples of Inductive Logic
You see that a lot in standardized tests !!!
Now, lets move to
deductive
and
inductive
reasoning
Examples of deductive logic
P1:

All men are mortal.
P2:
Joe is a man.
C:
Therefore Joe is mortal.

If the first two statements are true, then the conclusion must be true. 2
What is the next number in the sequence 6, 13, 20, 27,…

Here’s the sequence again 6, 13, 20, 27,…
Look at the difference of each term.
13 – 6 = 7, 20 – 13 = 7, 27 – 20 = 7
Thus the next term is 34, because 34 – 27 = 7.
However what if the sequence represents the dates. Then the next number could be 3 (31 days in a month).
The next number could be 4 (30 day month)
Or it could be 5 (29 day month – Feb. Leap year)
Or even 6 (28 day month – Feb.)

Deductive Reasoning
Examples:
All students eat pizza.
Claire is a student at ASU.
Therefore, Claire eats pizza.

2. All athletes work out in the gym.
Barry Bonds is an athlete.
Therefore, Barry Bonds works out in the gym

3.All math teachers are over 7 feet tall.
Mr. D. is a math teacher.
Therefore, Mr. D is over 7 feet tall.
The argument is valid, but is certainly not true.

The above examples are of the form
If p, then q. (major premise)
x is p. (minor premise)
Therefore, x is q. (conclusion)

Syllogism
All men are mortal. (major premise)
Socrates is a man. (minor premise)
Therefore, Socrates is mortal. (conclusion)


Syllogism
Syllogism:
An argument composed of two statements or premises (the major and minor premises), followed by a conclusion.
For any given set of premises, if the conclusion is guaranteed, the arguments is said to be valid.
If the conclusion is not guaranteed (at least one instance in which the conclusion does not follow), the argument is said to be invalid.
BE careful, DO NOT CONFUSE TRUTH WITH VALIDITY!

Lets have a break and watch one of the most illogical things you do every day when you are behind the wheels....

Then, we will have some practice on logic using the reading....
P1:
Saudi Arabia is the only country in the world where it is illegal for women to drive. ( Declarative Sentence).
P2:
But why is it illegal? ( Question)
P3:
Continuous protests and arguments have been going on since the law has been declared on May 2009 when Saudi Arabia banned them to drive ( Factually wrong, but it is a sentence)
P4:
Some argue that women should not drive due to health purposes and traditional obstacles in addition to cultural restrictions. ( Declarative Sentences despite the faulty reasons)
P5:
The question is, what is the solution for this problem?
P6:
Should Saudi women be authorized to drive or should they not?
Open the reading
" Who Says a Woman Cannot be Einstein" and lets do some logic"
How are things in logic named differently than writing?
P.S: they are practically the same.
How do students usually use inductive and deductive logic in writing and reading?
Why teach logic in a writing class, you ask?
Organizing and supporting the paragraphs:
1- When we learn about inductive and deductive logic, we know how to organize the support of the paragraphs.
2- Also, we learn to place our conclusions as our topic sentences.


How DO Logic & Writing Relate?
Conclusion
Topic Sentence
Premises

Supporting Sentences
Logic is What goes on Our Minds
In writing, we express these logical thoughts following
How to transfer the two types on logic into your writing?
Inductive Logic
Premises = Evidence
Conclusion = Topic sentence
How to Write the Paragraph?
Conclusion = Topic Sentence
Premises = Evidence
Conclusion = Topic sentence
Premises = Evidence
How to Write the Paragraph?
Conclusion = Topic Sentence
Premises = Evidence
Deductive Logic
Deductive
Writing
Inductive
Reading
Quick Revision before we begin fallacies
Definitions
1-
Either/or:
only two choices are possible.
( Very common is gender talks: girls either smart or beautiful)
2-
Avoiding the Issue:
To avoid this error , the solution must respond to the problem.
( Happened a lot in our debates, you bring irrelevant points that do not advance your arguments)
3-
Overgeneralizing
: Thinking that a valid idea extends beyond the limit of reasonableness.
( Gender, driving, racism)
( The use of qualifiers helps in lessening it)
4-
Oversimplifying
: distorting complex matters.
(Again, you do that a lot in our debates by making an issue simpler than it is.)
5-
Double-Standard
: judging the same action differently depending on who performs the action.
( Women!)
6-
Shifting the Burden of Truth:
Making an assertion and demanding the opposition to prove it false.
( Your debates)

7-
Irrational Appeals
: Basing your position on an appeal that is unreasonable.
( Everyone does it!)

Logical Fallacies
What is a Fallacy?
1- A fallacy is an error that affects the reasoning or the truth of an argument.
2- We need to learn about these errors in order to evaluate arguments and check their errors.
3- Also, we are learning about them in order to create arguments that are error-free.
Errors Affecting the Truth
1- Either/ Or Thinking
2- Avoiding the Issue
3-Overgeneralizing
4- Oversimplifying
5- Double Standard
6- Shifting the Burden of Truth
7- Irrational Appeals
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