Basics of Logic

[sravna]

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Dear Folks,

In the discussions we often hear the complaints that the arguments are not logical and are just mere assertions and own beliefs. I am going start a discussion in this thread regarding the basics of logic and what makes an argument logical.

Unlike intuition, logical reasoning can be taught because the latter is more of a conscious process and so we can prescribe some steps to be followed to present something in a logical way.

I will draw upon my experience as a tutor for the GMAT and the GRE exams which are nothing but entrance exams for admissions to higher studies in the U.S. and many other countries. These are reasoning tests and hence the methods used to score well in those exams can be used to enhance one's logical skills provided the methods used are not just some exam oriented tricks. In this thread we will be discussing how we can actually enhance the logical skills.

In a similar thread which I will be starting shortly, I would be discussing how the subject of Mathematics can be learnt in a different manner than we actually learn now. I would use the philosophy of ancient Indian teaching where a holistic approach is adopted.

I welcome contributions and suggestions from the members so that the threads can be very informative and useful.

 

[renuka]

Dear Sravna,

I am amazed..you are somehow able to handle so many heavy duty threads at the same time.

I really need an MRI of your brain..I must see how it works!

Come to Chit Chat section sometimes yaar..lots of nice stuff PJ sir puts there for relaxation.

 

[sravna]

Dear Sravna,

I am amazed..you are somehow able to handle so many heavy duty threads at the same time.

I really need an MRI of your brain..I must see how it works!

Come to Chit Chat section sometimes yaar..lots of nice stuff PJ sir puts there for relaxation.

Dear Renuka,

I don't compromise on relaxation. I get it somehow. But yes thanks for the suggestion. I will visit other sections too.

 

[auh]

Dear Sravna,

The first step to learn, in logic, is to know the fallacies...

I am sure that you would be aware, but would like to give a link to one of many such websites about logical fallacies Fallacies

If you would see carefully, many of these logical fallacies would be applicable to your arguments (conclusions).

I am sure you would consider this objectively...

 

[sravna]

Introduction


Logic is something that we so routinely use in everyday life without even knowing that we are doing that. Unless the principles of logic operate in our communation or in our understanding of a fact, we neither can possibly make a sensible conversation nor can make much out of any fact. If humans had lacked the ability to think logically, they would have been no different from other species. The jump from a chimpanzee to a Newton or a Sankara or even to a human who thinks in a rudimentary way was made possible because of the jump to the logical reasoning capability.

So what is logical reasoning?

Logical reasoning is a process of thinking which helps us to see, organize and present information or facts that we know in a coherent manner. At the end of such a thinking process we are able to conclude something which is different from what was said though the substance of what is concluded is based on what was said or what was known. There is always novelty in what is concluded because of logical reasoning unlike in rote presentation where the same stuff is repeated. That is the reason we use the term reasoning.

As a thinking process, logical reasoning has to be differentiated from intuition as in the latter, the conclusion arrived at is not a result of a conscious process but presents itself directly. In the case of intuition, an unexpected conclusion strikes you suddenly and without your cosncious effort. Intuition is generally associated with deep truths. In my view thinking happens between these two extremes too.

One interesting difference between logical reasoning and a strong intution is that since you directly access truths in the case of intuition , you need not have been exposed to such experiences which form the basis of your conclusions. For example one may not have been formally exposed to moral education or any such learning experience at all but can still know what is right or wrong in a way that he would have exactly learnt from such an experience. But in the case of logical reasoning you need to have some basis for your conclusions as the conclusions solely come out of such a basis. However even in intuitive thinking even though the conclusions are direct they have to have a basis because we are finally able to explain what we access through intuition.

Since logical reasoning is a conscious effort it is possible to imitate the process. For example, in the area of Artificial Intelligence there is a lot of activity going on to make computers think intelligently. I am sure the thought process they are trying to mimic is only the logical thinking process. One may argue that if we have enough facts we may arrive at the deepest truths. But in my view, creating and making such innumerable facts work to arrive at deep conclusions would be a truly mind boggling problem.

To comprehend how difficult the problem is, let us consider two men of equal and exceptional intelligence but who have totally different views on a number of topics. Who is ultimately right? That is the problem of getting at the deepest truth for even extremely intelligent men who have been thinking and debating for centuries if not for thousands of years. In my view, logical reasoning is a leap away from the other species and a perfect intuition would be yet another leap away.

Our focus in this thread will be on logical reasoning only.

 

[sravna]

Let us now take specific instances where logical reasoning is used and consider what the different types of logical reasoning are. Look at the following hypothetical conversation between two people,Ram and Shyam.

Ram: I study hard for the logic exams
Shyam : So you should pass the logic exams

Now, consider this conversation

Ram: Whenever I study hard for the logic exams , I pass
Shyam:So you should pass the logic exams if you study hard.

We do not see anything difficult to understand in the above conclusions that Shyam makes . It seems very natural and we do something like that all the time. Behind such understanding of Shyam and the way he responds are the principles of Logic. More specifically the first conclusion is an example of deductive reasoning and the second is an example of inductive reasoning.

In the former as the name suggests what we conclude is a deduction that is, the conclusion doesn't add any extra information to what is already said but only follows from it. The conclusion however is novel in the sense it was not evident to our consciousness before the logical reasoning was used. We will soon come to how the conclusion follows in the case of deductive reasoning. However in the second conclusion Shyam generalizes from what Ram said , that is, he takes the specific instances cited by Ram to conclude that is always the case. He says something more than what is said.

There is a third variety of logic called the abductive reasoning in which a conclusion which is a reasonable inference is made based on what is known or said. For example if Ram were very sad and Shyam makes the conclusion that Ram failed in his exam, then that would be a reasonable conclusion if it is known that Ram normally is not sad unless he does not do well in the exams. Note that in the case of abductive reasoning, the conclusion is only a good explanation but does not follow from what is given unlike in the case of deductive reasoning.

Though all the three types come under logic, we will restrict our discussion to deductive reasoning as it is more commonly associated with the term logic. We will start the discussion with what specific rules are involved, for example in the way Shyam comes to his conclusion in the first case. That is, we will discuss the rules of deductive reasoning.

 

[renuka]

In the case of intuition, an unexpected conclusion strikes you suddenly and without your cosncious effort. Intuition is generally associated with deep truths. In my view thinking happens between these two extremes too.

.

Dear Sravna,

Intuition is based on past experiences...past experiences are stored in the "microchip" of our mind.

For it to be stored that means that stored data had undergone logical reasoning once upon a time.

I do not agree about the deeper truth etc..in this world logic is the basis for everything.

It is just that we tend to dub things we do not know or have no idea about as deeper truth.

 

[sravna]

The following are some of the terms associated with a logical argument:

1. Premise: It is the fact or hypothesis explicitly stated and is used as the reason by the author of the argument for arriving at the conclusion. There can be many premises

2. Assumption: It is something like the premise in that, it is also a basis for the author of the argument to reach his conclusion but unlike the premise it is unstated. Again there can be many assumptions.

3. Conclusion: It is what the author of the argument tries to convey and is based on the premises and the assumptions only

4. Inference: It is what that follows automatically from the premises in the argument but unlike the conclusion it is not the main message of the author

An Illustration: Consider the following statements

1. Socrates is a man
2. Therefore Socrates is mortal

Premise: Socrates is a man

Assumption: Men are mortal

Conclusion Socrates is mortal

 

[auh]

W.r.t. # 8, I would like to submit that even though a valid conclusion can be arrived at logically by its premises, it may be a false conclusion due to its false premises:

All cups are green.
Socrates is a cup.

Therefore, Socrates is green.

So for the conclusion to be both true and logical, the premises should be undeniably true and should be universally acceptable, and not mere inferences. Let us consider this:

Socrates might be a man
All men are mortal
Socrates is mortal (conclusion does not necessarily follow from the premise and hence the argument is not sound)

 

[sravna]

W.r.t. # 8, I would like to submit that even though a valid conclusion can be arrived at logically by its premises, it may be a false conclusion due to its false premises:

All cups are green.
Socrates is a cup.

Therefore, Socrates is green.

So for the conclusion to be both true and logical, the premises should be undeniably true and should be universally acceptable, and not mere inferences. Let us consider this:

Socrates might be a man
All men are mortal
Socrates is mortal (conclusion does not necessarily follow from the premise and hence the argument is not sound)

Again your irresistible urge for finding faults. shri auh I will address your concerns in subsequent posts. Why can't you be patient till then!

 

[auh]

Again your irresistible urge for finding faults. shri auh I will address your concerns in subsequent posts. Why can't you be patient till then!

Please Sravna, have a broader outlook, will you? We are discussing logic and all I did was to show a variation. If it is your wish that only you will "enlighten" what needs to be said about logical arguments, and where, then I will desist.

 

[sravna]

Please Sravna, have a broader outlook, will you? We are discussing logic and all I did was to show a variation. If it is your wish that only you will "enlighten" what needs to be said about logical arguments, and where, then I will desist.

Shri auh,

All I said was that you have patience as I would be addressing them in subsequent posts. am I wrong in saying that?

 

[auh]

...All I said was that you have patience as I would be addressing them in subsequent posts. am I wrong in saying that?

Assuming that I am impatient is far from the truth ,..

One has to have enormous amounts of patience to deal with your posts and the theores therein...

 

[sravna]

Assuming that I am impatient is far from the truth ,..

One has to have enormous amounts of patience to deal with your posts and the theores therein...

It is not just an assumption. There is proof for it and that is what I pointed out.

 

[sravna]

How do we identify premises and the conclusion of an argument? Consider the following argument:

"We need a better idea than democracy. If people are mature enough to rise above their differences, the need for issue based parties and therefore an elected government is not important. If people are not mature enough then the will of the people is not in the best interests of the nation"

Let us first always try to identify the conclusion of an argument as what the author finally tries to say is easy to identify. In the above argument what does the author really want to convey? Is it the first statement? To determine that, see if it follows from the rest of the argument. It does unlike the second and the third statements which form the reasons for the first statement.

So the conclusion is :"We need a better idea than democracy" which is the first statement and which is what the author wants to finally convey.

Sometimes it needs more thought than the above to identify the conclusion. In the next discussion, we will see further examples to identify in a few arguments what the conclusion is.

 

[sangom]

How do we identify premises and the conclusion of an argument? Consider the following argument:

"We need a better idea than democracy. If people are mature enough to rise above their differences, the need for issue based parties and therefore an elected government is not important. If people are not mature enough then the will of the people is not in the best interests of the nation"

Let us first always try to identify the conclusion of an argument as what the author finally tries to say is easy to identify. In the above argument what does the author really want to convey? Is it the first statement? To determine that, see if it follows from the rest of the argument. It does unlike the second and the third statements which form the reasons for the first statement.

So the conclusion is :"We need a better idea than democracy" which is the first statement and which is what the author wants to finally convey.

Sometimes it needs more thought than the above to identify the conclusion. In the next discussion, we will see further examples to identify in a few arguments what the conclusion is.

My dear Shri Sravna,

I don't know whose sentences you have cited in your above post. Without any disrespect to the author, I find that the three sentences are not really related and that there is no cogency in what is said.

Taking the first sentence, "We need a better idea than democracy", the author has not spelt out why and what for. Democracy is, by dictionary meanings,
1. The doctrine that the numerical majority of an organized group can make decisions binding on the whole group.

2. A political system ruled by the people, either directly or through elected representatives.

3. A state under the direct or representative rule of its people.

There is no mention, nor any insistence, here that the people concerned have to be mature to rise above their differences in order to have an acceptable democracy. Secondly, there is no requirement of parties (issue based or other kinds) also. All that is required in a democracy is that the majority rules and its decisions are implemented and accepted by the minority also.

Thus, the second sentence (If people are mature enough to rise above their differences, the need for issue based parties and therefore an elected government is not important.) is without any relevance. Again, what does the writer mean when he says that If people are mature enough to rise above their differences, the need for ... an elected government is not important? Does he permit dictatorship or plutarchy or something like that? Not clear at all.

The third sentence is loosely said. "If people are not mature enough then the will of the people is not in the best interests of the nation" Even if the people are not mature enough (who decides such maturity - to rise above their differences, obviously, and what are the scientific yardsticks developed for this purpose? These have to be clarified first.), a democracy aims only at implementing the will of the majority and the minority is obliged to follow the majority decisions, even if they are not mature enough. The idea of the best interests of the nation is, once again, irrelevant or unconnected to the previous two sentences because the author has failed to define what he/she means by the best interests of the nation, as different from the decisions of the majority, which is all that democracy is concerned with. The decision of the majority will be what is the best interests of the nation.

Therefore, it appears to me as though you are selecting sentences of the very same kind which you yourself are giving in your posts, and trying to establish "logic" which is, unfortunately, lacking in all these pronouncements.

In the above example, the person who wrote those three lines seems to be talking from the pulpit. He has judged the maturity or the lack thereof of the people, whether the parties are issue based, whether an elected government is needed or not, and, above all, he/she pronounces judgment about what is or is not, in the best interests of the nation.

Kindly refrain from citing more such awkward examples to illustrate the basics of logic.

 

[sravna]

My dear Shri Sravna,

I don't know whose sentences you have cited in your above post. Without any disrespect to the author, I find that the three sentences are not really related and that there is no cogency in what is said.

Taking the first sentence, "We need a better idea than democracy", the author has not spelt out why and what for. Democracy is, by dictionary meanings,
1. The doctrine that the numerical majority of an organized group can make decisions binding on the whole group.

2. A political system ruled by the people, either directly or through elected representatives.

3. A state under the direct or representative rule of its people.

There is no mention, nor any insistence, here that the people concerned have to be mature to rise above their differences in order to have an acceptable democracy. Secondly, there is no requirement of parties (issue based or other kinds) also. All that is required in a democracy is that the majority rules and its decisions are implemented and accepted by the minority also.

Thus, the second sentence (If people are mature enough to rise above their differences, the need for issue based parties and therefore an elected government is not important.) is without any relevance. Again, what does the writer mean when he says that If people are mature enough to rise above their differences, the need for ... an elected government is not important? Does he permit dictatorship or plutarchy or something like that? Not clear at all.

The third sentence is loosely said. "If people are not mature enough then the will of the people is not in the best interests of the nation" Even if the people are not mature enough (who decides such maturity - to rise above their differences, obviously, and what are the scientific yardsticks developed for this purpose? These have to be clarified first.), a democracy aims only at implementing the will of the majority and the minority is obliged to follow the majority decisions, even if they are not mature enough. The idea of the best interests of the nation is, once again, irrelevant or unconnected to the previous two sentences because the author has failed to define what he/she means by the best interests of the nation, as different from the decisions of the majority, which is all that democracy is concerned with. The decision of the majority will be what is the best interests of the nation.

Therefore, it appears to me as though you are selecting sentences of the very same kind which you yourself are giving in your posts, and trying to establish "logic" which is, unfortunately, lacking in all these pronouncements.

In the above example, the person who wrote those three lines seems to be talking from the pulpit. He has judged the maturity or the lack thereof of the people, whether the parties are issue based, whether an elected government is needed or not, and, above all, he/she pronounces judgment about what is or is not, in the best interests of the nation.

Kindly refrain from citing more such awkward examples to illustrate the basics of logic.

Dear Shri Sangom,

My intention was only to illustrate something, Anyway let me answer why the argument is not awkward.

The first statement is just what the author thinks.Nobody can question if somebody doesn't find a democratic form of government a good idea.

The second and the third statements are the explanation for above opinion of the author. What the author means by the second statement is that when there are the issues on which a political parties fight such as minority rights, women's rights or caste and religious appeasements etc do not exist because people rise above such issues and live in harmony, and so there are no real social issues on which a party can claim to fight for. For economic and scientific matters you really do not need an elected government. That s better done by selection of the competent people. The author only talks about the idea of democracy. So his argument may be restricted to that and need not really talk about the alternatives.

The third statement means immaturity makes people make wrong decisions and hence be detrimental to their own cause. So if the majority of the people decide who rules then it would be detrimental to them .That is all there is to it

Let us say though not with reference to this argument, that an argument such as this is meant to be assessed. Thus for example the argument is tested for properties such as soundness and validity. So the argument need not be flawless and is generally not flawless as the purpose of our exercise is in many cases to expose the flaws in the argument.

I will come to the concepts of soundness and validity of an argument in the future posts.

 

[sravna]

We saw in the previous discussion an illustration that showed how a conclusion is identified. We will use another example and state the general approach to the problem.

Argument

"When an airplane is taken out of service for maintenance, it is often repainted as well, and during the repainting no other maintenance work can be done on the plane. In order to reduce maintenance time, airline officials are considering using a new nontoxic plastic film instead of paint. The film takes just as long to apply as paint does, but many other maintenance tasks can be carried out at the same time."

The General Approach:

Step 1:Try to identify which part of an argument is an explanation of something i.e., which part of the argument follows from some other part

We can see that the following two parts have that relation.

"the film takes just as long to apply as paint does but many other maintenance tasks can be carried out at the same time." in the last sentence

and

"reduce maintenance time," in the last but one sentence

The latter can be concluded from the former, that is, if unlike in the use of paints, many other maintenance tasks can be carried out while the film is being used, then the maintenance time is reduced.

Step 2: See if what is explained is what the author is mainly trying to convey. If not start with step 1 again.

In this case the above is what the author is trying to convey. The argument is about reducing the maintenance time, by using film in the place of paints.

 

[sangom]

Let us try to identify the conclusion which is not very obvious as in the following argument:

"When an airplane is taken out of service for maintenance, it is often repainted as well, and during the repainting no other maintenance work can be done on the plane. In order to reduce maintenance time, airline officials are considering using a new nontoxic plastic film instead of paint. The film takes just as long to apply as paint does, but many other maintenance tasks can be carried out at the same time."

< snipped >

Dear Shri Sravna,

Again, I find that this para does not say why "When an airplane is taken out of service for maintenance, it is often repainted as well"; this repainting every time the plane is taken our for maintenance, seems unnecessary from this statement. Hence, the whole purpose of this exercise seems to be to continue the rather unnecessary custom of repainting on every occasion of maintenance.

May be this is an ad or promo for the paint/film manufacturer!

 

[sravna]

Dear Shri Sravna,

Again, I find that this para does not say why "When an airplane is taken out of service for maintenance, it is often repainted as well"; this repainting every time the plane is taken our for maintenance, seems unnecessary from this statement. Hence, the whole purpose of this exercise seems to be to continue the rather unnecessary custom of repainting on every occasion of maintenance.

May be this is an ad or promo for the paint/film manufacturer!

Dear Shri Sangom,

Good point.

An argument consists of premise(s) and a conclusion and may be some assumptions. What I am trying to show in the last two posts is to identify the conclusion. The reason is, it is easier to identify the conclusion first than identifying other parts of the arguments. I will come to other parts of the argument also and try to explain how they fit into an argument.

The conclusion is the main idea for writing the argument and it is only the conclusion that needs explanation. Other statements are to be taken as facts. Right now just consider the statement as a fact that leads to what the author is trying to conclude.

I have modified my earlier post to include the above point.

Thanks.

 

[sangom]

< snipped >

In this case the above is what the author is trying to convey. The argument is about reducing the maintenance time, by using film in the place of paints.

If the argument is about "reducing the maintenance time", the fellow should have said the more obvious thing, viz., "don't paint/ repaint whenever a plane is taken out of service for maintenance". Instead, he seems to go round the head in order to touch the nose!! What kind of a logical argument is this?

 

[sravna]

If the argument is about "reducing the maintenance time", the fellow should have said the more obvious thing, viz., "don't paint/ repaint whenever a plane is taken out of service for maintenance". Instead, he seems to go round the head in order to touch the nose!! What kind of a logical argument is this?

Dear Shri Sangom,

The point is you are given a certain argument and given that argument you need to find what the author is trying to convey. Therefore it is about logically analyzing an argument and assessing it. Yes, in this case the author could have just said what you say. But the argument becomes simplistic and therefore our purpose of showing how to analyze an argument that is not simplistic would not be realized.

In fact in the subsequent posts I will discuss a number of cases where the arguments have flaws with the objective of showing how to identify such flaws.

 

[sravna]

Now let us try to identify the conclusion in the following two arguments. In the next two discussions we will see two more arguments along with the solutions and wind up the discussion on identifying the conclusion of an argument.

Argument 1

The ancient Nubians inhabited an area in which typhus occurs, yet surprisingly few of their skeletons show the usual evidence of this disease. The skeletons do show deposits of tetracycline, an antibiotic produced by a bacterium common in Nubian soil. This bacterium can flourish on the dried grain used for making two staples of the Nubian diet, beer and bread. Thus, tetracycline in their food probably explains the low incidence of typhus among ancient Nubians.

Argument 2

TrueSave is a mail-order company that ships electronic products from its warehouse to customers worldwide. The company’s shipping manager is proposing that customer orders be packed with newer, more expensive packing materials that virtually eliminate damage during shipping. The manager argues that overall costs would essentially remain unaffected, since the extra cost of the new packing materials roughly equals the current cost of replacing products returned by customers because they arrived in damaged condition.

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