Functions of Language :

Functions of Language :
The formal patterns of correct reasoning can all be conveyed through ordinary language, but then so can a lot of other things. In fact, we use language in many different ways, some of which are irrelevant to any attempt to provide reasons for what we believe. It is helpful to identify at least three distinct uses of language:
The informative use of language involves an effort to communicate some content. When I tell a child, "The fifth of May is a Mexican holiday," or write to you that "Logic is the study of correct reasoning," or jot a note to myself, "Jennifer—555-3769," I am using language informatively. This kind of use presumes that the content of what is being communicated is actually true, so it will be our central focus in the study of logic.
An expressive use of language, on the other hand, intends only to vent some feeling, or perhaps to evoke some feeling from other people. When I say, "Friday afternoons are dreary," or yell "Ouch!" I am using language expressively. Although such uses don't convey any information, they do serve an important function in everyday life, since how we feel sometimes matters as much as—or more than—what we hold to be true.
Finally, directive uses of language aim to cause or to prevent some overt action by a human agent. When I say "Shut the door," or write "Read the textbook," or memo myself, "Don't rely so heavily on the passive voice," I am using language directively. The point in each of these cases is to make someone perform (or forswear) a particular action. This is a significant linguistic function, too, but like the expressive use, it doesn't always relate logically to the truth of our beliefs.
Notice that the intended use in a particular instance often depends more on the specific context and tone of voice than it does on the grammatical form or vocabulary of what is said. The simple declarative sentence, "I'm hungry," for example, could be used to report on a physiological condition, or to express a feeling, or implicitly to request that someone feed me. In fact, uses of two or more varieties may be mixed together in a single utterance; "Stop that," for example, usually involves both expressive and directive functions jointly. In many cases, however, it is possible to identify a single use of language that is probably intended to be the primary function of a particular linguistic unit.
Literal and Emotive Meaning
Even single words or short phrases can exhibit the distinction between purely informative and partially expressive uses of language. Many of the most common words and phrases of any language have both a literal or descriptive meaning that refers to the way things are and an emotive meaning that expresses some (positive or negative) feeling about them. Thus, the choice of which word to use in making a statement can be used in hopes of evoking a particular emotional response.

This is a natural function of ordinary language, of course. We often do wish to convey some portion of our feelings along with information. There is a good deal of poetry in everyday communication, and poetry without emotive meaning is pretty dull. But when we are primarily interested in establishing the truth—as we are when assessing the logical merits of an argument—the use of words laden with emotive meaning can easily distract us from our purpose.
Kinds of Agreement and Disagreement
In fact, an excessive reliance on emotively charged language can create the appearance of disagreement between parties who do not differ on the facts at all, and it can just as easily disguise substantive disputes under a veneer of emotive agreement. Since the degrees of agreement in belief and attitude are independent of each other, there are four possible combinations at work here:
Agreement in belief and agreement in attitude: There aren't any problems in this instance, since both parties hold the same positions and have the same feelings about them.
Agreement in belief but disagreement in attitude: This case, if unnoticed, may become the cause of endless (but pointless) shouting between people whose feelings differ sharply about some fact upon which they are in total agreement.
Disagreement in belief but agreement in attitude: In this situation, parties may never recognize, much less resolve, their fundamental difference of opinion, since they are lulled by their shared feelings into supposing themselves allied.
Disagreement in belief and disagreement in attitude: Here the parties have so little in common that communication between them often breaks down entirely.
It is often valuable, then, to recognize the levels of agreement or disagreement at work in any exchange of views. That won't always resolve the dispute between two parties, of course, but it will ensure that they don't waste their time on an inappropriate method of argument or persuasion.
Emotively Neutral Language
For our purposes in assessing the validity of deductive arguments and the reliability of inductive reasoning, it will be most directly helpful to eliminate emotive meaning entirely whenever we can. Although it isn't always easy to achieve emotively neutral language in every instance, and the result often lacks the colorful character of our usual public discourse, it is worth the trouble and insipidity because it makes it much easier to arrive at a settled understanding of what is true.

In many instances, the informal fallacies we will consider next result from an improper use of emotionally charged language in the effort to persuade someone to accept a proposition at an emotional level, without becoming convinced that there are legitimate grounds for believing it to be true.

What is Language?

What is Language?
Language is a basic tool of communication. We often communicate our concepts, judgments and reasoning through language.

Wittgenstein says,

“ We use language while giving orders, describing an object or giving its measurements, reporting an event, speculating about an event, forming and testing hypothesis, presenting the result of an experiment, making up a story, play-acting, singing, guessing riddles, telling a joke, solving a problem in arithmetic, asking, cursing, greeting, and praying.”

Basic functions of Language;

There are following basic functions of language;

Informative function.
Expressive function.
Directive function.
1. Informative Function;

Language serves informative function when it is used to convey information. We are often informed or inform others about something. And this information is obviously in a language. So this function of language is informative function.
Now this information may include false propositions, true propositions, good arguments, bad arguments etc.

2. Expressive Function;
A language serves expressive functions when it is used to convey or evoke feelings. We often express sorrows, when we say “alas!” or “what a pity!” we express our enthusiasm when we say, “That is really great!” similarly we express our awe and wonder in our prayers.

The best example of expressive function of language is poetry in which a poet conveys his/her own feelings and also evokes our feelings too.

For example,
“Nisar mai teri galion kea e watan ke jahan
chali hai rasm ke koi na sar utha ke jiye
jo chahne wala koi tawaf ko nikle
nazar chara ke chale jism-o-jan bacha ke chale”

This stanza is a selection from the poetry of Faiz Ahmed Faiz in which he is expressing his feelings about the freedom (of thought and speech) in our country during dictatorship and is evoking feelings of others as well.

3. Directive Function;

Language serves directive function when it is used to cause or prevent an action.
For example when I say “please pass me the salt” my intentions here are neither to communicate information nor to express my feelings but to cause an action, that is to say, to get the salt.
Similarly when I say “shut the window” I am giving a command as I want some result and the result is to get the window closed.

We should note that commands can be disobeyed and in order to make them more directive in function we can add polite words such as ‘please’. So when we say “please shut the window” it is more likely to be obeyed.

What is an Argument?

What is an Argument?
Argument is a structured group of propositions which reflect an inference. And the inference is the process of linking propositions by affirming one proposition on the basis of another (one or more) proposition(s).

Propositions are the building blocks of an argument. And inference is the process which ties these building blocks (propositions) together. And to determine the correctness or incorrectness of an inference we examine propositions and their relationship.

Now we can define argument as a group of propositions of which one is claimed to follow from other(s) which are regarded as providing support or grounds for the other.

But it does not mean that argument is a mere collection of propositions. An argument has a structure in the group of propositions, and this structure captures some inferences. This structure uses the terms, premise and conclusion. Conclusion as it is evident by its name is the proposition which we affirm or derive on the basis of other propositions, and these supporting propositions are called premises.

The simplest kind of argument consists on one premise and a conclusion. For example;

The teacher is not coming today.
Therefore there is no class of logic today. Or it can be expressed in a single sentence;
Since the teacher is not coming today, there is no class of logic.

Sometime conclusion precedes its premise. For example;

There is no class of logic today.
Because teacher is not coming.

Just remember that it is not necessary that an argument is always in order where premise precedes conclusion it may be other way round. Also an argument may have more than one premise not necessarily only one or two.

A single proposition can never be an argument it is always a group of propositions which compose an argument. Some compound propositions may resemble an argument but they are not. For example;

If Ali had an umbrella while walking to market then it is likely that Amjad was home.

Now neither the first component of this proposition (if Ali had an umbrella while walking to market) nor the second component (it is likely Amjad was home) is asserted in this hypothetical proposition. It asserts only that the former implies the later, and both could be false. No inference is drawn and no conclusion is claimed to be true. So this is just a hypothetical proposition and not an argument. But if we put it like this;

Amjad was home when it rained because Ali had his umbrella while walking to market.

Now this is an argument because the first component (Amjad was home….) is asserted on the basis of second component (Ali had his umbrella….). the second component is the premise while the first component is the conclusion. Here it is claimed that the first component has been followed from the second one and if the second is true the first must be true.

So hypothetical propositions may look like, sometimes, arguments but it never can be an argument and the two should not be confused.

Deduction and Induction :

Deduction and Induction :
Arguments can be divided into two groups, that is to say, Deductive arguments and Inductive arguments.

A deductive argument is an argument that makes the claim that its premises support the conclusion conclusively. While on the other hand an inductive argument is the one which claims that its premises support the conclusion with some degree of probability.
For example

All men are mortal.
Ali is a man.
Therefore Ali is mortal.

The above argument is a deductive argument. Because here we can see that the premises of this argument support the conclusion conclusively, that is to say, there is some logical relationship, the conclusion necessarily follows from the premises.

On the other hand,

Ali is mortal.
Akbar is mortal.
Aslam is mortal.
Therefore All men are mortal.

This argument is an inductive argument as the premises of this argument support the conclusion with some degree of probability. Though it is highly probable but we cannot say with certainty that all men are mortal. To be certain we need future evidences too, that is the death of all human beings.

Another important thing to note is that we often assume or take for granted some premises in deduction to be true and then draw conclusion, while in induction we directly refer to the facts and then make a generalization.

For example;

All kings are mortal.
Faisal is a king.
Therefore Faisal is mortal.
In this deductive argument to find out whether its propositions are true or false, we will have to assume other two propositions for the truth of “All kings are mortal”
All men are mortal.
All kings are men.
Therefore all kings are mortal.
Now to prove that “All men are mortal” we will have to assume other two propositions that is to say;
All animals are mortal.
All men are animals.
Therefore All men are mortal.
Similarly to prove that All animals are mortal we will have to assume other two propositions and so on. It is rather better for us to see our premises and conclusions (propositions) inductively, that is, to go directly to the facts.

In spite of the above interpretation both are two different processes of reasoning and hence both are important. For example we can say deductively that
All patients of malaria are cured by quinine.
Mr X is a patient of malaria.
Therefore Mr. X is cured by quinine.

And inductively we can say,

Mr. X is being patient of malaria cured by quinine.
Mr. Y is being patient of malaria cured by quinine.
Mr. Z is being patient of malaria cured by quinine.
Therefore all patients of malaria are cured by quinine.

Difference between Deduction and Induction;

Deduction goes from general laws to particular facts and induction goes from particular facts to general laws.

The aim of induction is to see whether our argument tallies with the actual world
or not. While the aim of deduction to see the form of the argument, that is to say,
how it is formed. Deduction demands that thought should agree with itself and
Induction demands that thought should agree with the actual reality.

3. Deduction employs the methods of synthesis while induction employs the method
of analysis. Deduction is concerned with syllogism, which means putting the
premises together (process of synthesis) and then drawing a conclusion from them.
On the other hand induction has to discover the causal connection among the facts
for which analysis (a process to separate the relevant facts from the irrelevant
facts which go together) is necessary.

Induction is based upon the law of nature and the law of uniformity of nature,
while deduction is based on laws of thought.


Validity is the attribute of deductive argument while probability is the attribute of
Inductive argument. A deductive argument must be valid or invalid, while an inductive argument is more or less probable

Fallacy :

Fallacy :
Sometimes an argument seems to be valid and sound but in reality it is not so. It involves a violation of some rule of logic which is not apparent and which can be detected only on close examination. Such a piece of unsound reasoning is called a fallacy.
When the premise of an argument fails to support its conclusion we call the argument a fallacious argument. So a fallacy is an argument which appears to be valid but in fact it is not and which can mislead us.

In logic we use the term fallacy in narrower sense when we call it typical error that is made in reasoning. In this sense each fallacy is a type of incorrect argument. We call the argument committing fallacy in which such kind of mistake is made. And different arguments can commit same fallacy, and the argument which commits a fallacy is itself a fallacy because it is an example of that typical mistake.

A fallacy may be committed unintentionally or intentionally. When committed unintentionally it is called Paralogism, while when it is committed intentionally it is call Sophism. In paralogism the person committing fallacy himself is not aware, while in sophism is a fallacy which is employed with the intention in order to deceive or mislead someone. However a fallacy whether committed intentionally or unintentionally is a fallacy.
So the study of fallacy enables us to avoid these and fulfil the purpose of logic which is to differentiate between correct and incorrect reasoning. We understand, after studying these fallacies, what the valid thinking (reasoning) is, we recognise sound arguments and unsound arguments and the conditions for valid reasoning. Even when we are tricked by an (invalid) argument we wish to be able to show how we are tricked by it. If we are just able to see it and not solve the problem our mind is unable to proceed as Aristotle says. Hence it is necessary to study the fallacies.

We can avoid fallacies when we understand the kinds of reasoning mistakes made by different arguments. Therefore we need to understand different kinds of fallacies. Although there are many kinds of fallacies but there are two most common and important, namely:
Fallacies of Relevance.
Fallacies of Ambiguity.
1. Fallacies of Relevance:

These are the bald mistakes, that is to say there are the product of the missing connection between premises and conclusion. And since the connection is missing the premises cannot establish the truth of conclusion drawn. But the premises may look relevant to conclusion psychologically to the reader or hearer. Each fallacy of this kind has a traditional and modern name as follows;

a. The Appeal to Emotion or argument ad populum:

It is a kind of fallacy in which argument relies on emotions rather than on reason. Appeal to emotion of audience is the most common device used by people. In this kind of fallacy in place of evidence and rational argument expressive language (or emotive language) is used in order to excite emotions of audience. For example Love for a country is an honourable emotion but using this emotion to manipulate audience is not correct logically. As Samuel Johnson says “Patriotism is the last refuge of a scoundrel (villain)”
We can take example of this kind of fallacy in advertising commercials.
Beauty products are associated with youthfulness. Soft drinks are associated with high spirits, romance and adventure. Dairy products are associated with health and happy families. In short we are manipulated by relentless appeals to emotions of every kind.

b. The Appeal to Pity (argument ad misericordiam):

It is a fallacy in which the argument relies on generosity, altruism or mercy rather than reason. Misericordiam literally means ‘a pitying heart’. When the premises of an argument are an appeal to pity rather than reason the argument is fallacious. This is a very common kind of fallacy. We can say it’s a kind of subcategory of argument ad populum because in this we appeal to feelings/emotions of generosity, altruism and mercy.
A man who killed his parents himself after proving guilty pleads for mercy on the grounds that he is an orphan now.

c. The Appeal to Force (argument ad baculum):

It is a kind of fallacy in which the argument relies on threat of force rather than reason. We commit this fallacy when our evidence or rational methods fail, we use ‘might makes right’. As Stock says,” To knock a man down who differs from you in opinion may prove your strength, but hardly your Logic.”
Religious persecutions are examples of this kind of fallacy. The reformer who is prosecuted is not necessarily proved in error, it is only shown that his opponents are stronger than him. To make an end of a man by violence or bullying does not refute, by reason, or even make an end eventually of his conclusion.

d. Argument against the person (argument ad hominem):

It is a fallacy in which the argument relies on an attack against the person taking a position. It is an argument which rests, not upon the merits of the case but upon the character or position of the person who maintains it. It is an argument in which we tend to silence our opponent instead of convincing him (by attacking his personality). A man is accused of a crime; it is no answer to say that the prosecutor is as bad as the accused himself.

e. Irrelevant Conclusion (ignoratio elenchi):

It is a kind of fallacy in which the premises support a different conclusion than the one that is proposed. In a sense all the fallacies of relevance are ignoratio elenchi but this term is used chiefly when the point is missed substantively (actually) not merely with other kind of fallacies of relevance.
For example to prove the taste of dinner made by your wife she might name the difficulties she faced during making this dinner for you.

So these are the kinds and examples of Fallacies of Relevance.

2. Fallacies of Ambiguity;

These are the kinds of fallacies we commit due to confusion of the meanings of the words within argument. A term may have one sense in the premise but might be used in another sense in the conclusion. When an inference is drawn in this kind of argument it is fallacious and we call this fallacy, fallacy of ambiguity. There are five kinds of fallacies of ambiguity;

a. Equivocation:

The fallacy of equivocation arises from the ambiguous use of a term in an argument. It is a fallacy in which two or more meanings of a word or phrase are used in different parts of an argument (premise and conclusion).
For example;
No cat has two tails.
Every cat has one more tail than no cat.
Therefore every cat has three tails.
In this argument the term ‘no cat’ in premise is used in one sense while in the conclusion it is used in another sense.

b. Amphiboly;

It is a kind of fallacy in which a loose or awkward combination of words is used which can be interpreted more than one way. The argument contains a premise based on one interpretation and conclusion is based on another interpretation. A statement I amphibolous when it’s meaning is indeterminate because of the loose use of words combination. When we use ambiguous grammatical structure in a sentence. The ambiguity lies in the sentence and not in the word because of the construction of the sentence. For example the statement, “A piano for sale by a lady in an oak case with curved legs” can be interpreted both ways the curved legs of the oak case or the curved legs of the lady. Similarly a statement, “Dr. Arif donated along with his wife 5 million rupees to Govt College Lahore for research centre” can be interpreted both ways.

c. Accent;

It is a fallacy in which a phrase is used to convey two different meanings within an argument and difference is based on changes in emphasis given to words within the phrase. For example, “I never sold you this book” if we stress on ‘I’ it means something else and if we stress on ‘this book’ it means something else and if we stress on ‘you’ it means something else.

d. Composition;

It is a fallacy in which an inference is mistakenly drawn from the attributes of the parts of a whole, to the attributes of whole. In other words this fallacy consists in going from the distributive to the collective use of a term. For example;
Three and two are odd and even.
Five is three and two.
Therefore five is odd and even.
When it is said three and two are odd and even, ‘three and two’ are taken separately; but in conclusion ‘three and two’ (that is five) are taken collectively. Or if we say,
Ali is good.
Ali is sportsman.
Therefore Ali is good sportsman.

e. Division;

It is a fallacy in which a mistaken inference is drawn from the attributes of a whole to the attributes of the parts of the whole. This is actually converse of the fallacy of composition. It is committed when we pass from a statement about a group as a collective whole to the same statement about each individual or member of that group. For example;
Six is an even number.
Five and one are six.
Therefore five and one are even numbers.
Or we say;
Ali is a good sportsman.
Ali is sportsman.
Therefore he is a good man.
Or
Cheetahs are disappearing.
That animal is a cheetah.
Therefore that animal is disappearing.

So all above are the kinds and examples of Fallacies of Ambiguity.

Premise and Conclusion indicators :

Premise and Conclusion indicators :

Now the question is how we will determine which proposition is the conclusion and which one is premise?
It is not necessary that the premise must precede conclusion, we cannot rely upon the order of the propositions.
But there are certain words and phrases which we can use as indicators of conclusion of an argument such as:

Therefore For this (or these) reason(s)
Hence It follows that
So I conclude
Accordingly Which shows
Consequently Which means
Proves that Which entails
As a result Which implies
Thus Which allows us to infer that
Which points to the conclusion that
We may infer etc.

Some of the words and phrases are used to mark the premises of an argument and are called premise indicators. Usually, but not always, what follows any one of these will be the premise of an argument. Such as:

Since As indicated by
Because The reason is that
For For the reason that
As May be inferred from
Follows from May be derived from
As shown by May be deduced from
In as much as In view of the fact that

Rules of Categorical Syllogism:

Rules of Categorical Syllogism:

1. A syllogism must contain three and only three propositions, neither more nor less.
Syllogism is always composed of three propositions, namely the major premise in which major and middle terms are compared, minor premise in which minor and middle terms are compared; and a conclusion in which the minor and the major terms are related together.

2. A syllogism must contain three and only three terms, neither more nor less.
A syllogism is the comparison to two terms, major and minor, by means of third term that is middle term. From this rule it follows that no term should be ambiguous, because if it is ambiguous it equals to two terms and then syllogism will have four terms and will not remain syllogism any more. If it has less than three terms then it is the matter of immediate inference and not syllogism.

3. The middle term must be distributed at least once in the premises.
By this we mean that the whole of middle term must be referred to in one premise at least. It serves as a link between the two extremes, the major and the minor terms. If the middle term, with which the other two terms are compared, is undistributed it means that part of it is compared with major term and part of it with minor term, hence it fails to serve as a link between the two terms and we cannot draw a conclusion. For example if we say All Punjabis are men and All Bengalis are men. The middle term ‘men’ is undistributed in both so we cannot draw a conclusion.

4. No term must be distributed in the conclusion if it is not distributed in the premise which contains it. If a major term is undistributed in major premise it cannot be distributed in conclusion, similarly if minor term is undistributed in minor premise it cannot be distributed in conclusion. We have read that in syllogism conclusion is less general than the premises which mean no term can have greater extension in the conclusion than its premise.

5. From two negative premises there can be no conclusion. A negative proposition shows that there is no connection between its terms. Now if both the premises are negative it means the middle term do not have any connection with major and minor terms. And therefore we cannot draw any conclusion from it. The relation of major and minor terms is established through middle term. If both premises are negative the middle term will have no connection with both major and minor terms. Therefore in order that a syllogism may be valid one of its premises at least must be affirmative.
6. If one premise is negative, the conclusion must be negative; and if the conclusion is negative one premise must be negative. If one premise is negative and the other is affirmative it means that middle term agrees with one extreme and disagrees with the other extreme. So the extremes will obviously disagree with each other in conclusion, which follows that conclusion will be negative. For example
Men are not perfect.
Lawyers are men. The only conclusion that can be drawn is that,
Therefore lawyers are not perfect.

7. From two particular premises there can be no conclusion. Two particular premises cannot yield any conclusion, so in every valid syllogism at least one premise must be universal.

8. If one premise is particular the conclusion must be particular. A universal conclusion can be drawn only from two universal premises and if one premise is particular the conclusion must be particular.


9. From a particular major premise and a negative minor premise there can be no conclusion. No conclusion can be followed from a combination of a particular major premise and a negative minor premise.

The Mood and Figure of Syllogism

Mood: Every Syllogism has a mood. And its mood is determined by the type of its propositions that is to say, A, E, I, O. So the mood of syllogism is represented in three letters, and these letters are always given in standard form order. By order we mean the first letter names the major premise, the second letter minor premise and the third letter names the conclusion. For example we say
No politicians are professors. (E)
Some doctors are professors. (I)
Therefore some doctors are not politicians. (O)
The mood of the above syllogism is EIO.

Figure: The mood of a standard form syllogism is not enough to characterize its logical form. Two syllogisms with the same mood can be logically different. For example mood AII can both be valid and invalid. So their form can be shown more clearly by their figure. And this is the different possible positions of middle term which constitute the figures. There can be only four figures as there can be only four positions of combination of middle term
1. The middle term may be subject term of the major premise and predicate term of the minor premise.
All M P Figure-1
All S M
2. The middle term can be the predicate term of both premises.
All P M Figure-2
All S M
3. The middle term may be the subject of both premises.
All M P Figure-3
All M S
4. The middle term may be the predicate term of major premise and subject term of the minor premise.
All P M Figure-4
All M S

So the mood and figure of this syllogism is as follows;
All Men are mortal. (A)
All Students are men. (A)
Therefore All Students are mortal. (A)
AAA-1

Here the term ‘men’ is middle term and it is the subject of the major premise and the predicate of the minor premise therefore the figure of it is 1. And as all of the three propositions are universal affirmative that is why the mood of this syllogism is AAA.