# Scope of Logic

## The Scope of Logic

Question # 1

Define Logic, Scope of Logic, its needs, Importance and relation with

1             Grammer

2             Phsyhology

3             Metaphycis

What is Logic?

The science that investigates the principle governor correct or reliable in Terence.

“To prove something with false argument.”

“The System or principles of reasoning, applicable to any branch of knowledge or study.”

Scope of Logic?

The scope of logic is very wide. It covers always all types of knowledge weather it is related to science or arts: based or practice or theory, logic provides bases for them.

The nature of logic is simply like a tree and all the fields of knowledge are its branches Meaning that it is the minim main spring of all the learning. Net a single field of knowledge can be a parted from logic, because logic provides the reasoning for the existence of that knowledge. The wide range of branch of knowledge or learnings evolve from a single knowledge called the logic.

Value and uses of Logic:

It is of great value not only on individual  but a collective level. The scope, value and uses of logic are the things which cannot be separately discussed as where there as result shows the et value of it. Moreover, the scope vt value and uses of logic differently described by different school of thoughts as everyone defines it in a way he use it. At different levels the scope, value and used of logic can be emphasized as follows:

Scroll to Continue

For on Individual:

Logic is of great value for an individual person. When two ore more persons have a discussion on the some matter but give different arguments to defend or oppose the reasons or salutation of that matter, but only that person will be considered best or efficient who will be strong in his argument no matter whether the arguments are given as opponents or defended personality.

For a Mathematician:

Math is a tailor made to use logic in all its power, to set theory and number. Both logic and matr ae independent of reality because they have to make sense of words. In maths various formulas theories, and theorems are purely based on logic.

For a Scientist:

Some is also closely related to logic. The scientist we abstractions which are based on logic. There abstraction are them proved by experiments which as a result give rise to new theories and laws. Therefore the expansion of knowledge in field of science is only because of logic.

In the field of Law:

In the field of law, only those cases are acceptable which fulfill. The criteria of logic. Moreover the rules and law are developed on the bases of logical reasoning. The person how commit any action which is against the law, he would be given punishment.

For a Philosopher:

Philosophy provides explanation or reality. It is also based on the laws of logic.

Conclusion:

In Short, we may be say that logic is a touch, stone we can judge they rationality of the statements or arguments related to any field.

Relationship of Logic with Psychology Grammer and Mataphysics:

Logic:

It may aid us in obtaining a clearer view of what thinking is? If we compare the general standpoint of logic with the Psychology.

Both of there are science deal with what goes on in mind or consciousness and opposed to the so called objective Sciences which are concerned with some group are field of external fact. But inspite of this agreement there is an important distinction between logic and psychology.

Psychology:

Psychology deals with all that there is in mind. It describes pleasures,  and points, acts of will and association of ideas as well as what is usually called logical thinking.

The important difference is this. In Psychology we are interested in the content of consciousness for its own sake. We try to find out what actually goes  on in our minds, and to describes it just as we should any event which occurs in the external world, But in logic the question is not what ere mental process? But rather what knowledge do they give us and is this knowledge true on false? Logic in other worlds does not regared the way in which idea exist, and is not interested in them of what they are but rather in the purpose which they observe in affording us knowledge of something beyond themselves.

Psychology, in its description of conscious state, inquire regarding their quality intensity duration etc and the way which they combine with each other to form a complex ideas.

A logical idea or piece of knowledge is not a modification of consciousness which exists in the mind of some individual at a particulars time.

The relation between logic and psychology may perhaps be defined by referring to which exists between morphology and philology.

Morphology

Morphology deals with the form and structure of living organism.

Science of form and structure.

Physiology

Physiology deals with, the various acts and function which these organism discharge in fulfilling the end of life.

Science of function.

So, we can say that physiology deals with the actual structure of mental processes and logic with the part which they play in given us knowledge.

Relationship of Logic with Grammar:

In grammar we see the meanings of words but in logic we just see the thoughts these thoughts concern with concern.

In grammar we see the relationship of words Grammar has no concerned with logic but logic concerned directly or indirectly with logic.

Relationship of Logic with Mataphysics: Metaphysics:

Mata in great greek means over and since when you jump over something you find yourself behind or after it. The word metaphysics is said to originate from the mera fact that the corresponding part of work was positioned right after the part called physics.

Metaphysics generally refers to the branch of philosophy that attempts to understand the fundamental nature of all reality whether visible or invisible. It seeks a description. So basic so essentially simple, so all inclusive that it applies to everything whether divine or human as anything else.

Relationship:

Metaphysics and logic appear first glance to be different subject one concerned with the fundamental nature of everything that is, the offer with nature of validity. A closer look reveals that one’s view of the basic the nature of logic are if they are distinguishable at all, Simply different vantage points on the same land scope. For instance one can hardly provide a serious accounts of validly without presupposing something about the concepts of truth. Which is as debates that one cannot adegualty formalize our inferences about Metaphysics or human actions without committing one’s self on what are to be objects of quantification; neither can one. Characterize the meanings of the logical contents without finding one’s self in the middle for the realism antirealism debate nor can one even begin to have on adequate formalization of modal logic without taking a stand on the nature of modality, essence and accident such at least are the thems which inite much that is called analytical philosophy.

Question # 2

Horizons of Logic?

1                   Likelihood

2                   Induction

3                   Intnetion

4                   Deduction

5                   Truth and validity and solving problem

What is Logic?

Logic:

Logic is a branch of Philosophy is dedicated to the study of reasoning, Its systematic and rigorous nature has prompted some to describe it as science of reasoning.

What is reasoning?

Reasoning itself is a special kind of thinking any kind of mental activity.

Reasoning is characterized by the reach for evidence that is to say, for items

Example?

For example, I decided to get up early in morning at 6:00 Am for this I set the alarm clock and turned on the key and kept in beneath my pillow before set sleeping.

But I remained unable to getup at 6:00 Am as clock key didn’t\ turn.

Now question is that “Why the key didn’t turn?”

I used my mental power, started thinking and got point that there must be bed’s pressure that prevent the key from turning, So

1)     Nothing but (bed’s pressure prevent they key from turning (Reason).

2)     The key was prevented from moving by the bed’s pressure s (statement to be proved)

Horizons of Logic:

Aspects of Reasoning?

Horizons of logic Aspects of logic tell about what in involved in reasoning and what principle are needed for its critism.

1

Likelihood:

Likelihood is a hypothetical probability that an event that has already occurred would yield a specific outcome. This concept differ from probability.

Probability?

Probability reefer’s to the occurrence of future event.

White?

According to “White” Likelihood refers to the past event with known out-come.

Example?

Likelihood is a chance of something. E.g.

There a strong likelihood of his being elected. Its an indication of favorable and promise.

Likelihood show the appearance of truth or reality.

Use of logic likelihood:

In Logic:

This aspect of reasoning is used where the decision making is crucial, Such as management and medical diagnosis.

In Logic:

We use the logic “LL” “LL” can capture many properties of likelihood, in an intuitively appealing way Likelihood may be the quick to life.

Comparison of Likelihood with Probability:

Likelihood:

In logic, the likelihood is denoted by.

L(H, H / R)

H= Stands for hypothesis

R= Data

In Likelihood, hypothesis are variable and data are fixed.

Probability:

Probability denoted by

P=Probability

R=Data

H=Hypothesis

In probability data is variable and hypothesis is fixed i.e with known parameters and unknown outcomes.

Example:

For example occurrence of bays and girls in a family of two children either will be the one girls or on boy or two boys is determined by likelihood.

2

Induction:

“Induction is a process of reasoning in which a general is inferred from the particulars.”

OR

It is a process of reasoning from broad particulars specification to broad generalization.”

By means of induction. We try to discover those generalization that are true of world.

Kinds of Induction:

Induction is of two kinds

a-     Perfect Induction

b-    Imperfect Induction

Perfect Induction:

In perfect induction all the particulars are examined.

Imperfect Induction:

In imperfect Induction only so may a are held to----------------- from called scientific induction.

Example:

Ali says prayer

Ahsan says prayer

Abdullah says prayers

Ali, Ahsan an Abdullah are Muslims.

Therefore: All Muslims say prayers

3

Deducation:

“Deduction is process of reasoning in which we move from. Broad generalization to particular specification.”

Or

“An inference that purports to be conclusive is said to be deductive such an inference is known as deductive.”

In deduction proposition used as evidence  or reason are technically knows as premises.

And the proposition “Derived from premises by means of Argument is known as conclusion. In sound deduction, the conclusion is said to follow from premises.

So deductive logic in concerned with the validity or relative truth of proposition.

Example:

Al Mongolians have slant eyes

Chinese have slant eyes

Therefore

Chinese are Mongolians.

4

Intention:

“Intention is a course of action that one intend to follow or an aim that guides action, an objective.”

In Logic this refer to what  a person plans to do or achieve.

It simply signifies a course of action that one propose to follow e.g.

It is my intention to take vacation next month.

In Logic:

In logic intention is concept to describe a mode a being

“Relation between mind and objective.”

“The mind is said to intend or tend towards it objective.”

Whether an action in successful or unsuccessful depends at least on whether the intended result we brought about Intention behaviors can also just thought full and goal-directed ness.

It Subject to

“Knowledge without observation.”

Example:

1.     Before you start you car, you can intend to have a safe ride to work.

2.     Before you go to bed you intend to get up early in the morning and have a healthy walk in nearby park.

Steps for intentional Behavour:

Intention follows four steps fro process of reasoning.

i.                    Get clear about-something you want and write it down.

ii.                  Share your intention with someone in a way that will supportively hold you accountable to taking action.

iii.                Do something today to demonstrate your commitment to you intention.

Acknowledge that you did what you said you would. Then take next steps.

By Selling intention you make it clear to yourself and other what you plan to do. So it’s a mental picture or an imaged plan. Wish to create in your life whether it would be health, love, property  happiness, courage will power or anything you can imagine, intention is starting point.

Truth and Validity:

A deductive argument is valid when it is successful. Its validity refers to the relation between its proposition between the set of proposition that serve as the premises and the one proposition that serve as the conclusion of that argument. If the conclusion follows with logical necessity from the premises, we say that the argument is valid, therefore “validity can never apply to any single proposition by itself, because the needed relation cannot possible be found within any one proposition.

On the other hand. “Truth and falsity are attributes of individual proposition A single statement that serves as a premises in an argument may be true.” The statement that serve as its conclusion may be false.

Truth is the attributes of a proposition that asserts what really is the case. When I asserts what really is the case. When I asserts what lake superior is the largest of five Great lake, I assert what really is the case, what is true. If  I had claimed that lake Michigan is the largest of Great Lakes my assertion would not be in accord with the real world; therefore it would be false. This contrast between validity and truth is important.

“Truth and falsity are attributes of individual propositions or statements; validity and invalidity are attributes of arguments.”

“The relationship between true or false proposition and valid or invalid arguments are critical and complicated. Those relations lie at the heart of deductive logic.”

We begin by emphasizing that an argument may be valid even it one or more of its premises its not true. Every argument makes a claim about the relation between its premises and the conclusion drawn from them; that relation may hold even if the premises turn and to be false or the truth of the premises is in dispute.

There are many possible combinations of true and false premises and conclusions in both valid and invalid arguments.

i.            Some valid argument contain only true propositions. True  premises and a true conclusion

All mammals have lungs.

Al Whales are mammals.

Therefore all wholes or have lungs.

ii.            Some valid argument s contain only false propositions, false premises and a false conclusion.

All four legged creature have wings.

All spiders have four legs.

Therefore all spiders have wings.

iii.            Some invalid argument contain only true propositions. All their premises are true, and their conclusion are true as well.

If I owned all the gold in fort know then I would be wealthy.

I do not own all the gold in fort know.

Therefore I am not wealthy.

iv.            Some valid argument have false premises and a true conclusion.

All fishes are mammals.

All whales are fishes

Therefore: All whales are mammals.

v.            Some invalid argument also have false premises and a true conclusion.

All mammals have wings

All whales are mammals.

Therefore All whales have mammals/

vi.            Some invalid argument of course , contain all false propositions false premises and a false conclusion.

All mammals have wings.

All whales hare wings

Therefore All mammals are whales.

Question # 3

a:

Law of thoughts, Premises and conclusion.

b:

Diagram for single Argument Reconzing Argument:

What is Law?

Law means rules and regulations made by any authority. The authority have power to implement .the law.

Thought:

Thinking as process of thinking

Ideas produce by mental activity

Set of ideas, intellectual or philosophical ideas associated with a particular place time or group.

Law of Thoughts:

Law which collectively prescribe how a rational mind much think.

Rational:

The thinking based on reasons rather than emotion.

Explanation:

Law of thought deal with thinking of any individual this law never have sense meaning for all individuals. The thinking believe or ideas of everyone is different in nature.

Thoughts are necessary for formation of this law. Because the law does not exist without thoughts but the thoughts never have this restriction, they may be exist without law.

Every thought never come to law criteria because if the mind thinking is not rational it river fulfill the requirement of law.

Principles of Law of Thoughts:

They principle include three “Traditional law o thoughts”

Law of Identity.

Principle of Syllogism

Principle of deduction

Principle of Sufficient Reason

The Applicative Principle

1

Law of identity

“Everything what it is”

Explanation

The law says a person recognize a thing by its identity

Example:

We recognize a new place by its nameplate or a person by his name.

2

“A Cannot be so and so”

Sometime there is lack of agreement between opinion as action.

Example:

Sometime the opinion as actions never match with each other. If a teacher give an opinion to student to collect data about study through intent. But the student never have facility of interest so be prefer to collect data through Library books. Net research is teacher’s opinion the student action is study of book.

2

3

Law of Excluded Middle

“A thing may be so and so may not be so and so.”

Explanation:

According to this law an individual think all the possibilities related to situation and some time never think even one pross possibility.

Example:

If we think according to this law a person may perform two task accurately. A teacher is a good teacher and also a good poet.

Sometime these two possibilities never occur.

4

Principle of Syllogism:

This principle it a technique of assigning statement in such a way to prove a third statement is true.

Example:

If we compare two statements

1        All human must die.

2        I am a human

5

Principle of Deduction:

According to this principle information is used to understand a particular situation”

Example:

If we want to know the political condition of our Country. We gather information from TV, Newspapers and listen program about current affairs of Pakistan.

6

Principle of Sufficient Reason:

This principle say “Whatever exists is true must have a sufficient reason why the things or proposition should as it is not otherwise.

Example:

If crime in a country increase it have some reasons. The reason may be unemployment in a country, Law income of People increase in prices fo things nad sometime back of planning and control to some the crime.

7

The Applicative Principle:

Whatever can be asserted of any instars however chosen can be asserted about any given instance.

PREMISES AND CONCLUSION

Premises:

One pf two proposition from which inference is drawn.

Inference:

Inference is process that may be together cluster of proposions Some inference are correct other are not.

Conclusion:

A conclusion is a final decision opinion or judgment or act based on reasoning.

Explanation:

In writing or in speech a passage will often contain several proposition and yet contain an argument. An argument is not merely a collection of proposition.

The conclusion of the argument is the proposition that is different is the proposition that a affirmed on the basis of other proposition of argument.

Example:

We say that

All nammal’s have lungs.

All whales are mammals

Conclusion all whales have lungs.

Proposition which are affirmed (assumed) as providing support for the conclusion are the premises of argument.

Example:

Lawyer are rich. They get fee from their clients. If I am a lawyer I will rich.

Sometime because of structure or Formulation of proposition they contain sometime because of relations between the premises and sometime the premises and sometime because of relation between premises and conclusion.

The simplest Kind of argument consists of one premise and a conclusion that is claimed to follow from it. Both Premises and conclusion may be stated within the same sentence. We can indicated the conclusion of the argument frequently by following indicators.

Therefore              for these reasons

So                         I concluded that

Accordingly          which shows that

Proves that            which implies that

For this                 Reason which point to the conclusion that

Recognizing Argument:

Before we can evaluate an argument, we must recognize it. We must be able to distinguish argument argumentative passages in writing or speech. Even when we can be confident that an argument is intended in some context, We may be unsure about which proposition are serving as its premises and which as its conclusion. There are four things that must evaluate before. Recognizing  an argument.

Conclusion Indicators and Premises Indicators:

Contain words or phrases that typically serve to signal the appearance of an argument’s conclusion or of its premises. Here is a particle list of conclusion indicators.

There fore             For these reasons.

Hence                   it Follows that

So                         I conclude that

In congruently       which entails that

Premises Indictors:

Other words or phrases typically serve to mark the premises of anrgument and hence called premise indicators

Some Premises indicator are

Since           as indicated by

Because       The reason is that

For              for the reason

As               may be inferred from

Argument in Context:

The words and phrases help to indicated the presence of an argument or identity its premises or Conclusion but such indicators do not necessarily appears. Sometime it is just the meaning of the passage or its setting that indicate dthe presence of an argument.

No premise inditors or conclusion indicators are used here, yet the argument is clear. Indicators are also absent in the Following argument, recently offered by a notorious atheists, who Premises and conclusion are unmistaken able.

The full force of argument and counter argument can be grapes, in most circumstances. Only with an understanding of the context in which those argument are presented. In real life, context is critical.

Premises not in Declarative Form:

It is no uncommon for the premises of an argument to be presented in the from of question but if question assert nothing, and not express proposition how is this possible? On the surface they make no assertion, beneath the surface an interrogative sentence can serve as premise when its question is rhetorical that is when it suggests or assumes on answer that is made to serve as the premises of an argument. The sentence may be interrogative even though its meaning is declarative.

Unstated Proposition:

The chairman of the Department of Sociology at city college, CUNY present two strong but controversial argument in parallel, regarding the justifiability  of the death penalty. The first premises of each argument is the hypothesis that the featured belief about what does in fact deter homicide is mistaken. The second premises of each argument of each argument although entirely plausible is not stated, leaving the reader the task of reconstructing it.

The first argument goes like this. If the proponent of the death penalty is incorrect in his belief that the penalty deters homicide, then he is responsible for the execution of murderers. Who would not be exacted.

The second argument goes like this. If the opponent of the death penalty is incorrect in his belief that the death penalty does not he is responsible for the murder of innocent individual who would not have been murdered if the death penalty had been invoked.

Diagramming Arguments

“A technique for analysis of argument is diagramming.” With diagram we can represent the structure of an argument.

1.                 Number all the proposition which the argument contains in the order in which they Appear.

2.                 Circling each number

3.                 Using arrows between the circled numbers.

Example:

Premises      1                 Most flowers smell nice

Premises      2                 Rose is a flower

Premises      3                 A rose smell nice

2

1

3

By bracketing the premises in the diagram this argument we exhibit the fact that its premises give support only. Because they are jointed together premises are dependent with each other.

Premises      1                 All men are mortal.

Premises      2                 Socrates is a man.

Premises      3                 Socrates is mortal

Example:

1.  Contrary to what many people think positive test for IIIV is not necessarily a death sentence. For one thing.

2.  The time form the development antibodies to clinical symptoms averages nearly then years for anther.

3.  Many support are now suggesting that a significant number of develop clinical aids.

These premises are independently supported with each other.

1

2

3

Question # 4

Fallacies of Revelance, Fallacies of Ambiguity, Extension Intention and Intuition

Fallacies of Revelance

Informal Fallacies

Assessing the legitimacy of arguments embedded in ordinary language is rather like diagnosing whether a living human being has any broken bones, only the internal structured matters, but is a difficult to see through the layers of flesh that cover it. Soon we shall begin to develop methods, like the tools of radiology that enables us to see the skeletal form of an argument beneath the language that expresses it but compound Fractures are usually evident to the most casual observer, and some logical defeats are equally apparent.

The informal Fallacies considered here are patterns of reasoning that are obviously incorrect the fallaies of revelance for example, clearly fail to provide adequate reason fro believing the truth of their conclusion. Although, they are often used in attempts to persuade people by non-logical means. Only the unwary, the predisposed and the gullible are apt to be fooled by their illegitimate appeals. Many of them were identified by medieval are renaissance logicians, whose Latin names for them have passed into common use Its worthwhile to consider the structure, offer an example, and point out the invalidity of each of them in turn.

Appeal to Force:  or

In the appeal to force. Someone in a position of power threatens to brings down unfortunate consequence upon anyone who daves to disagree with a proffered proposition, Although it is rarely developed so explicity a fallacries of the type might propose.

If you do not agree with my political opinions, you will receive a grade of “F” for this course.

I believe that Herbert Hoover was the greatest president of the United States.

Therefore, Herbert Hoover was the greatest President of United States. It Should be clear that even ‘if all of the premises were true, the conclusion could nevertheless be false. Since that is possible arguments of this Form are plainly involved while this might be an effective way to get you the agree with my position it to be true.

Appeal to Pity: Or

Turning this on its head on appeal to pity tries to win acceptance by pointing out the unfortunate consequence that will otherwise fall upon the speaker and others for whom we would then Feel sorry.

I am single parents, solely responsible for the Financial support of my children.

If you give me his traffic ticket, I will lose my license and be unable to drive to work.

If I can’t work my children and I will become homeless and my strave to death.

Therefore you should not give me this traffic ticket Again conclusion may be false even if the premises are all true, so the argument is Fallacious.

Appeal to Emotion:

Or

In a general fashion, the appeal to motion relies upon emotively charged Language to arouse strong feelings that may lead an audience to accept its conclusion.

As all clear thinking residents of our fine state have already realized the Governor’s plan for financing public education is nothing but the bloody fanged wolf of Socialism cleverly disguised the harmless sheep’s clothing of concern for children.

Therefore.

The Governor’s plan is bad public policy. The problem here is that although the flowery language of the premise might arouse strong feelings in many members of its intended audience the widespread occurrence of those feelings has nothing to do with the truth of conclusion.

Appeals to Authority:

Or

These fallacies involves the mistaken Supposition that there is some connection between the truth of a proposition and some feature of the person who asserts or denies it In an appeal to authority. The opinion of someone famouse or an accomplice in another area of expertise is supposed to guarantee the truth of a conclusion. Thus

For example:

Federal Reserve chair Alan Greenspan believes that spiders are insects

Therefore

Spiders are insects.

As a patterns of reasoning. This is clearly mistaken; no proposition must be true because some individual happens to believes it:

Even an area where they have some special knowledge or skill expert authorities could be mistaken we may accept their testimony as inductive evidence but never a deductive evidence but never as deductive prof of the truth of a conclusion. Personally is Levant the truth.

Appeal to Ignorance:

Or

Argumentum od Ignoration.

An appeals to ignorance propose that we accept the truth of a proposition unless on opponent can prove otherwise Thus

For Example.

No one has conclusively proven that here is no intelligent Life on the man of Jupiter.

There is intelligent Life on the moons of Jupiter.

But of course,  the absence of evidence against a proposition is not enough to secure its truth. What we don’t know could nevertheless be so.

Irrelevant Conclusion:

Finally the Fallcy of the irrelevant conclusion tries to  establish the truth of a proposition by offering an argument that actually provides support for an entirely different conclusion.

All children should have ample attention from their parents.

Parents who work full-time cannot give ample attention to their children

Therefore

Mothers should not work full time. Here the premises might support some conclusion about working parents generally but do not secure the truth of a conclusion focused on woman alone and not on men. Although clearly Fallacious, this procedure may succeed in distracting its audience from the point that is really at issue.

Fallacies of Ambiguity

Ambiguous Language:

In addition to the fallacies of relevance and presumption. We examined in our previous lessons, there are several patterns of incorrect reasoning that aris from the imprecise use of Language. An ambiguous word Pharase or Sentence is not that has two or more distinct meanings. The inferential relationship between the proposition included in a single argument will be sure to hold only if we are careful to employ exactly the same meaning in each of them. The fallacies of ambiguity all involve a confusion of two or more of two or more different senses.

Equivocation:

An equivocation trades upon the use of an ambiguous word or phrase in one of its meaning in one of the proposition of an argument but also in an other of its meaning in a second proposition.

Really exciting novels are rare

But a rare books expsive expensive

Therefore,

Really exciting novels are expensive there, the word “rare” is used in different ways in the two premises of the argument So the link they seem to establish between the terms of the conclusion is spurious. In its more subtle occurrence this fallacy can undermine the reliablilty of otherwise valid deductive argument.

Amphiboly:

An amphiboly can occur even when every term in an Argument is univocal if the grammatical construction of a sentence create its own ambiguity.

A reckless motorist Thursday struck and injured a struck and injured a student who was Jogging through the campus in his pickup truck therefore,

It is unsafe to jog in your pickup truck

In this example

The Premises could be interpreted in different ways creating the possibility of fallacies inference to the conclusion.

Assent:

The fallacy of accent arises from an ambiguity produced by a shuft of  spoken or written emphasis. Thus for example

Jorge turned in his assignment on time today.

Therefore

Jorge usually turns in his assignment late.

Here the premise may be true if read without inflection, but if it is read with heavy stress on the last word seems ot imply the truth of the conclusion.

Composition:

The fallacy of composition involves an inference from the attribution of some feature to every individual member of a class to the possession oft eh same feature by the entire class.

Every course I took in college well-organized.

Therefore:

My college education was well organized.

Even if the premises is true of each and every component of my curriculum, the whole could have been a chaotic mess; so this reasoning is defective.

Division:

Similarly, the fallacies of division involves an inference from the attribution of some feature to an entire class to the possession of the same feature by each of its individual members.

Ocelots are now dying out

Sparky is an ocelots

Therefore

Sparky is no dying out

Although the premises is true of the species as a whole, this unfortunate fact does not reflect poorly upon the health of any of its individual members.

Again be sure to distinguish this from the fallacy of accident, which mistakenly apples a general rule to an ocelot; therefore sparkly is in poor healthy.

The essential point in the fallacy of dividion is that even when something can be truly said of a whole class it does not follow that the same can be truly said of each of its individual parts.

Avoiding fallacies:

Informal fallacies of all seventeen varieties can seriously interfere with our ability to arrive at the truth. Whether they are committed inadvertently in the course of an individual’s own thinking or deliberately employed in an efforts to manipulate others each may persuade without providing legitimate grounds for the truth of its conclusion. But knowing what the fallacies are affords us some protection in either case. If we can identify several of the most common patterns of incorrect, reasoning, we are less likely to slip into them ourselves or to be fooled by anyone else.

Extension:

Prep

Predicate logic

The extension of a predicate a truth valued function is the set of tuples of a values that, used as argument satisfy the predicate such a set of tuples is a relation for example

The statement “d2” is the weekday following “d1” can be seen as. A truth function associating to each tuple (d2, d1) the value true or false. The extension of this truth function is, by co mention, the set of tuples is associated with the value true.

Monday                Sunday

Tuesday                Monday

Wednesday           Tuesday

Thursday               Wednesday

Friday                             Thursday

Saturday                Friday

Sunday                  Saturday

By examining this extension we can conclude that Tuesday is the weekday following Saturday is false.

Using set builder notation the extension of the n ary predicate O can be writer as.

{(x……….xn)} |  (x,……….xn)

Relationship with Characteristic Function:

If the values O and 1 and in the range of a characteristic function are identified with the values false and True, respectively-making the characteristic function a predicate then for all relation R and predicate O the Following two statement are equivalent.

O is the characteristic function of R.

R is the extension of O.

Question # 5

Consistent set of beliefs,

Beliefs words and declarative sentences

Ambiguity, Predictable Proposition and their division:

Consistent Set of beliefs

Knowledge

Knowledge is a lable for the particular way of having acquired information.

Belief:

Belief is likewise an achievement word wired to a different set of criteria related to when the agent is ready to act on the information in question, In Sum information belief conviction etc. all are derivatives with information as the basis.

In Logic:

We are dealing with is concerned with sort of things which can be true or false, such as beliefs and declarative sentence, Truth and falsehood are the truth values. However logic is not much concerned with truth values of beliefs and declarative Sentence but rather with such questions as

Is such and such a set of belief is consistent?

Is such an argument is valid?

Consistency and Inconsistency

“A set of belief is consists just if it would be possible for them all to be two together that is if they are either in fact all true or could all have been true.”

“A set of beliefs is inconsistent just if it would be impossible for them all to be true.”

“A single beliefs which could not be false is said to express a necessary truth.”

A Single belief which is not inconsistent and does not express a necessary truth is said to be contigent.

Note:

We are dealing with a very week sort of possibility or a very strong sort of impossibility. For the purpose, these definition it is possible for human being to run a mile under a minute (human might have been stronger or laws of nature may be different. But it is not possible for 2 and 2 to make 5. It is not possible for it to be both raining and not raining at the some time in the place.

Declarative Sentences

“A set of sentence is consistent just if it would be possible for the sentence as being used all to be true.”

“A set of sentence is consistent just it would be impossible for the sentence as being used all to be true.”

“A single sentence may also be inconsistent in which case it is said to be self contradictory Or a contradiction.”

“A single sentence which is neither inconsistent nor a necessary truth is said to be contingent.”

Note:

We have added “as being used” This is to take care of fact that, for instance the fact it is raining it is not raining could be used to refer the different time and placed or to the same time and places. For later case they would be inconsistent But in the former case they would be consistent. It is very common for the truth of the sentence to depend on who and what is being referred so Ali is tall or not will depend on which person is being referred to by Ali.

For the same reason whether Ali is tall is consistent with “Ali” is not tall depend on whether Ali is being referred to the some person each time or whether the time reference is same. Given this we may often be unable to tell wether a set of sentences is consistence or not without knowing how they are were being used

E.g.

Socrates is a man  all men are mortal, Socrates is not mortal) but we should not doubt add. (If we want to make things absolutely clear) that are assuming that Socrates is beings used to refer to the some person throughout.

Exercise: 1.1

John says marry is coming at dinner to night, David says marry is not coming at dinner tonight is what hey say consistent?

Is not If they are referring to the same person and the same “No”. If they are referring to the same person and the same day. Otherwise Yes Is following set of beliefs is consistent?

(Socrates is a Philosopher, Socrates is a baler)

Yes whether the same person is being referred or not there is not impossibility in being both.

Peter believes that 2+2=5 Is what be believe consistent?

“No what he believes could not be true.”

Consistent set of Words

“Words” is a small Single meaningful unit of a Sentence. If words have no meaning they just don’t exist for us. Words which used in Sentence should avoid ambiguity and complex city.

Ambiguity:

When considering whether a set of Sentence is consistent we need to remember that sentence can be ambiguous. There are two types of ambiguity in a sentence.

Lexical ambiguity:

Occurs when there is more than one way of taking the structure of the sentence; For instance when there is more then one way in which the words might be grouped

E.g

She went to a pretty little girl’s camp.

A particular type of structure ambiguity occurs, when there is ambiguity of cross reference

E.g

Ali asked Ahmed because be likes him.

Exercise: 1.2

What sort of ambiguity occurs in the Following?

John Likes swing more than Peter?

Stur structural ambiguity. It could mean that John like swing more than be likes Peter; or than he Likes Swing more than he likes to swing swim more than Peter Swims.

2

Whether life is worth living depends on the liver?

Lexical ambiguity. Liver can mean someone who lives or bodily orgin.

3

John and marry are Just friends.

Structural ambiguity. It could mean that they are friends of each other or they are friends of the speaker.

4

Structural ambiguity. In particular ambiguity of cross reference. (Does the “She” refer to marry to a susan.”

Complexity:

Words used in a Sentence should be as much simple as possible, sometime complex words create confusion in understanding meaning consistent words. Should be clear, well grouped and simple.

Anita on April 18, 2019:

Thanks.....

M. Malik on September 23, 2015:

Jizak ALLAH awsome work thanks for posting it u solved my problem

zaheer on November 28, 2012:

i don't understand that what is logic because i don't know that what's the logic bahined logic can you help meeeeeeeeeeee if u can then tell me why you help meeeee.

logic on January 31, 2012:

kis na up load kiye he

Arslan on January 07, 2012:

u r right mohson bhai but he saw in august;if he saw well in time then he must told us even it was important for him or not.

Mohsin on January 05, 2012:

Zeeshan should be hanged as had seen this page five moths ago and he never told anyone how much it was important for all of us.

Arslan on January 04, 2012:

Really nice work yar ...

Shan on July 26, 2011:

aalaaaa