SOLVE IT IF YOU CAN

On a certain train, the crew consists of three men, the break man, the fireman and the engineer. Their names listed alphabetically are Jones, Robinson and Smith. On the train also three passengers with corresponding names, Mr. Jones, Mr. Robinson, and Mr.Smith. The following facts are known.
a. Mr. Robinson lives in Detroit.
b. The brakeman lives halfway between Detroit and Chicago. 
c. Mr. Jones earns exactly $20000 a year.
d. Smith once beat the fireman at chess.
e. The brakeman's next door neighbour, one of the three passengers mentioned, earns exactly three times as much as the brakeman.
f. The passenger living in Chicago has the same name as the brakeman.

          WHAT IS THE ENGINEER'S NAME ?

      

LANGUAGE IN LOGIC

Whether the actual process of thinking or reasoning requires language or not is an open question. It may be that thinking requires the use of symbols of some sort, words or images or what not.We all feel a certain sympathy with the girl who was told to think before she spoke, and replied," But how can I know what I think until I hear what I say?". Perhaps all thinking does require words or some other kind of symbols, but that is not a question that concerns us here. It is obvious that the communication of any proposition or any argument requires symbols, and involves language.
The use of language, however, complicates our problems. Certain accidental or misleading features of their formulations in language may make more difficult the task of investing the logical relations between prepositions. It is part of the task of the logician therefore, to examine language itself, primarily from the point of view of discovering and describing those aspects of which tend to obscure the difference between correct and incorrect argument. .

DEDUCTIVE AND INDUCTIVE ARGUMENT

Arguments are traditionally divided into two different types, Deductive and Inductive. Although every argument involves the claim that its premisses provide some ground for the truth of its conclusion, only a Deductive Argument involves the claim that its premisses provide conclusive grounds.When premisses and conclusions are related that it is absolutely impossible for the premisses to be true unless the conclusion is true also. Every Deductive argument is either valid or invalid ; the task of deductive logic is to clarify the nature of the relation between premisses and conclusion in valid arguments and thus to allow us to discriminate valid from invalid arguments.
On the other hand, an inductive argument involves the claim, not that its premisses give conclusive grounds for truth of its conclusion but only that they provide some grounds for it. Inductive Arguments are neither "valid" nor "invalid" in the sense in which those terms are applied to deductive arguments. Inductive arguments may, of course, be evaluated as better or worse, according to the degree of likelyhood or probablity which their premises confer upon their conclusion.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
"If Sylvester Stallone owened all the gold in Fort Knox, then Sylvester Stallone will be wealthy.
Sylvester Stellone does not own all the gold in Fort Knox.
Threfore Sylvester Stallone is not wealthy."

The premisses of this argument are true, and its concusion is false. Such an argument cannot be valid, because it is impossible for the premisses of a valid argument to be true while its conclusion is false.
Determining the correctness of arguments falls frequently within the province of logic. The logician is interested in the correctness even of arguments whose premisses might be wrong.

Exambles For Deductive & Inductive

In Deductive we infer particular from General Truths; While in Induction we infer General from Particular.


Example for Deductive Argument:


       1   All men are martal
            Socrates is a man
            Therefore Socrates is mortal.
                                            (valid)
                                       * * * * * * * * * * * * * *
       2  Puthukkudy is a violent place
           Johnny is from puthukkudy
          Therefore Johnny is violent.
                                             (invalid)
Here a particular conclusion inferred from premisses the first of which is a general proposition.
                                      * * * * * * * * * * * * * *
Example for Inductive Argument:

       1 Socrates is a man and is mortal

          Plato is a man and is mortal
         Aristotle is a man and is mortal
        Therefore probably all men are mortal
                                                (valid)
    2  Mr.D.P.Mony is a Puthukkudy man and famous
       Mr.Rajan is a Puthukkudy man and famous
        Mr.Johnny is a Puthukkudy man and famous
       Therefore probably all Puthukkudy men are famous.
                                                 (invalid)
Here a general conclusion is inferred from premisses all of which are particular proposition.


                                             Q because P
                                             -------------
If we are interested in establishing the truth of Q, and P is offered as evidence for it, then "Q because P" formulates agreement. However, if we regard the truth of Q as being unprobablematic, as being at least as well established as the truth of P but are interested in explaining why Q is the case, then "Q because P"is not an argument but an explanation.The two examples discussed are fairly easy to distinguish, the first being an explanation and the second an argument.But not all examples are so easily classified. In each case the context may help to make clear the intention of the writer or speaker. If his purpose to establish the truth he
formulates an argument. if his purpose is to explain , then he formulates an explanation.


                                      

HOW LOGICAL ARE THEY

"---------You have at your club all day, I perceive."
" My dear Sherlock Holmes !"
"Am I right..?"
"Certainly but how.......?"
He laughed at my bewildered expression.
"There is a delightful freshness about you, Watson,which makes  it a pleasure to exercise any small powers which I possess at your expense. A gentleman goes forth on a showery and miry day. He returns immaculate with a gloss still on his boots.He has been a fixture, therefore, all day. He is not a man with intimate friends, where, then, could he have been? Is it not obvious?
                                                       Arthur Conan Doyle(Hound of Baskervilles)
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Whether our argument concerns public affair or some other subject we must know some, if not all, of the facts about the subject on which we are to speak and argue.Otherwise we can have no material out of which to construct arguments.

Every Art and every inquiry, and similarly every action and pursuit is thought to aim at some good; and for this  reason the good has rightly been declared to be at which all things aim.
                                                        Aristotle, Rhetoric.
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On examining the apparently solid shell of a hen's egg, one may wonder how the egg can absorb the oxygen necessary to sustain the life and development of the embryo inside it. Obviously the shell must be permeable to oxygen; it must therefore have holes that are big enough to allow oxygen molecules to enter.
                                                                 H.E.Hinton (Insect Eggshells)

RECOGNIZING ARGUMENTS

We turn now to the problem of recognizing  'arguments'. In every argument one or more premisses and a conclusion are asserted. But not every assertion of several propositions constitutes an argument. Newspapers, Magazines and history books abound in assertions, though they tend to contain relatively few arguments. Containing several assertions is a necessary condition for discourse to express an argument, but it is not a sufficient condition.Nevertheless that that necessary condition distinguishes arguments from several kinds of non-arguments with which they are sometimes confused.

Consider the statement :

If objects of art are expressive, they are a language.

   

(If objects of art are expressive -- Premiss)

(they are a language---- Conclusion)

Such proposal is called conditional.            

Its component proposition 'objects of art are expressive' is not asserted, nor its other component proposition 'they are a language'. It asserts only that the former implies the latter, but both could be false for all the statement in question asserts. No premiss is asserted, No inference is made, No conclusion is claimed to be true. There is no argument here.

But consider the following quotation from John Dewey.

Because objects of art are expressive, they are a language.

(Because objects of art are expressive---- Premiss)

(they are a language.-------- Conclusion)

Here we do have an argument. The proposition 'objects of art are expressive' is asserted as premiss and the proposition 'they are a language' is claimed to follow from the premiss and is therefore asserted to be true. A conditional statement may look like an arguments, but it is not an argument; and the two should not be confused.

Consider another passage that looks - at first glance- even more like an argument.

"Synonyms are good servants but bad masters; therefore select them with care". 

In spite of the presence of the standard 'conclusion-indicator' "therefore"in the above passage, we do not generally regard such utterances as expressive arguments. What follows the "therefore"is a command rather than a proposition and since a command is neither true nor false, it cannot be claimed to be true on the basis of what is asserted in the rest of the passage. Wherever a command rather than an assertion occupies the place appropriate to a conclusion, we do not have an argument. Premisses and conclusions must be asserted in an argument and that is why such passages as these do not express arguments.  

LOGIC: PRIMISSES & CONCLUSIONS

To carry out the logician's task of distinguishing correct from incorrect arguments, one must first be able to recognize arguments when they occur, and to identify their premises and conclusions.An Argument can be stated with its conclusion first, or last,or in between its several premises.How can it be recognized? There are certain words or phrases that typically serve to introduce the conclusion of an argument.
Among the most common of these CONCLUSION INDICATORS are " Therefore", "Hence", "Thus", "So", "Consequently", "it follows that", "We may infer" and "We may conclude". Other words or phrases typically serve to mark the PREMISES of an argument .Among the most common of these PREMISS-INDICATORS are "since', "because", "for", "as", "inasmuchas", and  "for the reason that". Once an argument has been recognised, these words and phrases help us to identify its premiss and conclusion.

HOW LOGICAL ARE THEY ?

...When a man sees a mirage in the desert, he is not thereby perceiving any material thing; FOR the oasis which he is perceiving does not exist. 
                                                                                Alfred J. Ayer

No man will take counsel, but every man will take money; THEREFORE money is better than counsel.
                                                                                                                Jonathan Swift

The conscious objector ........ has no place in a republic like ours, and should be expelled from it, FOR no man who won't pull his weight in the boat has a right in the boat.
                                                                                                               Theodore Roosevelt

Since happiness consists in peace of mind, and since durable peace of mind depends on the confidence we have in the future, and since that confidence is based on the science we should have the nature of God and the soul,IT FOLLOWS THAT science is necessary for true happiness.
                                                                                                Gottfried Leibniz 

As good almost kill a man as kill a good book; who kills a man kills a reasonable creature , God's image;BUT he who destroys a good book kills reason itself.
                                                                                                       John Milton

 A tiger has a natural right to eat a man; but if he may eat one man he may eat another ,SO that a tiger has a right of property in all men, as potential tiger meat.
                                                                                                       Thomas Henry Huxley. 
                                                                                                (Natural Right And Political Right)


All censorship exist to prevent anyone from challenging current conceptions and existing institutions. All progress is initiated by challenging current conceptions and executed by supplanting existing institutions.CONSEQUENTLY the first condition of progress is the removal of censorship. There is the whole case against censorship in a nutshell.
                                                                                                              George Bernard Shaw.

The western window through which he had stared so intently has, I noticed, one peculiarity above all other windows in the house - it commands the nearest outlook on the moor. There is an opening between two trees which enables one from this point of view to look right down upon it, while from all the other windows it is only a distant glimpse which can be obtained. It follows,       THEREFORE ,that Barrymore, since only this window would serve his purpose, must have been looking out for something or somebody upon the moor.
                                                                           Arthur Conan Doyle, The Hound Of Baskervilles.

LOGIC

The study of the methods and principles used to distinguish Good (correct) Reasoning from Bad (incorrect)Reasoning is 

called LOGIC. How logical are we ?

* If truth is to be sought in every division of Philosophy, we must , before all else, possess trustworthy principles

   and methods for the discernment of truth. Now the logical branch is that which includes the theory of criteria                       

   and of proofs; so it is with this that we ought to make our beginnings.

                                                                                                     --Sextus Empiricus.

*All reasoning is thinking, but not all thinking is reasoning.

*Logic cannot be "the" science of the laws of thought, because psychology is also a science which deals with

  laws of thought(among other things). And Logic is not a branch of psychology; it is a separate and distinct 

  field of study.

*One may remember something, or imagine it, without doing any reasoning about it. Or one may let his       thoughts

   "drift along" in a day dream or a reverie, building castles in the air, or following what psychologists call

    Free Association, in which one image is replaced by another in an order that is anything but logical. There

    is often great significance to the sequence of thoughts in such Free Association, and some psychiatric tech-

   -iques make use of it. One need not be a psychiatrist to gain insight into a person's character by observing

    the flow of his stream of consciosness.   
* The distinction between correct and incorrect reasoning is the central problem with which logic deals.
   The logician's methods and techniques have been developed primarily for the purpose of making this 
   distinctions clear. The logician is interested in all reasoning regardless of its subject matter but only
   from  this special point of view. 

HOW LOGICAL ARE THEY ?

I am an American therefore what I do , however small, is of importance.
                                                                                     -Struthers Burt.


A nation without a conscience is a nation  without a soul. A nation without a soul
is a nation that cannot live.
                                                                                         -Winston Churchill.


Liberty means responsibility. That's why most men dread it.
                                                                                       --George Bernard Shaw.


I do not believe we can have any freedom at all in the philosophical sense, for we act 
not only under external compulsion but also by inner necessity.
                                                                                           -Albert Einstein


Only demonstrative proof should be able to make you abandon the theory of the creation;
but such a proof does not exist in nature.
                                                                        Moses Maimonides, The Guide For The Perplexed. 

HUNCH

A Hunch comes from a man's subconscious mind wherein he has stored every sense impression and thought impulse which ever reach the brain through any of the five senses. It comes from the infinitely intelligent mind's subconscious storehouse. It also comes from the mind of some other person who has just released the thought or picture of the idea or concept through conscious thought from his subconscious storehouse.


"The Sixth Sense" is the faculty which marks the difference between a genius and an ordinary individual. People who have keen imagination always say that their best idea come from their "HUNCHES". Some successful people have stated that they always close their eyes and listen to their Hunches or inner voice that comes to them   within. One such remarkable man says, "with my eyes close, I am able to draw ideas from a source of superior intelligence"