Nisar Kidwai’s lecture on 05/27/2012

 

THE LOGIC

PRELUDE.

This study is intended to introduce the subject of Logic, its scope and some preliminary concepts and terminology for the interested partners of our forum.

A BRIEF HISTORY OF LOGIC.

History of Logic goes back to 300 BC. It is the study of the development of the science of valid inference (logic). Formal logic was developed in ancient times in China, India, and Greece. Greek logic, particularly Aristotelian logic, found wide application and acceptance in science and mathematics. I would rather skip this part of the subject and  dare to suggest to read the History of Logic on Wikipedia.org or any other source as deemed fit.

THE MEANING OF LOGIC.

Here are some  basic  definition of logic.

A science that investigates the principles governing correct or reliable inference.

A particular method of reasoning or argumentation: We were unable to follow his logic.

The system or principles of reasoning applicable to any branch of knowledge or study.

Reason or sound judgment, as in utterances or actions: There wasn’t much logic in her move.

Convincing forcefulness; inexorable truth or persuasiveness: the irresistible logic of the facts.

As you will see that the logic is used to conclude the truth valid, invalid,  strong, weak,  out of relevance set of statements etc. There is another term namely ONTOLOGY  within the realm of logic and is described as “ the set of entities presupposed by a theory.”  I feel it is pertinent to briefly mention its scope which is specification of a conceptualization like a formal specification of program.  A broader definition is within philosophy.  “An explicit formal specification of how to represent the objects, concepts and other entities that are assumed to exist in some area of interest and the relationships that hold among them. There are a slew of definitions and applications of this area of science which we will discuss some  later time.  But now let’s begin  first with “The Logic.”

BASIC CONCEPTS OF LOGIC.

Logic facilitates, as a science, in distinguishing correct reasoning from the reasoning that is incorrect.  I add to remind the readers that RHETORIC also deals with reasoning but limits within the realm of persuasive and non-persuasive reasoning. The analysis for the correctness of the persuasive and non-persuasive reasoning will again fall within the logical field of inquiry.

 

INFERENCES AND ARGUMENTS.

Infer is to draw conclusions from premises e.g. you can see smoke and infer that there is fire.  Another example is you count 9 people out of a group of 10, and infer that someone is missing. Make a note that smoke implies the fire and but does not infer the fire. We infer the fire on the basis of smoke. So there is a difference between infer and imply. The beginning of the reasoning process may be considered inputting premises, data etc. and producing output which is the conclusion. Logic’s main and only concerns is whether the conclusion on the basis of premises is warranted.

An argument is a collection of statements one of which is designated as conclusion and the remainder are  designated as premises. The premises  of an argument are intended to support  the conclusion of the argument.

Also note that a statement is a declarative sentence, which is a sentence capable of being true or false.  Take example of the following statement.

It’s sunny.

5+6 = 11

However the following are sentences which are not statements.

Please handover the pen.

Are you retiring?

Note that statements are capable of being true or false a question or command is not capable of being true or false.

 

 

CATEGORIES.

The experts have sub-divided the process of logical analysis  in several different ways.  There are two different types of reasoning process and as a result two main branches of logic  have evolved.  Some reasoning is  often argued  with certainty, assuming the evidence is correct.  Others establish the claim for the reasoning being with greater or lesser degree of likelihood. This division based on certainty and likelihood is titled as Deductive and Inductive respectively.  The evidence in support of the reasoning  determine the category.

There are two different types of reasoning process as such there came two main branches of logic. Some claims are argues for ‘certainty’ and some claims are argues as ‘likelihood’.  The first category falls under the heading of deductive Logic. The other falls under the heading Inductive logic. The logical analysis is done in Formal and Informal ways. Formal logic starts by translating reasoning from English to symbolic  language.  In informal process, no such translation takes place. We simply examine and evaluate the reasoning process in ordinary English.  Thus logic can be distinguished from 1) Formal Deductive logic, 2) Informal Deductive logic 3) Formal inductive logic and Informal Inductive logic.   An example formal logic is presented here Via diagramming.

To help understand how multiple arguments interrelate with in a passage, diagramming is used Take the example of the following passage.

“ I saw Jim looking at Amy’s paper during the exam. He must have cheated, because they got the same question wrong. We cannot tolerate cheating. So someone should discipline him”.

This passage contains 5 statements that function as either premises or conclusions. Diagramming begins by simply identifying and numbering each of these claims. And number them as follows.

(1)I saw Jim looking at Amy’s paper during the exam. 2) He must have cheated,  3)because they got the same question wrong. 4) We can not tolerate cheating.  5) So someone should discipline him”.

The main point is that someone should discipline Jim. Since it’s the conclusion of the passage, give the last (highest) number in this case  5 and we will write it at the bottom of line.

Claim 2 and 4 are evidently required to get to the final conclusion so we will write  as  2  4 above the line of the conclusion. Claim 3 is premise as it starts with the world “because”. This word is known as premise-indicator.  Claim 1 is also supporting claim 2. As we see claim 3 is supporting claim 2 .  so claim 1 and 3 are the basic premises and will  be written parallel on top line. Now we can draw a diagram  by basic premises on the top of the line , supporting premises underneath the basic premises and conclusion at the bottom. Any multiple supporting argument is written on the same line as sister premise or evidently(qualifying) argument.  Remember conclusion can be only one.

2       4                    Evidentiary statements.

I

\I/

  1         3            Premises

\I/

5              Conclusion

The logic is also classified as ‘Standard logic’ and  ‘Non-standard logic’. This classification is done on the basis of assumptions presupposed by it.  To keep this discussion brief, I will keep this study with the Standard logic only. I will try to explain the assumptions associated with one example of standard logic.

THE BEARERS OF TRUTH AND FALSITY.

Its already clear, I hope, that logic has to do with discovering truth. The things that we call true and false, are the old philosophical  issue.  We say things like Obama is President and we say it is falls that Biden is President. These sentences are bearers of the truth and falsity.  Some philosophers argued that indicative sentences are the bearer of truth and falsity, some have asserted that proposition  of the sentences are the bearers of truth and still others suggested that statements are bearers of truth and falsity. Now it’s imperative that the understanding of these terms, i.e. Indicative sentences, a proposition, and a statement need be understood.  Statements must be carefully distinguished from proposition  they express when they are uttered. Intuitively statements stand in the same relation to propositions as nouns stand to the object they donate. Like the word “Gold” consists of 4 letters G O L D  and gold is a precious  metal.

The indicative is a simple factual statement and positive believe. Let’s evaluate two sentences. 1) I love my grandson. 2) My grandson is loved by me. These are two sentences. Both sentences carry the same meaning. The difference between  these sentences and proposition statements  have  embedded information, revealing the statement to whom it is referred to. It gets little more complicated than what I could describe for our audience simply because it’s for applied logic which matters for our readers and not for academia.  Just to make sure at this point what matter most  when we want to talk about bearers of truth and falsity we are going to call them statements instead of sentences or propositions. In standard logic, which presupposes the laws of excluded middle and non-contradiction, we got to be committed to hold every statement  to be either true(and if true, not false) or false ( and if false not true).

SETS OF STATEMENTS.

We also need to understand that sets in day-to-day life bear different meaning than the sets in  logic and mathematics.  Sets in daily life have  color, location and are subject to change in their membership  and finally must have several members, where  as set in logic and mathematics have no special location.  In logic several statements of a claim constitute a whole, then those statements constitute a set. In mathematics and logic, a set can be empty or even may consist of only one member.

ARGUMENTS.

Although statements and sets of statements are important  objects of study, the most important entities that logicians study are the argument. As an example, for exercise consider the following:

Since all men are mortal.

Socrates is a  man.

It follows that Socrates is mortal

Some statements are presented as  evidence in an attempt to establish another statements. The first two statements are presented to establish the claim that Socrates is mortal.  There is significant difference between arguments and explanation. Look at the following example.

 ARGUMENTS                                                     EXPLANATIONS 

Since all men are mortal                              Because he drank hemlock,

And Socrates is a man,                                  and hemlock is poison,

Socrates is mortal.                                          Socrates died.

The explanation is not convincing the reason or the cause of death (as it could not be determined if Socrates  survived the poison and died later for some other reason.)

PREMISES AND CONCLUSION.

Our job as logicians begins after identifying the arguments.  The analysis will require to set up the statements as premise-indicators  and conclusion-indicators.  This exercise is lengthy, time-consuming and should be  part of a class room session  or research center.  Just brief example of

EVALUATING ARGUMENTS.

Different terms are used in evaluating deductive and inductive arguments. For deductive conclusion of the argument with the level of certainty from its premises the word “valid”  or “invalid “ ,  “sound”  or “unsound”.

CONCLUSION.

From here on,` students would need to do some tedious exercises . I think at this juncture of the subject matter, interested parties would search the appropriate books to learn how to format  the analysis of the statements.  Again, for historical information, please  search on Google for “history of logic” and go to Wikipedia.org.l

 

 

Nisar kidwai