Some Terms in Logic

With the definition and the context of logic in scientific research now understood, let us look at some terms used in logic and their context in reasoning:

1. Definition: a group of words that assigns a mean­ing to some word or group of words. Every defini­tion consists of two parts: (a) the word or group of words that is supposed to be defined, known as the definiendum, and (b) the word or group of words that does the defining, known as the For example, in the sentence “Elephant means a large, herbivorous, gray-colored mammal on four legs,” “elephant” is the definiendum, and all other words following the word “means” together constitute the definiens.
2. Term: any word or arrangement of words that serve as the subject of a statement. Terms may be proper names, such as Washington, South Ameri­can, or Somerset Maugham; common names, such as bridge, behavior, city; or descriptive phrases, such as “pages of this book,” “those who can vote,” “winner of Nobel Peace Prize.” Words or combina­tions of words that cannot serve as terms include verbs (e.g., sings), adverbs (e.g., courageously), adjectives (e.g., beautiful), prepositions (e.g., beyond), conjunctions (e.g., and), and nonsystem­atic arrangements of words (e.g., signature like camel if).
3. Propose: to offer for consideration, discussion, acceptance, or adoption.
4. Proposition: that which is offered (as above).
5. Premise: a proposition laid down as a basis of argu­ment.

Example: All snakes are reptiles

Curly is a snake.

Therefore, Curly is a reptile.

In the above argument, the statements of the first two lines are premises, and the statement in the third line is the conclusion.

6. Conclusion: the statement in an argument that fol­lows from the evidence presented in the premises (see [5] above).

Conclusions appear in literature dealing with research in several forms, beginning with, to name a few,

“It follows from . . .”

“It is evident . . . “

“One may observe . . .”

“Therefore . . .”

“Based on…”

“Hence . . .”

7. Argument: a group of statements, one of which, the conclusion, is intended to follow from the other statement or statements, the premises.

It should be noted that there is similarity between the arguments used in the way of forming “conclusions” from “experimental results” by scien­tists and the arguments presented by attorneys in courts of law.

8. Evidence: that which enables the mind to see the truth. It may be from perception by senses, from the testimony of others, or from induction of reason.

In the context of experimental results, percep­tion is mostly by eyesight in the form of observing something happening or reading a measurement. Hearing, smelling, tasting, and touching have yet to become common modes of observation in sci­entific research. Relative to testimony of others, all research is, in a sense, an addition to, or modi­fication of, the existing body of knowledge in a particular area or areas of science. To the extent that a particular researcher’s findings or argu­ments substantiate or conform to the existing body of knowledge, that finding or argument is considered to be sound evidence. The inductive argument (yet to be defined and described here) based on reason is, as mentioned above, a finding derived not from observation alone but from a chain of reasoning (conclusions of one argument may serve as the premise for another argument, and so on) until the final conclusion is proposed to be in conformity with the existing and accepted body of knowledge.

9. Implicate (the act of implication)-, to show or prove to be connected or concerned (with something).

There may be a statement in scientific arguments beginning with, for instance,

“It can be implied . . .”

“The implication of this . . .”

10. Inference: the process of reasoning, whereby start­ing from one or more propositions accepted as true, the mind passes to another proposition or propositions, whose truth is believed to be involved in the truth of the former. For example, in scientific writings, one may see statements like

“It may be inferred . . .”

“The inference from this is . . .”

“This leads to the inference . . .”

11. Truth: conformity to facts or reality, as of state­ments to facts, of words to thought, of motives (or actions) to profession.

The first part of this definition, namely, con­formity to facts or reality, is especially significant

to scientific research in that the effort of science, in the broadest sense, is to add to or correct our knowledge relative to facts or reality. The next part of the definition, namely, statement of facts, becomes significant in a research report, a confer­ence presentation, a thesis, or another form of publication.

Incidentally, “truth” is a much broader term than implied above. Another bunch of dictionary meanings of “truth” includes honesty, sincerity, virtue, and uprightness. Though these qualities are also required in the pursuit of science, their rele­vance is more “societal” in the broadest sense.

I remember an incident in childhood of getting fact and truth confused. I, like many other chil­dren, had been told that to speak the truth is a vir­tue; the more truth, the more virtue. Truth in my mind became equivalent to fact. So, I and a bunch of children gathered together, sat on a mat in front of the house from where we could watch the slow traffic in the road, and competed in the serious game of gathering virtue. We tried to outdo each other by narrating facts like

There is a man with a turban.

A girl is walking behind him.

There is a donkey carrying a load.

I see a dog behind the donkey.

There is a stick in the hand of the man.

I see a woman far away.

There is a bundle on the head of the woman. I see a boy pulling a goat.

He has tied a rope to the goat.

Whoever uttered a fact first was entitled to the virtue assigned to that part of the truth. People got

virtue points proportional to the number of such statements made.

12. Reality: actual being or existence of anything in distinction from mere appearance.

Simple though it seems, philosophers have long wrestled with distinguishing reality from appearance. Several “isms,” such as idealism, real­ism, empiricism, and existentialism, all center on the concept of reality. As is well known, there is no “proof” in philosophy; hence, one may say with­out embarrassment that all the efforts relative to separating reality and appearance are so far unsuc­cessful and quite likely to remain so. And what is significant is that, fortunately for the experimental scientist, in most of his routine undertakings, such a tangle is uncalled for.

13. Inductive arguments (induction): not, as it is sup­posed to be, an argument that proceeds from par­ticular to the general, but an argument in which the conclusion is intended (by its author) to follow only probably from the premises.

Example:

Premises:

Russell came from New Bedford High. He was a good student.

Goethe came from New Bedford High. He was a good student.

Monet came from New Bedford High. He was a good student.

Conclusion: All students coming from New Bedford High are good students.

But Fermi, who is coming this year from New Bedford High, may turn out to be a dud.

Inductive arguments are very common in experimental research. We do not, and often can­not, exhaust listing all members of a class. After testing “sufficient” (but limited) members of a class, we feel emboldened to make a general state­ment about all members of that class. With a lim­ited number of experiments, we claim to have found the truth. For example, consider a simple experiment testing the effect of an independent variable, x, on a dependent variable, y. We take several values of x within the required range and find by experimentation the corresponding values ofy. Then, we plot a graphical relation between x and y. A straight-line relation of the form

y = ax + p

is the easiest possible. Otherwise, we attempt a general relation of the form

for a curved line. Relative to the number of (x, y) combinations, we decide, on an arbitrary basis, what is sufficient. However large this sufficient number may be, we are far from exhausting the possibilities. Such decisions are very common in experimental research, particularly in technology, where our inquiry is directed more toward know­ing the empirical, meaning “likely,” relation, rather than the truth of the relation.

14. Deductive arguments (deduction): not, as it is sup­posed to be, an argument that proceeds from the general to the particular, but an argument in which the conclusion is intended to follow neces­sarily from the premises.

Example:

Premises:

All engineers are intelligent.

Chrysler is an engineer.

Conclusion-. Chrysler is intelligent.

Though less often than inductive arguments, deductive arguments are often used to validate experimental results.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.