What Reasoning Is and How It Works

KINDS of Reasoning

When the term reasoning is called to mind, we might think of what's rather facetiously known as common sense, which in many cases turns out neither to be very common nor to have much to do with the senses, but rather with established practices and prejudices.  Or we might think of rhetoric, that ancient art of crafty persuasion that appeals to emotion, and is used at least as often to mislead as to lead.  But in this work, we prefer to think of true reasoning as the methodical connecting of evidence and related ideas in such a way as to lead systematically and convincingly to an ultimate implication or inference.  This disciplined approach to reasoning is known as logic.  It's also referred to as critical thinking, particularly when the task at hand is investigating traditional, popular, or authoritarian assumptions.

We use so-called commonsense reasoning mostly when we're just following established procedure without worrying much about how or why.  We use rhetorical reasoning to persuade others of a viewpoint, generally assuming it to be true on the basis of its appeal and popularity, rather than on a sober and impartial consideration of factual evidence.  We use logic when our real need is to learn what is consistent, real, and true—even when reality and truth turn out not to be as pleasant or appealing as we might like.

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Statements—the Building Blocks of Reasoning

Basic Grammar

Although it used be standard procedure to teach English grammar in American public schools, this appears no longer to be the case.  Therefore, because the workings of logic correlate to grammatical construction, we must undertake a brief review of (or for some, an introduction to) basic grammar principles, in the context of how they apply to reasoning.

 What a statement is, and what it isn't  A statement is a declarative sentence that makes a claim.

"You are looking at my cat."

declarative

states a claim, is a statement

Sentences that do not make claims, such as interrogatives, directives, and exclamations, are not statements.

"Why are you looking at my cat?"	interrogative	asks a question; is not a statement
"Please look at my cat."	directive	gives an order or makes a request; is not a statement
"Holy cats!"	exclamation	expresses emotion or surprise; is not a statement

 Truth value  In logic, a statement evaluates as either true or false.  This condition of being true or false is called a statement's truth value.  Questions, directives, and exclamations make no claims.  So they are neither true nor false, and thus have no truth value.  Only statements, either individually or as interrelated groups, have truth values.  Furthermore, only well-formed statements, i.e., those which are not inherently nonsensical, can have truth values.  (Thus, when we speak of "logical statements" we mean only "well-formed statements.")

"Abraham Lincoln was the 16th U.S. president."	The truth value of this statement is true.  Lincoln was indeed the 16th U.S. president under the nation's present constitution.
"Abraham Lincoln was born in Lincoln, Nebraska."	The truth value of this statement is false.  Lincoln was born in Kentucky.
"Abraham Lincoln was born in Lincoln, Nebraska, and also was the 16th U.S. president."	Though it's true that Lincoln was the 16th U.S. president, it's false that he was born in Lincoln, Nebraska.  Since this statement asserts that both claims are true when in fact one is false, the truth value of statement as a whole is false.
"It's raining in Lincoln, Nebraska."	The truth value of this statement might be unknown to anyone outside Lincoln, Nebraska, but it's still either true (if it is actually raining there) or false (if it isn't actually raining there).
"There's a rock on the moon that resembles Abraham Lincoln."	The truth value of this statement might never be known; however, in reality there either is or is not such a rock on the moon.  The statement's truth value is true if there is such a rock there, or false if there isn't, regardless whether anyone knows about it.
"The President of Nebraska is Abraham Lincoln." "Nebraska is zero."	These two statements have no truth values because they're nonsensical.  In the first example, there's no such thing as "the President of Nebraska."  In the second, "zero" isn't a meaningful quality of Nebraska.

While on the topic of truth value, it belabors the obvious to state that truth itself is the quality of an idea's being in close accord with an accepted standard of reference.  However, what is often not so obvious is that accepted standards vary with context.  Standards of truth are typically dogma with respect to ideology, coherently consistent reasoning with respect to logic, and observed evidence of reality with respect to empiricism.  We should be aware that such differences in standards sometimes lead to conflicting notions of truth.  Methods of dealing with such conflicts include compartmentalization (the mental segregation of opposing lines of thought into exclusive categories), reconciliation (the reinterpretation of ideas in a way—such as compromise—that renders the conflict effectively moot), and resolution (the use of evidence and reason to determine which concept of truth is most consistent, both with itself and with reality).

 Parts of a statement: subject and predicate  A statement consists of two major parts: a subject and a predicate.  The subject of a statement contains a noun or pronoun indicating the person, place, thing, or concept that the statement is about.  The predicate contains a verb specifying an action or state of being, plus other material indicating what the subject is or does, or what happens to the subject.  In the statement, "John has a long mustache," "John" is a noun, which is the name of the subject of the statement.  The statement's predicate is "has a long mustache."  The statement is about "John;" "has" is the predicate's verb; and "a long mustache" specifies what it is that John has.  In each of the following statements, the subject is highlighted in yellow, and the predicate in aqua:

The ugly duckling has become a beautiful swan.
The waiter is clumsy.
The dog chases the ball.
The ball is chased by the dog.

 The agent-patient relationship  Note in the last example that, although the dog is still doing the chasing, the verb in this case isn't "chases," but "is chased," and it's the ball, not the dog, which "is chased."  Therefore, in this case "the ball" is the subject, even though it receives the action rather than performs it.  This illustrates what's called an agent-patient relationship.  In such a relationship, the agent is always the entity performing an action, while the patient is always the entity upon which the action is performed.  Whether the dog chases the ball or the ball is chased by the dog, the relationship is the same: the dog is doing the chasing and is thus the agent, while the ball is being chased and is therefore the patient.  (Sometimes it happens that the agent and the patient are the same thing, in which case we use a reflexive pronoun to indicate that they're identical.  For example, in the statement, "Joe injures himself," Joe is the one both causing and receiving the injury.  Thus, the agent is Joe, and the patient is himself—poor Joe again.)

 Active and passive mood  Although it's the agent that's the subject of most statements, that's not always the case.  The difference depends on whether the statement is in active or passive mood.  In active mood, the subject is the agent (in this case the dog), the acting entity: "The dog chases the ball."  In passive mood, the subject is the patient (the ball), the entity acted upon: "The ball is chased by the dog."  In some cases, passive mood can be used to express a relationship in which the speaker or writer either doesn't know, or doesn't choose to reveal, the identity of the agent: "The ball is chased."

 Function versus syntax  In the normal syntax (word order) of English statements, the subject typically precedes the predicate.  However (often in poetry), the normal word order sometimes gets shuffled.  Consider: "Beneath the spreading chestnut tree the village smithy stands."  If we assumed, simply because of its position in the statement, that "the spreading chestnut tree" is the subject, we'd be mistaken.  It's not the relative positions of subject and predicate, but rather the functional relationship between the two, that determines which is which.  Here the main verb of the statement is "stands," and clearly it's the smithy, not the tree, that's doing the standing.  (Indeed, there would be no meaningful difference if we were to shuffle things even further, as in "Beneath the spreading chestnut tree stands the village smithy."  Therefore, "the village smithy" is truly the subject, and "beneath the spreading chestnut tree" is simply a part of the predicate that clarifies where the smithy "stands."  If we rearrange the sentence in standard syntax, we get: "The village smithy stands beneath the spreading chestnut tree"—a bit less charming and colorful, but more like what we'd expect to hear—if smithies hadn't been replaced by auto repair shops a century ago.  (Besides, in a different configuration, "stands" wouldn't be the final word in this line of the poem, and thus there'd be no rhyme for "hands" in the next line.  But that's beside the point in this discussion of grammar.)

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Arguments—Linking Statements to Make a Point

Most people tend to think of an argument as a kind of dispute, ranging from a heated difference of opinion to wild accusations, insults, mayhem, and general ill will.  In logic, however, argument is none of the above.  Logical argument is the connecting of related statements in such a way that, taken together, they coherently lead step-by-step to an ultimate claim, commonly called a conclusion, since it typically occurs at or near the end of an argument.  Although logical arguments are often used in an effort to resolve disputes, sometimes they don't involve any sort of disagreement at all, but simply constitute methodical support for, and confirmation of, widely accepted ideas.  And sometimes logical argumentation is simply used as a tool to discover truth, as by reasoning through a problem to which the solution isn't initially known; indeed, careful reasoning might reveal the solution to be something wholly unanticipated.

 What are linkages, and what role do they play?  To see what's meant by logically related statements, consider this timeworn example:

All men are mortal.
Socrates is a man.
So, Socrates is mortal.

The first statement presents two concepts to be considered: men and mortal.  The second statement introduces another concept, Socrates, and links it to one of the concepts, men, introduced in the first statement.  The third statement then links the new concept, Socrates, to the other initial concept, mortal.

To some readers this might seem so simple and instinctive as to be hardly worth mentioning.  The logical linkages that methodically lead from assumptions and evidence to a conclusion are what make an argument coherent.  Yet many people (even some who are supposedly well educated) apparently have little, if any, inkling of how to interlink ideas.  Their notion of making a point is simply to throw out assertion after assertion, with no attempt to show either how these ideas are supported by evidence or how they're logically interrelated, let alone how they lead to a conclusion.  This isn't reasoning; it's simply preaching.  Still, many people are eagerly taken in by it, and so it persists.  An argument whose statements are not adequately linked is incoherent.

 Functions of statements within an argument  A statement that introduces information or a relationship is called a premise.  Kinds of information and relationships stated in premises include assertions, beliefs, evidence, facts, judgments, relationships, speculation, and more.  A statement that expresses the overall implication or inference of an argument's combined and interconnected premises is called a conclusion.  A conclusion presents an idea that is shown to be very probably or even inescapably true, by the information and linkages provided by the premises.

Very often, arguments contain material that serves functions other than premises and conclusion.  These include analogies, clarifications, definitions, descriptions, examples, explanations, illustrations, limitations, rhetoric, refutation of challenges, and other material.  Technically, these aren't part of the line of reasoning, but are intended to assist in understanding the argument.

In the real world, most arguments run somewhat longer than three simple sentences, and sometimes there are multiple lines of linkage that converge at some point prior to the conclusion.  Aside from formal tradition, there are no hard and fast rules that determine each statement's exact position in an argument.  As to the conclusion, perhaps most often it comes near the end of an argument, after the various premises have led up to it.  But sometimes (particularly when it's anticipated that the target audience will agree readily), the conclusion is presented first, and the premises are then added to provide explanation and justification.  Occasionally, the conclusion is found somewhere in the middle of an argument, or it may appear more than once, bolstered both before and after by different trains of thought.  Sometimes, an argument is more effective when parallel lines of linkage are pursued concurrently a step at a time.  But when our primary interest is in clarity rather than some other effect, an argument is usually easiest to follow when each line of thought is traced individually from start to finish, or at least to a point where the various lines converge.

 A note of caution  We can't do much about how others manipulate reasoning for less than ethical purposes, except to be aware of various common ploys.  For some, their business is preying on the gullible, their method is deception, and their sole ethical guideline is whatever they can get away with.  But as for ourselves, we ought not to use artful wordings or arrangements of material in an effort to disguise weaknesses in an argument.  If what we seek is truth, then we should look to the strength and sufficiency of our evidence, and the solidity of the logical framework we build upon it.  If what we seek isn't truth, if we can successfully argue our point only through deception, diversion, and deliberate omission, then we ought to reconsider whether that point is actually one worth making.  In a few cases—thwarting a criminal, for example—perhaps such tactics would be justified.  But when we're dealing with honest people, we ought to behave in good faith ourselves, and that means being open and honest about both the strong and weak points in our reasoning.

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THE CONTENT OF PREMISES: Assumptions, Facts, and Evidence 

Human knowledge is plentiful, but there are rather severe limits on what we can know with absolute certainty—for example, that we (by direct experience) exist, or that a triangle (by definition) is a geometric figure with exactly three straight sides.  Most of what we assume to be factual knowledge we've gleaned from observations made using our imperfect sensory apparatus and filtered through our cultural and personal biases, or we've learned from sources we're inclined to trust despite hidden agendas and sometimes spotty expertise.

 Assumptions  are ideas that we're prepared to consider true, despite that support for their being true might be insufficient or lacking altogether.  Assumptions include what we believe or speculate, and even much of what we presume we know, but would be hard pressed to verify against an impartial standard.

 Facts, strictly speaking, are ideas that are independently verifiable by an impartial observer.  However, most people aren't that demanding about what they call "facts."  So we're well justified in challenging any alleged fact unless and until we're satisfied that it is indeed independently verified.  If it isn't verifiable, then it's an assumption, not a fact.  The same goes for any subjective interpretation or evaluation of a fact: to the extent that it's subjective, it's an assumption, not a fact.

 Evidence  encompasses many sorts of facts and data—physical, mathematical, recorded, and so forth.  Evidence is a term we typically apply to things that furnish independent, plausible support for believing something to be true.  For example, fossilized bones are physical evidence of ancient creatures; the divisibility of all even numbers by two is mathematical evidence that two itself is the only even prime number; the religiously critical writings of Jefferson and Madison are evidence that some of the most prominent founders of the United States weren't Christians.  (Note that writing constitutes evidence that an idea has been believed, but not that the belief is true.)

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PROGRESSION: Deductive versus Inductive Reasoning 

Deduction and induction are often described as two progressions of reasoning.  Deduction progresses from the general to the particular, while Induction progresses from the particular to the general.  While this isn't always the case, it's true in most instances, and so should be good enough for our purposes.  Consider the following sample premise as a starting point:

All life forms we've observed are carbon-based.

What can we make of this?  We could consider it as either a particular or a general statement, depending on where we'd like to go with it.  To use it as general evidence of something more particular, we could work toward a conclusion like:

So, humans are carbon-based.

On the other hand, to use it as particular evidence of something more general, we might work toward a broader conclusion, such as:

So, all life forms are carbon-based.

Of these two conclusions, the first, illustrating deduction, is based on an unspoken second premise: Humans are a life form we've observed.  The second, an example of induction, requires a slight leap of faith, based on the plausible assumption that the same pattern, which we've observed without exception in each of the millions of life forms so far studied, most probably holds true as well for any life forms we haven't yet observed. 

 Deductive reasoning  uses generally known and accepted truths to establish a specific point.  We use deduction to demonstrate or prove particular ideas to be either true or false.  Our earlier example, All men are mortal, and Socrates is a man; so, Socrates is mortal, is an example of deductive reasoning.  It begins with a general statement, All men are mortal, which we may suppose to be universally true, since no exceptions have been observed and confirmed.  From this premise, the argument progresses toward the case of a particular individual, Socrates, who, being a man, we may deduce to be mortal.  If the argument is valid (it is), and if all of its premises are true, then we can say, with the same degree of certainty that we know the premises are true, that the conclusion must also be true.

 Inductive reasoning  works in the opposite direction, starting from some particular things that are known and progressing toward a broader truth about similar things of the same general kind.  We use induction to figure out general patterns from representative sample observations and relationships.  Physicist Isaac Newton famously developed his general laws of motion from observations of individual physical objects.  Subsequently, he inferred his principle of universal gravitation by applying those laws to the motions of the planets (as previously recorded by Johannes Kepler), guided by an assumption that the principles of physics are constant throughout the natural universe.  In contrast to implications of deductive reasoning, the conclusive inferences of an inductive argument are never an air-tight certainty, but rather a matter of statistics.

Inductive arguments are often perched on statistical probabilities, or on the supposed reliability of an expert authority.  With probabilities, our confidence in an inductive conclusion depends on how many examples we've observed and how consistent they are with the pattern we propose to establish, and on whether we've adequately accounted for any examples that deviate significantly from the expected pattern.  With authority, the case hinges on whether the source is indeed a confirmed reliable authority in the field in question, and to what degree that authority might be fallible.  In either case, there is a possibility that the argument's conclusion could turn out to be false in some instances, even when the probability leans strongly toward truth.

(Fans of Sherlock Holmes will be devastated to learn that their fictional hero's forte was not deduction, but rather induction, as in the shrewd assessment of the highest probability from an assortment of plausible alternative possibilities.  There is always a chance that an answer with the highest probability—if even a minuscule fraction less than 100 percent—is not the correct one.)

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TERMS

Click a term to review its definition or explanation in the text.

• common sense

• rhetoric

• logic

• statement

• truth value

• subject and predicate

• agent-patient relationship

• mood: active and passive

• argument

• conclusion

• premise

• coherence

• linkage

• content: assumptions, facts, and evidence

• progression: deductive and inductive reasoning

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