What Is Logic?

© 2011 By Paul Herrick

A “Cook's Tour” of the Fundamental Ideas
of Logical Theory

Introduction

The word “logic” is used in two different ways. We often say things like this: “His logic seems faulty to me” or “I don’t agree with her logic.” In such cases, we are using the word “logic” to refer to someone’s reasoning. However, the word “logic” is also used as the name of an academic subject taught in colleges around the world, as in “Philosophy 106: Introduction to Logic.” Logic, as an academic discipline, may be defined as “the systematic study of the standards of good reasoning.”

Human beings have certainly been thinking logically since before the dawn of recorded history. But the academic discipline named logic dates back only to the 4th century B.C., to the city of Athens, Greece. For it was there that the ancient Greek philosopher Aristotle (384-322 B.C.) wrote the first known treatises of logical theory and began teaching the first logic classes in history. The subject matter of the new academic subject was not specific reasoning about a particular topic, rather, it was the standards any reasoning must follow if it is to be good reasoning. 

In sum, logical thinking has been around as long as human beings have been reasoning, but the academic discipline named “logic” only dates to the 4th century B.C., to the creative genius of one of the greatest of the ancient Greek philosophers, Aristotle.   

Incidentally, the subject founded by Aristotle was not called “logic” at first and apparently did not have a formal name during his lifetime. Several decades after the death of Aristotle, it was named “Logos” by a school of philosophers who met every day in downtown Athens on a painted porch (Greek: “stoa”), the philosophers known to history as the Stoics.

Back to Top

And Aristotle said, “Let there be logic.”

We always understand something better when we understand its origin and logic is no exception. Let us now take a brief look at how the academic subject named logic began. The story, as they say, is worth recounting.

The founder of logic as an academic subject was born and spent his early years in Macedonia, a state located on the northeastern part of the Greek peninsula. After his father died, Aristotle was sent to Athens, to study philosophy at Plato’s Academy, the first recognizable university in world history. (The name of the school came from its location: the grove of Akademos, a garden of olive trees named after a legendary Greek hero.)  Aristotle studied under the great philosopher Plato (429-347 B.C.) for nearly 20 years before leaving to found his own university and research institute, the Lyceum.

It is likely that the seed idea for a subject devoted solely to the study of reasoning occurred to Aristotle while he was studying philosophy at Plato’s Academy. In order to see why the study of philosophy might inspire the birth of logical theory, let us take a brief look at the discipline the Greeks named philosophy (from the Greek words “philo” for love and “sophia” for wisdom, literally, “the love of wisdom”).  

At the dawn of the 6th century B.C., ancient people everywhere made sense of the world on the basis of customary myths (stories passed down orally from generation to generation) and by obediently believing what priestly and political authorities told them to believe. Beginning with Thales of Miletus (c. 625- 546 B.C), a group of individuals in ancient Greece began questioning the customary myths and the traditional explanations of the universe. In written works and in discussions recorded in the historical record, these individuals pioneered a radically new way to make sense of the world. Named “philosophers” by the Greeks, Thales and his associates were the first persons in history to do all three of the following:

  • They rejected the explanations of the world contained in the traditional myths and the claims of religious and political authorities, on the grounds that there was no good reason to believe that unbacked myths and unquestioned claims of authorities are true, that is, in correspondence with reality.
  • In place of mythical stories and authoritative pronouncements, they sought explanations based on unaided reasoning and on observations that could in principle be made by anyone.
  • They put their theories and the supporting evidence for their theories into written form and passed this around for critical comments, reasoned discussion, and intellectual debate. Philosophical theories were to be proposed, criticized, defended, revised, and / or rejected on the basis of reasoning and observable evidence, without reference to unbacked myth and authorities whose statements could not be questioned. 

In short, the first philosophers sought rational explanations of the world and of things within the world—accounts justified on the basis of evidence and reasoning alone. The birth of the philosophical tradition, in ancient Greece during the 6th century B.C., was one of the first intellectual revolutions in world history.

Now picture young Aristotle sitting in philosophy class at the Academy, weighing the evidence  for and against each of the competing philosophical theories of the universe. Like college students today, he is trying to make up his mind: Which theory makes the best sense of things overall? Which explanation best fits the evidence? It is easy to imagine the young Aristotle thinking to himself, in this context:  

“The reasons for and against each theory are complicated and it is difficult to sort them all out. What we need is a separate discipline that studies the universal standards of reason itself, not reasoning about this or that theory but pure reason no matter what it is about.”

Aristotle would eventually write five thick treatises of logical theory, known collectively as the organon (“tool of thought”), most of it as valid today as it was 2,300 years ago. Indeed, there are scholars today who spend their entire academic lives studying and probing his fascinating works on logic, doctoral dissertations are still being written on the logical theory of Aristotle, and new books and articles on Aristotle’s logic still appear every year, resulting in new logical insights over two millennia after his death. For teaching the first logic classes on record, and for writing the first logic textbooks, Aristotle deserves the title history has conferred on him: He is the founder of logic as an academic discipline.

Incidentally, while teaching at the Lyceum, Aristotle conducted research in, and wrote academic treatises on, nearly every subject known at the time, including physics, metaphysics, ethical theory, political theory, linguistics, biology, zoology, music, rhetoric, poetry, aesthetics, and scientific methodology. He wrote the first history of philosophy. He not only criticized the most important theory proposed by his teacher Plato, the theory of forms, he also proposed and argued extensively for a radically different theory of forms. The theories of Plato and Aristotle, on the nature of abstract objects, compete even today, powerful arguments are still being traded. Because of his extensive scientific research on sea life, the first such research in world history, Aristotle is also known as the founder of marine biology. Logic is a fascinating subject; the history of logic is equally fascinating. And so is its founder.

Back to Top

But Isn’t All Reasoning Equal?

When first exposed to the claim that there are objective standards of good reasoning, some people reply with something like this:

“But isn’t all reasoning equal? What gives you, or anyone else, the right to say that some reasoning is good and other reasoning is bad? How can you say that one person’s reasoning is wrong and someone else’s is right? All human beings are equal, and all human reasoning is equally good. Only a logical imperialist would put down someone’s reasoning.” 

However, this attitude is easily dispelled. Can anyone honestly say that the following is a piece of good or correct reasoning?

Premise: Some apples are red.
Conclusion: Therefore it follows that President Obama was actually born in the old Soviet Union, which makes him ineligible to be President of the United States.

Does anyone seriously think that the reasoning from the premise to the conclusion, in this case, is good reasoning? Does the fact that some apples are red provide solid evidence for the claim that the President was born in the former USSR?  How about this reasoning:

Premise: The Earth is larger than a typical acorn.
Conclusion: Therefore it follows that the Moon does not exist--it is nothing more than a bright reflection of something floating in a pond on Earth.

The premise does not really support the conclusion does it? Now compare this to the following reasoning:

Premise: Ann and Bob are not both home.
Premise: But Ann is home.
Conclusion: Therefore, it follows that Bob must not be home.

The interesting property of this argument is this: If the premises are true, the conclusion must be true. On the basis of only the information contained in the premises, the conclusion is completely certain. In this case, the premises conclusively establish the conclusion. Logicians call this type of argument a “deductively valid argument.”

Certainly not all reasoning is equal. Surely some acts of reasoning are better than others. The reasoning Einstein gave in support of his Special Theory of Relativity is an example of extremely good reasoning, while the case for the claim that the Earth is hollow (and harbors inside itself a secret, advanced civilization) is just foolish. Logic seeks the universal standards reasoning ought to follow if it is to be correct or good reasoning, no matter what the subject matter.

Back to Top

The Value of Logic

The principles of logic are thus no mere academic exercise. They are guides to correct reasoning just as the principles of accounting are guides to keeping a correct set of books, the principles of arithmetic are guides to correctly adding, subtracting, multiplying and dividing numbers, the principles of photography are guides to taking good pictures, the principles of physics are guides to correctly landing a manned spacecraft on the moon and getting it back home again afterwards, and so on. Not everyone reasons correctly all the time. Everyone makes logical errors at least sometimes. We all need to pay attention to the principles of logic, at least when matters get complicated and things get hard to sort out.

What Does a Standard of Reasoning Look Like?

Let us examine a few sample standards of correct reasoning. Our first example was discovered and first formulated in ancient times, by logicians belonging to the Stoic school of philosophy in Athens, Greece. Where P and Q represent declarative sentences, that is, sentences expressing something that is either true or false, the following pattern of reasoning is correct:

  1. If P is true, then Q is true.
  2. But P is true.
  3. Therefore, Q must be true.

If we uniformly substitute two declarative sentences of our choice for the variables P and Q, and make a few obvious grammatical adjustments, we produce what logicians call a “substitution instance” of this structure of reasoning:

  1. If Plato is lecturing, then Aristotle is in the audience.
  2. But Plato is lecturing.
  3. Therefore, Aristotle must be in the audience.

I substituted “Plato is lecturing” for P, “Aristotle is in the audience” for Q, and left the rest unchanged. Here is a different substitution instance of the same general pattern of reasoning:

  1. If Ann is swimming, then Bob is swimming.
  2. But Ann is swimming.
  3. Therefore Bob must be swimming.

Here P was replaced by “Ann is swimming,” Q was replaced by “Bob is swimming,” while everything else (“If…then” and so on) was left unchanged. Logicians in the Middle Ages named this pattern of reasoning “Modus Ponens” (Latin for “Method of Affirmation”).

In contrast, the following form of reasoning is simply not correct reasoning:

  1. If P is true then Q is true.
  2. But Q is true.
  3. Therefore P must be true.

If you are not sure that this pattern of reasoning is illogical, consider the following substitution instance:

  1. If it is noon then Ann is swimming.
  2. But Ann is swimming.
  3. Therefore it must be noon.

Not good reasoning. (Can you explain why?) In logic, this form of reasoning is known as the “fallacy of affirming the consequent.” A fallacy is an error in reasoning.

So, not all reasoning is good reasoning. Logic seeks the principles that distinguish correct from incorrect reasoning: the standards reasoning must follow if it is to be good reasoning no matter what it is about.

Back to Top