Logical Reasoning

I. Definition

Logical reasoning (or just “logic” for short) is one of the fundamental skills of effective thinking. It works by raising questions like:

If this is true, what else must be true?
If this is true, what else is probably true?
If this isn’t true, what else can’t be true?

These are all inferences: they’re connections between a given sentence (the “premise”) and some other sentence (the “conclusion”). Inferences are the basic building blocks of logical reasoning, and there are strict rules governing what counts as a valid inference and what doesn’t — it’s a lot like math, but applied to sentences rather than numbers.

Example:

If there is someone at the door, the dog will bark.

Assuming this sentence holds true, there are some other sentences that must also be true.

If the dog didn’t bark, there is no one at the door.
Just because the dog barked doesn’t mean there’s someone at the door.

There are also a few sentences that are probably true, such as:

The dog can sense (hear or smell) when someone is at the door.
The dog belongs to the people who live in the house where the door is located.

II. Types of Logical Reasoning

There are two basic types of logic, each defined by its own type of inference. They correspond to the two categories in the example from section 1.

Deduction is when the conclusion, based on the premises, must be true. For example, if it’s true that the dog always barks when someone is at the door and it’s true that there’s someone at the door, then it must be true that the dog will bark. Of course, the real world is messy and doesn’t always conform to the strictures of deductive reasoning (there are probably no actual dogs who always bark when someone’s at the door), but deductive reasoning is still important in fields like law, engineering, and science, where strict truths still hold. All math is deductive.
Induction is when the conclusion, based on the premises, is probably The answers are less definitive than they are in deductive reasoning, but they are often more useful. Induction is our only way of predicting what will happen in the future: we look at the way things are, and the way they have been in the past, and we make an educated guess about what will probably happen. But all predictions are based on probability, not certainty: for example, it’s extremely probable that the sun will rise tomorrow morning. But it’s not certain, since there are all sorts of catastrophes that could happen in between now and then.

III. Logical Reasoning vs. Critical Thinking

Logic is one of the main pillars of critical thinking. And there’s no question that critical thinking would be impossible without some understanding of logical reasoning. However, there are many other skills involved in critical thinking, such as:

Empathy, or the ability to imagine what someone else is feeling or experiencing. This is a crucial skill for critical thinking, since it allows you to broaden your perspective and reflect on your actions and beliefs. Empathy also makes you a better student of philosophy because it enables you to put yourself in the author’s shoes and understand the argument from within.
Analogy, or noticing similarities and thinking them through. Analogies allow us to draw conclusions about, for example, the similarity between our own time and some moment in history, and thus try to make better decisions in the future. This skill is closely related to inductive logic.
Creativity. Critical thinking is all about innovative problem-solving and coming up with new ideas, so it’s heavily dependent on creativity. Just like a creative art, critical thinking depends on assembling old parts in new ways, working inventively within constraints, and matching moments of inspiration with hours of rigorous craft.

III. Quotes About Logical Reasoning

Quote 1

“I am convinced that the act of thinking logically cannot possibly be natural to the human mind. If it were, then mathematics would be everybody’s easiest course at school and our species would not have taken several millennia to figure out the scientific method.” (Neil Degrasse Tyson)

Neil Degrasse Tyson is an astrophysicist and TV personality who passionately advocates for science and critical thinking. In this quote, he suggests that science and logical reasoning are inherently difficult tasks for the human mind, an organ that evolved to perform a very different set of tasks under very different conditions from the ones we live in today.

Quote 2

“Logic takes care of itself; all we have to do is to look and see how it does it.” (Ludwig Wittgenstein)

Wittgenstein was probably the most influential philosopher of the 20th century, but his views changed dramatically over the course of his life, leading to some controversy as to what he actually thought. This quote is a good example. Early on, Wittgenstein believed that logical reasoning was autonomous — that logical truth was an objective truth, out there in the world for anyone to see if they knew how to look. Later on, though, Wittgenstein started to believe that culture and nature influence the way we see logic, and that logic is therefore not perfectly objective. It’s a tricky question, whether logical reasoning is universal or cultural — it must be tricky if a genius like Wittgenstein couldn’t make up his mind on it!

IV. The History and Importance of Logical Reasoning

Logic is a universal part of the human experience — agriculture would be impossible without inductive reasoning about weather and sunlight, and construction would be impossible without mathematics and deductive reasoning about what makes a structure sturdy.

Formalized logic has appeared in several places with more or less similar results. The Greek philosopher Aristotle is credited with being the first to develop a formal system of logical reasoning, but there were already people in India and China working on formal logic long before Aristotle was born. The Indian, Chinese, and Greek systems were all remarkably similar in their rules, which suggests that there may have been some mutual influence despite the distance. Traders and travelling scholars may have brought ideas about logical reasoning with them all over the world, allowing for rapid development of new ideas.

Logic may seem like a stuffy, abstract discipline used only by philosophers and lawyers, but it has had a profound influence on the history of science and technology as well. Alan Turing, the inventor of the modern computer, was a logician rather than a tinkerer or engineer, and his famous “Turing Machine” was a product of his rigorous training in formal logical reasoning.

V. Logical reasoning in Popular Culture

Example 1

“Vulcanians do not speculate. I speak from pure logic.” (Spock, Star Trek)

Mr. Spock was raised on Vulcan and trained to be perfectly rational, ignoring all emotion and concentrating on logical reasoning instead. This represents a widespread trope in popular culture — that logic and the emotions are at odds with each other (the head pulling one way and the heart pulling in another). But there’s no reason why logic and the emotions have to be enemies. Uncontrolled emotion certainly clouds logical reasoning — it’s difficult to think rationally if you’re in a rage, for example — but many traditions argue that logic and the emotions should be partners rather than rivals, each providing its own sort of insight in harmony with the other.

Example 2

On Sherlock, the great detective Sherlock Holmes has a website called “The Art of Deduction,” in which he explains his methods for solving crimes. However, the website has the wrong name — nearly all of Sherlock’s inferences are inductive rather than deductive. That is, they bring together bits and pieces of evidence to develop a theory about what probably happened in a particular crime. They’re not based on the kind of logical certainty that we saw in section 1, but rather on reasoning about likelihoods and probabilities. It’s always logically possible that Sherlock could have it wrong, even though that rarely seems to happen.