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Simply put, logic is the study of human reasoning. The laws of logic are those patterns of reasoning that will allow you reliably to stick to the truth if you’ve started with the truth. In other words, logic itself is not an ultimate source of substantive truth of any sort at all, but it’s like a mechanism, or a set of universal rules, or procedures, for moving from known truths to previously undetected truths.

The subject matter of logic is arguments. In a logical argument, no one actually needs to be disagreeing with anyone. It can be simply a search for truth.

In logic, an argument is a series of propositions, or statements about reality, one of which is a conclusion drawn from the others, the latter thereby serving in that context as premises or starting points for arriving at the conclusion.

Here’s a little lingo to impress your friends. In deductive logic, a valid argument is an argument of such a form or nature that, if all its premises are true, then you have an absolute 100 percent guarantee that its conclusion is, too. Here is an example of a valid argument, based on a simple, reliable form of deductive reasoning, or inference, called by logicians modus ponens:

  (1) If A, then B

  (2) A

  Therefore

  (3) B

Suppose it’s true that (1) If it’s raining, then your car is getting wet (because you parked outside). If it’s also true that (2) It is raining, then the conclusion follows logically from (1) and (2) that (3) Your car is getting wet. Now, that’s not an exciting conclusion, unless the car is a nice convertible and you remember leaving the top down.

A valid argument with all true premises is called a sound argument. Simply put, in arguments, soundness = validity + truth. Only a sound argument completely guarantees the truth of its conclusion. An argument can be unsound in either of two ways. It can have a false premise. Or it can be invalid, involving the sort of faulty reasoning that, even if all its premises were true, its conclusion could still be false.

With inductive logic, the truth of the premises just raises the probability of, or renders more likely, or gives evidential support to, the conclusion, without giving a 100-percent guarantee that it is true. Here is an example of inductive reasoning:

  (1) All objects of type A that we have seen have had property B.

  (2) There is likely nothing atypical about any A-type objects not yet seen.

  Therefore, probably,

  (3) The next A that we see will have property B.

Inductive logic is not as ironclad as deductive reasoning, but it is the basis for most science and technology, and has achieved tremendous results.

The standard philosophical analysis of knowledge presents it as nothing more, or less, than properly justified true belief. The concept of justification here is that of rational justification. So philosophers have asked throughout the centuries, “What is required for rational justification?” The question is what might be needed to support a belief if that conviction is to have a chance of qualifying as knowledge. And the question can be put in other ways: What makes a belief rational or reasonable to hold? What indicators of truth does rationality demand?

There are people who seem to think that something like strict logical proof is required for rationality. Their mantra is “Prove it.” An old friend, who was a distinguished professor at Yale, once recounted that he had received an unexpected phone call from his son’s Sunday School teacher. The man had reported, “Professor, every time I say anything new in our class, your little boy blurts out, ‘Prove it!’ Could you please have a talk with him and explain that no one can prove everything?” My friend had to laugh and go have a chat with his demanding young rationalist. As the philosopher John Locke concluded from his own research into the nature of proof, “He that, in the ordinary affairs of life, would admit of nothing but direct plain demonstration would be sure of nothing in this world but of perishing quickly.” Solid proof, or in Locke’s language, demonstration in life is rare and so is not ordinarily required.

It seems clearly excessive to think that no belief is rational to hold unless the believer is in possession of some decisive and compelling proof that it’s true. You have beliefs about the galaxy, nuclear energy, your computer, and even your own body that you can’t prove in any decisive sense. You can most often produce some bit of evidence, or the reported testimony of some expert, or at least a vague memory of having once had either evidence or testimony for the truth of what you believe, but you are rarely in possession of a knock-down, incontrovertible proof. Life just doesn’t work like that.

As a result of this realization, some philosophers have suggested that perhaps it is excessive to require proof for rationality, but it may indeed be necessary to have at least sufficient evidence in order to be justified in believing anything.

On this philosophy, widely known as evidentialism, it is irrational ever to believe anything without sufficient evidence that it’s true. Hearsay is not enough, sheer faith is never alone to be trusted, and an unsupported intuition is not admissible at all. Hard evidence or nothing is the demand. But this may itself not be a reasonable demand. Rational belief may not even always dependent on evidence. And that’s a surprise to many people. It’s a matter that Chapter 5 in this book explores.

Philosophy involves an exploration of the biggest questions about human life and its context, as well as a determined search to find answers. Any possible answer or belief on these big issues must be assessed carefully for its truth, and that most often means examining any evidence or argument or any other serious consideration we can find that might indicate its truth. And this requires logical thinking. Logic is vital. You can’t just go with a hunch or a feeling, but have to test ideas logically, first to understand them fully, and then to evaluate them well. It will take you on one of the most unusual intellectual journeys of your life to answer the biggest, deepest questions about evidence and rationality and what logical scrutiny can tell us about them, a journey to be undertaken in the next two chapters. So, if you’re up to it, buckle up your mental seat belt, keep reading, and prepare for the philosophical ride of your life.