In the last section we learned about logical entailment, which happens when the premises guarantee that the conclusion is true. That is the fundamental concept of this book. But it's not the only sort of logic you can study with formal tools.
Your next task is to assess this argument:
1. There are one million tickets in a fair lottery.
2. Sergeant bought one ticket.
3. Sergeant won’t win.
If you realized this isn’t a fair question, you're right. The argument is good in one sense but bad in another. We just have to be clear about what we mean.
If you answered “bad”, you probably realized that the argument isn't valid. You are right: those premises do not entail that he won’t win. Since he has a ticket, at least he has a chance.
If you answered “good”, you probably realized it is still highly likely that the conclusion is true.
The logic of likelihood and probability is called inductive logic.
The logic of entailment and validity, by contrast, is called deductive logic.
So what we can say is that the argument is deductively bad but inductively good.
Let's see if you've got the idea.
Unfortunately, the person making an argument doesn't always tell you so clearly whether they are doing induction or deduction. Sometimes we have to use contextual clues and the principle of charity to figure it out.
For example, imagine that a crime scene investigator has examined the bank robbery, and makes the following argument:
“Gunpowder traces were found on the chair in the middle of the room, and the bullet hole is on the north wall. So the perpetrator fired from the south side of the room.”
Inductive and deductive logic can both be studied with the formal tools we learn in this book. Our focus, however, will be on deduction: the notions of entailment and validity.
The main reason why is that you have to learn deductive logic first. Inductive logic is more complicated and presupposes a grasp of deductive logic.
That shouldn’t be surprising: in a sense, deduction is just a special case of induction. A good inductive argument makes the conclusion likely to be true. If the premises guarantee that the conclusion is true, then that is maximally likely.
Now here's a slightly harder question. The American legal standard for a criminal conviction is “beyond a reasonable doubt”.
Finally, let's apply what you've learned.
Great work--you're almost done with Chapter 1.