Hello. I'm Glenn. And this is the ethics tutorial on deductive and inductive inference. Let's go over a couple ideas to keep in mind, and then cover the topics for this tutorial.
Things to keep in mind for this tutorial are the definition of an argument and the definition of an inferential claim.
In this tutorial, we will cover several statements about arguments and inferential claims. We'll clarify different levels of logical certainty. And we'll provide several examples of both deductive and inductive arguments.
Key terms for this tutorial. Deductive argument-- an argument whose inferential claim is a claim of logical certainty. Inductive argument-- an argument whose inferential claim is a claim less than logical certainty. Logical certainty-- inconceivable that the conclusion is not entailed by the premises.
First, a few statements about arguments and inferential claims. Arguments are evaluated on the type of inferential claim that they make. Important to remember is that inferential claims are always about the whole argument. An inferential claim is about the argument's type.
And in that respect, we need to determine which of the two main categories the argument falls into. The main categories are that it is either deductive or inductive. We need to determine this first because it will be the basis of the evaluation. And once we know which type it is-- either deductive or inductive-- we can then assess its strengths and make a clearer evaluation of it.
The way we determine whether an argument is deductive or inductive is to address what level of logical certainty it exhibits. There are two ways of looking at this-- either the argument expresses a degree of probability or it presents itself as coming to a conclusion that is certain. This is how we tell the difference.
Now, deductive arguments present a conclusion that is a logical certainty. Another way of understanding this is that when an argument is logically certain, it is inconceivable that the conclusion is not entailed by the premises.
Inductive arguments, on the other hand, entail a degree of probability. It may be highly probable, it may be minimally probable, but it is always a degree of probability. So inductive arguments are an argument whose inferential claim is less than logical certainty.
One thing to note in this respect is that when we look at it, most of our day-to-day reasoning is inductive. Rarely do we deal with deductive arguments. We rely on probabilities to predict what is the case and what will be the case.
For example, we assume that the sun is going to rise tomorrow. And the evidence for that is that it always has. Well, this is an inductive argument because it is probable that the sun will rise tomorrow. However, it is not 100% certain.
If every quiz we take so far is easy, it's reasonable to believe that the next quiz will be easy, but this is only probable. So this is where most of our reasoning is, and that's OK. We don't have to be certain all of the time.
So let's look at two examples of inductive arguments and two examples of deductive arguments. First, inductive-- the first argument is the chair in the living room is red, the chair in the dining room is red, all the chairs in the house are therefore red. This is not deductive because it's not certain. There is a possibility that there are other rooms and other chairs. So although it is probable that the chairs in the house are all red, it is not certain.
Second, I got up at 5:00 AM today, I got up at 5:00 AM yesterday, therefore I will get up at 5:00 AM tomorrow. The past is, of course, a predictor of the future, but it is not 100% certain. I may very well get up at 5:00 tomorrow, but I may sleep in.
Two deductive arguments-- first, all oranges are fruits, all fruits grow on trees, therefore all oranges grow on trees. Given the premises, the conclusion necessarily follows from them. It is 100% certain.
Notice, however, that the second premise is false. Grapes, for example, don't grow on trees. They grow on vines. However, a deductive argument is only in reference to the conclusion following with certainty from the premises.
Deduction does not deal with truth. That's a different issue. So we can have a Deductive argument with a necessary conclusion that does contain a false premise. That's OK.
Second, Jeff is a bachelor, all bachelors are single, therefore Jeff is single. This presents a conclusion that is 100% certain.
In summary, we have looked at distinctions between inductive and deductive inferences. We've seen how they are different in the type of inferential claim they make. We understand that they operate on different levels of logical certainty. And the examples have shown us the distinctions in how they operate.
An argument whose inferential claim is a claim of logical certainty
An argument whose inferential claim is a claim less than logical certainty.
Inconceivable that the conclusion is not entailed by the premises