To begin with, recall the nature of an argument. If you want to make an argument, then you want someone to agree with something. In order to do that, you must give them a reason to agree with you. In other words, you must give some support for whatever it is that you want someone to accept. What does the supporting are called the premises, and what is supported by the premises is called the conclusion.
The premises are statements that claim to say something true of the world. This is called a factual claim. The way you get from the factual claim to the conclusion is by saying that the conclusion follows from the supposed facts you provide. When you say that a premise supports a conclusion in this way, you are making an inferential claim.
With this in view we can now distinguish two types of argument: deductive and inductive. It is only the inferential claim that is being distinguished when arguments are separated into deductive and inductive, not the factual claims.
In deductive arguments, the premises support the conclusion so well that, assuming the premises are true, it would be inconceivable for the conclusion to be false. In other words, a successful deductive argument will have logical certainty.
Inductive arguments do not have logical certainty. This is because they only claim to show that, assuming the premises are true, it is likely that the conclusion is also true, not that it is necessarily true. An inductive argument, then, does not have logical certainty.
But there is nothing wrong with inductive arguments. We use inductive reasoning all the time.
In this example, the conclusion establishes probability rather than certainty. As long as you only try to establish probability with inductive arguments, they are powerful and useful. It is only if you believe that you have established logical certainty with an inductive argument that it becomes problematic.
You need to be sure, then, to identify what type of argument you are dealing with before you can properly evaluate it. Once you know which type of argument you are dealing with, you can find out if it is successful or not.
The first two examples are inductive and the second two are deductive. This is because the conclusions in the first two are not guaranteed by the premises, whereas the conclusions are guaranteed by the premises in the last two.
For this reason, an inductive argument will always be unsuccessful as a deductive argument. A deductive argument fails if it doesn’t establish logical necessity. Since an inductive argument never establishes logical necessity, it must always fail as a deductive argument.
You can see this clearly in argument (2). The premises of this argument tell you two things: that Sofia was hungry and that she was holding a burger. These things alone do not tell you that she necessarily ate the burger, only that it’s likely.
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