ID1050– Quantitative & Qualitative Reasoning Example Arguments ID1050– Quantitative & Qualitative Reasoning

First Steps to Analyzing an Argument In the following slides, some simple arguments will be given. The steps to begin analyzing each argument are: Eliminate any non-statements. Identify the conclusion and the premises. Determine if the argument is inductive or deductive Deductive arguments can be valid or invalid. We will learn later how to prove validity of an argument. In this presentation I will simply discuss its validity/invalidity. Valid arguments can be sound or unsound. We will not be learning how to decide if an argument is sound or not, but I will discuss it during this presentation. Inductive arguments are analyzed for fallacies, or know bad argument types.

Dogs, Animals, and Things That Eat Here is an argument: All dogs are animals. All animals must eat. So, all dogs must eat. There are no non-statements in this argument. There is a conclusion indicator, “So”. The last statement is the conclusion, and the others are premises. This argument is Deductive. The intention of the argument is that if the premises are true, they will lead with certainty to the conclusion. It will turn out that this argument is Valid. For now, consider the diagram above. We would probably all agree that the premises are true, so this argument is Sound. P Dogs P C

Bloops, Gleeks, and Zorgs Here is an argument: All Bloops are Gleeks. All Gleeks are Zorgs. Therefore, all Bloops are also Zorgs. There are no non-statements in this argument. There is a conclusion indicator, “Therefore”. The last statement is the conclusion, and the others are premises. This argument is Deductive. The intention of the argument is that if the premises are true, they will lead with certainty to the conclusions. It will turn out that this argument is Valid. For now, consider the diagram above. We have no idea if the premises are true, so we can’t decide about its soundness. P Bloops P C

Dogs, Animals, and Four-Legged Things Things with 4 legs Here is an argument: All dogs are animals. All (normal) dogs have four legs. Thus, all animals have four legs. This sounds like a previous argument about dogs, but something seems to be wrong! The conclusion indicator, “Thus”, tells us the last statement is the conclusion. This argument is Deductive. The intention of the argument is that if the premises are true, they will lead with certainty to the conclusions. (Although it is flawed.) It is clear that this argument is Invalid. We will prove this later, but consider the diagram . We can’t discuss soundness because the argument is invalid. P Dogs P C

Logical People, Part I P P C Here is an argument: My grandfather was logical. My father was logical. So, I am logical. This argument is Inductive. The intention of the argument is to give supporting premises, but even if they are true, they do not guarantee that the conclusion is true, only that it is likely to be true. We cannot discuss either validity or soundness of inductive arguments. These terms apply only to deductive arguments. P P C

Logical People, Part II P P C Here is a similar argument: Children of logical people are always logical. My father was logical. So, I am logical. The only change to the previous argument is the first premise. The conclusion is exactly the same as before. This argument is Deductive. The intention of the argument is to guarantee that the conclusion is true. This is, in fact, a Valid argument. If the premises are true, they invariably lead to the conclusion. However, I think you’ll agree that this argument is Unsound. The first premise is not generally agreed upon to be true. P P C

Conclusion Analyzing an argument begins with finding the conclusion and premises, then determining whether the argument is Deductive (premises guarantee the conclusion) or Inductive (premises make the conclusion likely). You can’t determine whether an argument is Valid or Invalid simply by looking at the Truth or Falseness of the conclusion alone. Validity is a matter of the entire structure of the argument. Validity only applies to Deductive arguments. We will learn to prove or disprove validity later. Soundness only applies to Valid Deductive arguments. We won’t be working with soundness of arguments in this course. Inductive arguments may have fallacies that defeat them. If they don’t, then all that is left is to argue against the strength of the premises.