Date: 12/17/2002 at 22:06:31 From: Siamak Subject: Valid Arguments What are the real-life applications for valid arguments? I understand the concept of valid arguments and the theorems associated with them but I can't see the big picture. It seems like we use it subconsciously, but what are the specific uses in the modern world?
Date: 12/18/2002 at 12:53:19 From: Doctor Achilles Subject: Re: Valid Arguments Hi Siamak, Thanks for writing to Dr. Math. That's a very rich question. Valid arguments allow us to start with a set of statements and reason our way to a conclusion or to a set of conclusions. The statements we start with can be knowledge that we already have, such as conclusions from other arguments or statements that we know are true. The starting statements can also be assumptions that we pretend are true for the time being (a sort of logical fantasy to see what our assumptions might mean if they were true). Or the starting statements can be pieces of scientific ("empirical") data such as observations about certain phenomena. Often (perhaps always) the set of statements we start with consists of a mix of these three types. The rules we use to get from starting statements to conclusion(s) depend somewhat on the field we are in. The basic rules of logic - see the Dr. Math crash course in symbolic logic: http://www.mathforum.com/dr.math/faq/symbolic_logic.html are used in all arguments. There are often other rules associated with reasoning in other fields. What makes an argument valid (or invalid) is the proper (or improper) application of the rules of reasoning. The conclusion(s) we reach from our starting statements is(are) guaranteed to be true if (1) the starting statements were true and (2) the argument was valid (i.e. the rules of reasoning were properly applied). I would assert that every field of work requires the ability to make valid inferences. In fact, in order to get through life, one must be comfortable reasoning. Consider the following exchange: Mother: Go mow the lawn. Child: I already did the dishes, so my brother should mow the lawn. This may sound like a natural and obvious exchange. But there is actually some fairly involved reasoning going on on the part of the mother and child. Let's just consider what the child had to reason through in order to produce her reply. First, she had to recognize that mowing the lawn was part of a set of household chores. Then she had to go from that abstract set (household chores) back to a different concrete example (doing the dishes). She then brought in an assumption that chores should be split evenly between children, as well as the knowledge that there is one other child in the family, to reason that in order to make the chores even, the brother should mow the lawn. Notice that the mother could use the same set of starting statements together with a few others to turn the argument around: Mother: Your brother already did laundry, vacuumed the house, and walked the dog; you should mow the lawn instead of him. Notice also that neither mother nor child ever explicitly states that the number of chores each child does should be equal, but this assumption is clear in both of their reasoning. Aside from daily life, valid reasoning is vital to all fields of work. I am a biologist. There is a certain set of facts about how cells work that is taken as true. From these facts and the experimental observations in the laboratory, I have to infer conclusions about other details of how cells work that have not yet been discovered by anyone. All the sciences (including social sciences like polital science and psychology) use an analogous process in making conclusions. Valid inferences are vital in law and medicine as well. As a lawyer, you are given the laws themselves, the history of all the cases that have happened so far, and the particular facts of a case. From that, your goal is to convince a judge (and/or a jury) to come to a certain conclusion about what action the law requires. In medicine you are given the set of knowledge about how the human body works, the set of treatments that have been used and how they have worked, and the particular symptoms a patient has. From that, you must make valid inferences about what treatments will most help the patient (this always requires first inferring what is wrong with the patient - which can be difficult - and then deciding the best treatment). Valid inferences are necessary for us to get through life. Any time we ever need to convince or persuade another person, the ability to make valid arguments - to understand what is taken as given and to explain how a certain conclusion must be true - is vital. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/
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