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Deductive arguments

Intro

People whose lives revolve around their beliefs, no matter how strange these beliefs may be, tend not to listen to logic and reason or anything else that undermines their beliefs. To accept that they are wrong means that they lose what they think makes them special. When discussing martial arts fraud, it helps to use deductive arguments but, even then, a lot of people will still stand by their illogical, irrational beliefs.

This article examines the structure of a sound deductive argument, from its premise to its conclusion. However, the conclusion is only as compelling as the premises upon which it is based.

Logic does not solve the problem of verifying the basic assertions that are used to support arguments, for that, we need to use scientific inquiry. Since the philosophy of science and the scientific method are complicated topics, they are not covered in this discussion.

Propositions

A proposition is a statement that is either true or false. It pertains to the meaning of the statement, not to the arrangement of words used to convey that meaning. For example, "There a master in our school who claims to have a Ph. D." is a proposition. "Our school has a master in it who claims to have a Ph. D." is a rephrasing of the same proposition. Care must be used in rephrasing since it is easy to change the meaning of a statement unintentionally by rephrasing it.

Arguments

An argument is a set of premises and a conclusion where the conclusion and premises are separated by some trigger word, phrase, or mark known as a turnstile.

Premises

A deductive argument requires many core assumptions, called premises, on which the argument is built. They are the reasons for accepting the argument. Premises are only premises in the context of a particular argument; in another argument, they might be conclusions.

You should always explicitly state the premises of the argument. Failing to do so is often viewed as suspicious, and will likely reduce acceptance of your argument.

The premises of an argument are often introduced with words such as "assume", "since", "obviously," and "because." For example, “Let’s assume that the master’s Ph.D. is legitimate.” You should get your opponent to agree with the premises of your argument before proceeding.

Using the word "obviously" in a premise is often viewed with suspicion since it is sometimes used to persuade people to accept false statements rather than admit that they do not understand why something is obvious. Do not be afraid to question statements that people tell you should be obvious.

Inferences

Once the premises have been agreed upon, the argument proceeds using a step-by-step process called inference. In an inference, you start with one or more propositions that have been accepted, and then you use these propositions to arrive at a new proposition. If the inference is valid, the new proposition should also be accepted.

You may later use the new proposition for inference. This means that initially, you can only infer things from the premises of the argument. However, as the argument proceeds, the number of statements available for inference increases.

Inference steps are often identified by using phrases such as "therefore" or "implies that." For example, “Therefore, the master should have a diploma and transcript from an accredited university.”

Conclusion

If all goes well, you will arrive at a proposition that is the conclusion of the argument (the result you were trying to prove). The conclusion is the result of the final step of inference. It is only a conclusion in the context of a particular argument; it could be a premise or an assumption in another argument. The conclusion is said to be affirmed based on the premises, and the inference from them. For example, “Since the master does not have a diploma and transcript from an accredited university, he must not be a Ph. D.”

Complications

Clearly, you may build a valid argument from true premises and arrive at a true conclusion. You may also build a valid argument from false premises, and arrive at a false conclusion. You may also start with false premises, proceed using valid inference, and reach a true conclusion. However, you cannot start with true premises, proceed using valid deductive inference, and then reach a false conclusion.

If an argument is valid, and it started from true premises, then it is called a sound argument and a sound argument must arrive at a true conclusion.

The following is an example of an argument that has an invalid inference:
  1. Premise: Taekwondo students are martial artists that workout in a dojang. (True)
  2. Premise: Karate students are martial artists. (True)
  3. Inference: Therefore, karate students workout in a dojang. (False)
  4. Conclusion: Both taekwondo students and karate students workout in a dojang. (False)
The following is an example of an argument that is valid but may or may not be sound:
  1. Premise: Every event has a cause.
  2. Premise: The universe has a beginning.
  3. Premise: All beginnings involve an event.
  4. Inference: This implies that the beginning of the universe involved an event.
  5. Inference: Therefore, the beginning of the universe had a cause.
  6. Conclusion: The universe had a cause.

The proposition in statement 4 is inferred from statements 2 and 3. Statement 1 is then used, with the proposition derived in statement 4, to infer a new proposition in statement 5. The result of the inference in statement 5 is then restated as the conclusion in statement 6.

Spotting arguments

Spotting an argument is harder than spotting a premise or a conclusion. Many people pepper their writing with assertions, without ever producing anything that might reasonably be called an argument.

Sometimes arguments do not follow the pattern described above. For example, people may state their conclusions first, and then justify them. This is valid, but it may be a bit confusing.

Some statements look like arguments but are not. For example:
"If the history of taekwondo is accurate, then General Choi must either have been a power-hungry pretender, or the founder of taekwondo."
This is not an argument; it is a conditional statement. It does not state the premises necessary to support its conclusion, and, even if you add those assertions, it still suffers from many other flaws.
An argument is also not the same as an explanation. Suppose that you are trying to argue that John believes that taekwondo is an ancient art, and you state:
"John said taekwondo is an ancient art because he believes taekwondo has its roots in the ancient art of subak"
This may appear to be a relevant argument, but it is not; it is an explanation of John's statement. To see this, remember that a statement of the form "X because Y" may be rephrased as an equivalent statement, of the form "Y, therefore, X." Doing this with this statement results in:
"John believes that taekwondo has its roots in the ancient art of subak, therefore he said that taekwondo was an ancient art."
Now it is clear that the statement, which seemed to be an argument, is actually assuming the result which it is supposed to be proving.

SOURCES
  • The Secular Web. [Online]. Available: http://www.infidels.org/news/atheism/logic.html.

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