Deductive and Inductive Arguments & Reasoning.

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A valid argument.

A proposition can only be said to be true if it corresponds to reality. For example, if I told my friend that I ate eggs and bacon for breakfast this morning, it is only true if I really did eat eggs and bacon this morning. To show that a proposition is true, one needs to be able to present evidence and arguments, a process of reasoning that can be either deductive or inductive.

Deductive Arguments.

Using deductive reasoning the conclusion to an argument will follow from the premises. However, the premises to the argument have to be true and logically valid for the conclusion to follow. It might be the case that the premises are true but the logic is erroneous, then the argument is invalid. A simple example would be as follows:

1. If someone owns a castle, then he is rich.
2. John is rich.
3. Therefore, John owns a castle.

It is quite clear that there is an error here, namely, that one can be rich but not own a castle.

Example 2: Now, using an invalid form of the Moral Argument for God’s existence, it might be presented as follows:

1) If God exists, objective moral values exist.
2) Objective moral values exist.
3) Therefore, God exists.

Both premises 1 and 2 are true, but the conclusion cannot be said to follow logically from them. The argument, in this form, commits the fallacy known as “affirming the consequent” (1). Alternatively, it is possible that an argument can be logically valid but still unsound given that it has false premises. C.S. Lewis has been criticized on his Liar, Lunatic, or Lord Trilemma argument for Jesus’ deity. For example, one might present his argument as follows:

1) If Jesus were not Lord, he would be a liar or a lunatic.
2) Jesus was neither a liar nor a lunatic.
3) Therefore, Jesus is Lord.

This is a valid argument. It infers the negation of the first premise’s antecedent based on the negation of its consequent. However, the argument is still erroneous given that premise 1 is false. There could be other alternatives for premise 1, for example, there is the option that the historical Jesus as he comes down to us in the gospel accounts is a legend.

Inductive Arguments.

A further way of reasoning is through inductive reasoning. The difference between a deductive and inductive argument is that whereas the former, in a logically valid form, has a conclusion that is certain, the latter’s conclusion is only probable and credible given the evidence. The evidence presented within the premises of the inductive argument is viewed as supplying persuasive evidence for the truth of the conclusion, but the conclusion is never certain in the same way as is within deductive argument. An example of an inductive argument is as follows (2):

1) Groups A, B, and C were composed of similar persons suffering from the same disease.

2) Group A was administered a certain new drug, group B was administered a placebo, and group C was not given any treatment.

3) The rate of death from the disease was subsequently lower in group A by 75 percent in comparison with both groups B and C.

4) Therefore, the new drug is effective in reducing the death rate from said disease.

Though inductive reasoning is debated among philosophers, most people tend to find it useful. For example, the conclusion to this argument is likely true given the rules of inductive reasoning. However, it cannot be said to be absolutely true. It might be the case that the participants in group A who were believed to demonstrate that the new drug is effective, might have improved simply due to luck or some unknown variable.

References.

1. Damer, E. 2001. “Confusion of a Necessary with a Sufficient Condition,” in Attacking Faulty Reasoning (4th ed.). p. 150.

2. Craig, W. 2008. Reasonable Faith (3rd ed.). p. 92 (Scribd ebook format)

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