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Deductive arguments are those whose premises are said to entail their conclusions (see lesson 1). If the premises of a deductive argument do entail their conclusion, the argument is valid. (The term valid is not used by most logicians when referring to inductive arguments, but that is a topic for another mini-lesson.) If not, the argument is invalid.
Here's an example of a valid argument:
Shermer and Randi are skeptics.
Shermer and Randi are writers.
So, some skeptics are writers.
To say the argument is valid is to say that it is logically impossible for its premises to be true and its conclusion false. So, if the premises of my example are true, then the conclusion must be true also. The premises of this argument happen to be true, so this argument is not only valid, but sound or cogent. A sound or cogent deductive argument is defined as one that is valid and has true premises.
A valid argument may have false premises, however. For example,
All Protestants are bigots.
All bigots are Italian.
So, all Protestants are Italian.
Being valid is not the same as being sound. Validity is determined by the relationship of premises to conclusion in a deductive argument. This relationship, in a valid argument, is referred to as implication or inference. The premises of a valid argument are said to imply their conclusion. The conclusion of a valid argument may be inferred from its premises.
While many errors in deduction are due to making unjustified inferences from premises, the vast majority of unsound deductive arguments are probably due to premises that are questionable or false. For example, many researchers on psi have found statistical anomalies and have inferred from this data that they have found evidence for psi. The error, however, is one of assumption, not inference. The researchers assume that psi is the best explanation for the statistical anomaly. If one makes this assumption, then one's inference from the data is justified. However, the assumption is questionable and the arguments based on it are unsound. Similar unsound reasoning occurs in the arguments that intercessory prayer heals and that psychics get messages from the dead. Researchers assume that a statistically significant correlation between praying and healing is best explained by assuming prayer is a causative agent, but this assumption is questionable. Researchers also assume that results that are statistically improbable if explained by chance, guessing, or cold reading, are best explained by positing communication from the dead, but this assumption is questionable. These researchers reason well enough. That is, they draw correct inferences from their data. But the reasons on which they base their reasoning are faulty because questionable.
I am not suggesting by the above comments that the data and methods of these researchers are beyond criticism. In fact, I find it interesting that skeptics seem to divide into two camps when criticizing such things as Gary Schwartz's so-called afterlife experiments. One camp attacks the assumptions. The other camp attacks the data or the methods used to gather the data. The former camp finds errors of assumption and fallacies such as begging the question, argument to ignorance, or false dilemma. The other finds cheating, sensory leakage, poor use of statistics, inadequate controls, and that sort of thing.
Finally, some deductive arguments are unsound because they are invalid, not because their premises are false or questionable. Here is an unsound deductive argument whose premises may well be true:
If my astrologer is clairvoyant, then she predicted my travel plans correctly.
She predicted my travel plans correctly.
So, my astrologer is clairvoyant.
This conclusion is not entailed by these premises, so the argument is invalid. It is possible that both these premises are true but the conclusion is false. (She may have predicted my travel plans because she got information from my travel agent, for example.) This argument is said to commit the fallacy of affirming the consequent. Another example of this fallacy would be:
If a god created the universe, we should observe order and design in Nature.
We do observe order and design in Nature.
So, a god created the universe.
The premises of this argument may be true, but they do not entail their conclusion. This conclusion could be false even if the premises are true. (We should also observe order and design in Nature if something like Darwin's theory of natural selection is true.)
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