Deductive and Syllogistic Reasoning

Deductive reasoning, or deduction, starts with a general case and deduces specific instances.

Deduction starts with an assumed hypothesis or theory, which is why it has been called 'hypothetico-deduction'. This assumption may be well-accepted or it may be rather more shaky -- nevertheless, for the argument it is not questioned.

Deduction is used by scientists who take a general scientific law and apply it to a certain case, as they assume that the law is true. Deduction can also be used to test an induction by applying it elsewhere, although in this case the initial theory is assumed to be true only temporarily.

(Source: Changingminds.org)

Syllogisms have three parts:

1. Major premise. (Generally, a universally accepted fact.)
2. Minor premise. (A more specific, related fact.)
3. Conclusion: Necessary truth drawn about the minor premise in consideratino of the major premise.

For example:

Major Premise: All mammals are warm-blooded.

Minor Premise: A whale is a mammal

Conclusion: Whales are warm-blooded. 

Major Premise: Some watercolors are masterpieces.

Minor Premise: All watercolors are paintings.

Conclusion: Therefore, some paintings are masterpieces.

Syllogistic traps

(The following explanation and examples are taken from changingminds.org)

We each make many statements in conversation and written statements, implying logical connections between them. Sadly, the logic and truth that we assume is not always there.

Consider the following statements and conclusion:

    Statement 1: All men are animals

    Statement 2: Some animals are aggressive

    Conclusion: Some men are aggressive

This seems to be a reasonable conclusion, but then consider the following:

    Statement 1: All men are animals

    Statement 2: Some animals are female

    Conclusion: Some men are female

Now the conclusion appears to be ridiculous and false - yet the reasoning is exactly the same as in the first example. The first example thus has a false conclusion. The animals who are aggressive are not necessarily men.

What is happening here is that we are using what we know to be true as a substitute for the logic of the statement. In less certain situations, we use the same unspoken assumptions and beliefs to less acceptable ends.

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