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Syllogistic Reasoning

 

Disciplines Argument > Types of Reasoning > Syllogistic Reasoning

Syllogistic traps | Using Venn diagrams | So what?

 

Syllogistic reasoning is concerned with using syllogisms to draw conclusions from premises.

Syllogistic traps

We each make many statements in both conversation and writing where we imply logical connections between unrelated points. 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.

There are a number of other syllogistic fallacies that can trap the unwary logician.

Using Venn diagrams

Syllogistic reasoning uses rational logic and hence set theory applies and the best way to visualize it is to draw a Venn Diagram. The diagram below is a valid drawing that explains the first two statements in the example.

 

 

The conclusion of the example falls into the traps of making the assumption that the 'aggressive animals' and 'men' subsets necessarily overlap, whereas there is no necessity for this in statements one and two. Although the conclusion could be true it does not have to be true.

So what?

Beware of making linked assertions that seem reasonable but in fact are logically incorrect.

You can, of course, make such assertions deliberately, using logic that seems valid to persuade. If you do this, of course, you run the risk of the other person exposing your false logic.

See also

Syllogisms, Set Theory, Syllogistic Fallacies, Belief Bias, Conditional Reasoning

 

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