Syllogistic Reasoning

By Andrew Dart, author of 'Building Your Skeptical Toolkit'.

Syllogistic reasoning is a form of logical reasoning based upon, unsurprisingly, syllogisms, which are arguments made up of several parts. Typically, a syllogism is made up of a couple of statements, or premises, that are taken to be true and a conclusion based upon these premises. A syllogism starts with a Major Premise, which is a general statement that as stated is taken to be true, at least within the boundaries of the argument. Next you have the Minor Premise, which is a more specific statement that relates to the major premise and again is always treated as being a true statement. For the conclusion, referred to as a putative conclusion within a syllogism, to be logically valid it must be guaranteed by the premises. It is not enough for the premises to simply suggest the conclusion, it must 100% guarantee it to be the case.

 

Let me give you a classic example:

Major Premise: All men are mortal.
Minor Premise: Socrates is a man.

therefore...

Putative Conclusion = Socrates is mortal.

In this example the conclusion is guaranteed by the two premises. If all men are mortal and Socrates is a man then it is logical to conclude that Socrates is mortal.

 

Let’s look at another example:

Major Premise: All men are animals.
Minor Premise: Some animals can fly.

therefore...

Putative Conclusion = Some men can fly.

Once again we know that our two premises are true, all men are animals and yes some animals, such as bats and birds, can indeed fly. However, this time it should be easier to see that the conclusion does not follow from the premises, because we know that men cannot in fact fly. In these two examples we can start to see how validity and truth are not the same thing. In the first example it is true that some men can swim, however the logic of this argument is not valid. In the second one the conclusion is both invalid and untrue. And, as I am sure you have guessed, it is possible to have a conclusion that is valid and yet untrue at the same time.

 

For example:

Major Premise: If unicorns exists, then dragons exist.
Minor Premise: Unicorns exist.

therefore...

Putative Conclusion = Dragons exist.

The logic of this example is perfectly valid, the conclusion is 100% guaranteed by the premises, however sadly in the real world neither the premises nor the conclusion are true. This is where a lot of people fall down. They assume that if the conclusion is true in the real world, i.e. some men can actually swim, then it must therefore be logically valid as well; and vice versa if the conclusion is not true in the real world, alas dragons do not exist, then they assume the logic must be invalid. This is not the case. Syllogistic arguments should be treated as their own separate little universes in which all that matters is whether the argument is logically valid. Everything discussed in these little universes is treated as true, even if this truth is not reflected in the real world.


Now some of you may be scratching your head after that and trying to work out why therefore the some men can fly example is invalid. I mean if an argument does not have to be true in the real world in order to be valid then it doesn’t matter than men can’t really fly, all that matters is the logic. Well you would be completely correct, the fact that men can’t really fly does not matter at all. However, the conclusion is still logically invalid.

 

Let me show you why with a Venn diagram, oh the excitement.

As you can see from this graphical representation of the syllogistic argument just because “Men” fall within the “Animals” bubble does not mean that they also fall within the “Flying Animals” bubble as well. These two things remain separate and thus the conclusion that some men can fly is logically invalid, as well as being untrue. Now all of that can be a bit tricky to follow at first, and believe me I have only scratched the surface of syllogistic reasoning, so let me leave you with another example. Here we have a line of reasoning that is a little closer to what you might encounter as a skeptic.

 

Keeping in mind what we have learnt about truth and validity see if you can work out if the following syllogism is logical valid or not. I’ll even throw in a Venn diagram to help you.

Major Premise: All homeopathic remedies are alternative medical modalities.
Minor Premise: Some alternative medical modalities are effective treatments.

therefore...

Putative Conclusion = Some homeopathic remedies are effective treatments.

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