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What is a ‘logical progression’ and how do I make one?

Western logical structures, which developed from the Ancient Greeks and were then developed by the Church Fathers and Enlightenment philosophers, tend to be what we mean when we say we want your argument to ‘progress logically’.

Of course there are other forms of logic, both forms that are equally ancient and newer forms that challenge this pattern. So if you are doing quantum physics, post-modern philosophy, or Indigenous stonework, among others, you will be challenging these logical norms. It is important to understand what readers are expecting as ‘normal’ to establish what you are doing and why its right for your project.

For everyone else, understanding these logical norms means you can finally crack the code of why your supervisor keeps writing ‘I’m not sure this is a logical progression’ on your manuscript.

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Perhaps the easiest and best known form of logical progression is the syllogism.

If you don’t know about syllogisms, they are a very simple kind of logical structure that can be very helpful to work out what claims you are making, what deductions you are making from those claims, and where you might be going wrong.

The Ancient Greek philosopher and father of the syllogism, Aristotle, uses the formula:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

This is a very neat logical argument. Yay!

The syllogism is a good way to run through a logical checklist. Every time we ask if something is ‘logical’, we are asking questions like:

  • What are you assuming? Is it correct?
  • What are the facts? Do you fully understand them?
  • What is the order in which things occur?
  • Is there causation, correlation or just coincidence?
  • What conclusions can we draw from our argument?

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As you have probably noticed when trying to construct your arguments for your thesis, there are lots of ways you could go wrong with your logical progression. 

The main ways you could go wrong with your logical progressions:

  1. you assume things are true when they are not true;
  2. you assume things are true for everything and they are only true for a specific set of those things;
  3. or you leave out an assumption that means you have a serious logical gap.

A tool like the syllogism can help you identify what they are, and then fix them.

It can be easier to understand this with some examples:

  1. For example, if you assume things are true when they are not true, your logical fallacy (mistake) might be:
Claim Comments
Aristotle died in 322 BCE. (BCE = before the common era.)
This is a historical fact.
The Classical period in Ancient Greece ended in 323 BCE. This is widely accepted to be a valid definition of the Classical period.
Therefore the death of Aristotle led to the end of the Classical Period. False. Years BCE go backwards, so Aristotle’s death happened after the end of the Classical era.

2. If you assume things are true for everything and they are only true for a specific set of those things, your logical fallacy might be:

Claim Comments
All mammals have tails. Only some mammals have tails, though all have vestiges of tails.
Humans are mammals. This is a fact.
Therefore, humans have tails. False. Only some mammals have tails. Humans are among the mammals that do not have tails.

3. If you leave out an assumption (or step) which means you have a serious logical gap, your logical fallacy might be:

Claim Comments
Aristotle died in 322 BCE. As before, this is a historical fact.
The Classical period in Ancient Greece ended in 323 BCE. Again, this is widely accepted to be a valid definition of the Classical period.

 

However, the reason Classical period ends in 323 BCE is because this is the date of the death of Alexander the Great. Aristotle was Alexander the Great’s tutor, and therefore he fled Athens after the new rulers took power. Nonetheless, he is believed to have died of natural causes.
Therefore, the death of Aristotle was caused by the end of the Classical Period. False. While this fixes the chronology problem of the first syllogism, we have left out quite a lot of important other information. With the extra information put in, we can see that our argument is incorrect.

Try it for yourself!

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I hope this post helped you to have the ‘ahah!!’ moment to sort out your logical arguments. This is something that got cut from my new book, with the Thesis Boot Camp gang, called Your PhD Survival Guide. If this is what we cut, imagine what we’re keeping!

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