Formal logic originated in many parts of the Ancient World and in many ways Aristotle looms large simply because much of what he wrote survived and found application later. Thus, for convenience key elements, including deductive reasoning, are grouped with him on this site.
There is a technical language with Latin names and also mathematical expressions for describing logic, but I am not going to use it, because the aim here is to create a simple description of this tool for thought.
The first element of deduction is some kind of statement about relationships.
- So, for example - All squares have four sides.
- Following that we have a descriptive statement e.g. This field is a square.
- Finally we can make a deduction : - This field has four sides.
There are further rules about how negative statements and chains of deduction work in deductive reasoning. A simple source is the Wikipedia page. This form of reasoning is also the basis of some popular games, e.g. Cluedo and of course, the Sherlock Holmes stories. The purpose is to use what we know to "deduce" information that allows us to answer other questions.
Even without going deeper into it, we can identify some key possible problems.
First would be "what if there are squares that don't have four sides" - this turns up in the messier categories of real life. You might try out "all humans have two eyes" to see how it's hard to create a simple rule to define complex things. The field of predicate logic began as a way to develop statements that avoid this problem, but can become complex in use.
Second is that particularly we create an involved chain of deduction using negatives and chains, we may make invalid deductions. A simple common example mistake that you would never make: "All cats have four legs, my dog has four legs, therefore my dog is a cat" can happen more easily as the list of statements becomes longer and more complicated.
The third is an information problem - again crucial as we move from constrained examples into real life. We are told "This field is a square" but what if the person telling us that is wrong about it?
Being aware of the problems is useful but deduction is a foundation for thinking, it lets us go from some things we know are correct to other things. Without that it's hard to go forward. Of course, if we don't know, we may need something else and the first place we go next is induction.
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