Do good explanations have to be true?
Good explanations
Thesis
Truth
Understanding
Widely accepted, has been through testing
When something is true, will generally be seen as more credible
Truth differs between subjects; some truth has greater subjective value than others.
Corresponds to real life (correspondence, coherence)
AOKs
For example, “x explains y” could be true, although the explican x itself is false.
A possible talking point is the distinction between the phenomena and the explicans
Mathematics
Human Science
Understanding refers to a feeling/grasp of a phenomena.
An explanation is a description of a phenomena
The goal of an explanation is for someone to understand the phenomena
Understanding is very subjective, different people understand differently
Naturally, a good explanation will be on that allows the person in question to understand the phenomena more effectively.
A “false/untrue” explanation can also produce the feeling of understanding, and at times can explain phenomena it better than a true but ineffective explanation
Many times models are used to represent and rationalize thinking
Purpose is for ease of understanding, for teaching, etc...
Despite explaining concepts well, these models/explanations are usually not accurate representations of real life.
Mathematics as a subject/area of knowledge is one rooted on logic and knowledge that has already been proven as being mathematically true.
Much of higher level mathematics is based around proof. Proof only works when each step/axiom utilized is completely correct, otherwise the proof falls apart.
True explanations can include false explicantia, while still maintaining verity.
All good explanations are rooted in truth, despite occasionally using false explicans to describe phenomena. False explicans are used to ensure easier understanding for the reader.
A good explanation that is not necessarily true can create the same feeling of understanding