New answer, as of 30 July
If there is a deliberate attempt to deceive, I believe the word casuistry is applicable, as it describes subtle but misleading reasoning that is superficially correct. An abridged version of the definition according to vocabulary.com is:
- n argumentation that is specious or excessively subtle and intended to be misleading
- n moral philosophy based on the application of general ethical principles to resolve moral dilemmas
If you allow words that don't start with the letter "c", then sophistry might also be a good choice. The Merriam-Webster definition thereof:
noun soph·ist·ry \ˈsä-fə-strē\
: the use of reasoning or arguments that sound correct but are actually false
: a reason or argument that sounds correct but is actually false
In other words, someone can take an established fact and concoct an argument showing it is true based on a false premise and a fallacious proposition (e.g., calculating 16/64 = 1/4 by canceling the sixes).
According to the four stages of competence theory, such a person may be unconsciously competent, particularly if the knowledge is skill-based and so can be acquired through repetition, or through trial-and-error rather than education. It is then feasible to have knowledge that cannot be verbalised.
According to Steven Aitchison, the four stages of competence can be summarised as:
- Unconscious incompetence – The individual neither understands nor knows how to do something, nor recognizes the deficit, nor has a desire to address it. In short, you don’t know what you don’t know.
- Conscious incompetence – Though the individual does not understand or know how to do something, he or she does recognize the deficit, without yet addressing it. This is the stage where you know what you don’t know.
- Conscious competence – The individual understands or knows how to do something. However, demonstrating the skill or knowledge requires a great deal of consciousness or concentration. You know how to do it, but you have to think your way through it.
- Unconscious competence – The individual has had so much practice with a skill that it becomes “second nature” and can be performed easily (often without concentrating too deeply). This is the stage where you can do it without thinking. You just know what to do.