[2] The noun was frequently used to describe a condition of strictness or stiffness, which arises from a situation or constraint either chosen or experienced passively.
For example, the title of the book Theologia Moralis Inter Rigorem et Laxitatem Medi roughly translates as "mediating theological morality between rigour and laxness".
Intellectual rigour is a process of thought which is consistent, does not contain self-contradiction, and takes into account the entire scope of available knowledge on the topic.
This method, when followed correctly, helps to prevent against circular reasoning and other fallacies which frequently plague conclusions within academia.
During the 19th century, the term "rigorous" began to be used to describe increasing levels of abstraction when dealing with calculus which eventually became known as mathematical analysis.
Published mathematical arguments have to conform to a standard of rigour, but are written in a mixture of symbolic and natural language.
The reason often cited by mathematicians for writing informally is that completely formal proofs tend to be longer and more unwieldy, thereby obscuring the line of argument.
An argument that appears obvious to human intuition may in fact require fairly long formal derivations from the axioms.
A particularly well-known example is how in Principia Mathematica, Whitehead and Russell have to expend a number of lines of rather opaque effort in order to establish that, indeed, it is sensical to say: "1+1=2".
Still, advocates of automated theorem provers may argue that the formalisation of proof does improve the mathematical rigour by disclosing gaps or flaws in informal written discourse.
[citation needed] Students who have not reached that final stage of cognitive development, according to developmental psychologist Jean Piaget, can build upon those skills with the help of a properly trained teacher.
It is instruction that requires students to construct meaning for themselves, impose structure on information, integrate individual skills into processes, operate within but at the outer edge of their abilities, and apply what they learn in more than one context and to unpredictable situations.