Critical Thinking, Formal Logic, and Mathematics

According to Ennis (1990), “Critical thinking is reasonable, reflective thinking that is focused on deciding what to do or believe” (as cited in University of Western Sydney, n.d.). While according to Moon (2008), “Critical thinking is a capacity to work with complex ideas whereby a person can make effective provision of evidence to justify a reasonable judgment. The evidence, and therefore the judgment, will pay appropriate attention to context” (as cited in University of Western Sydney, n.d.).

However, both of these influential definitions seem to be too vague and narrow to be useful. In fact, they don’t even make a distinction between deductive and inductive reasoning. Deductive reasoning involves deciding (using any number of fixed rules of deductive logic) what conclusions must follow from a given set of premises/propositions. In a correctly performed deductive thread of thoughts, a conclusion is guaranteed to be true, if the premises from which it was deduced are true. On the other hand, inductive reasoning involves deciding (using few, if any, definite rules) what conclusions may follow from a given set of premises/propositions. Hence, no matter how well an inductive thread of thoughts is performed, the conclusion is never guaranteed to be true, even if the premises from which it was induced are known to be true. Most scientific theories are good examples of high-level inductive reasoning; while most, complete solutions to complex mathematical problems are good examples of high-level deductive reasoning. And this seems to pose a problem for the definitions of critical thinking given by Ennis (1990) and Moon (2008).

After all, solving complex mathematical problems definitely requires “reasonable, reflective thinking that is focused on deciding what to do or believe” (Ennis, 1990). Similarly, solving complex mathematical problems definitely requires “a capacity to work with complex ideas,” making “effective provision of evidence to justify a reasonable [or even undeniable] judgment,” and paying attention to context (Moon, 2008). Anyone who doubts that solving complex mathematical problems, even by simply following the rules/steps developed for their solution, requires all these skills, should only take a look at the following flowchart -  http://www.nature.com/protocolexchange/system/uploads/2626/original/flowchart.jpg?1372325178,  which graphically and textually represents a mathematical algorithm (i.e. a sequence of steps required for reaching the correct solution) “for the control of complex networks and other nonlinear, high-dimensional dynamical systems” (Cornelius & Motter, 2013). In this respect it is important to note that computers, who only run on algorithms, have long become unrivaled (with regards to speed) in solving complex mathematical problems, by simply following the rules/steps developed for their solution (i.e. the algorithms).

Thus, it seems possible to be considered a critical thinker, according to the definitions of Ennis (1990) and Moon (2008), despite being completely incapable of inductive reasoning (which humans actually use at every corner) and independent thought, like most computers.    

References

Cornelius, S. P., & Motter, A. E. (2013). NECO – A scalable algorithm for NEtwork COntrol. Protocol Exchange. doi:10.1038/protex.2013.063

 

University of Western Sydney. (n.d.). Develop your skills in critical thinking and analysis. Retrieved from https://www.uws.edu.au/hall/hall/critical_thinking.