Natural Deduction

Natural deduction is a somewhat elusive concept to define, yet it is entirely essential to practical applications of logic. As a response to the limited use of deductive logic in real-world situations, where premises and conclusions are necessarily disconnected by the need to be axiomatic, natural deduction relies on inferences to reach valid conclusions in a more organic way (Pelletier, n.d., pg. 107). Because it is more abstract, however, there is no one system of natural deduction that is agreed upon. Many methods that follow the vague structure of natural deduction fall under the term despite their particulars being somewhat contradictory (Pelletier and Hazen, n.d., pg. 1). For example, critical applications of deduction are seen in the field of forensics, where detail-oriented detectives look for inferences in the scene and circumstance in order to piece together a picture of what happened.

In its most basic form, natural deduction bypasses the need for axiomatic premises by breaking down the premises of a conclusion into components to prove their validity, thus the conclusion is inferred to also be true (“Lecture 15”, n.d.). In applying this kind of logic, it is necessary to identify where the limitation of an argument lies. If a statement can be proved valid except it is not known that one of its premises is axiomatic, then it is a candidate for natural deduction (“Natural deduction for sentence logic fundamentals”, n.d., pg. 59). A simple example of a natural deduction argument could be: if John wants pizza for dinner, then John will order pizza for dinner. Deductively, this would be valid if the premise “John has for dinner what he wants for dinner” is axiomatic. Since it is not, we can apply natural deduction to determine if the components of the premises are true. Will John have what he wants for dinner? Does John want pizza for dinner? If those premises are true, then it can be inferred that John will order pizza for dinner.

References

Lecture 15: Natural deduction. (n.d.). Cornell University. Retrieved April 28, 2013, from http://www.cs.cornell.edu/courses/cs3110/2012sp/lectures/lec15-logic-contd/lec15.html 

Natural deduction for sentence logic fundamentals. (n.d.). UC Davis. Retrieved April 28, 2013, from tellerprimer.ucdavis.edu/pdf/1ch5.pdf 

Pelletier, F. J. (n.d.). A history of natural deduction and elementary logic textbooks. Simon Fraser University. Retrieved April 28, 2013, from www.sfu.ca/~jeffpell/papers/pelletierNDtexts.pdf 

Pelletier, F. J., & Hazen, A. P. (n.d.). Natural deduction. University of Alberta. Retrieved April 28, 2013, from www.ualberta.ca/~francisp/papers/PellHazenSubmittedv2.pdf