Research Article
For Mathematical Truth to Be Known: A Provability-based Condition Construction
Abstract
One of the defining characteristics of mathematics is its emphasis on proof, which is the process of demonstrating the truth or falsehood of a mathematical claim through a rigorous and logical argument. However, while the concept of proof is central to mathematics, it is also a complex and multifaceted notion that raises a range of philosophical and practical questions. This article proposed a condition beyond the JTB framework for mathematical knowledge by using mathematics provability with a careful reflection on Gettier cases.
Keywords: justified true belief theory; provability; mathematical knowledge
References
- Gulley, Norman. Plato’s theory of knowledge. Routledge, 2013.
- Parikh, Rohit, and Adriana Renero. “Justified true belief: plato, gettier, and turing.” Philosophical Explorations of the Legacy of Alan Turing: Turing 100 (2017): 93-102.
- Whitesmith, Martha. “Justified true belief theory for intelligence analysis.” Intelligence and National Security 37.6 (2022): 835-849.
- Turri, John. “In Gettier’s wake.” Epistemology: The key thinkers (2012): 214-229.
- Gettier, Edmund. “Is justified true belief knowledge?.” Arguing about knowledge. Routledge, 2020. 14-15.
- Goldman, Alvin. “A causal theory of knowing.” en (5), pgs (1976): 138-153.
- Benacerraf, Paul. “Mathematical truth.” The Journal of Philosophy 70.19 (1973): 661-679.
- Noonan, Harold. Routledge Philosophy Guidebook to Kripke and Naming and Necessity. Routledge, 2014.
- Beziau, Jean-Yves. “What is an axiom?.” A True Polymath-A Tribute to Francisco Antonio Doria, College Publications, London (2020): 122-142.
- Price, Huw. “Why ‘not’?.” Mind 99.394 (1990): 221-238.