Abstract
Abstract Two crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of mathematics (in metamathematics). Their role, features and interconnections are discussed. They are confronted with the concept of truth in mathematics. Relations between proofs and truth are analysed.
Highlights
Concepts of proof and truth play an important role in metamathematics, especially in the methodology and the foundations of mathematics
We indicated above that “normal” mathematicians do not distinguish in their research practice between provability and truth
For example, a specialist in number theory who investigates the structure of the natural numbers (i.e., the structure (N, S, +, ⋅, 0) where N is the set {0, 1, 2, 3, ...}, S denotes the successor function, + and ⋅ denote, resp., addition and multiplication of natural numebrs and 0 denotes the distinguished element called “zero“) is not working in the framework of a fixed axiomatized formal system of arithmetic but is using any correct mathematical methods in order to decide whether a considered property is true/holds in the investigated structure
Summary
Concepts of proof and truth play an important role in metamathematics, especially in the methodology and the foundations of mathematics. What does it mean in mathematics that a given statement is true? In mathematical research practice proof is a sequence of arguments that should demonstrate the truth of the claim. In practice mathematicians generally agree on whether a given argumentation is a proof. ISSN 2299-0518 intellectus et rei, secundum quod intellectus dicit esse quad est vel non esse quod non est” (De veritate, 1, 2). What does it mean that a mathematical statement (for example: “2 + 2 = 4”) agrees with the reality?
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
