The meaning of the term "Axiom" from Plato to Modernity
A study on the relationship between language and maths
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We present the results of a doctoral research project of a historical-bibliographical nature, which used a qualitative research methodology with an interpretative approach based on the Semiotics of Ottean Complementarity Thought - PsCO, to shed light on the evolution of the meaning of the term Axiom from Plato to Modernity. Studying the evolution in the meaning of the term Axiom made it possible to clarify issues related to a change in the character of the foundations of Mathematical Knowledge and which involves the relationship between Language and Mathematics. Analysing this relationship, we...
We present the results of a doctoral research project of a historical-bibliographical nature, which used a qualitative research methodology with an interpretative approach based on the Semiotics of Ottean Complementarity Thought - PsCO, to shed light on the evolution of the meaning of the term Axiom from Plato to Modernity. Studying the evolution in the meaning of the term Axiom made it possible to clarify issues related to a change in the character of the foundations of Mathematical Knowledge and which involves the relationship between Language and Mathematics. Analysing this relationship, we sought to investigate what a possible change in the understanding of the term axiom meant which, according to Otte (2011), from Antiquity to Modernity, was taken as an antonym for hypothesis, assumed essentially as truths and, from Modernity onwards, it came to be understood as a synonym for hypothesis. The highlight of our study was that redirections in the relationship between Language and Mathematics, operationalised by approximations and distancing between philosophical thought and Mathematical thought, significantly influenced the promotion of change in the meaning of the term Axiom.
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