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silenzer
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I was just wondering, is it possible? It's regarding a debate on whether mathematics is an invention or discovery.
silenzer said:Thanks for the reply. What I mean is that I'm debating with someone about whether mathematics is an invention or discovery, and he said that there is only one set of axioms in mathematics that produces results in physics. Is this true? So that, if we were to alter some of those mathematical axioms, the results would be incorrect.
silenzer said:I was just wondering, is it possible? It's regarding a debate on whether mathematics is an invention or discovery.
Yes, different sets of axioms can be used in physics to calculate various phenomena. Axioms are fundamental principles or assumptions that serve as the basis for a mathematical or logical system. As long as the chosen set of axioms is consistent and complete, it can be used to make calculations in physics.
Different sets of axioms can lead to different mathematical models and theories, which can result in different calculations and predictions. For example, using Euclidean geometry as opposed to non-Euclidean geometry can produce different results when calculating the curvature of space in general relativity.
It is not a matter of accuracy, but rather the relevance and applicability of the chosen set of axioms to the specific problem at hand. Some sets of axioms may be more suitable for certain phenomena, while others may be better for different situations. The validity and usefulness of an axiom set is determined by its ability to accurately describe and make predictions about the physical world.
Yes, it is possible to combine different sets of axioms in physics. This can be seen in the development of new theories and models that build upon previously established axioms. For example, classical mechanics and quantum mechanics use different sets of axioms but can be combined to create the more comprehensive theory of quantum mechanics.
The choice of axioms depends on the specific problem being studied and the desired level of accuracy and complexity. Scientists often use well-established and tested sets of axioms that have been shown to accurately describe physical phenomena. However, in some cases, new sets of axioms may need to be developed to better explain or predict a particular phenomenon. Ultimately, the choice of axioms is based on their ability to accurately describe and explain the physical world.