Are the statements which we make true?…and, if they are true, how do we know that they are true? To address these two questions let us first note that this book is interested in two types of truth: mathematical truth and scientific truth. Mathematical truth applies to statements within a mathematical theory. A statement is true within a theory either if it is one of the axioms of the theory or if it can be deduced from the axioms of the theory (see Chapter 3). Scientific truth applies to statements about the real world. A statement about the real world is true if it corresponds to what happens in the real world. A theory about the real world is true if all of its statements correspond to what happens in the real world. Given a mathematical theory which is consistent (i.e. true within itself) or a specific statement which is true within the theory, we can enquire whether or not the theory or statement is true in relation to reality.
Burt, G. (2010), "Chapter 5 Theory, evidence and reality: The mean and median ideals of competing groups", Burt, G. (Ed.) Conflict, Complexity and Mathematical Social Science (Contributions to Conflict Management, Peace Economics and Development, Vol. 15), Emerald Group Publishing Limited, Bingley, pp. 67-86. https://doi.org/10.1108/S1572-8323(2010)0000015008Download as .RIS
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