Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Justifying Definitions in Mathematics---Going Beyond Lakatos   This paper addresses the actual practice of justifying definitions in
mathematics. First, I introduce the main account of this issue, namely
Lakatos's proof-generated definitions. Based on a case study of definitions of
randomness in ergodic theory, I identify three other common ways of justifying
definitions: natural-world-justification, condition-justification and
redundancy-justification. Also, I clarify the interrelationships between the
different kinds of justification. Finally, I point out how Lakatos's ideas are
limited: they fail to show that various kinds of justification can be found and
can be reasonable, and they fail to acknowledge the interplay between the
different kinds of justification.

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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol