What constitutes a definition and what is a mere property?

Question

If a triangle is defined as a plane figure with 3 straight sides and 3 angles, would it be part of its definition that it has one less side than a square?

Or is that just a property of it?

How do I know which is part of the definition and which is a property?

Like, for example, the angles must add up to 180 degrees, is this part of the definition or is it a property? Also, is having 3 straight sides, which is part of the definition, also a property? I read the pages on definition and properties on plato.stanford, but they were no help. Thanking you in advance.

Answer 1

How do I know which is part of the definition and which is a property?

You don't. A mathematician chooses the definition, and other properties then follow from that. A neat example is the determinant, which, as wikipedia notes, has various equivalent definitions. Not all mathematicians choose the same definition, although they do tend to choose equivalent definitions (I know of no exceptions).

This is also why you sometimes see comments on this site which ask the OP's definition of some concept: a question can be trivial to answer, or even true by definition, using one definition, but much more difficult using another equivalent definition.

Answer 2

Like Jmoravitz says, whatever you are defining, it should be well defined. Once defined, there should be no ambiguity about what object would be. Example: A definition of a square is that it is a quadrilateral with all equal sides and all equal angles. A property that follows is that the sum of a pair of opposing angles is 180 degrees. Now Lets change "property" into "definition": A definition of a square is that a pair of opposing angles is 180 degrees. Is this a well defined definition of a square? Does that mean we are talking about a square? Could be, or not. After all, a cyclic quadrilateral also has pairs of opposing angles summing 180 degrees. Cyclic quadrilaterals often are not squares. So using a definition to introduce a particular entity should be subject to a more stringent "test of correctness" than a introducing this entity by revealing one of its properties

Answer 3

Accidental properties and essential properties is what I was after.

An essential property is one that an entity, without, would not be itself. An accidental property is one which, without, it would still be itself.