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My mathematical knowledge is limited, so I am wondering if mathematicians have come up with a theory for this kind of thing before.

Chidi
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    Way to vague. This can cover the natural numbers to CW complexes. Can you give more specific examples? – Thomas Andrews May 31 '22 at 14:35
  • @ThomasAndrews To be specific, I was thinking about physical objects e.g building a wall out of bricks and mortar. – Chidi May 31 '22 at 16:40

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Most mathematical constructions are actually definitions. We define a new object by specifying its properties, possibly with reference to other objects, and justify the validity of the definition. Then, everything we can prove about an object is a logical consequence of the properties given in the definition. Metamathematics is the formal study of the logical systems in which we carry out these constructions and proofs.

What it means (if anything) for an object to have "constituent parts" will vary from one field to another, and the concept is often irrelevant. Math doesn't require metaphysical explanations of its objects.

Karl
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  • Alright, so you're saying there is no one way to define construction. If I specified that I was talking about geometrical objects, is there a way to define it for that? – Chidi May 31 '22 at 17:11
  • It's common to think of a geometric object as a set of points in space. From this perspective, combining multiple objects to form a new object is just the operation of union of sets. – Karl May 31 '22 at 19:51