Is composition more than the composite parts

Question

Sorry for the somewhat dumb question! Please do see if you can make sense of the latter, and put it in formal or whatever terms.

If a chariot is equal to its parts then the chariot is not its "being" equal to its parts. Else changing the parts of a chariot would be impossible – and would (?) that mean that every referent of “chariot” is composed of the same axle and wheel etc..

[P1 P2 P3 ↔ C] ← C as opposed to P1 P2 P3 ↔ C ← C The chariot is (let's suppose) just the chariot's parts, but that fact is not something about the chariot.

Answer 1

At minimum, composition is the specific composite parts plus their configuration, i.e. their position relative to each other and/or the way they are joined.

Additionally (and much more interestingly), you can have emergence of qualities that the composition exhibits.

Answer 2

The answer to your question depends on how one spells out certain supplementation intuitions about composites. This can be done in precise terms in mereology, a theory (or rather class of theories) dealing with the parthood relation.

Intuitions first: The supplementation intuition says that a composite, i.e. a whole having proper parts (parts distinct from the whole) cannot consist of a single proper part. In other words proper parts are always 'supplemented' by certain other proper parts.

This intuition can be formalized in a first-order theory whose signature only contains = and the two place relation symbol P representing the parthood relation. The first three axioms capture the intuition that parthood is a partial order:

1. ∀xPxx
2. ∀xyz(Pxy & Pyz → Pxz)
3. ∀xy(Pxy & Pyx → x = y)

Now one quite strong way to represent the supplementation intuition is by adding the axiom

1. ∀xy(¬Pyx → ∃z(Pzy ∧ ¬Ozx))

where Oxy := ∃z(Pzx & Pzy) ('x and y overlap' in the sense of sharing some part). This axiom says that in case y is no part of x there is some part of y such that this part and x do not overlap. Lets call 1.-4. extensional mereology (EM). Now it is easily seen that 4. and so EM entails

1. ∀xy(PPxy → ∃z(Pzy ∧ ¬Ozx))

where PPxy := Pxy & x ≠ y. 5. seems to be a proper rendering of the supplementation intuition. But EM also entails that composites having exactly the same proper parts cannot be distinguished:

1. ∀xy(∃zPPzx ∨ ∃zPPzy) → (x=y ↔ ∀z(PPzx ↔ PPzy)).

So, as long as your chosen mereology contains 4. it is extensional in the sense that composites are nothing more than their proper parts.

Answer 3

Much more often than not the sum of parts is much more than than the collection of parts.

A house is made of bricks; but its much more than a collection of bricks.

A novel is made of letters from the alphabet; but its much more than the mere collection of letters.

A molecule of water is made of two hydrogen atoms and one oxygen atom; but again its not just the collection of those atoms.

Only in simple arithmetic do we get 1+1=2; that is the sum is the collection. This simplicity is vital to its utility; so much so that many parts of mathematics implicitly use this or try to generalise it so thats its true. This is what is called the principle of linearity - and is the key idea in the theory of Linear Algebra - and its many avatars. Quantum Mechanics, strangely enough given its bizarre behaviour is a linear theory. The differential calculus, or its geometric avatar - differential geometry - is linear in the small.