Argument against best possible composed entities

Last revised: 06/14/25

These are in progress and subject to revision. Feedback welcomed.
The subpoints provide further clarifying thoughts or definitions.

Presuppositions

1. Self-contradictions cannot take place or be true.

2. The argument employs the S5 Axiom of modal logic, which states that if something is possible, it is possible in all possible worlds, and if something is necessary, it is necessary in all possible worlds. This argument employs metaphysical modality by considering what is possible or necessary across all comprehensive ways reality could be. Metaphysical possibility applies to an entity or state of affairs that (a) is free from logical contradiction and (b) conforms to eternal or necessary truths and the nature of things, such as the requirement that a triangle must have three sides and cannot have four.

Premises

1. Either something (including a world) composed of items of reality (S) is the best possible within its kind or not.

   1. “World” refers to the totality or a collection of existents, as in the sum or framework in which things exist.

   2. “Composed” refers to consisting of or is made up of parts. For the sake of this argument, these could be physical or metaphysical parts.

   3. “Items of reality” refer to entities, relations, or states of affairs.

      1. Entities may be objects, persons, numbers (if abstracta exist), etc.

      2. Relations are the ways entities are connected, either causally, spatially, temporally, or logically.

      3. States of affairs are particular ways things are—this person sitting, that object moving, two events coinciding.

   4. Let S denote “something (including a world) composed of finite entity, including worlds.”

2. Assume for reductio that S is the best possible within its kind.

3. If true, then S is better than all other possibilities within its kind.

4. Therefore, assuming S is the best possible within its kind, S is better than all other possibilities within its kind. (Hypothetical Syllogism on #2-3)

5. S is better than all other possibilities within its kind if and only if no other possible configuration within that kind includes a set of finite entities who, taken together with their relations and structure, result in a better whole.

   1. The fallacy of composition is assuming that because each part has a certain property, the whole must have that property. This premise does not say that each finite entities is better, therefore the whole is better. It says the combination of the entities with their structure and relations results in a better whole. The point is not that better parts automatically make a better whole. It says the whole is better based on how the parts are arranged and interact.

   2. The premise also doesn’t does not say because this whole is better, each finite entity in it must be better. It allows that the relations and structure could account for the better overall outcome, even if the individual entities are not better on their own.

6. Therefore, assuming S is the best possible within its kind, no other possible configuration within that kind includes a set of finite entities who, taken together with their relations and structure, result in a better whole. (Definitional Substitution on #4-5)

7. Some other possible configuration within any kind includes a set of finite entities who, taken together with their relations and structure, result in a better whole.

   1. Suppose you have a world W₁ with a large number of good finite entities arranged harmoniously. Now imagine a world W₂ that adds one more good entity without loss of harmony or value. W₂ is better than W₁. Now try W₃, which adds another. This process can continue indefinitely. So for any world, there's another with a slightly better composition. So "best" keeps moving forward, like a line that never ends. You can keep adding to it.

   2. Even if a pizza has endless slices with every kind of flavor and topping, new kinds of properties can always appear. Can the farm where the cheese is produced treat its animals better or pay better wages to laborers? Does consuming endless slices of pizza support a local community or put other small businesses in jeopardy? A better pizza could improve people’s lives beyond just taste. How much energy and water go into making the pizza? Could the environmental benefit of the pizza be improved? I think so. Just as you can never reach the last cardinal number, you can never reach the last “best” pizza property.

8. Therefore, assuming S is the best possible within its kind, no other and some other possible configuration within that kind includes a set of finite entities who, taken together with their relations and structure, result in a better whole, which is a contradiction. (Definitional Substitution on #6-7)

9. Therefore, the assumption that S is the best possible within its kind is false. (Reductio ad Absurdum on #2 & 8)

10. Therefore, S (including a world) is not the best possible within its kind. (Disjunctive Syllogism on #1 & #9)