# What use is the Principle of Plentitude?

I am having trouble wrapping my head around the principle of plentitude. It was explained to me thus: "Everything which could exist does exist".

What is the use of this untestable notion?

• See a discussion here. Oct 19, 2015 at 11:21
• IMO, it's useless. Oct 19, 2015 at 12:53
• @R.Barzell Then have I identified another intuitionist? The LEM is really convenient, and immediately creates this universe of 'plenty', if you think it through. Modalities aside, something either can't exist, or it must, in every case. These things that 'must' exist don't have to be simple objects and clutter up your world, but they have to be there.
– user9166
Oct 19, 2015 at 19:39
• What is the relationship to Kant?
– user9166
Oct 19, 2015 at 19:49
• @jobermark I have sympathy for the intuitionists/constructivists, although I don't know if I would go as far as to say I'm one of them. On the one hand, I have issues with proof by negation and infinity (as a "completed object"). On the other hand, the LEM in and of itself doesn't bother me. Granted, I'm sure I'm missing some subtleties, but I think there should be some middle ground. Why must using the LEM commit one to a position that said entities must exist? Why not just show their existence is not incompatible with the premises and call it a day? Oct 19, 2015 at 19:56

There are several places in philosophy where the principle of plenitude is used in different ways:

1. In Liebniz's theodicy, that his attempt to solve the problem of evil; he posits a plenitude of possible worlds.

2. In formalism in the philosophy of mathematics which posits the plenitude of all logically consistent mathematical systems as the ground for all possible mathematics.

3. In Lewis plural worlds where he contemplates the actual existence of all logically consistent worlds to solve traditional problems in causality and the like.

It's the third example that most closely matches the principle as you put it; though I can't say exactly how Lewis uses the actuality of these possible worlds to solve or make intelligible the philosophical problems he sets himself.

This is the principle used in classical mathematics that is created by presuming the Law of the Excluded Middle. Whatever does not lead into contradiction must already exist, and can be used as needed. Its existence does not need to be further defended or derived in any way.

The primary use is to let us generalize more freely about things that we cannot enumerate or identify, so we can imagine what kinds of combinations those imaginary things might participate in. We can imagine different configurations of infinities or spaces by starting from what they would have to be like if they existed, without feeling silly about it, because we have already decided that they exist.

This is very convenient -- until it isn't. It leads directly into traps like Russell's paradox and other confusing aspects of negation. Does 'nothing' exist? Well, it must, unless that would be impossible, and the impossibility seems unlikely. But what is it like, this absolute nothing? It verily seeths with internal contradictions, and we would like to be rid of it, except we have accepted that whatever is not impossible is already real.

Lifting this principle from Platonic mathematics and transplanting it into other kinds of philosophy has the same effect. It broadens our horizon, but threatens to confuse us.