## What use is the Principle of Plentitude?

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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.

– Mauro ALLEGRANZA – 2015-10-19T11:21:32.297

IMO, it's useless. – R. Barzell – 2015-10-19T12:53:12.857

@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. – None – 2015-10-19T19:39:23.247

What is the relationship to Kant? – None – 2015-10-19T19:49:52.633

@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? – R. Barzell – 2015-10-19T19:56:30.513

@R.Barzell I guess you also have to decide that existence is a predicate, but I am a math person, so I assume that automatically. But if existence is a predicate, "Everything that can exist, must exist." because everything either does or does not (already) exist, whether or not you notice it or use it. I gues outside math, folks don't believe that existence is a predicate -- but to me that is just cheating. – None – 2015-10-19T20:13:02.927

@jobermark how can existence be a predicate when existence is the subject for the predicate? – R. Barzell – 2015-10-19T20:15:32.570

Because exists('green dragons') is subject to the laws of logic. – None – 2015-10-19T20:19:12.553

– R. Barzell – 2015-10-19T20:20:24.573

@jobermark Why treat it as a predicate? Why not just treat it as the value of a bound variable in a quantification? While we're at it, we should make it clear that our sets over which our variables are bound are well defined. – R. Barzell – 2015-10-19T20:25:07.113

Occam's razor, we know we already have predicates, why complicate life? Unification-based semantics are cleaner than quantifiers. This is a math person, I want it pretty, I don't need it to work... – None – 2015-10-19T20:32:56.813

@jobermark because using predicates for existence could lead to problems. Didn't Kant cite the use of "existence as a predicate" as the fundamental flaw behind the Ontological Argument? – R. Barzell – 2015-10-19T20:46:46.967

But not doing so does not escape the problems, it just moves them. We are way off topic here... – None – 2015-10-19T20:57:36.453

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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.

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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.