1

Notice that I'm not talking here about the actual existence of something, but the possibility of existence.

About such ways, I only know one that is argumentative (which is the kind I would like to have as answer), which is to point out that the thing in question exists (if it exists, then it's the case it's possible for it to exists) and one personal (that is to say, one can use for himself but not in an argument), which is the union of

  • not seeing any explicit contradiction in the concept in question,
  • having no reason to think there is a implicit contradiction in the concept and
  • having no known reason to think there is something in the actual world that would make the existence of that thing impossible

. What other methods apart from this two exists? (specially that are valid for arguing (in an argument) that it's possible for something to exist)

3

There is always proof by contradiction:

  • If it is not possible for X to exist, then Y could not exist. But Y does exist, so X must be able to.

For example: if it were not possible for eggs to exist, then omelettes could not exist. Here is an omelette. (In this case, we can conclude further that eggs have existed recently.)

1

As a definition of 'possible', if something exists in an extension of our world that is internally consistent, but it is uncertain whether that world is our world, you are certain the corresponding thing is possible.

Less evasively, if you establish a strong enough analogy between two things, and there is a role played by something in one of them, things that play a corresponding role in the other one cannot be judged absolutely impossible, without knowing more.

There might be a particle for gravity because other fields like electricity are borne by particles. In fact we know a lot about how such a thing would work if it existed. But we cannot find one to point at.

This kind of potential existence by analogy has a certain force in arguments beyond the mere imagination rules you enumerate, in that it can debunk incomplete proofs that are pretending to be definitive. A real proof someone thinks they have made, that would fail if such an object exists, is not a actually water-tight unless it also proves the object would not exist.

Assumptions about particles that would rule out gravitons are always questionable on their face, even though we are not sure gravitons are real.

1

How about I think therefore I am?

without doubt I exist also if he deceives me, and let him deceive me as much as he will, he can never cause me to be nothing so long as I think that I am something.

- from Meditation II: http://www.sacred-texts.com/phi/desc/med.txt

  • How does this escape pointing at yourself? (Reality => Possibility is one of the methods already covered in the OP, and thus excluded.) – jobermark Nov 15 '14 at 1:21

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