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Quod sic: The Statue of Zeus no longer exists (it was destroyed by fire in the 5th century A.D.) Therefore, there is something (the Statue of Zeus) that does not exist.

Contra: How can there be anything which does not exist?

[edit] This question was put 'on hold' by five of the more experienced members of this site, as being unclear as to what was being asked. I am not clear what is unclear about the question, but I will provide a bit of background. I was actually repeating one of the medieval questions that the scholastics asked. The question is whether 'everything exists' is true, i.e. so that whatever thing in the range of quantification you select, is an existent thing, or whether you could find something in the domain that doesn't exist.

That is the question, and it is a deep and fundamental one for our understanding of quantification. I then gave one argument for (quod sic – it is so) and one argument against (contra). The argument for is that the Statue of Zeus does not exist (it was destroyed), therefore, on the grounds that

Fa implies Ex Fx

it follows that something does not exist (where F = exists).

The argument against is that there cannot be anything which does not exist, for to 'be' something is to be, and to be is to exist.

So we have two opposing arguments on the question, what is the correct answer? I provided an answer myself, see below.

I hope this helps.

closed as unclear what you're asking by Paul Ross, virmaior, Hunan Rostomyan, shane, Mauro ALLEGRANZA Aug 20 '14 at 14:09

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    both can be true by equivocating on the meaning of "exists" – Dave Aug 13 '14 at 16:03
  • Captain Ahab doesn't exist. Purple unicorns don't exist. The number 3, abstracted from the physical world, doesn't exist. Lots of things don't have physical existence yet we can speak sensibly about them. – user4894 Aug 13 '14 at 16:44
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    Can I just be clear - is the temporal aspect of your example important to the question you want to ask? Is it a sufficient answer to say "you would be correct to say that there is not such a thing that is both The Statue of Zeus and that is located somewhere in the world at the present time" and to explain how such a statement is sensible despite an apparent lack of reference? Or would you rather seek an existential claim that actually isn't sensible despite having the surface appearance of something sensible? – Paul Ross Aug 13 '14 at 18:35
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    Santa Claus does not exist, but I am sure that he usually wears a red coat. – Bob Aug 13 '14 at 21:26
  • The question is perfectly clear. It is asking whether it is possible that some things do not exist. It is giving one possible reason why some things do not exist (quod sic), and one possible reason why that is impossible (contra). – quis est ille Aug 20 '14 at 14:46
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This was a well-known problem in the middle ages. They solved it by distinguishing the existential import of affirmative from negative propositions. An affirmative proposition does have existential import. If we read "there is something that does not exist" as

(1) something is non-existent

then it is false, because it is affirmative, and thus implies the existence of a non-existing thing, which is contradictory. On the other hand if we read it as the negative proposition

(2) something no longer exists

then it can be true, if 'something' is satisfied by the Statue, which no longer exists, and therefore doesn't exist now. I.e. the domain of quantification can include non-existent things, but not in such a way that we can say anything positive about them.

I still see a problem here, however. What do we mean by the 'domain of quantification'? What do we mean by 'including' such things as the Statue? If the domain includes the Statue now, i.e. if at this very moment in time it still includes it, then surely we are saying something positive about the statue, namely that it is now in the domain. But if conversely we say it is no longer in the domain, then how can we quantify over it, even to make a negative statement about it?

Interesting how many of the answers above say that what exists is the idea of the Statue. This is wrong. It is not the idea which no longer exists, for the idea still does exist. What no longer exists is the statue, not the idea.

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Let's take the set of everything. A member of the set of everything has an attribute on a state transition diagram:

Not yet existing -> existing -> formerly existing

Not that any member of the set that never transitions from not yet existing to existing is not a part of everything, a contradiction, and there was once (presumably) nothing, so all members of everything experience at least one state transition.

Ah hah, no we're getting into the subtleties of grammar.

Is the Statue of Zeus a concept? In which case, the concept still exists.

Is the Statue of Zeus an arrangement of matter? If so, no matter still exists in that arrangement, but the actual nature of the arrangement still exists as a possibility.

Is the Statue of Zeus a specific incidence of an arrangement of matter? If so, then that specific incidence has experienced in second transition into formerly existing.

So let's take members of the set of everything to also have the following attributes: an arrangement (for concepts we can use bit-modeled neural arrangements) and an incidence.

So every member of the set of everything has a state, an arrangement, and an incidence.

Take anything to be a member of the set of everything that is either in the state of not yet existing or formerly existing. Then anything does not exist but is still anything because it exists at another point in time.

Similarly, the corollary for space would bundle a location with a member, so that if the Statue of Zeus at Olympia were moved to say, Missoula, then the Statue of Zeus at Olympia would no longer exist and therefore not exist, even though a member of everything with the same arrangement, incidence, and state would still exist. Alternatively, incidence could be tied to location.

  • Wouldn't logical paradox follow the existence of a "set of everything"? – Paul Ross Aug 13 '14 at 18:46
  • It would if we manipulated it directly, but we're only using it to introduce anything (members) and ascribe them attributes, so we should be alright. Note we can protect the set from containing itself by a restriction to everything composed of matter and still have an equivalent result. Likewise, the set containing itself violates no assumptions taken here. – Calvin Aug 13 '14 at 19:49
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The idea of the statue of zeus exists. The statue itself used to exist. If there is evidence that something existed, then those things are not around anymore but a record of them being around exists. By "is" we mean the idea of the object exists (in this case a statue), not the object itself.

  • I don't think putting the emphasis on the existence of ideas is quite right. We can have ideas of lots of things that not only don't currently exist, but also that never have or will exist in fact, and perhaps even some things that are logically impossible. We don't want to trivialize the notion of something existing if we want it to do useful philosophical work. – Paul Ross Aug 13 '14 at 18:44
  • Paul, my answer explains how we can refer to physical objects that no longer exist. I am not sure how your comment pertains to what I am trying to say. – user8669 Aug 14 '14 at 0:04
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Depends on what the observer considers existence to mean. There are several ways to determine existence:

1.In physics (atomically, made of matter, being capable of observance, etc.);

2.Existence as in a particular form (e.g. the statue no longer exists since it was broken, but SI atoms it's composed of still exist);

3.Existence as life (e.g. you kill something and it "no longer exists", but without decomposing entirely its matter still does).

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