### Necessary Existence Revisited

Accepting premise 1 that we can quantify over everything, let's look at premise 2: If (1) then it's not possible that there's something such that, possibly, absolutely everything is distinct from it."

I think, in its current form, premise 2 may be denied. Indeed, there isn't actually something such that absolutely everything is distinct from it, however it may be possible that there is something such that, possibly everything is distinct from it. Take an arbitrary x in the domain (which includes all existent things).

1. It is not necessary that x be in the domain (that x exist)

2. If (1) then (3)

3. It is possible for x to not be in the domain

4. If (3) then (5)

5. It is possible for everything in the domain to be distinct from x

6. If (5) then (7)

7. There is something such that possibly, absolutely everything is distinct from it

8. If (7) then (9)

9. It is possible that there is something such that possibly, absolutely everything is distinct from it

Why is this argument able to fly in the face of the good reasoning that gave us premise 2? I think the answer lies in the notion of "possible". To say something possibly doesn't exist is roughly equivalent to saying that possibly everything that exists is distinct from it. For any existent object this obviously isn't the case, but that doesn't exclude the possibility for it being the case. Note, that the case in which the possibility is fulfilled, it is not contradictory to the necessity of identity. If the object were to not exist, it wouldn't be in the domain anyway, and thus would need not be distinct from itself. The argument for Necessary Existence depends on a rigid domain, but the notion of possible non-existence depends on the domain being flexible. So clearly, if we hold the domain rigid in our logic, it will look like the domain can't possibly be other than it is.

So, let's reformulate premise 2 of the original argument to see if it can still cause trouble:

2*: If (1) then it's not possible that there's something such that absolutely everything is distinct from it.

Here I removed the possibility operator I exploited in my argument. If we follow the original argument through using 2* instead of 2 we get the conclusion:

C: Necessarily everything exists.

Let's rephrase that in terms of the domain (which still includes all existing things).

C*: Necessarily, everything in the domain is in the domain.

This is beggining to look a little less threatening let's rephrase it one more time.

C**: Necessarily, for every x in the domain, x is in the domain.

Does this still say that necessarily everything that exists exists? No, this is little more than the law of identity applied to the domain itself. It doesn't exclude the possibility of different things being in the domain, but if those things are in the domain they better be in the domain.

To sum up, I deny premise 2 of the argument previously presented in the blog, but maintain the necessity of identity. I do this with the simple obvervation that in possible scenarios, it's possible that the domain be different than it actually is.

I think, in its current form, premise 2 may be denied. Indeed, there isn't actually something such that absolutely everything is distinct from it, however it may be possible that there is something such that, possibly everything is distinct from it. Take an arbitrary x in the domain (which includes all existent things).

1. It is not necessary that x be in the domain (that x exist)

2. If (1) then (3)

3. It is possible for x to not be in the domain

4. If (3) then (5)

5. It is possible for everything in the domain to be distinct from x

6. If (5) then (7)

7. There is something such that possibly, absolutely everything is distinct from it

8. If (7) then (9)

9. It is possible that there is something such that possibly, absolutely everything is distinct from it

Why is this argument able to fly in the face of the good reasoning that gave us premise 2? I think the answer lies in the notion of "possible". To say something possibly doesn't exist is roughly equivalent to saying that possibly everything that exists is distinct from it. For any existent object this obviously isn't the case, but that doesn't exclude the possibility for it being the case. Note, that the case in which the possibility is fulfilled, it is not contradictory to the necessity of identity. If the object were to not exist, it wouldn't be in the domain anyway, and thus would need not be distinct from itself. The argument for Necessary Existence depends on a rigid domain, but the notion of possible non-existence depends on the domain being flexible. So clearly, if we hold the domain rigid in our logic, it will look like the domain can't possibly be other than it is.

So, let's reformulate premise 2 of the original argument to see if it can still cause trouble:

2*: If (1) then it's not possible that there's something such that absolutely everything is distinct from it.

Here I removed the possibility operator I exploited in my argument. If we follow the original argument through using 2* instead of 2 we get the conclusion:

C: Necessarily everything exists.

Let's rephrase that in terms of the domain (which still includes all existing things).

C*: Necessarily, everything in the domain is in the domain.

This is beggining to look a little less threatening let's rephrase it one more time.

C**: Necessarily, for every x in the domain, x is in the domain.

Does this still say that necessarily everything that exists exists? No, this is little more than the law of identity applied to the domain itself. It doesn't exclude the possibility of different things being in the domain, but if those things are in the domain they better be in the domain.

To sum up, I deny premise 2 of the argument previously presented in the blog, but maintain the necessity of identity. I do this with the simple obvervation that in possible scenarios, it's possible that the domain be different than it actually is.

## 1 Comments:

This reply is incompatible with premise 1. If there is a possible object such that possibly absolutely everything is distinct from it, and necessity of identity holds, it follows that this object is not a member of the domain, contradicting premise 1.

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