Dominus Paradoxum

Just as there are Cambridge properties, which don't “add” anything to the things of which they are properties, and can even “accrue” to the non-existent, I'm beginning to suspect that there might also be Cambridge relations. A Cambridge relation does not “link” the terms it relates, and at least one of them can even be non-existent. For example, the ancient Greeks worshipped Zeus quite irrespectively of the fact that Zeus does not exist. In this case ‘worshipping’ is a Cambridge relation. I think that ‘difference’ might also be a Cambridge relation. For example, everything which exists is different from (or ‘is other than’) a phoenix. But if this relation were a real, i.e., a ‘linking’ relation, this would entail that a phoenix exists. Real relations can only link existing terms. So if difference were a real relation, and phoenixes do not exist, we would have to say that everything was not different from a phoenix, in which case, they are phoenixes! Nor can this ‘relation’ subsist between them and a ‘platonic’ phoenix, for just as surely as everything differs from a platonic phoenix, a platonic phoenix itself differs from a living, breathing, instantiated phoenix, and the latter certainly does not exist. (And it is hard to conceive how a phoenix could exist “outside” of space-time.) So at least this latter relation of difference must be Cambridge. Or perhaps a lack of difference can only entail identity if both of the terms exist. So x and y could be said to be different in two cases: 1. Where x and y exist and a relation of difference subsists between them and 2. Where either x or y does not exist. Even so, though, there is certainly more that’s different about them than the mere fact that one exists and the other doesn’t. Also, everything that exists is 'not nothing', but this certainly does not mean that everything is untied to ‘nothing’ by ‘a relation of difference’. And mightn’t we also say that everything which exists is different from a square circle? But I do not expect even the most committed Platonist to countenance square circles in his ontology.

Luiseach

It certainly would be rather difficult to conceive of such a paradox.

SlateGreySky

Would the introduction of modal operators help to ressurrect the difference relation with respect to entities that do not actually exist?

I'm thinking here not necessarily of a thesis as strong as possibilism (indeed, I don't think one needs to commit even to modal realism to make this work). I just mean that, given that ExPx (that is, there is some existing thing that is a phoenix) is false, that doesn't imply the falsehood of <>ExPx (that is, it is possible that there exist a phoenix). From the possibility operator, one could then assert a difference relation between the phoenix that exists in world "w" and the man that exists in the actual world.

Even if modality is not introduced, it seems possible that a Russellian analysis of the statement "My cat differs physically from a phoenix" could be performed such that the difference relation holds between "cat" and "phoenix," even if "phoenix" does not actually refer.

Thoughts?

Dominus Paradoxum

But that's the thing: A real relation can only link exising terms. So if the "phoenix" in world w has no ontological status, how can "it" bear a real relation to anything?

John Page

The relation is in the mind/brain. If you think of some concept that I have not and am not experiencing then there is no relation in my mind to (the concept/image) of that thing.

The brings into question the distinction between a "relation" and a "real relation".

Cheers, john

Dominus Paradoxum

Sorry, but you haven't done anything to show that relations exist only in the mind. Why don't you think relations exist in reality?

John Page

Relations do exist in reality, but in the "mind" part of reality. Can you demonstrate that they exist outside the mind?

I contend that only differences exist in "non-mind entities". Our sensors detect and we can measure the differences between entities. In performing this analysis within our minds we create or discover relations. We correlate the differences detected and their relations in order to conceptualize more and more complex entities.

So we arrive at a set of observed differences and the relations between them to produce mental objects.

Am I making sense so far?

Cheers, John

Dominus Paradoxum

I think so. Your computer moniter is probably about five feet distant from your celing, an this relation of distance does not depend in any way upon your conciving it or being conscious of it. Unless, that is, you happen to be some sort of idealist. Otherwise, I think you're commited to saying at least spatio-temporal relations exist in reality.

John Page

Agin, in the reality of the mind. It is the mind that receives information about the differences in reality and imputes there to be distance, time, computers etc. through the relations between these differences. I don't think the idealist charge stands, I'm not saying the mind creates "stuff", just that it conceives of the stuff in a certain way.

For example, I venture a sheep would not see "the computer".
Cheers, John

Witt

SlateGreySky:
Would the introduction of modal operators help to ressurrect the difference relation with respect to entities that do not actually exist?

I'm thinking here not necessarily of a thesis as strong as possibilism (indeed, I don't think one needs to commit even to modal realism to make this work). I just mean that, given that ExPx (that is, there is some existing thing that is a phoenix) is false, that doesn't imply the falsehood of <>ExPx (that is, it is possible that there exist a phoenix).
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If Px is false for all existent x's then ExPx is contradictory.
i.e. <>(ExPx) is also contradictory.
<>p is false, iff, p is contrdictory.

<>Px must be true before we can assert Ex(<>Px) or its equivalent <>(ExPx).

Phoenix is a phoenix, or phoenix=phoenix, implies phoenix exists.

~(phoenix=phoenix).

Ficticious or mythical objects are not values of the individual variable, they are descriptions..therefore their existence is required before we can deal with them in logic.

SlateGreySky:
From the possibility operator, one could then assert a difference relation between the phoenix that exists in world "w" and the man that exists in the actual world.

Even if modality is not introduced, it seems possible that a Russellian analysis of the statement "My cat differs physically from a phoenix" could be performed such that the difference relation holds between "cat" and "phoenix," even if "phoenix" does not actually refer.
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Yes, if there is no difference then they are identical.
There is clearly a difference, since your cat has attributes that the phoenix does not have.

~(Fx <-> Fy) -> ~(x=y), for all objects described or given.

Witt