Obviously the problem cannot be expressed in formal logic, because the nature of the problem is that it renders the formal logic as fundamentally unsound. — Metaphysician Undercover

:rofl:

If your argument cannot be expressed clearly, then the obvious implication is that it is unsound. Again, S4 and S5 and derivatives have been shown to be complete and consistent. You appear to be simply wrong here.

The demonstration is like this. If the world is describable as state A, and then it becomes state B, we can conclude that change occurred between A and B, We could then assume a state C as the intermediary between A and B and describe the change as state C, but this would imply that change occurred between A and C, and also between C and B. We could posit state D between A and C, and state E between C and B, but we would still have the same problem again. As you can see, this indicates an infinite regress, and we never get to the point of understanding what change, activity, or motion, really is. Activity, change, motion, is what occurs between states of affairs, when one becomes the other. — Metaphysician Undercover

:lol: Have you thought of going in to writing the jokes for Christmas crackers?

I agree that a State of Affairs can only capture one moment in time, — RussellA

maybe take care here, too. Why shouldn't a state of affairs list the positions some object occupies over time? As, 'The ball rolled east at 2m/s'?

Meta would have to disagree with this, because he can't make sense of instantaneous velocity, or of calculus or any sort of limit or infinitesimal in general. See the Christmas Cracker above, where Meta treats change as a series of static instances rather than as dynamic, and as a result discovers that motion is impossible. :wink:

Change cannot be reduced to a sequence of instantaneous states - but no one is claiming that.

All this by way of mostly agreeing with you. Including the suspicion that Plantinga is misled by his faith. — Banno

From what I've seen, it does seem very likely that Plantinga thinks that there is a connection between his philosophy and his faith. But I'm pretty sure that there are Christians who accept his faith but not his philosophy, I suspect it is not really the faith that is misleading him, but good old-fashioned philosophical mistakes.

It may be. However the penchant for a modal ontological argument gives me pause.

However the penchant for a modal ontological argument gives me pause. — Banno

I looked this up. I see what you mean. His argument feels like a construction for a pre-determined outcome - as does his theodicy. Perhaps I'm being too black-and-white. Most likely, with Christians who indulge in philosophy, there is influence both ways.

That is not consistent with empirical observations. We see activities, things moving. — Metaphysician Undercover

I am not saying that time does not exist, but even if time does exist, there is only one actual moment in time.

Suppose a train enters a station at t1 and leaves the station at t2.

What does “we see things moving” mean?

At t2 we see the train leaving the station and at t2 we have the memory of the train entering the station at t1.

It cannot mean that at t2 we see the train leaving the station and then nip back in time to see the train entering the station at t1. Time travel is not possible.

It means that at t2 we see the train leaving the station and at t2 we have the memory of the train entering the station at t1.

Why shouldn't. state of affairs list the positions some object occupies over time? As, 'The ball rolled east at 2m/s'? — Banno

It could. A State of Affairs could list the position of an object through time, such as on an Excel spreadsheet. But we look at this spreadsheet in our present moment in time. We don't need to travel through time in order to understand that the object had different positions through time.

Similarly with the proposition “the ball rolled east at 2 m/s”. We look at this proposition in our present moment in time. Again, we don't need to travel through time to understand that the object had different positions through time.

We only exist at the present moment in time, and have memories about the past.

So far as I can see, "haecceity" has no meaning beyond "the property that accounts for the uniqueness of entities". It is just a label for the problem. Since non-existent objects don't exist, they can't possess haeccity". So it is doesn't help with non-existent objects. . — Ludwig V

I agree that haecceity is just a label for the problem. Though haecceity might be something other than a property.

In Ordinary language, when we say “there is no apple on the table”, we mean that the apple does not exist.

However in modal logic, the apple exists even though it does not obtain.

This makes logical sense, because the apple must exist in some sense if we are able to refer to it.

Yes, non-existent objects cannot have haecceity.

However, non-obtaining objects can exist, and it is these that have haecceity.

For Plantinga, even though there is no apple on the table, this apple can have haecceity.

But we look at this spreadsheet in our present moment in time. — RussellA

A state of affairs isn't perspectival. The expression of a proposition will generally have the hallmarks of a certain POV, but a state of affairs is not an expression. A state of affairs that obtains is a fact.

A state of affairs isn't perspectival. The expression of a proposition will generally have the hallmarks of a certain POV, but a state of affairs is not an expression. A state of affairs that obtains is a fact. — frank

As I see it:

Suppose in the world are the States of Affairs i) the apple is on the table ii) the apple is not on the table. These States of Affairs are not perspectival.

If the State of Affairs, the apple is on the table, obtains, then it is a fact. This is also not perspectival.

A State of Affairs exists even if it does not obtain.

A State of Affairs expresses a possible world.

When I say “the apple is not on the table”, this is perspectival from my point of view.

Then my proposition “the apple is not on the table” is false because the apple is on the table.

3 and 6 appear to be identical — Ludwig V

True, in ordinary language
Possibility 1 - the apple is on the table
Possibility 2 - the apple is not on the table
=====================================================

"There is no apple on the table" which doesn't refer to anything non-existent and "There is an apple on the table", which refers to the apple on the table, which does exist. — Ludwig V

In ordinary language, if “there is no apple on the table” is true, then there is no apple. The proposition is referring to something that is non-existent. This seems like a puzzle.

As you say “I don't see how one can say anything at all about non-existent objects. They have to exist in some sense if we are to talk about them at all.”

This is the problem that modal logic solves. The apple exists even if it does not obtain. If it exists then it can be included within modal equations.
==================================================

But whether the apple in W3 is the same apple as the apple in W6 or the apple in W9 is the same as the apple in W12, - or perhaps the same apple is in question in all four worlds - is a question of trans-world identity. That's an awkward question — Ludwig V

Yes, in modal logic, if in W3 the apple exists but does not obtain, and in W6 the apple exists but does not obtain, is this the same apple or a different apple even though it is identical.

Plantinga suggests that the apples in W3 and W6 are different even though they may otherwise be identical. This is why he attaches a haecceity to each entity that exists.

This makes sense, in that how can two entities that exist but not obtain be the same thing.

In ordinary language, if x does not exist and y does not exist, how can there ever be the possibility of x and y being the same thing. This is why it becomes a problem for logic to solve.

:up:

I am not saying that time does not exist, but even if time does exist, there is only one actual moment in time.

Suppose a train enters a station at t1 and leaves the station at t2.

What does “we see things moving” mean? — RussellA

I am asserting the very opposite of what you are saying. There is no "actual moment in time". Time is continuous duration, or flow, without any moments. You see the train enter the station, stop, passengers come and go, then the time leaves the station. Your proposals of t1 and t2 are just mental products, useful fictions, which are not at all representative of the real independent world.

What does “we see things moving” mean?

At t2 we see the train leaving the station and at t2 we have the memory of the train entering the station at t1.

It cannot mean that at t2 we see the train leaving the station and then nip back in time to see the train entering the station at t1. Time travel is not possible.

It means that at t2 we see the train leaving the station and at t2 we have the memory of the train entering the station at t1. — RussellA

It means that the use of "t1" and "t2" do not provide the grounds for a true representation of the real world.

maybe take care here, too. Why shouldn't a state of affairs list the positions some object occupies over time? As, 'The ball rolled east at 2m/s'?

Meta would have to disagree with this, because he can't make sense of instantaneous velocity, or of calculus or any sort of limit or infinitesimal in general. See the Christmas Cracker above, where Meta treats change as a series of static instances rather than as dynamic, and as a result discovers that motion is impossible. :wink:

Change cannot be reduced to a sequence of instantaneous states - but no one is claiming that. — Banno

In your twisted mind, what does "state" mean?

The reason why "a state of affairs" cannot list "the positions" some object occupies over time, is because this is explicitly a compilation of a multitude of states. Therefore it is not "a state". Do you recognize the fundamental distinction between one and many? If not, you could read Plato's Parmenides, where he examines this distinction in his arguments against sophistry. This is why "one" was not considered to be a number by ancient Greeks. And, even now "one" is excluded from the primes because inclusion would render a meaningful definition of "prime number" as impossible.

And Merry Christmas to you Cracker Jack!

In Ordinary language, when we say “there is no apple on the table”, we mean that the apple does not exist. — RussellA

Do you mean that the apple that might be on the table does not exist? Clearly, there is not, in this world, any apple that might be on the table. That apple only exists in the possible world in which there's an apple on the table. If there are many apples that might be on the table, each apple will exist in a different possible world.

In ordinary language, if “there is no apple on the table” is true, then there is no apple. The proposition is referring to something that is non-existent. This seems like a puzzle. — RussellA

No, this seems like a muddle. "There is no apple" needs a context to be meaningful.

Yes, in modal logic, if in W3 the apple exists but does not obtain, and in W6 the apple exists but does not obtain, is this the same apple or a different apple even though it is identical. — RussellA

I don't know which apple you are referring to as "the apple". Are you using "does not obtain" to mean "does not exist in the actual world"? In general, IMO, the identity or difference of objects across different worlds depends on the specific details of the case. One cannot generalize.

This is the problem that modal logic solves. The apple exists even if it does not obtain. If it exists then it can be included within modal equations. — RussellA

Yes, but you have to specify in which world these apples exist.

Again, I'll state the relevant point. Some, especially Banno prefer denial, so I'll make it clear.

Motion, change, becoming, or activity, cannot be understood with the terminology of "states". This is because change is what occurs between states, therefore does not get described by "a state". To describe the change which happens between states, with another state, produces the need to describe what happened between those states, causing the appearance of an infinite regress, without ever addressing the issue of what "change" is, change being when one state ends and the next begins.

So, even if we take Banno's example "The ball rolled east at 2m/s", and consider this to be "a state", the next "state" might be "the ball rolled northeast at 1.5m/s. Notice, that what happens in between is not described. We can posit an intermediate state, "the ball was hit by a ball moving north". This still does not provide a description of the change. We could posit many more intermediary states, indentation of the ball, elasticity, difference in molecular activity, electrons, whatever, and all those intermediary states will never produce an understanding of the "change" which occurred between one state and another. So, the simple solution is to employ the concept of "force". There was an exchange of "force". But "force" is not a state of affairs, nor can it be understood as a part of a state of affairs, because it describes something about the relation between distinct states of affairs.

Now Banno will have you believe that a compilation of "states", such as "The ball rolled east at 2m/s'", since it is a compilation of distinct states, could have "force" included within that compilation. The rolling ball had a specific force. But of course, apprehending a compilation of states as "a state", is an ontological misunderstanding.

And Merry Christmas to all!

There is no "actual moment in time". Time is continuous duration, or flow, without any moments. — Metaphysician Undercover

Your only direct and immediate knowledge of time is that of the present, the present moment in time. Within your present, you have memories of the past. You can theorise, hypothesise, that time is a continuous duration, but you have no direct or immediate knowledge that this is the case.

Do you mean that the apple that might be on the table does not exist? — Ludwig V

As I understand it:

In ordinary language we can say “there is no apple on the table”, so we seem to be referring to an apple that does not exist, which is a puzzle.

But we must be referring to something.

In logic, this problem is avoided by treating the apple as existing regardless of whether it obtains or not

The proposition "There is something that is an apple and this something is not on the table" can be written as ∃x(P(x)∧¬Q(x)) where P(x) means "x is an apple" and Q(x) means "x is on the table"

We can then refer to an apple that exists regardless of whether or not it is on the table.

The italics phrase reflects a proposition; the bold phrase represents an element of actual reality.
— Relativist

But there is nothing which you are calling "actual reality" in the modal model, that's the problem. " — Metaphysician Undercover

Are you referring to concretism?("for the concretist, there is no special property of the actual world — actuality — that distinguishes it, in any absolute sense, from all of the others; it is simply the world that we inhabit.")

I agree that is a problem with concretism.

n ordinary language we can say “there is no apple on the table”, so we seem to be referring to an apple that does not exist, which is a puzzle.

But we must be referring to something.

In logic, this problem is avoided by treating the apple as existing regardless of whether it obtains or not — RussellA

The problem with this is that:
There is no X on the table, for every conceivable X.

I suggest that it's simpler to semantically equate, “there is no apple on the table” with the fact that apples are not in the set of objects on the table.

His argument feels like a construction for a pre-determined outcome — Ludwig V

Like most such arguments.

Meta has dragged the argument over to his misunderstanding of physics. This was I suppose inevitable, given that it underpins much of his miscomprehension. I should know better than to respond.

A State of Affairs could list the position of an object through time, — RussellA

Yes, it could, but if that were the only possibility then it would indeed be subject to Zeno's paradoxes.

There is a very profound difference between listing the position of the ball at, say, 1/10th second intervals, and saying that it has a velocity of 2m/s. The latter tells us were the ball is for any point we might choose.

There seems to be an unstated presumption that a state of affairs is how things are at some instant. But the logic does not make this presumption. The state of affairs can be how things re over time.

So it might say that the train arrived at t1 and left at t2.

I'm somewhat surprised to find myself pointing this out.

In Ordinary language, when we say “there is no apple on the table”, we mean that the apple does not exist. — RussellA

If that were so, then we could ask which apple is not on the table. But “there is no apple on the table” is not about an individual apple.

This makes logical sense, because the apple must exist in some sense if we are able to refer to it. — RussellA

But the sentence "there is no apple on the table” is not referring to an individual apple. And nor is it referring to the haecceity of some absent individual apple. It's not saying "There is an x such that x is an apple and x is not on the table", but that "for all x, if x is an apple then x is not on the table".

Formally, the following is invalid:
¬∃x (A(x) ∧ T(x)) ↔ ∃x (A(x) ∧ ¬T(x))

The proposition "There is something that is an apple and this something is not on the table" can be written as ∃x(P(x)∧¬Q(x)) where P(x) means "x is an apple" and Q(x) means "x is on the table" — RussellA

That might be true, when, for example, there is only one apple around or when I mean that the apple I'm holding in my hand. But ¬∃x(P(x)∧Q(x)) identifies a different state of affairs, which does not refer to any apples.

EDIT
I'm not saying that there is no problem about referring to non-existent objects. I am saying that this isn't it.

I suggest that it's simpler to semantically equate, “there is no apple on the table” with the fact that apples are not in the set of objects on the table. — Relativist

Thank you. That's much better.

However in modal logic, the apple exists even though it does not obtain. — RussellA

In this and what follows, it would pay to make clear in which world the apple exists. That was the bit we discussed way back where truth and existence are both relative to a world; sentences are true at a world, and things exist at a world. The addition of "obtaining" is unnecessary. It is a somewhat confused proxy of "actual", and a part of Plantinga's erroneous metaphysics, which treats actuality as a property rather than an index... in order, I might add, to procure a dubious ontological argument for there being a god.

The common error in ontological arguments is to treat existence as a predicate. Plantinga avoids treating existence simpliciter as a predicate, but reintroduces the same error by treating actuality and necessary existence as properties that do the existential work ontological arguments require.

A state of affairs that obtains is a fact. — frank

Exactly.

And we might add that a state of affairs need not be at an instant, but may be over a period of time.

And we might add that a state of affairs need not be at an instant, but may be over a period of time. — Banno

Yep. Whales evolved during the Eocene. That's a fact.

Suppose in the world are the States of Affairs i) the apple is on the table ii) the apple is not on the table. These States of Affairs are not perspectival.

If the State of Affairs, the apple is on the table, obtains, then it is a fact. This is also not perspectival.

A State of Affairs exists even if it does not obtain.

A State of Affairs expresses a possible world.

When I say “the apple is not on the table”, this is perspectival from my point of view.

Then my proposition “the apple is not on the table” is false because the apple is on the table. — RussellA

This apparently presumes only one possible world.

We cannot have a possible world in which (i) and (ii) are both true. We can have w₀ in which there is not an apple on the table and w₁ in which some apple is on the table. And here there is no contradiction.

We don't here need "obtain". Just that "An apple is on the table" is true at w₀ but not at w₁; and so SOA₀ exists at w₀ but not at w₁.

We may index our possible worlds by saying that w₀ is the actual world. Calling that "adopting a perspective" suggests an unneeded subjectivism. All we are doing is saying that we are speaking from w₀

“The apple is not on the table” is true at w₀ and false at w₁.

:wink: Yep. And we are very pleased that they did. Isn't it odd that we needed to point this out?

:grin: