# Necessarily, the number of planets is nine. ?!

Emil

Fri 29 Jan, 2010 02:39 pm
@ACB,
ACB;123516 wrote:
As I see it, a statement is contingent if it is actually true but could have been false (i.e. it is logically possible for it to have been false). Thus "the capital of France is Paris" is true, but could have been false; the capital could have been (say) Lyon. That is to say, there is one (actual) world in which the capital is Paris, and simultaneously another (possible) world in which it is not. Hence "the capital of France is Paris" is contingently true. Note that this has nothing to do with error.

Now, "water is H2O" and "the atomic number of gold is 79" could logically be false in the actual world (if the physicists are wrong). But that is not the point. The point is: could they be true in the actual world while at the same time being false in a possible world? That, I think, is the test for contingency.

The question to ask is not "Could it logically be false that water is H2O", but "If it is true that water is H2O, could it logically have been false?" And that remains an open question.

Kennethamy - I wrote the above before I saw your post #59.

You have slightly misunderstood the concept of (logical) contingency. For any P, that P is contingent does not logically imply that P is true. There is a concept that has this implication though, it is the concept of contingently true. It seems to be this concept you are speaking about, not that of contingency.

This point was also made in Swartz and Bradley (1979). I don't have a page reference since I don't have the work in my possession right now. I think I will order it at my library again just to be able to give better references. The work cited above employs PWS. In PWS contingent may be defined like this:
[INDENT]Logical contingent. For any P, P is logically contingent iff (there exists a possible world where P is the case and there exists a possible world where P is not the case).

[/INDENT]And contingently true like this:
[INDENT]Logical contingently true. For any P, P is logically contingently true iff (P is the case and there exists a possible world where P is not the case).[/INDENT]

---------- Post added 01-29-2010 at 09:40 PM ----------

kennethamy;123509 wrote:
Yes. I agree. Here, I am nearly betwixt-and-between. But my inclination is to say they are contingent truths.

I agree with this, but I haven't read Kripke etc.

Angra Mainyu

Fri 29 Jan, 2010 03:17 pm
@Emil,
ACB wrote:

As I see it, a statement is contingent if it is actually true but could have been false (i.e. it is logically possible for it to have been false).

It has nothing to do with error, but still, I'm not sure why you introduce "logically possible" here.

For instance, "Water is H2O" is true, but it's not clear that it's not logically possible for it to have been false. It's not clear that it entails a contradiction to disagree with Putnam and Kripke and say that "water is H2O" is a contingent true (it may be an error, but is it a contradiction?).
ACB wrote:

Thus "the capital of France is Paris" is true, but could have been false; the capital could have been (say) Lyon. That is to say, there is one (actual) world in which the capital is Paris, and simultaneously another (possible) world in which it is not. Hence "the capital of France is Paris" is contingently true. Note that this has nothing to do with error.

Right, so here you're not using the definition in terms of logical possibility; rather, what you seem to be saying is that a necessary true statement is one that is true at every possible world (including the actual world), whereas a contingently true statement is one that is true at the actual world, but there is a possible world at which it's false.

The question is, then: what's a possible world?

ACB wrote:

Now, "water is H2O" and "the atomic number of gold is 79" could logically be false in the actual world (if the physicists are wrong).

I think the "logically" is unnecessary. They could be false in the actual world if physicists are wrong (but they're not). It may also be logically possible that it's true at the actual world but not at some other world.

It's not clear at all that it's contradictory to disagree with Putnam, Kripke, etc., and claim that "water is H2O" is contingent. And if it's not contradictory (even if it's false) to claim that "Water is H2O" is contingently true, then it's logically possible for "Water is H2O" to be true at the actual world, but not at some other world.

ACB wrote:

But that is not the point. The point is: could they be true in the actual world while at the same time being false[/i] in a possible world? That, I think, is the test for contingency.

If that "could" is a "is it logically possible?" then maybe it could. But I think you're actually very close to what Putnam, Kripke and others say (even though I think your introduction of "logically possible", etc., is complicating matters).

The criteria I think you may be using (if you want to use possible worlds) is: proposition P is contingently true if it's true at the actual world, but false at some other world (not "could be false", or "could have been false" at another world, but it is false at another world), and it's necessarily true if it's true at the actual world and at every possible world.

But then, the question is: what's a possible world?

If it's "some scenario that could have happened", then we'd have to discuss what that "could have happened" means.

ACB wrote:

The question to ask is not "Could it logically be false that water is H2O", but "If it is true that water is H2O, could it logically have been false?" And that remains an open question.

I think you're mixing two different criteria. The question would be: if it's true that water is H2O (or, to be precise, the molecular composition of water is H2O; and that's true), could it have been false? (leaving the "logically" aside here).

But then again, the question is: what do we mean by "could have been false", or "could have been different"?

Emil

Fri 29 Jan, 2010 04:13 pm
@Angra Mainyu,
Angra Mainyu;123528 wrote:
It has nothing to do with error, but still, I'm not sure why you introduce "logically possible" here.

For instance, "Water is H2O" is true, but it's not clear that it's not logically possible for it to have been false. It's not clear that it entails a contradiction to disagree with Putnam and Kripke and say that "water is H2O" is a contingent true (it may be an error, but is it a contradiction?).

Because contingency/necessity is usually defined in logical possibility. Disregard any metaphysical contingency/necessity whatever that means if anything.

Quote:
Right, so here you're not using the definition in terms of logical possibility; rather, what you seem to be saying is that a necessary true statement is one that is true at every possible world (including the actual world), whereas a contingently true statement is one that is true at the actual world, but there is a possible world at which it's false.

The question is, then: what's a possible world?
That definition of contingent is false. See my post above.

I have never seen anyone define possible world in something other than terms of logical possibility. A possible world = a set of propositions that completely describes a world and that is consistent.

Quote:
I think the "logically" is unnecessary. They could be false in the actual world if physicists are wrong (but they're not). It may also be logically possible that it's true at the actual world but not at some other world.
Quote:
It's not clear at all that it's contradictory to disagree with Putnam, Kripke, etc., and claim that "water is H2O" is contingent. And if it's not contradictory (even if it's false) to claim that "Water is H2O" is contingently true, then it's logically possible for "Water is H2O" to be true at the actual world, but not at some other world.
Still more of this mixing with PWS and TS, "it's logically possible for "Water is H2O" to be true at the actual world, but not at some other world.". Translated to PWS "There is a possible world where "Water is H2O" is true and that world is the actual world, and for all possible worlds, if "Water is H2O" is true in that world, then it is the actual world.

The latter claim is false. There is not only one possible world where it is true that "Water is H2O". There are infinitely many and only one of them is the actual world.

Quote:
If that "could" is a "is it logically possible?" then maybe it could. But I think you're actually very close to what Putnam, Kripke and others say (even though I think your introduction of "logically possible", etc., is complicating matters).
I think it is your confusion of PWS with TS that complicates matters. Keep to one of them and there will be less confusion.

Quote:
If it's "some scenario that could have happened", then we'd have to discuss what that "could have happened" means.
It can mean many things depending on context. Sometimes logical possibility, sometimes physical, sometimes epistemic, sometimes practical sometimes...

kennethamy

Fri 29 Jan, 2010 04:19 pm
@Emil,
Emil;123518 wrote:
You have slightly misunderstood the concept of (logical) contingency. For any P, that P is contingent does not logically imply that P is true. There is a concept that has this implication though, it is the concept of contingently true. It seems to be this concept you are speaking about, not that of contingency.

This point was also made in Swartz and Bradley (1979). I don't have a page reference since I don't have the work in my possession right now. I think I will order it at my library again just to be able to give better references. The work cited above employs PWS. In PWS contingent may be defined like this:[INDENT]Logical contingent. For any P, P is logically contingent iff (there exists a possible world where P is the case and there exists a possible world where P is not the case).

[/INDENT]And contingently true like this:[INDENT]Logical contingently true. For any P, P is logically contingently true iff (P is the case and there exists a possible world where P is not the case).[/INDENT]

---------- Post added 01-29-2010 at 09:40 PM ----------

I agree with this, but I haven't read Kripke etc.

How could it be that a statement is contingent only if it is true? What mode would its negation be, then?

Emil

Fri 29 Jan, 2010 04:48 pm
@kennethamy,
kennethamy;123540 wrote:
How could it be that a statement is contingent only if it is true? What mode would its negation be, then?

Non-contingent and false I suppose, that is, necessarily false.

ACB

Fri 29 Jan, 2010 04:55 pm
@Emil,
Emil;123518 wrote:
You have slightly misunderstood the concept of (logical) contingency. For any P, that P is contingent does not logically imply that P is true.

Yes, I did know that. When I said in my post #60 "a statement is contingent if...", I did not mean "only if". I was talking about a contingently true statement. Sorry for misleading you.

Otherwise, I stand by what I said in that post.

Emil

Fri 29 Jan, 2010 04:59 pm
@ACB,
ACB;123548 wrote:
Yes, I did know that. When I said in my post #60 "a statement is contingent if...", I did not mean "only if". I was talking about a contingently true statement. Sorry for misleading you.

Otherwise, I stand by what I said in that post.

Ok. So you merely wanted to state the conditional:
[INDENT]If a proposition is true and could have been false, then that proposition is contingent.

[/INDENT]? In that case I agree with you. However it is not a definition of contingent as I thought you were giving.

kennethamy

Fri 29 Jan, 2010 05:27 pm
@Emil,
Emil;123545 wrote:
Non-contingent and false I suppose, that is, necessarily false.

Why necessarily false? So denying a contingent statement changes the modality of the statement? Hmmm. Magic.

Emil

Fri 29 Jan, 2010 05:37 pm
@kennethamy,
kennethamy;123553 wrote:
Why necessarily false? So denying a contingent statement changes the modality of the statement? Hmmm. Magic.

Don't ask me. Besides it was not what he meant. See his post above.

kennethamy

Fri 29 Jan, 2010 05:39 pm
@Emil,
Emil;123557 wrote:
Don't ask me. Besides it was not what he meant. See his post above.

I don't know the post you are referring to. But there are false contingent statements, are there not?

Emil

Fri 29 Jan, 2010 05:40 pm
@kennethamy,
kennethamy;123558 wrote:
I don't know the post you are referring to. But there are false contingent statements, are there not?

#66. Pretty much his only post just above.

Sure.

kennethamy

Fri 29 Jan, 2010 06:26 pm
@Emil,
Emil;123559 wrote:
#66. Pretty much his only post just above.

Sure.

As I see it, a statement is contingent if it is actually true but could have been false

How about, if it is false, but could have been true? But why isn't the "could" in "could have been true" a categorical true, and not an hypothetical "could"? No "ifs". The statement that there is a fly in the room could have been false, if it is true, and could have been true, if it is false. And nothing else need be true or false.

ACB

Fri 29 Jan, 2010 08:07 pm
@kennethamy,
kennethamy;123580 wrote:
How about, if it is false, but could have been true? But why isn't the "could" in "could have been true" a categorical true, and not an hypothetical "could"? No "ifs". The statement that there is a fly in the room could have been false, if it is true, and could have been true, if it is false. And nothing else need be true or false.

A statement (or proposition) is contingent if it is true but could have been false (e.g. "the capital of France is Paris"), or if it is false but could have been true (e.g. "the capital of France is Lyon").

If you refer back to my post #60, you will see that I was responding to earlier posts about such statements as "Water is H2O" or "The atomic number of gold is 79". My point was that the fact that "The capital of France is Paris" is contingent does not prove that "Water is H2O" is contingent. Angra Mainyu was arguing that "Water is H2O" is contingent because it is logically possible that physicists have erred and that it is actually false. But this is not analogous to saying that "The capital of France is Paris" could have been false. Thus the contingency of the "Paris" statement does not prove that the "water" statement is contingent.

Angra Mainyu's argument amounted to saying that any statement that may be wrong is contingent. But that confuses logical with epistemic possibility. Do you agree?

Emil

Fri 29 Jan, 2010 08:23 pm
@kennethamy,
kennethamy;123580 wrote:
As I see it, a statement is contingent if it is actually true but could have been false

How about, if it is false, but could have been true? But why isn't the "could" in "could have been true" a categorical true, and not an hypothetical "could"? No "ifs". The statement that there is a fly in the room could have been false, if it is true, and could have been true, if it is false. And nothing else need be true or false.

ACB just expressed himself poorly and said something misleading but he has clarified what he meant, so why are you still going on about that post?

---------- Post added 01-30-2010 at 03:35 AM ----------

ACB;123601 wrote:
A statement (or proposition) is contingent if it is true but could have been false (e.g. "the capital of France is Paris"), or if it is false but could have been true (e.g. "the capital of France is Lyon").

If you refer back to my post #60, you will see that I was responding to earlier posts about such statements as "Water is H2O" or "The atomic number of gold is 79". My point was that the fact that "The capital of France is Paris" is contingent does not prove that "Water is H2O" is contingent. Angra Mainyu was arguing that "Water is H2O" is contingent because it is logically possible that physicists have erred and that it is actually false. But this is not analogous to saying that "The capital of France is Paris" could have been false. Thus the contingency of the "Paris" statement does not prove that the "water" statement is contingent.

Angra Mainyu's argument amounted to saying that any statement that may be wrong is contingent. But that confuses logical with epistemic possibility. Do you agree?
P⇒

ACB

Fri 29 Jan, 2010 09:35 pm
@Emil,
Emil;123603 wrote:
P⇒

Good. We are agreed on that. Also, with regard to the point I was making:

1a. That it is epistemically possible that not-P does not logically imply that P is contingent.

Right?

Emil

Fri 29 Jan, 2010 10:55 pm
@ACB,
ACB;123606 wrote:
Good. We are agreed on that. Also, with regard to the point I was making:

1a. That it is epistemically possible that not-P does not logically imply that P is contingent.

Right?

Right. [more characters]

Angra Mainyu

Sat 30 Jan, 2010 12:15 am
@Emil,
Emil wrote:
Because contingency/necessity is usually defined in logical possibility. Disregard any metaphysical contingency/necessity whatever that means if anything.

I don't agree that that's how it's usually defined. Maybe we could agree to disagree?

Emil wrote:

This is confused. To say that it is logically possible that it is true in a possible world is just to say that ◊◊TP.

No, remember, I'm not equating "logically possible" with "true at a world". However, I don't know how to make my explanation of my points in post #64 any clearer, so maybe we could agree to disagree?
Emil wrote:

I think it is your confusion of PWS with TS that complicates matters. Keep to one of them and there will be less confusion.

I'm not confusing them. I'm considering ACB's post. But as I said, I don't know how to make those points any clearer, so I'll leave it at that.

Emil wrote:

The latter claim is false. There is not only one possible world where it is true that "Water is H2O". There are infinitely many and only one of them is the actual world.

No, the claim is true, and I never said that there is only one possible world at which "Water is H2O" is true. But I don't know how to make it clearer, so I guess we have to agree to disagree.

ACB wrote:

Angra Mainyu was arguing that "Water is H2O" is contingent because it is logically possible that physicists have erred and that it is actually false.

No, I never argued that. What I pointed out was that, in accordance to the definition of "contingent" provided by kennethamy and Emil, with which I disagree, "Water is H2O" would be contingent, since it's not contradictory to claim that "Water is H2O" is false.

But I'm withdrawing from this thread soon. I tried to explain my position and explore the meaning of "contingent" and "necessary", but I wasn't understood, and I'm not sure how to make my position clearer, so I have to leave it at that.

Pepijn Sweep

Sat 30 Jan, 2010 04:25 am
@Owen phil,
Pluto was defined as a planet between 1930 (discovery) and 2006 when we discovered object heavier and further away from the Sun. By consensus Pluto in now a dwarf-planet, so the number of Solar-planets is agreed upon as eight.

If a premises is no longer true, how about the arguments?

kennethamy

Sat 30 Jan, 2010 06:24 am
@ACB,
ACB;123601 wrote:
A statement (or proposition) is contingent if it is true but could have been false (e.g. "the capital of France is Paris"), or if it is false but could have been true (e.g. "the capital of France is Lyon").

If you refer back to my post #60, you will see that I was responding to earlier posts about such statements as "Water is H2O" or "The atomic number of gold is 79". My point was that the fact that "The capital of France is Paris" is contingent does not prove that "Water is H2O" is contingent. Angra Mainyu was arguing that "Water is H2O" is contingent because it is logically possible that physicists have erred and that it is actually false. But this is not analogous to saying that "The capital of France is Paris" could have been false. Thus the contingency of the "Paris" statement does not prove that the "water" statement is contingent.

Angra Mainyu's argument amounted to saying that any statement that may be wrong is contingent. But that confuses logical with epistemic possibility. Do you agree?

Yes, I agree with all of this.

Magnus phil

Sun 31 Jan, 2010 04:19 pm
@Owen phil,
Pluto isn't really a planet, so the number is actually 8.