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

Owen phil

Sun 27 Dec, 2009 08:26 am
@Emil,
Emil;114629 wrote:
The last is false.

Why? Can you show why it is false?

---------- Post added 12-27-2009 at 09:30 AM ----------

kennethamy;114627 wrote:
You mean that it was impossible that that we should have discovered that there were only 5 planets? Or 12 planets? 9 was the magic number? Hmmm.

It is true that we DID discover that there were 9 planets.

Should we have discovered that there were 5 planets, then we would have said so.

kennethamy

Sun 27 Dec, 2009 08:39 am
@Owen phil,
Owen;114631 wrote:
Why? Can you show why it is false?

---------- Post added 12-27-2009 at 09:30 AM ----------

It is true that we DID discover that there were 9 planets.

Should we have discovered that there were 5 planets, then we would have said so.

An axiom of S5 is that necessary statements are necessarily necessary.

What has your answer to do with my question? My question was, would it have been possible for us to discover that there were 8 planets, or 10 planets? Was it necessary that there be 9 and only 9 planets? Why? That there are 9 planets is a contingent truth. Not a necessary truth.

Owen phil

Sun 27 Dec, 2009 09:06 am
@kennethamy,
kennethamy;114635 wrote:
An axiom of S5 is that necessary statements are necessarily necessary.

Quote:
Originally Posted by kennethamy
You mean that it was impossible that that we should have discovered that there were only 5 planets? Or 12 planets? 9 was the magic number? Hmmm.

What has your answer to do with my question? My question was, would it have been possible for us to discover that there were 8 planets, or 10 planets? Was it necessary that there be 9 and only 9 planets? Why? That there are 9 planets is a contingent truth. Not a necessary truth.

[]p ->[][]p, is a theorem of S5 not an axiom.

We have agreed that [](the number of planets is 9) is false.
ie. [][](the number of planets is 9), is false too.

[](the number of planets is > 7) is false.
[][](the number of planets is > 7) is false too.

Obviously, if we had dicovered the number of planets to be different from 9 we would have said so.

Ken
"You mean that it was impossible that that we should have discovered that there were only 5 planets? Or 12 planets?"

No, I don't mean that it was 'impossible' that we should have discovered that there were a different number of planets rather than 9.
Whatever number was dicovered is contingent, and stating other values eg.(the number of planets is 5) would be contingently false not impossible.

(the number of planets) = 9, is a contingent truth.
(the number of planets) []= 9, is a contingent truth.
(the number of planets) > 7, is a contingent truth.
(the number of planets) []> 7, is a contingent truth.

Angra Mainyu

Wed 27 Jan, 2010 08:22 pm
@Emil,

Emil

Thu 28 Jan, 2010 02:39 am
@Angra Mainyu,
Angra Mainyu;123148 wrote:

Hi Angra.

I'm not sure you will like this board more than the other one. It is still full of idiots. But there are many religionists here for you to play with.

Also, I'd like to see what you wrote as I'm not exactly sure how to solve this problem, except by talking about opaque contexts.

Angra Mainyu

Thu 28 Jan, 2010 05:48 am
@Emil,
Emil;123185 wrote:
Hi Angra.

I'm not sure you will like this board more than the other one. It is still full of idiots. But there are many religionists here for you to play with.

Also, I'd like to see what you wrote as I'm not exactly sure how to solve this problem, except by talking about opaque contexts.

Hi, Emil

I'm not planning to participate in many debates with religionists here; I was just perusing the threads and I thought I'd post in this one, so I registered.

As for what I wrote, I didn't present an alternative to opaque contexts, but I was just trying to tackle another angle of the issue, as an opportunity to discuss what it is for something to be necessary (or contingent), but without taking a stance myself, but I have no objection to the previous replies to the argument by you and kennethamy.

Plus, I did some nitpicking by pointing out that "the number of planets is 9" is actually false.

Anyway, I'll repost it if you're interested:

Slight astronomical nit-picking:

The number of planets is actually 8.

Pluto is a dwarf planet, which is a different astronomical classification (i.e., "dwarf planet" is not some type of planet, but actually not a planet - maybe astronomers should have come up with another name).

Still, if we count dwarf planets too, the number is still not 9, since there are other dwarf planets, like Eris, so the number of (planets + dwarf planets) is at least 11 (since Ceres and Eris are dwarf planets too), and there might be up to 2000 of them.

In short, the number of planets (going by the definition in astronomy) is 8, and if we want to count planets + dwarf planets, the number is at least 11, and perhaps up to 2000.

I'll use "planet" in the stricter sense, so the number of planets is 8 (of course, I'm talking about planets in our planetary system, there are plenty more in other planetary systems), and the number of dwarf planets is unknown.

As for the philosophical question, I'd like to discuss what it is for something to be contingent or necessary:

On the issue of whether the number of planets could have been something other than 8, then a question is whether that "could have been" means "if the past had been different up to some point", or "given the same past", or something else.

But, perhaps, the issue is clearer with a closer example:

Is "Obama was the POTUS in DEC-2009" contingent? Could it have been different?

If (for instance) McCain had won, then Obama would not have been the POTUS in DEC-2009. But could McCain have won, if the past up to the election had been the same? And would the question of whether "Obama was the POTUS in DEC-2009" is contingent hinges on the matter of determinism?

Someone could say that "the number of planets is 8" or "Obama was the POTUS in DEC-2009" is contingently true if it's true and there is a possible world at which it's false, but then the question is what a possible world is, and if a possible world is a scenario that could have happened, then it seems to me that we're back to the previous case:

A question is whether the number of planets could have been different from 8, or whether Obama could have not been the POTUS, and whether that "could have been different" has something to do (or not) with determinism (i.e., what kind of "could have been different" we're talking about).

kennethamy

Thu 28 Jan, 2010 07:04 am
@Angra Mainyu,
Angra Mainyu;123200 wrote:
Hi, Emil

I'm not planning to participate in many debates with religionists here; I was just perusing the threads and I thought I'd post in this one, so I registered.

As for what I wrote, I didn't present an alternative to opaque contexts, but I was just trying to tackle another angle of the issue, as an opportunity to discuss what it is for something to be necessary (or contingent), but without taking a stance myself, but I have no objection to the previous replies to the argument by you and kennethamy.

Plus, I did some nitpicking by pointing out that "the number of planets is 9" is actually false.

Anyway, I'll repost it if you're interested:

Slight astronomical nit-picking:

The number of planets is actually 8.

Pluto is a dwarf planet, which is a different astronomical classification (i.e., "dwarf planet" is not some type of planet, but actually not a planet - maybe astronomers should have come up with another name).

Still, if we count dwarf planets too, the number is still not 9, since there are other dwarf planets, like Eris, so the number of (planets + dwarf planets) is at least 11 (since Ceres and Eris are dwarf planets too), and there might be up to 2000 of them.

In short, the number of planets (going by the definition in astronomy) is 8, and if we want to count planets + dwarf planets, the number is at least 11, and perhaps up to 2000.

I'll use "planet" in the stricter sense, so the number of planets is 8 (of course, I'm talking about planets in our planetary system, there are plenty more in other planetary systems), and the number of dwarf planets is unknown.

As for the philosophical question, I'd like to discuss what it is for something to be contingent or necessary:

On the issue of whether the number of planets could have been something other than 8, then a question is whether that "could have been" means "if the past had been different up to some point", or "given the same past", or something else.

But, perhaps, the issue is clearer with a closer example:

Is "Obama was the POTUS in DEC-2009" contingent? Could it have been different?

If (for instance) McCain had won, then Obama would not have been the POTUS in DEC-2009. But could McCain have won, if the past up to the election had been the same? And would the question of whether "Obama was the POTUS in DEC-2009" is contingent hinges on the matter of determinism?

Someone could say that "the number of planets is 8" or "Obama was the POTUS in DEC-2009" is contingently true if it's true and there is a possible world at which it's false, but then the question is what a possible world is, and if a possible world is a scenario that could have happened, then it seems to me that we're back to the previous case:

A question is whether the number of planets could have been different from 8, or whether Obama could have not been the POTUS, and whether that "could have been different" has something to do (or not) with determinism (i.e., what kind of "could have been different" we're talking about).

I would have thought that since the Obama-POTUS statement is contingent, it is true that the statement could have been false. Do you no think it is a contingent statement?

By the way, welcome. There are some smart people here too. But some of them are not conversant with logic. (Which is what Emil means. He confuses not being conversant with logic with stupidity).

ACB

Thu 28 Jan, 2010 07:42 am
@Owen phil,
Owen;114640 wrote:
(the number of planets) = 9, is a contingent truth.
(the number of planets) []= 9, is a contingent truth.
(the number of planets) > 7, is a contingent truth.
(the number of planets) []> 7, is a contingent truth.

Can you please explain why you think the second and fourth statements above are true?

Zetherin

Thu 28 Jan, 2010 09:00 am
@Emil,
Emil;123185 wrote:
Hi Angra.

I'm not sure you will like this board more than the other one. It is still full of idiots. But there are many religionists here for you to play with.

Also, I'd like to see what you wrote as I'm not exactly sure how to solve this problem, except by talking about opaque contexts.

We don't need formal logic to tell us how offensive this is! Man, Emil, that's harsh.

kennethamy

Thu 28 Jan, 2010 09:23 am
@Zetherin,
Zetherin;123234 wrote:
We don't need formal logic to tell us how offensive this is! Man, Emil, that's harsh.

Emil's universe of discourse is, logicians. You have to understand that.

Angra Mainyu

Thu 28 Jan, 2010 09:29 am
@Owen phil,
kennethamy wrote:

I would have thought that since the Obama-POTUS statement is contingent, it is true that the statement could have been false. Do you no think it is a contingent statement?

The statement could have been false if the past had been different, but if determinism is true, then it seems there is a sense in which the past couldn't have been different - and thus the same goes for the Obama-POTUS statement; it seems there is a sense (under determinism) in which it couldn't have been false.

What I was trying to discuss (rather than taking a stance on the matter) was the meaning of the expressions "could have been false", "could have been different", etc., when used in the context of the contingent-necessary distinction.

In other words, the question I was trying to explore is: is it sufficient for a statement to be contingently true the fact that it is true but could have been false if the past had been different, or is it required that the past could have been different as well?

kennethamy wrote:

By the way, welcome.

Thank you.

kennethamy

Thu 28 Jan, 2010 09:53 am
@Angra Mainyu,
Angra Mainyu;123243 wrote:
The statement could have been false if the past had been different, but if determinism is true, then it seems there is a sense in which the past couldn't have been different - and thus the same goes for the Obama-POTUS statement; it seems there is a sense (under determinism) in which it couldn't have been false.

Thank you.

But to say that a statement is contingent, is to say that it is logically possible for it to be false. It's negation does not imply a contradiction. There is a conditional sense in which the statement "could have been false" in the sense that if the past had been different it would have been false. But we are not talking (or, at least, I am not talking) of this conditional sense. I am talking of the categorical sense in which P could be false, simply means, that its negation does not imply a contradiction. I don't know whether the planet statement could have been false in your (conditional) sense. But I know it could have been false in my categorical sense. (There is also, by the way, an epistemic sense in which it could have been false, too).

Zetherin

Thu 28 Jan, 2010 10:15 am
@kennethamy,
kennethamy;123241 wrote:
Emil's universe of discourse is, logicians. You have to understand that.

You say that as if it excuses his brash demeanor. Logicians, like anyone else, can be polite enough not refer to others in such a condescending manner. Or, do you think that because his passion is logic, it is necessary that he be a prick?

kennethamy

Thu 28 Jan, 2010 10:20 am
@Zetherin,
Zetherin;123257 wrote:
You say that as if it excuses his brash demeanor. Logicians, like anyone else, can be polite enough not refer to others in such a condescending manner. Or, do you think that because his passion is logic, it is necessary that he be a prick?

I was not excusing him. I was explaining him. Madame de Stael once wrote that to understand all is to forgive all. But I don't believe that. All he said was, "full of idiots", and I imagine even he would allow it is hyperbole. No one should take it personally. It is a general proposition.

Zetherin

Thu 28 Jan, 2010 10:33 am
@kennethamy,
kennethamy;123258 wrote:
I was not excusing him. I was explaining him. Madame de Stael once wrote that to understand all is to forgive all. But I don't believe that. All he said was, "full of idiots", and I imagine even he would allow it is hyperbole. No one should take it personally. It is a general proposition.

You should be able to see how offensive it can be to members of the community. And I'm not sure why you mention about general propositions. General propositions can be just as offensive.

Emil

Thu 28 Jan, 2010 10:39 am
@Zetherin,
Zetherin;123234 wrote:
We don't need formal logic to tell us how offensive this is! Man, Emil, that's harsh.

I don't think it is particularly harsh. I did not insult anyone in particular so I don't think it is against the rules either. At least such 'broad' utterances have not been punished at the other forums I have been it, so I expect this one to be just like that.

Besides, you're not an idiot.

---------- Post added 01-28-2010 at 05:42 PM ----------

Angra Mainyu;123200 wrote:
Hi, Emil

I'm not planning to participate in many debates with religionists here; I was just perusing the threads and I thought I'd post in this one, so I registered.

As for what I wrote, I didn't present an alternative to opaque contexts, but I was just trying to tackle another angle of the issue, as an opportunity to discuss what it is for something to be necessary (or contingent), but without taking a stance myself, but I have no objection to the previous replies to the argument by you and kennethamy.

Plus, I did some nitpicking by pointing out that "the number of planets is 9" is actually false.

Anyway, I'll repost it if you're interested:

Slight astronomical nit-picking:

The number of planets is actually 8.

Pluto is a dwarf planet, which is a different astronomical classification (i.e., "dwarf planet" is not some type of planet, but actually not a planet - maybe astronomers should have come up with another name).

Still, if we count dwarf planets too, the number is still not 9, since there are other dwarf planets, like Eris, so the number of (planets + dwarf planets) is at least 11 (since Ceres and Eris are dwarf planets too), and there might be up to 2000 of them.

In short, the number of planets (going by the definition in astronomy) is 8, and if we want to count planets + dwarf planets, the number is at least 11, and perhaps up to 2000.

I'll use "planet" in the stricter sense, so the number of planets is 8 (of course, I'm talking about planets in our planetary system, there are plenty more in other planetary systems), and the number of dwarf planets is unknown.

As for the philosophical question, I'd like to discuss what it is for something to be contingent or necessary:

On the issue of whether the number of planets could have been something other than 8, then a question is whether that "could have been" means "if the past had been different up to some point", or "given the same past", or something else.

But, perhaps, the issue is clearer with a closer example:

Is "Obama was the POTUS in DEC-2009" contingent? Could it have been different?

If (for instance) McCain had won, then Obama would not have been the POTUS in DEC-2009. But could McCain have won, if the past up to the election had been the same? And would the question of whether "Obama was the POTUS in DEC-2009" is contingent hinges on the matter of determinism?

Someone could say that "the number of planets is 8" or "Obama was the POTUS in DEC-2009" is contingently true if it's true and there is a possible world at which it's false, but then the question is what a possible world is, and if a possible world is a scenario that could have happened, then it seems to me that we're back to the previous case:

A question is whether the number of planets could have been different from 8, or whether Obama could have not been the POTUS, and whether that "could have been different" has something to do (or not) with determinism (i.e., what kind of "could have been different" we're talking about).

None of the above is what philosophers commonly mean with "contingent". To say that a proposition is contingent means that there is a possible world where it is the case and a possible world where it is not the case. Also, the proposition does not imply a contradiction and neither does it negation.

---------- Post added 01-28-2010 at 05:45 PM ----------

kennethamy;123208 wrote:
[...]

By the way, welcome. There are some smart people here too. But some of them are not conversant with logic. (Which is what Emil means. He confuses not being conversant with logic with stupidity).

That's not what I meant and I'm not that conversant (never heard that word before) with logic yet since I couldn't understand much of Graham Priest's book In Contradiction. It is exceedingly technical.

I did not mean it literally either. I meant that there are many persons that fit the first meaning of "idiot" given on Wiktionary:[INDENT]
1. (pejorative) A common term for a person of low general intelligence. usage note This may be used pejoratively, as an insult. It is a weak insult, however, and between close friends, family members, or lovers, is often completely nonaggressive.

[/INDENT]

---------- Post added 01-28-2010 at 05:49 PM ----------

ACB;123214 wrote:
Can you please explain why you think the second and fourth statements above are true?

Actually the second and forth sentences here are not well formed formula and they do not mean anything in standard notation. The reason being the that necessity operator (the box, [] for the lazy and □ for pros) is placed in a place it cannot meaningfully be. In this case in the middle of a dyadic operator ("dyadic operator" means an operator that works on two things, the opposite is a monadic operator which works on one thing. The necessity operator is a monadic operator.).

Oh and by the way. My idiots remark was not targeted at ACB or Kennethamy either.

Angra Mainyu

Thu 28 Jan, 2010 11:23 am
@Emil,
kennethamy wrote:
But to say that a statement is contingent, is to say that it is logically possible for it to be false. It's negation does not imply a contradiction.

For instance, statements like "Water is H2O?", or "The atomic number of gold is 79" are often regarded as necessary, not contingent, even though it is logically possible for them to be false - i.e., there is no logical contradiction involved in, say, claiming that modern physics got it wrong, and the statements in question are false.

I'm not suggesting that they're false, of course, but my point is that philosophers (like Kripke, Putnam, and many anonymous on-line debaters) claim that such statements are necessary, even though their negation involves no contradiction.

What they say is that it's not metaphysically possible (rather than logically possible) for them to be false. I've seen that distinction in on-line debates, the works of a number of professional philosophers, and particularly in arguments made by theologians to try to show that God exists.

Also, it is my impression that the statement "Necessarily, the number of planets is nine" (or rather eight) in this thread, also refers to metaphysical necessity, rather than logical necessity, even if this thread is in the subforum "Logic" (perhaps, it should be in "Metaphysics"?).

So, what I'm trying to discuss is this category of statements, "metaphysically possible" vs. "metaphysically necessary", which seems all but clear in my view, and the status of planets according to such classification.

kennethamy wrote:

But we are not talking (or, at least, I am not talking) of this conditional sense. I am talking of the categorical sense in which P could be false, simply means, that its negation does not imply a contradiction. I don't know whether the planet statement could have been false in your (conditional) sense. But I know it could have been false in my categorical sense. (There is also, by the way, an epistemic sense in which it could have been false, too).

I agree, of course, that in the sense in which you're using "necessary", that the number of planets is eight is not necessary, since there is no contradiction involved in claiming that they're not eight.

However, as I mentioned, I think that kind of categorical sense that you're using is not the one used in this thread.

On the other hand, I'm not sure the conditional sense ("it could have been false if the past had been different") is what "metaphysically contingent" means. I'm just proposing alternatives, trying to elucidate the concepts of metaphysical contingency and metaphysical necessity, which I find rather unclear.

---------- Post added 01-28-2010 at 02:24 PM ----------

Emil wrote:
None of the above is what philosophers commonly mean with "contingent". To say that a proposition is contingent means that there is a possible world where it is the case and a possible world where it is not the case. Also, the proposition does not imply a contradiction and neither does it negation.

I considered that possibility in the post you're quoting. Not all metaphysicians are possible world theorists, though many are. But as I mentioned, the question then becomes "what's a possible world?", and if that's a scenario that could have happened, then the question is the same as before: what kind of "could have happened" is that?

Is it "it could have happened if the past had been different?"

But it seems not, based on usage, since possible worlds have their own past. But it looks kind of mysterious to me.

Emil

Thu 28 Jan, 2010 11:44 am
@Angra Mainyu,
Angra Mainyu;123269 wrote:
I considered that possibility in the post you're quoting. Not all metaphysicians are possible world theorists, though many are. But as I mentioned, the question then becomes "what's a possible world?", and if that's a scenario that could have happened, then the question is the same as before: what kind of "could have happened" is that?

Is it "it could have happened if the past had been different?"

But it seems not, based on usage, since possible worlds have their own past. But it looks kind of mysterious to me.

Only slightly and not explicitly enough for my taste.

I don't want to try to teach you how the possible world semantics works in detail. You may know already and are just pretending not to know for the sake of argument. For an introduction to logic using PWS see Swartz and Bradley (1979).

As for a non-PWS definition of contingent. Here:
[INDENT]Contingency 1.Contingency 2. For all propositions, that a proposition is contingent is logically equivalent with that it is logically possible that it is true and it is logically possible that it is false. [(∀P)(∇P⇔(◊TP∧◊FP)]

[/INDENT]I have never seen anyone talk of contingency in the sense you keep referring to, that is, "if the past had been different" or something like that. Contingency has nothing to do with the past. But perhaps you've met some odd and non-standard deterministic contingency concept that I have never heard of.

Angra Mainyu

Thu 28 Jan, 2010 12:19 pm
@Owen phil,
Emil wrote:

I don't want to try to teach you how the possible world semantics works in detail. You may know already and are just pretending not to know for the sake of argument. For an introduction to logic using PWS see Swartz and Bradley (1979).

PWS only moves the question one step back, but the question becomes "what's a possible world?", and we're back with the same problem (or a similar one), as far as I can tell, if "possible world" is defined in terms of what "could have happened" (if not, I'm not sure how they'll define it).

Emil wrote:
[INDENT]Contingency 1.

That one does not seem to match usage among metaphysicians, or in many on-line debates (see the examples of water and gold in my reply to kennethamy); I don't think that this is what Owen meant.

Emil wrote:

Contingency 2. For all propositions, that a proposition is contingent is logically equivalent with that it is logically possible that it is true and it is logically possible that it is false. [(∀P)(∇P⇔(◊TP∧◊FP)]

This one has the same problem as the previous one.

Emil wrote:
I have never seen anyone talk of contingency in the sense you keep referring to, that is, "if the past had been different" or something like that. Contingency has nothing to do with the past. But perhaps you've met some odd and non-standard deterministic contingency concept that I have never heard of.

I've never seen anyone try to figure what "contingent" mean by proposing that example, but they often say that P is contingently true if it's true and could have been false, and an entity exists contingently if it exists but could have not existed.

Now, that "could have been false", and "could have not existed" may mean "if the past had been different", or "even with the same past"; but I'm not sure what else that might mean; so, I'm trying to figure that out.

Emil

Thu 28 Jan, 2010 01:32 pm
@Angra Mainyu,
Angra Mainyu;123286 wrote:
PWS only moves the question one step back, but the question becomes "what's a possible world?", and we're back with the same problem (or a similar one), as far as I can tell, if "possible world" is defined in terms of what "could have happened" (if not, I'm not sure how they'll define it).

It is impossible to keep giving non-circular definitions. This is called the dictionary problem. I'm fine with PWS being a framework to understand logic but you should read Swartz and Bradley (1979) for an introduction to logic using PWS.

Quote:
That one does not seem to match usage among metaphysicians, or in many on-line debates (see the examples of water and gold in my reply to kennethamy); I don't think that this is what Owen meant.

This one has the same problem as the previous one.

No? I think it matches exactly what the common meaning is. Again see the work referred to before and this site. All of them agree in essence with the two definitions that I mentioned above.

Quote:
I've never seen anyone try to figure what "contingent" mean by proposing that example, but they often say that P is contingently true if it's true and could have been false, and an entity exists contingently if it exists but could have not existed.
Quote:
Now, that "could have been false", and "could have not existed" may mean "if the past had been different", or "even with the same past"; but I'm not sure what else that might mean; so, I'm trying to figure that out.

That's not what they commonly mean. Where'd you get this whole past idea? Though the past might be different and if it was, then certain contingent things would not exist and others would, etc.