The last is false.

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.

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.

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.

Sorry, I didn't realize the thread was old. Please disregard.

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).

(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.

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.

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.

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.

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?

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.

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

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).

[...]

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).

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

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.

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).

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.

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).

[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)]

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.

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).

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.

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.