# Analytic propositions

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2. » Logic
3. » Analytic propositions

Wed 6 Jan, 2010 04:03 am
An(p), means, p is analytic.

D1. An(p) =df <>p -> []p.
D2. (p => q) =df [](p -> q).
D3. (p <=> q) =df [](p <-> q).

1. An(p) => (p <-> []p).
2. An(p) => (p <-> <>p).
3. An(p) => (<>p <-> []p).

4. An(p) <=> (<>p <=> []p).
5. An(p) <=> (p <=> <>p).
6. An(p) <=> (<>p <=> []p).

7. (An(p) & <>p) -> p, is a theorem.

These definitions and theorems show that some modal arguments are circular.
For example, Hartshorne (1962), claims proof of God's existence with the following argument.

Hartshorne:
G = God exists.

8. (An(G) & <>G) -> G.

(God exists is analytic. & God exists is possible.) implies, God exists is actual.

This argument which is an instance of 7, is valid and not sound.
But, if G is analytic then <>G <=> G, (by 5.)
That is, the argument becomes..

8a. (An(G) & G) -> G) which is a circular argument. The premise includes the conclusion.

Note that...
Since (An(p) & <>~p) -> ~p, is also a theorem...

8b. (An(G) & <>~G) => ~G, is also valid and not sound.

ie. God exists is analytic & God does not exist is possible, implies God does not exist is actual.

Hartshorne's modal ontological argument proves nothing.

kennethamy

Wed 6 Jan, 2010 06:57 am
@Owen phil,
Owen;117619 wrote:
An(p), means, p is analytic.

D1. An(p) =df <>p -> []p.
D2. (p => q) =df [](p -> q).
D3. (p <=> q) =df [](p <-> q).

1. An(p) => (p <-> []p).
2. An(p) => (p <-> <>p).
3. An(p) => (<>p <-> []p).

4. An(p) <=> (<>p <=> []p).
5. An(p) <=> (p <=> <>p).
6. An(p) <=> (<>p <=> []p).

7. (An(p) & <>p) -> p, is a theorem.

These definitions and theorems show that some modal arguments are circular.
For example, Hartshorne (1962), claims proof of God's existence with the following argument.

Hartshorne:
G = God exists.

8. (An(G) & <>G) -> G.

(God exists is analytic. & God exists is possible.) implies, God exists is actual.

This argument which is an instance of 7, is valid and not sound.
But, if G is analytic then <>G <=> G, (by 5.)
That is, the argument becomes..

8a. (An(G) & G) -> G) which is a circular argument. The premise includes the conclusion.

Note that...
Since (An(p) & <>~p) -> ~p, is also a theorem...

8b. (An(G) & <>~G) => ~G, is also valid and not sound.

ie. God exists is analytic & God does not exist is possible, implies God does not exist is actual.

Hartshorne's modal ontological argument proves nothing.

Harshorne, and no one else, ever assumed that God exists is analytic.

Owen phil

Wed 6 Jan, 2010 08:21 am
@kennethamy,
kennethamy;117645 wrote:
Harshorne, and no one else, ever assumed that God exists is analytic.

What does this stupid remark mean??

kennethamy

Wed 6 Jan, 2010 08:28 am
@Owen phil,
Owen;117666 wrote:
What does this stupid remark mean??

It is not stupid. It is true. And it means exactly what it says. No one thinks that the proposition that God exists is analytic. Necessary, yes, but not analytic. There is a distinction, you know.

fast

Wed 6 Jan, 2010 08:28 am
@Owen phil,
edited out
................

Owen phil

Wed 6 Jan, 2010 08:45 am
@kennethamy,
kennethamy;117672 wrote:
It is not stupid. It is true. And it means exactly what it says. No one thinks that the proposition that God exists is analytic. Necessary, yes, but not analytic. There is a distinction, you know.

A proposition is analytic if it is either impossible or it is necessary.

If p is necessary then it surely is analytic.
[]p -> ([]p v []~p), is tautologous.

What distinction did you have in mind?

kennethamy

Wed 6 Jan, 2010 08:51 am
@Owen phil,
Owen;117680 wrote:
A proposition is analytic if it is either impossible or it is necessary.

If p is necessary then it surely is analytic.
[]p -> ([]p v []~p), is tautologous.

What distinction did you have in mind?

The proposition that every event must have a cause, if true, is necessary, but it is not analytic. The proposition that all dogs must be animals is necessary, but not analytic. Have you ever read philosophers like Kripke or Quine?* You should sometimes try philosophizing in English. You might be missing some things.

Not even to mention, Kant, or Spinoza, or Descartes?

Emil

Wed 6 Jan, 2010 11:22 am
@Owen phil,
Don't you mean "The proposition that all dogs must be animals is necessary, but analytic."? That seems to me to be an example of an analytic proposition. While the first one you mention is not.

---------- Post added 01-06-2010 at 06:27 PM ----------

Owen;117619 wrote:
An(p), means, p is analytic.

D1. An(p) =df <>p -> []p.
D2. (p => q) =df [](p -> q).
D3. (p <=> q) =df [](p <-> q).

1. An(p) => (p <-> []p).
2. An(p) => (p <-> <>p).
3. An(p) => (<>p <-> []p).

4. An(p) <=> (<>p <=> []p).
5. An(p) <=> (p <=> <>p).
6. An(p) <=> (<>p <=> []p).

7. (An(p) & <>p) -> p, is a theorem.

These definitions and theorems show that some modal arguments are circular.
For example, Hartshorne (1962), claims proof of God's existence with the following argument.

Hartshorne:
G = God exists.

8. (An(G) & <>G) -> G.

(God exists is analytic. & God exists is possible.) implies, God exists is actual.

This argument which is an instance of 7, is valid and not sound.
But, if G is analytic then <>G <=> G, (by 5.)
That is, the argument becomes..

8a. (An(G) & G) -> G) which is a circular argument. The premise includes the conclusion.

Note that...
Since (An(p) & <>~p) -> ~p, is also a theorem...

8b. (An(G) & <>~G) => ~G, is also valid and not sound.

ie. God exists is analytic & God does not exist is possible, implies God does not exist is actual.

Hartshorne's modal ontological argument proves nothing.

Careful not to confuse circular logic with begging the question. His argument begs the question but it is not circular. A circularly argument, you may recall, is one where the conclusion is a premise of the argument. Being a conjunct of a conjunction that is a premise is question begging and not circularity.

Your formulas are unclear. I'm guessing that "=>" means logical implication, and "->" means material implication, "<>" logically possible, "[]" logically necessary. I prefer to use proper symbols such as "⇒" and "→" (and "◊" and "□"). I already linked you earlier to a site where you can find them but you don't seem to want to use them.

Otherwise I agree with you.

kennethamy

Wed 6 Jan, 2010 11:40 am
@Emil,
Emil;117749 wrote:
Don't you mean "The proposition that all dogs must be animals is necessary, but analytic."? That seems to me to be an example of an analytic proposition. While the first one you mention is not.

---------- Post added 01-06-2010 at 06:27 PM ----------

I guess this is one example we don't agree on. But it is only an example. Red is a color is not analytic but is necessary. Things equal to the same thing are equal to each other is not analytic, but necessary. And so on. Therefore, all necessary propositions are analytic is false. And certainly, as fast pointed out, God exists is not a necessary truth. It may not even be true. So how could it possibly be analytic even if all necessary truths were analytic, which, as we have seen, they are not?

So what did you agree on with Owen?

Emil

Wed 6 Jan, 2010 11:45 am
@kennethamy,
kennethamy;117764 wrote:
I guess this is one example we don't agree on. But it is only an example. Red is a color is not analytic but is necessary. Things equal to the same thing are equal to each other is not analytic, but necessary. And so on. Therefore, all necessary propositions are analytic is false. And certainly, as fast pointed out, God exists is not a necessary truth. It may not even be true. So how could it possibly be analytic even if all necessary truths were analytic, which, as we have seen, they are not?

So what did you agree on with Owen?

I think that "Red is a color" is analytic and necessary.

"Things equal to the same thing are equal to each other" seems to me to be non-analytic and necessary. Though I'm unsure.

I agree that all necessary propositions are analytic is false. I also agree that God exists is not a necessary truth, and I think it is not analytic either.

Everything else he wrote.

kennethamy

Wed 6 Jan, 2010 11:49 am
@Emil,
Emil;117767 wrote:
I think that "Red is a color" is analytic and necessary.

"Things equal to the same thing are equal to each other" seems to me to be non-analytic and necessary. Though I'm unsure.

I agree that all necessary propositions are analytic is false. I also agree that God exists is not a necessary truth, and I think it is not analytic either.

Everything else he wrote.

Why "red" is a color? Not that it matters. What else did he write? Never mind.

1. Philosophy Forum
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3. » Analytic propositions