A General Argument Against Evil - Part II

Now, since M is itself a state of affairs, either M is logically possible or logically impossible.

Suppose M is logically possible.

If so, then it is logically possible that God cannot cause X to obtain.

Thus, it is logically possible that X is logically impossible.

Thus, X is logically impossible.

Alternatively, suppose M is logically impossible.

If so, then it is logically im ...[text shortened]... oth[/b] M and X). This is your mistake, and it has nothing to do with my argument.

Cheers.
[/b]

Let's look at the basic assumptions of the system you are talking about:

(a) God can cause any logically possible state of affairs to obtain.
(b) <Some assumption I'm making about M/X>

Your claim is that, by making assumption (b), I am deliberately introducing a proposition that is inconsistent with (a). Correct so far?

Originally posted by bbarr
M = ‘God cannot cause X to obtain’

Presumably, the variable ‘X’ in M just denotes some state of affairs or other.

Now, there is no reason to suppose that X cannot be M itself. Clearly, whatever system of logic we are using is capable of having states of affairs that refer to other states of affairs (otherwise, we would not be able to define M as you did above). By the same token, the system of logic is capable of expressing/defining self-referential states of affairs as well.

Hence, if we consider the state of affairs such that the M and X we are talking about are identical, this state of affairs (M/X) can be properly expressed in the system of logic we are using.

So, what is the assumption I am making?

(b) X is logically possible (impossible) iff X is logically possible (impossible)

which is a tautology.

If (a) and (b) lead to a contradiction; and (b) is a tautology, then it follows that (a) must be a falsehood.

Originally posted by lucifershammer
Originally posted by bbarr
[b]Consider the following state of affairs (call it X):

"God cannot cause X to attain."

If X is logically possible, then God can cause X to attain. If God can cause X to attain, however, then it is logically impossible that God cannot cause X to attain; i.e. X is logically impossible.

Huh?
...[text shortened]... ain (double negative)
=> X is logically attainable
=> X is logically possible

Cheers,

LH[/b]

OK, so let's keep this simple, stupid:

You claim:

"X is logically possible
=> God can cause X to attain (God's omnipotence)
=> It is logically impossible that God cannot cause X to attain (essentially a double negative)
=> "God cannot cause X to attain" is logically impossible (just re-ordering the sentence)
=> X is logically impossible (definition of X) "

Let us give meaning to proposition 'X'.
X= "LucifersHammer talking sense".

Thus your argument becomes:

1. LucifersHammer talking sense is logically possible.
2. Therefore God can cause LucifersHammer talking sense to attain (God's omnipotence).
3. Therefore It is logically impossible that God cannot cause LucifersHammer talking sense to attain.
4. Therefore God cannot cause LucifersHammer talking sense to attain is logically impossible. (just re-ordering the sentence)
5. Therefore LucifersHammer talking sense is logically impossible.

It is obvious that 5 does not follow from 4.
Just because the fact that "God cannot cause LH to talk sense is impossible", does not entail "LH can talk sense" to be impossible.

All that we can ascertain from the statement that ""God cannot cause LH to talk sense is impossible" is that "God can cause LH to talk sense". It does NOT imply that "LH cannot talk sense".
It may well be the case that "LH talks nonsense".

If you still cannot see this LucifersHammer, then look at the structure of your argument:

You have one premise (1) and four conclusions (2), (3), (4) and (5) from this single assumption.
Ultimately (removing the intermediate, unnecessary explanatory 'deductive' chains) therefore your argument simplifies down to:

1. LucifersHammer talking sense is logically possible.
2. Therefore LucifersHammer talking sense is logically impossible.

If you cannot see the fallaciousness of this argument, then you really have proved beyond a shadow of doubt that :

"LucifersHammer talking sense is logically impossible"

Originally posted by bbarr
You have shown nothing concerning my notion of omnipotence other than that you can get yourself confused.

Alright, let's see what we're talking about here.

If A is the set of all states of affairs, and M is some relationship on AxA such that:

M(x,y) when y is a state of affairs such that God cannot cause x to attain

Then, does there exist some state of affairs X such that M(X,X)?

Or, in other words, does the relationship M have a fixed point?

I believe it does (verbally expressed as "God cannot cause the state of affairs defined by this statement to attain"😉.

I haven't formulated a full formal proof yet, but I think it would go something like this:

Let P be the set of all propositions. It can be shown that P is countably infinite (i.e. isomorphic with N, the set of all natural numbers). The most obvious definition for A would be 2^P, i.e. the set of all subsets of P. Then A would be uncountably infinite or isomorphic with R, the set of all reals.

Now, one can define M such that it is an function M:A->A without losing its semantics. If A is mapped on to R such that M is monotone on R, then we know (from Tarski's Fixed Point Theorem) that M has a fixed point.

Hence, state X exists and the paradox in my previous post remains.

No confusion here.

Originally posted by howardgee
OK, so let's keep this simple, stupid:

You claim:

"X is logically possible
=> God can cause X to attain (God's omnipotence)
=> It is logically impossible that God cannot cause X to attain (essentially a double negative)
=> "God cannot cause X to attain" is logically impossible (just re-ordering the sentence)
=> X is logically impossible ...[text shortened]... oved beyond a shadow of doubt that :

"LucifersHammer talking sense is logically impossible"

You actually paid to do philosophical logic in college??

Your argument is specious because the final step does not follow from your definition of X.

Originally posted by lucifershammer
Alright, let's see what we're talking about here.

If A is the set of all states of affairs, and M is some relationship on AxA such that:

M(x,y) when y is a state of affairs such that God cannot cause x to attain

Then, does there exist some state of affairs X such that M(X,X)?

Or, in other words, does the relationship M have a fixed point ...[text shortened]...

Hence, state X exists and the paradox in my previous post remains.

No confusion here.

Let's take this step by step.

Given my definition of omnipotence as premise 1, you think you can produce a reductio. Fine. What is the second premise, and only the second premise, of this supposed reductio?

Your turn.

Originally posted by lucifershammer
Alright, let's see what we're talking about here.

If A is the set of all states of affairs, and M is some relationship on AxA such that:

M(x,y) when y is a state of affairs such that God cannot cause x to attain

Then, does there exist some state of affairs X such that M(X,X)?

Or, in other words, does the relationship M have a fixed point ...[text shortened]...

Hence, state X exists and the paradox in my previous post remains.

No confusion here.

You probably shouldn't base any arguments on the assumption that there is a set of all propositions. Such an assumption entails that there is a set of all turhts (which would, of course, be a proper subset of the set of all propositions). But the supposition that there is a set of all truths runs afoul of Cantor's theorem. Here's an instructive exchange on the matter:

http://www.sunysb.edu/philosophy/faculty/pgrim/exchange.html

Note that my definition of omniscience doesn't presuppose the existence of such a set.

Originally posted by lucifershammer
Let's look at the basic assumptions of the system you are talking about:

(a) God can cause any logically possible state of affairs to obtain.
(b) <Some assumption I'm making about M/X>

Your claim is that, by making assumptio ...[text shortened]... (b) is a tautology, then it follows that (a) must be a falsehood.

You are just so confused, I don't know what to say other than "re-read the argument I presented above". Eep!

Originally posted by bbarr
You are just so confused, I don't know what to say other than "re-read the argument I presented above". Eep!

It is very unbecoming to simply say "you are confused" and leave it at that. The M you stated is some kind of function in A (the set of all states of affairs). Why is it impossible that M have a fixed point?

Originally posted by lucifershammer
Since this argument has come up in some recent posts, I thought it might be worthwhile to take another look at it.

For anyone with the stomach for the whole discussion, you can find it here:

http://www.redhotpawn.com/board/showthread.php?threadid=21886

Some key corollaries of the argument can be seen in bbarr's posts on these pages:

http: ...[text shortened]... To sum up:

A theist can commit to the truth of (2) by rejecting either of (3) or (5.1/5.1'😉.

Nietzsche "Genealogy of Morals"

Originally posted by bbarr
Let's take this step by step.

Given my definition of omnipotence as premise 1, you think you can produce a reductio. Fine. What is the second premise, and only the second premise, of this supposed reductio?

Your turn.

I suppose the second step would be:

2. Suppose X is logically possible.

where X is a fixed point of the relation

M(x) = A state of affairs such that God cannot cause a state of affairs x to attain.

LH

EDIT: The alternative line would be

2'. Suppose X were logically impossible.

Originally posted by bbarr
You probably shouldn't base any arguments on the assumption that there is a set of all propositions. Such an assumption entails that there is a set of all turhts (which would, of course, be a proper subset of the set of all propositions). ...[text shortened]... omniscience doesn't presuppose the existence of such a set.

Thanks for the link. Two quick observations:

1. It is not entirely clear to me why the set of all truths (T) must be a proper subset of the set of all propositions (P); i.e. there might be truths that cannot be expressed as propositions. Certainly the set of all true propositions is a proper subset of P.

2. Does Cantor's theorem work with uncountably infinite sets? e.g. Is 2^R of a higher cardinality than R? I don't think his diagonalisation argument can be directly applied to an uncountably infinite set; but I could be wrong here.

Would appreciate any pointers/links on this.

LH

EDIT: Also, in the system I am thinking of, a proposition is a finite string of symbols. Such a system would be incapable of expressing universal propositions or propositions about infinite sets of propositions.

Originally posted by lucifershammer
You actually paid to do philosophical logic in college??

Your argument is specious because the final step does not follow from your definition of X.

The last sentence was a humurous conclusion based on the analysis of your fallacious argument.

Did you follow the steps 1 - 5 in my post?

Originally posted by howardgee
The last sentence was a humurous conclusion based on the analysis of your fallacious argument.

Did you follow the steps 1 - 5 in my post?

I meant your step 5 does not follow from your definition of Y (let's call "LH talking sense" Y to avoid confusion). But my step 5 follows from my definition of X.

Originally posted by lucifershammer
Since this argument has come up in some recent posts, I thought it might be worthwhile to take another look at it.

For anyone with the stomach for the whole discussion, you can find it here:

http://www.redhotpawn.com/board/showthread.php?threadid=21886

Some key corollaries of the argument can be seen in bbarr's posts on these pages:

http: ...[text shortened]... To sum up:

A theist can commit to the truth of (2) by rejecting either of (3) or (5.1/5.1'😉.

Why would any action be necessary or unnecessary to God as far as
our universe is concern? If God desires a certain outcome through
whatever means He designs; doesn’t it follow that all things will be
as He deems them worthwhile, not how we perceive them to be
necessary or not? God after all sees all the variables in play, while
we some times miss those things right in front of our faces.

How does suffering even fit with the words necessary or unnecessary?
Reason I ask about suffering is that suffering (pain) is simply a
reaction to nerve impulses, but so too is pleasure. It is the degree and
manner which the body is affected causes both. So don’t all feelings
be they pleasurable or painful fall into just the result of other actions
like a caress or kiss from a lover, or a slap or stab wound from an
enemy?

Morally perfect is defined how? Within human debates we see a lot
of dividing ourselves up into different types of categories; we have
labeled ourselves liberal, conservative, moderates, or whatever else
is out there. Do we see that within just human mindsets there are
different views on how things should be done, along with many of
the reasons why? What makes us think we can perceive God’s views
on how to act toward man? We don’t even agree on how man should
act toward man, or what man should allow to occur simply because
man likes certain things and others do not, like the death penalty,
abortion, slavery, prostitution, religious freedom, drug use for fun,
and so on.

Many people don’t accept evil the same way, some may not even
accept it at all. I understand for the sake of this discussion evil or
for that matter good does not have to be defined. As I see this
discussion it is more like that of if the unstoppable force strikes
the unmovable object what happens, and as such is just an
exercise in what ifs. I am not sure we can prove anything but if
my reasoning on this is flawed in some manner, please correct
it.
Kelly

Originally posted by lucifershammer
I meant your step 5 does not follow from your definition of Y (let's call "LH talking sense" Y to avoid confusion). But my step 5 follows from my definition of X.

Here is what you wrote, and you do not define X at all!:

"To complete the argument:

Suppose X is logically impossible.
Then it is impossible that God cannot cause X to attain.
i.e. God can cause X to attain.
Hence, X is logically attainable.
Hence, X is logically possible.

You get a contradiction either way."

The reason you get a contradiction is because of your fallacious logic.
Please read my earlier post, and think hard, and TRY to understand your confusion.