Modal Logic

[ppar3566]

I have recently joined the Richard Dawkins discussion forum in order to understand a little better other people's points of view and how people explain the non-existence of God. Many people there are exceptionally intelligent and it is a little intimidating for an admitted Christian to be there. But one thing on there got me thinking. That is that much of the logic (read non positivist arguments) are based on modual logic i.e. that if a=b and b=c then a must equal c. For example:
a) if God is all knowing, all loving, and all powerful he must know about evil, want to stop it and be able to stop it.
b) evil exists
c) therefore God does not exist.

Now leaving aside the validity of that argument (which is one of the weaker modular arguments but the only one i can think of of the top of my head). I wanted to know whether such arguments are based on axiomatic treatment of logic and thus must be based on a closed system. i.e. a=b, b=c, and therefore a only = c if they exist in a system in which no other variable can interfere with A,B, or C. If this is correct I think it spells out the easiest way to destroy such arguments as you dont have to argue about whether God exists only that the argument is based on an open system and thus not relevant.

I would love to use this argument but I dont know enough about philosophy to know if I am thinking right. If you are familiar with this sort of treatment of logic then could you help me.

 

[Odale]

I think you mean Modal Logic.

That confused me there =X.

One of their examples:

One basic version of the modal argument is a modal version of the problem of evil:

1) If God is possible, then God is a necessary being.
2) If God is a necessary being, then unjustified evil is impossible.
3) Unjustified evil is possible.
Therefore, God is not possible.

Edit:

I read a few more posts from there and the more I read the more confused I get.

 

[Kidan]

Ah.. the joys of higher mathematics, and yes, logic is a math.

And before I start waxing eloquent, let's remind everyone that it's been over 5 years since I got out of college, and getting pretty close to 10 since the last time I did logic and proofs....

The thing is that the logic, and their corresponding proofs, are a shorthand, a way to prove two statements, via a set of other statements.

Logical proofs have the following structure:
given statement
proving statements
Proved statement

There are a couple of ways to disprove these statements. One is the Law of Syllogism, the other the law of Detachment.

Let's explore this in a bit more depth, with a problem.

Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

(1) If you are a skateboarder, then you are a criminal.
(2) If you are a teenager, then you are a criminal.
(3) If you are a teenager, then you are a skateboarder.


There are two if... then statements here in (1) and (2). The Law of Detachment requires only one, so let's try syllogism.

Let p be the statement "you are a skateboarder".
Let q be the statement "you are a criminal".
Let r be the statement "you are a teenager".

Next we rewrite the three statements in terms of p and q.

(1) p->q
(2) r->q
(3) r->p


Now compare with the Law of Syllogism. You'll find that it doesn't match. (3) and (1) together imply (2) by the Law of Syllogism, but we can't use (1) and (2) to conclude (3).

The conclusion is invalid.



So, to touch on your original "proof:"

a) if God is all knowing, all loving, and all powerful he must know about evil, want to stop it and be able to stop it.
b) evil exists
c) therefore God does not exist.

First, let's simplify this a bit:

1) If God Exists, Then He would want to stop Evil
2) If Evil Exists Then There is No God


r = God Exists
b = Stop Evil
c = Evil Exists

1) r -> b
2) c -> !r

You can see that this was a poorly constructed logic structure to start with, and now you can see why. To disprove this, you would explain why.

Basically, why b does not yield c.



For more info on this stuff, here's a PDF file dealing with Logic and Proofs: http://www.mathsci.appstate.edu/~jlh/primer/hirst.pdf

 

[Odale]

/faint

 

[ppar3566]

I think you mean Modal Logic.

That confused me there =X.

rofl yes that is what i meant, thanks. And yes that was one of the better Modal logic arguments I was referring too. It just seemed to me that such a system is inherently open in that 'unjustified evil' (hello tautology) seems a very subjective term. Hence the system is not closed as human subjectivity influences b and therefore the system can not hold.

For more info on this stuff, here's a PDF file dealing with Logic and Proofs: http://www.mathsci.appstate.edu/~jlh/primer/hirst.pdf

Excellent. I have a background in matrix algebra but not much else except basic probability theory hence it is hard for me to argue on equal footing. Thanks for the reference (saved it to desktop).

Just to recap though. Is what you are saying the same as requiring a closed system. The example I usually use is as follows:
1. My neighbors roof is always wet when it is raining.
2. My neighbors roof is wet.
3. Therefore it must be raining.

In this case 1 and 2 are true but as they lie in a open system (i.e. the roof could get wet by means other than rain) the fact that they are true is not sufficient to prove that a wet roof = rain. Is this the same logic as your example?

 

[Neirai the Forgiven]

Largely, my view is:

a) God loves humans.
b) humans commit acts of evil.
c) God wishes to destroy evil.
d) Destroying evil would require the destruction of humans
e) God loves humans more than he wants immediate gratification of his hatred of evil.
f) God bides his time until he can separate evil from humanity as much as is going to happen.

aka,
love > evil
therefore, evil exists.

 

[ppar3566]

Largely, my view is:

a) God loves humans.
b) humans commit acts of evil.
c) God wishes to destroy evil.
d) Destroying evil would require the destruction of humans
e) God loves humans more than he wants immediate gratification of his hatred of evil.
f) God bides his time until he can separate evil from humanity as much as is going to happen.

aka,
love > evil
therefore, evil exists.

Yes that would be my theory as well but for the fact that as Christians it is inherent in our system of thinking (by the term faith) that we do not claim to be able to prove God true. Hence I suppose my theory is that as a Christian attempts should not be made to justify the existence of God but rather to show that proving the existence of God is a futile endevour. Thus I think it is very dangerous to set up our own axiomatic proofs of God, particularly when we as humans cannot close the system.


The Dawkins website also smells of positivism, which i simply can not abide. if ppl are interested i would like to post my reasons for my loathing of positivism here for discussion. But one thing at a time I suppose.

I want to go back to Kidan's stuff now and see if I can find the holes in the modal logic system Odale referred too.

 

[Odale]

When I take time and look at these logical analyses I can't help but see loop holes. The fact that they use large-scale (its midnight here and I forgot the word I am looking for) ideals and other topics (mainly such as evil and God) to make these logistical analyses does not make any valid point from a Christian view.

a) if God is all knowing, all loving, and all powerful he must know about evil, want to stop it and be able to stop it.
b) evil exists
c) therefore God does not exist.

Free will anyone?

Just an example.

Yeah I would like to hear why you dislike Positivism. It seems that abiding to positivism is counter productive to understanding God in a philosophical sort of way, which, in a way is what these people are doing (I think).

 

[Durruck]

The problem with closed logical proofs is that you cannot allow any outside evidence into the proof. a=b and b=c therefore a=c. You can only imply things you have asserted as truth from a & b into c.

Without the premise of God Exists in either a or b... You cannot deduce that God exists in c.

Open proofs allow for external forces, but likely using the open proof negates your credibility in the argument because you're using a source that the audience does not recognize.

If I recall correctly, it's GodsPeon's signature here on the forums that brings up what is quite likely the most logical conclusion from any argument: For those that believe, no proof is necessary. For those that do not believe, no proof is possible. (or something like that).

You can talk yourself blue in the face, but the logical crowd that wants a tangible god will never find one. On the other hand, we find God in everything we see around us.

 

[ppar3566]

@ Odale

Free will in many ways is also difficult as Christians themselves are not really sure whether we have free will or not. Indeed, if one plays the free will card in such a debate it leaves one open to the seemingly contradictory statements in the bible that lend themselves to either free-will or determinism. In this case one would need to take a free-will argument and explain away the determinism stuff in the bible or take the more dangerous approach entitled 'middle knowledge', which seems to me to be 'convenient knowledge' more than anything as it tries to marry determinism by God to free will by man - this leads to the difficult question of "if free will is so important that God allowed evil, why did he hedge his bets with an equal helping of determinism". All of this can be overcome with careful argumentation but it is something that I have yet to find a definitive or even useful answer to, despite my Dad being one of the more dominate middle knowledge proponents in my country.

Just quickly: Positivism states that there is an objective truth and that it is directly perceivable through our senses. There is also a implicit claim that the scientific method is the only way of determining those objective truths and that constraint refinement of that method will lead to our ability to directly perceive the bare and naked truth.

I hold that for a number of reasons (which I will discuss in brief below) that one can only logically hold a position in which, there is a truth (so not relativism) but that that truth cannot be directly perceived by humans (so not positivism). In essence then human knowledge and science is a set of interpretations of that truth, which are altered on the basis of science, knowledge, and trial and error on the basis of how useful those interpretations are to the way we live our lives. The major difference to positivism is that useful is not akin to truthful, and thus science may lead to a less truthful position because it is more useful than a more truthful position. It is true to say that the collection and overlapping of these interpretations give rise to reality as socially constructed. Such that where one scientists specific needs might lead to a gross misinterpretation of reality for the sake of convenience, the overlapping of scientific knowledge will give rise to a socially constructed reality that is often but not always closer to the real truth but it will never be the same as real truth nor will it be always be close to reality, particularly in a society that values utility over accuracy. For example society values and promotes extroversion and high self-esteem in our children despite the overwhelming evidence that introverted and depressed people are more accurate judges of reality.

Why is this so. Well the problem of course is cognitive load. i.e. the human mind has a finite ability to process new information (which i presume is where positivism wants to be - at the forefront of new knowledge). This limited ability to utalise large amounts of new information simultaneously leads to mental shortcuts, activation of sterotypes and heuristics, and biases in information processing which in essence means that we do not directly perceive reality at all but a constructed reality or a reality of our own making. This is true at a biological level where we often claim to see colour at night time when night vision is essentially colour blind and where we automatically fill in missing gaps in our visual field. It is also true at an intellectual level where scientists are often arguing about the relative usefulness of alternative constructed realities rather than relative truths as the truth can never be completely and totally perceived, only interpreted.

Christians originally rejected the idea of socially constructed reality where they ironically asserted an absolutist position. The irony comes from the fact that that same absolutism is now responsible for the logical and scientific arguments that assert there is no God. It is my strong belief that socially constructed reality is in essence the most acceptable logical position to hold as a Christian, which is encapsulated with the saying "faith seeking reason".

@ Durrick

I dont think that people that use such logic are cowards, I think some of them might be hiding behind sophistry, but i think many seriously hold these positions but as i mentioned before reality is socially constructed and these folk hold to a reality that we do not share (i.e. that a loving God can allow evil). In essence I am a strong supporter of logic and reason (and see positivism as a destruction of reason) because i think it leads to a better faith. After all, correctly translated Romans 12 reads "Therefore, in view of Gods mercy offer yourselves as a living sacrifice, this is your rational (not spiritual) act of worship". In essence Paul, coming to the end of one of the most forceful rhetorics in written history suggests as Christians we should find Christ through reason and then live our lives out by logically applying Christian teaching to our daily lives.

 

[Elader Arkon]

Here's something fun for naturalists (which athiests are by definition) that I learned from my professor in my Biblical theology and Ethics class.

If Naturalism is true, one must accept the following as true:
1.)The material world is all there is (nothing exists outside the box)
----------------
| Material World| <--look an illustration!
----------------
2.) Everything inside the box must be caused by something else inside the box, i.e. everything is contingent and the result of material causes.
3.) Since nothing can exist outside the box, reason and logic must be 'inside' the box.
4.) Since reason and logic must be inside the box, they must be a result of material causes (and therefore contingent and non-essential)
5.) Since reason and logic are contingent upon material causes, they are not fundamentally true.
6.) Thus reason and logic only 'feel' true because of some material causation (the feeling that logic is true is a chemical delusion)
7.) Thus we have no compelling reason to believe the results of any logical or rational inquiry, because it cannot be superior to superstition (both may 'feel' true)
8.) Thus no real knowledge is possible, including scientific knowledge, since we have no reason to trust science over superstition (though we might prefer science)*
9.) Thus science cannot prove that Naturalism is true or credible.
10.) Thus if Naturalism is correct(true), we can never know it to be correct and there is no reason to accept it as correct.


NB:A v B

~B​

----------

A​

*Had a note to see Alvin Plantinga. Apparently he was the one that thought of this.

 

[Durruck]

Don't get me wrong, I agree completely and function very similarly to you. But most of the people that want to have God proved to them via logic won't accept the premises that you will present for the proof.

At some point, faith has to enter the logical argument. Sure, Paul makes a great statement about logical belief, but it still points back to his faith that Jesus was who He claimed to be. And it doesn't matter how many times that Paul saw Jesus perform miracles, the naysayers continued to refuse to believe that they were real. Your experience doesn't count (to them) if they can't see it for themselves. The problem is that until they learn to listen to God, they continue to believe that they control the power of belief (and it's actually their disbelief that limits them). They will find any other "logical" way to explain away phenomena rather than to accept that there could be an all powerful, all knowing supernatural being.

Yet those same people believe in mother nature, ghosts, divination, etc. Those same people are just short of Baalists and Ra-ists that are talked about frequently through the Old Testament. They just don't realize that they're using a different false god and a different set of masters.

Something to wrap your mind around is the idea that the "faithless" are actually very little different than you and I. They still have faith, tons of it in fact. They just choose to put it into different things. Self-righteousness. Self-sufficiency. Financial freedom. They're all ideas that people have that they don't need anything beyond themselves, that they are powerful enough to control what happens to them. They put their faith into broken ideas instead of one that completes them. That's how they're different. But they still have faith in their idea.

 

[Neirai the Forgiven]

It is mildly amusing how much time and effort is spent trying to prove that God exists or does not, from both sides of the fence.

I've been a member of CGA for 3 years and not once has somebody tried to prove whether or not I exist.

I really appreciate it when I come across Christians who don't even let the question of God's existence cross their minds. I, unfortunately, can't say I am one of them, but I'm trying.

 

[Durruck]

Heh. When someone comes at me with the "logic" argument about proving my own existence, I just tell them to talk to one of the other voices in their head, because I'm already bored with them.

 

[ppar3566]

If Naturalism is true, one must accept the following as true:
1.)The material world is all there is (nothing exists outside the box)
----------------
| Material World| <--look an illustration!
----------------
2.) Everything inside the box must be caused by something else inside the box, i.e. everything is contingent and the result of material causes.
3.) Since nothing can exist outside the box, reason and logic must be 'inside' the box.
4.) Since reason and logic must be inside the box, they must be a result of material causes (and therefore contingent and non-essential)
5.) Since reason and logic are contingent upon material causes, they are not fundamentally true.
6.) Thus reason and logic only 'feel' true because of some material causation (the feeling that logic is true is a chemical delusion)
7.) Thus we have no compelling reason to believe the results of any logical or rational inquiry, because it cannot be superior to superstition (both may 'feel' true)
8.) Thus no real knowledge is possible, including scientific knowledge, since we have no reason to trust science over superstition (though we might prefer science)*
9.) Thus science cannot prove that Naturalism is true or credible.
10.) Thus if Naturalism is correct(true), we can never know it to be correct and there is no reason to accept it as correct.

Yes but there is a standard,even for materialism (on a side note i think it would be worth going to the Dawkins forum just to see how many and varied the opinions are - not all are materialists). In this case the standard is utility, or that which leads to the greatest adaptation to life - this is reason. Individuals holding such a position would never claim there theories to be true, just more true than previous ones. The underlying assumption is that adaptability to the environment is akin to truth and thus the useful a theory the closer it is to objective reaility (a point I disagree on). The other problem as i see it is that reason has been replaced by many atheists by the idea of fact or evidence. Here individuals seek to distance themselves as far from the mode of understanding as possible, with the assumption that distance leads to less bias and thus places there faith in the hope that the scientific method will one day by-pass our biases and show us the world as it is. One thing I have always wanted to say about this is that it seems that for the positivist atheist the fairies at the bottom of the garden have been replaced by the fairies in their own head (I suppose this is the same as what durruck said about everyone has faith, just in different things).

Don't get me wrong, I agree completely and function very similarly to you. But most of the people that want to have God proved to them via logic won't accept the premises that you will present for the proof.

True enough, and you have also presented logical supporting statements in the posts of your i have read. But I want to reiterate my belief this does not mean we should abandon logic ( as a previous thread on this topic in CGA suggested - suggesting we should rely on affect and experience alone). Christians used to be at the forefront of rational thinking (e.g. Lewis) and now we lag so far behind that I sometimes wonder whether Christians reject logical reasoning because they can't play with the big boys anymore. I know I lag miles behind and have just started my way toward wanting to play with the big boys, starting with metaphysics and moving to ascetics. By the time i am 60 I think I will have caught up

Something to wrap your mind around is the idea that the "faithless" are actually very little different than you and I. They still have faith, tons of it in fact. They just choose to put it into different things. Self-righteousness. Self-sufficiency. Financial freedom. They're all ideas that people have that they don't need anything beyond themselves, that they are powerful enough to control what happens to them. They put their faith into broken ideas instead of one that completes them. That's how they're different. But they still have faith in their idea.

Yes this is something I have been interested in for a while. Is there something quantitatively (difference in degree of belief) different about those with faith and those without, or is the difference like you say qualitative (different in kind). I think I hold the methodist position (though I am not methodist - dont have methodist church here from what i can tell) that Jesus death resulted in cosmic changes, one of which was that every person was put on the same scale and thus differences in belief are quantitative. I wont' list my reason why here but it is something that has been bugging me for a while. How does this play out in my life. Well, i dont know how this will go down, but i believe Christ's death restored to everyone a little something of what we were before the fall and that it is that leads people to Christ - what allows for people to believe in the full restoration to come. I see this coming through in every area in life and thus we need to show Christ holistically to non-Christians on the basis of cognitive, behavioural, and affective evidence. People decide for or against Christ on their own, our job is to fill out the evidence (for want of a better word) to assist them by helping to provide a context by which they can make the most informed choice possible.

 

[ppar3566]

I really appreciate it when I come across Christians who don't even let the question of God's existence cross their minds. I, unfortunately, can't say I am one of them, but I'm trying.

See I disagree, I dont see no doubt as particularly more healthy than doubt (I sometimes see it as wholly unhealthy, when some people believe cause they have never really thought of it). If you are in the world and don't live cooped up in a life that almost entirely consists of interactions with other like minded Christians I can't see how you can not have doubts. At univiersity I have seen the various ways in which different ways in which young folk deal with doubt. I am not sure which i think is more unhealthy, those that squash all doubt and refuse to entertain it or think about it in any way or those that throw it away cause it is just easier. My wife and i have some strong doubts but we still believe and i think my faith, though more doubt filled, is the stronger for it.

 

[Neirai the Forgiven]

I really appreciate it when I come across Christians who don't even let the question of God's existence cross their minds.

To clarify, I don't mean they don't have doubts. I mean they don't allow themselves to get embroiled with the question of existence.

For example, I read the book Bono in Conversation. At one point the author (a post-Jewish agnostic) mentions the existence of God. Bono doesn't even try to prove God exists, he simply talks about all the great things God has been doing in his life.

There's no need to prove what is real.

 

[Elader Arkon]

My post was addressing the general atheist view (and usually most common from my experiences. In a way the wannabe pure naturalist atheist is kindof like the general american church: they don't really know what they believe.), in a discussion the path tread would be to find just what they believe, point out contradictions (if any), then dive straight into what the ramifications of their way of belief is.


And Neirai, I'm just the opposite. I tend to find those who haven't questioned the very existence of God haven't questioned much else either. (no offense I'm not referring to you, just people I've known and worked with in general)

 

[ppar3566]

In a way the wannabe pure naturalist atheist is kindof like the general american church: they don't really know what they believe.)

QFT. Though i still think that materialism has an answer to both your and my arguments. If there is nothing beyond the material, then the only 'truth' that matters is that which leads to greater adaption to ones environment (what ever that may mean).

I tend to find those who haven't questioned the very existence of God haven't questioned much else either. (no offense I'm not referring to you, just people I've known and worked with in general)

Yes and the people I have met like this tend to be much more dogmatic and frankly unloving (Bono excluded - though he is hardly the poster boy for religion that I would like).

 

[Odale]

QFT. Though i still think that materialism has an answer to both your and my arguments. If there is nothing beyond the material, then the only 'truth' that matters is that which leads to greater adaption to ones environment (what ever that may mean)....

If you cannot touch it, taste it, hear it, smell it or see it then it must not be real.

If you do not believe (read as if you do not have a Christian mind-set) then you will never be able to touch God, taste God, hear God, smell God or even see God.

Edit: I think that experiencing God falls into all of those categories... lol The 6th sense... except God isn't a dead person.