# Is Modal Logic evil?



## Civbert (Nov 10, 2006)

Please read this article and and the rest before you answer.
Possible world
Here's an excerpt:


> Those who use the concept of possible worlds consider the actual world to be one of the many possible worlds. For each distinct way the world could have been, there is said to be a distinct possible world; the actual world is the one we in fact live in.


 Be careful. This does not mean that possible worlds exist, but that possible worlds could have been.

Now add these premises: 
A *possible world* is a universe as God _could_ have made it.
The *actual world* is the universe God did make.

In a prior thread I included "god" as something within the scope of a possible world. But I'd like us to consider God as transcending possible worlds. Here's another excerpt:


> The idea of possible worlds is most commonly attributed to Gottfried Leibniz, who spoke of possible worlds as ideas in the mind of God and (in)famously used the notion to argue that our actually created world must be "the best of all possible worlds".


I'm not interested in the conclusion that this is the "best possible world" since that's too ambiguous a statement. I just want to consider the idea of possible worlds being the way God _could_ have made the world should He have chosen to do so.

The reason I want to know if the idea of Modal Logic is evil is because I think it can conceptually include a different revelation - a different scripture. It could include God not revealing himself at all. The only thing that a possible world of modal logic requires is God not being apposed to the law of contradiction. From this we can still use the ideas of "possibility", "necessity", and "contingency" as described in the article. 

Intellectually, many will have trouble with the idea of "possible worlds" and God. Some will insist on "actualism". That is - God could not have made the world any different than the way He did. In model logic, Christianity is not necessary - since it is defined by the world as God made it - that is, it included the Scriptures. I don't think the Bible is necessary in possible worlds. Does that make the idea of model logic evil? I'm not sure. It does make it un-biblical. But is not the only alternative to modal logic "actualism" and all it implies?

P.S. Consider Option 3 to read: *Not sure.* I think there _may_ be another alternative way of looking at this.


----------



## tewilder (Nov 12, 2006)

It seems to me that the syntax of modal logic is subject to more than one interpretation. You can take it as metaphysical possibility or you can take it as epistemic. In the latter case it would be reasoning about what is possible or necessary relative to what we know, and thus about the status of our knowledge.

Another way to look at this is with some of the medieval scholastics who would discuss what is possible or necessary relative to the will of God, but not take things as equally open relative to the wisdom of God. (To overlook this is to misunderstand the discussions about pssibility under the will.)


----------



## Civbert (Nov 13, 2006)

tewilder said:


> It seems to me that the syntax of modal logic is subject to more than one interpretation. You can take it as metaphysical possibility or you can take it as epistemic. The the latter case it would be reasoning about what is possible or necessary relative to what we know, and thus about the status of our knowledge.
> 
> Another was to look at this is with some of the medieval scholastics who would discuss what is possible or necessary relative to the will of God, but not take things as equally open relative to the wisdom of God. (To overlook this is to misunderstand the discussions about possibility under the will.)



I think you are correct. I've read more about modal logic and see that it has more applications. I guess I'm looking strictly at the use of modal logic when it speaks of logically possible worlds - and the assumption that the world (actual) could have been different than it is (possible). 

I'm surprised more people have not answered in the affirmative. Does not the implications of modal logic (actual/possible worlds) imply that the bible (the propositions of scripture) is merely a contingent truth. Can we say that revelation, and particularly the revelation given in the Word, is necessary with modal logic? Can we even rightly presume that the God defined in Scripture is necessarily true? Model logic seems to imply that it is logically possible that Christianity false. That is, we can not say Christianity is a necessary true worldview.


----------



## tewilder (Nov 13, 2006)

Civbert said:


> I'm surprised more people have not answered in the affirmative. Does not the implications of modal logic (actual/possible worlds) imply that the bible (the propositions of scripture) is merely a contingent truth. Can we say that revelation, and particularly the revelation given in the Word, is necessary with modal logic? Can we even rightly presume that the God defined in Scripture is necessarily true? Model logic seems to imply that it is logically possible that Christianity false. That is, we can not say Christianity is a necessary true worldview.



In the eighties there was a big stir over possible worlds theory, although in the end it turned out to be another way to say the same old things. Plantinga wrote some stuff on it, perhaps the most peculiar of which was his article "Bringing About the Past" where he argued that it was possible, though unlikely to change the past. I think I recall his example being causing Abraham not to have existed.

But this is old old stuff. In the middle ages people debated whether God was not free to have devised a completely different plan of salvation, for example.


----------



## Vytautas (Nov 13, 2006)

Civbert said:


> Does not the implications of modal logic (actual/possible worlds) imply that the bible (the propositions of scripture) is merely a contingent truth. Can we say that revelation, and particularly the revelation given in the Word, is necessary with modal logic? Can we even rightly presume that the God defined in Scripture is necessarily true? Model logic seems to imply that it is logically possible that Christianity false. That is, we can not say Christianity is a necessary true worldview.



Why would it be a problem that the Bible and Christianity are contingent truths and not necessary truths?


----------



## Civbert (Nov 14, 2006)

Vytautas said:


> Why would it be a problem that the Bible and Christianity are contingent truths and not necessary truths?



It appears to undermine the idea that Christianity is the only true worldview.


----------



## tewilder (Nov 14, 2006)

Civbert said:


> It appears to undermine the idea that Christianity is the only true worldview.



In the first place it is not a question of whether just "Biblical" truths are contingent. If there is no modality then no truths are contingent.

Now, is the fact that I overslept this morning a contingent truth or a necessary one? Is it part of the Christian and Biblical world view that I necessarily overslept this morning?


----------



## Brian Bosse (Nov 14, 2006)

Hello Gentlemen,

Anthony (Civbert) is a friend of mine. He and I see things quite eye to eye. However, on this point I disagree with him. Modal logic is not evil. Modal logic is just a system of thought that can be applied to some given metaphysical system. I can express my Christianity in terms of modal logic. 



> Now, is the fact that I overslept this morning a contingent truth or a necessary one? Is it part of the Christian and Biblical world view that I necessarily overslept this morning?



I would say yes. If God ordains every event, then all events are necessary. Applying modal logic to my Christianity, God is necessary in every world. Since this God who is necessary in every world is the God of the Bible, and since this God of the Bible ordains every event, then every event in every possible world is ordained by God. I would also argue that God neccessarily acts in a manner consistent with His nature. This works out to be that God always acts in a manner that maximizes His glory. Therefore, in the set of all possible worlds, these worlds are worlds in which God's glory is maximized. Is it possible that there is more than one world where God's glory is maximized? Perhaps. If this is the case, then there may be more than one possible world. I tend to think that there is only one possible world. All of this fits with modal logic. So, in what sense is modal logic evil?


----------



## tewilder (Nov 14, 2006)

Brian Bosse said:


> Hello Gentlemen,
> 
> Anthony (Civbert) is a friend of mine. He and I see things quite eye to eye. However, on this point I disagree with him. Modal logic is not evil. Modal logic is just a system of thought that can be applied to some given metaphysical system. I can express my Christianity in terms of modal logic.
> 
> ...



This is what we used to call, in logic class, "collapse into PC". When you try to strengthen modal logic past the Lewis S5 system (as I recall) everything becomes necessary, so there in only predicate calculus and no modal distinctions for a modal logic to take account of.


----------



## Brian Bosse (Nov 14, 2006)

Hello T.E. Wilder,



> This is what we used to call, in logic class, "collapse into PC". When you try to strengthen modal logic past the Lewis S5 system (as I recall) everything becomes necessary, so there in only predicate calculus and no modal distinctions for a modal logic to take account of.



I do not mean to be rude, but I am not sure how this applies to what I wrote. I was not speaking about the systems of modal logic. Rather, my point was that Modal systems can be applied to the axioms of Christianity just like propositional logic, or first order predicate calculus, or second order predicate calculus, etc...can be applied to the axioms of Christianity. I used the following axioms in my previous post: God ordains all events; God is necessary; and God ordains events in such a manner that maximizes His glory. My whole point was to show that Modal logic does not ential that truths regarding God are contigent. 

The following comes from the Stanford Encyclopedia of Philosophy. The most familar family of modal logics begins with the rather weak 'K' system that is basic propositional logic with a necessitation rule and distribution axiom. This system can be strengthened by the addition of the idea that the necessity of A implies that A is actual. This new system is called 'M'. The system S4 is adding to 'M' the idea that the necessity of A implies that it is necessary that A is necessary. The system S5 is adding to 'M' that the possibility of A implies that it is necessary that A is possible. 

Again, Modal logic is just a system of thought that can be applied to many different metaphysical systems. I will grant that the distinctions of modal logic are moot if the actual world is necessary, which I tend to think it is. Modal Logic is not in itself bad. 

Sincerely,

Brian


----------



## LadyFlynt (Nov 15, 2006)

“Sometimes I think the surest sign that intelligent life exists elsewhere in the universe is that none of it has tried to contact us.” Calvin & Hobbes


----------



## tewilder (Nov 15, 2006)

Brian Bosse said:


> Hello T.E. Wilder,
> 
> 
> 
> ...



If everything is necessary there is no point to modal logic, as everything has the same modality. Anything true would also be necessary and possible, and anything false would also be impossible.

But then one wonders about the odd fact that we have the ablity to reason modally. What's that for?


----------



## Brian Bosse (Nov 15, 2006)

Hello T.E.,



> If everything is necessary there is no point to modal logic, as everything has the same modality.



I agree.



> But then one wonders about the odd fact that we have the ablity to reason modally. What's that for?



If you are asking why we reason modally, then my answer would be because we think in terms of necessity and possibility. For instance, I can speak of the necessity of getting either a heads or tails when I flip a coin, and at the same time speak of the possibility of getting heads. Since we make these distinctions someone decided to formalize it. 

Brian


----------



## Magma2 (Nov 16, 2006)

Civbert said:


> Intellectually, many will have trouble with the idea of "possible worlds" and God. Some will insist on "actualism". That is - God could not have made the world any different than the way He did. In model logic, Christianity is not necessary - since it is defined by the world as God made it - that is, it included the Scriptures. I don't think the Bible is necessary in possible worlds. Does that make the idea of model logic evil? I'm not sure. It does make it un-biblical. But is not the only alternative to modal logic "actualism" and all it implies?



While this thread is probably old, smelly and dead, I am curious as to the reason why you’re asking the question? Is it your concern that modal logic when applied to God or the Scriptures by necessity (would that a modal pun) be a denial of immutability? For example, GHC wrote:



> From the immutability and omniscience of God, it follows necessarily that there is indeed no other possible method of salvation-not, however, for the reasons Hodge gives, but simply because of this immutability. In much of this discussion, the authors speak as if God on one occasion produced an act of will and on another occasion he made another voluntary act. The Westminster Standards, however, reproduce the Biblical position that God is immutable. Therefore, not only is the propitiatory method of atonement absolutely necessary, but also the number of mosquitoes in the world at any given instant. Every detail is a part of the all-comprehensive divine decree. God foreordains whatever comes to pass. Everything is necessary. [The Sovereignty of God, http://www.trinityfoundation.org/journal.php?id=54]



I suppose whether it's methods of salvation or possible worlds it makes no difference, but I'm just curious if this is the source of your concern?


----------



## tewilder (Nov 17, 2006)

Brian Bosse said:


> Hello T.E.,
> 
> 
> 
> ...



"To reason modally" = "to think in terms of necessity and possibility". So when you say" "If you are asking why we reason modally, then my answer would be because we think in terms of necessity and possibility. ", what are you saying?


----------



## Brian Bosse (Nov 17, 2006)

Hello T.E.,



> So when you say" "If you are asking why we reason modally, then my answer would be because we think in terms of necessity and possibility. ", what are you saying?



Perhaps, I am being a little pedantic in this post, but I will break it down for you as explicitly as I can. 

*If you are asking why we reason modally…*

I am qualifying the answer I am about to give. How am I qualifying my answer? My answer should only be taken within the context of my understanding of your question. What was your question? It was, “What’s the ability to reason modally for?” My understanding of this question is the bolded antecedent above. 

*…then my answer would be…*

Now that the qualification is laid out, I am now going to give my answer. Again, this is only within the content of my understanding of your question. If I misunderstood your question, then my answer may or may not be applicable. If I have properly understood your question, then my answer is applicable. (Note: This a subtle example of 'possible' and 'necessary'.) 

*… because we think in terms of necessity and possibility.*

The reason we reason modally is because we use concepts such as ‘necessity’ and ‘possibility’. We may even do this necessarily.  I gave a subtle example of this above using 'may or may not apply' versus 'is applicable'. Here is a more explicit example: If we flip a coin, then we know that we will _necessarily_ end up with either heads or tails. At the same time we know that we _possibly_ will end up with heads. Since we think in terms of ‘necessity’ and ‘possibility’ as was just illustrated, then someone decided to formalize it. Wala! Modal Logic was born. It is no different from someone formalizing sentential connectives such as ‘and’, ‘or’, ‘not’, ‘if…then…’, etc… bringing into existence propositional or sentential logic. 

Brian


----------



## tewilder (Nov 17, 2006)

Brian Bosse said:


> Since we think in terms of ‘necessity’ and ‘possibility’ as was just illustrated...



Why do we do this?


----------



## Brian Bosse (Nov 17, 2006)

Hello T.E.,



> Why do we do this?



I suppose it is because we are rational creatures. I am not sure I understand where you are going with this, if anywhere. Are you leading to a point, and if so, does the point have something to do with Modal logic being evil?

Brian


----------



## tewilder (Nov 19, 2006)

Brian Bosse said:


> Hello T.E.,
> 
> 
> 
> ...



If there are no modal differences in reality, would reasonning modally be the mark of an _irrational_ creature?


----------



## Brian Bosse (Nov 20, 2006)

Hello T.E.!



> If there are no modal differences in reality, would reasonning modally be the mark of an irrational creature?



It is not clear what you mean by there being no modal difference in reality. I suspect you mean this:

If every event is necessary, would the event of reasoning modally be the mark of an irrational creature?

Consider this: God ordains that when I reach into a bag made up of one green ball and one red ball that I will grab the green ball. It is _necessarily_ the case that I will grab the green ball. However, I don't know this - only God does. What I do know is that if I reach into the bag I will _possibly_ get a green ball. Even if I believe that every event is necessary, I only know what the necessary outcome is regarding my grabbing a ball _after_ it has happened. Prior to the event I can only speak of possibilities. So, it is not the mark of irrationality to think in modal terms in a universe where every event is necessary. 

Brian


----------



## Civbert (Nov 20, 2006)

Magma2 said:


> While this thread is probably old, smelly and dead, I am curious as to the reason why you’re asking the question? Is it your concern that modal logic when applied to God or the Scriptures by necessity (would that a modal pun) be a denial of immutability? For example, GHC wrote:
> 
> I suppose whether it's methods of salvation or possible worlds it makes no difference, but I'm just curious if this is the source of your concern?


I actually hadn't thought of God's immutability (that is an interesting point though). And I'm not terribly concerned about modal logic being evil. My questions were made to start people thinking about they way we reason and the limitations of reason for finding "ultimate answers" like is world-view X true. I don't think we can really know all the ultimate answers. 

But I'm interested in how many Christians seem to believe there is something sinful about asking the "unanswerable questions." Even David seemed to say that it is wrong to ponder things too great for us to really know. 



> Lord, my heart is not haughty, Nor my eyes lofty. Neither do I concern myself with great matters, Nor with things too profound for me.
> (Psa 131:1 nkj)



What got me interested in the modal logic was Paul Manta's coming out of the TAG closet. I'll need to find the thread and link to it. I started to read more about modal logic on the scope of "possible worlds" and found that if we consider anything to be sufficient if it is logically coherent in some "possible world", then there is very little left that is "necessarily" true. This seems to be a challenge to those who want to believe their worldview is the only possibly valid worldview. 

Interestingly enough, Brain Bosse started bloging on Van Til's apologetic method. I don't think I read his blog before I read about "possible worlds" in modal logic - but you can see how it is relevant. The only way to validate the TAG is by proving the improvable using modal logic - that only Christianity provided the necessary preconditions of intelligibility. That is, no other worldview "possibly" valid. 


Brain, 

I know... I still haven't responded to your posts. I'm just getting the easy answers out of the way first.


----------



## Civbert (Nov 20, 2006)

P.S. Doesn't Calvin also warn against asking questions we can not answer? I don't know where, but I read it in Calvin's Institutes somewhere regarding knowledge.


----------



## Civbert (Nov 20, 2006)

Brian Bosse said:


> Hello Gentlemen,
> 
> Anthony (Civbert) is a friend of mine. He and I see things quite eye to eye. However, on this point I disagree with him. Modal logic is not evil. Modal logic is just a system of thought that can be applied to some given metaphysical system. I can express my Christianity in terms of modal logic.



I know you agree with me. It's just a matter of getting you around to my point of view. 

But, no, I don't really think modal logic is evil. But it does bring up some uncomfortable issues. 




Brian Bosse said:


> I would say yes. If God ordains every event, then all events are necessary. Applying modal logic to my Christianity, God is necessary in every world.
> Since this God who is necessary in every world is the God of the Bible, and since this God of the Bible ordains every event, then every event in every possible world is ordained by God.


But only by first taking Christianity as a given.



Brian Bosse said:


> I would also argue that God necessarily acts in a manner consistent with His nature. This works out to be that God always acts in a manner that maximizes His glory. Therefore, in the set of all possible worlds, these worlds are worlds in which God's glory is maximized. Is it possible that there is more than one world where God's glory is maximized? .



That's very interesting because it sounds a lot like the Leibniz quote in the article I liked too at the start, that this is the "best possible world". I must ask - is it? Must it be? And if we say God has created this world to maximize His glory, are we not presuming the God of Scripture? Are there not other definitions of God wherein God is not interested in maximizing His own glory. Some would claim that ultimately, God wants to maximize the happiness of mankind. Not me though! I don't think this is the God of Scripture. But then, I'm assuming Scripture again. So the position is only provably true from within my own worldview.



Brian Bosse said:


> Perhaps. If this is the case, then there may be more than one possible world. I tend to think that there is only one possible world. All of this fits with modal logic. So, in what sense is modal logic evil?



I don't really think "modal logic" is itself evil. But I do think modal logic and "possible words" do make things less sure. When arguing for the case of a particular "world-view" using the modal idea of "possible worlds", one can not assume that particular worldview to prove that worldview is necessarily true.


----------



## tewilder (Nov 21, 2006)

Brian Bosse said:


> Hello T.E.!
> 
> 
> 
> ...



It is really a very simple point, and entirely obvious. If, as some people suggest, everything is necessary, why did God create us with the ability and proclivity to think in terms of a contrast of possibility and necessity (if, in fact that is what modality is, as is the standard interpretation)?

Why do our minds work in terms of a distinction that, according to some, is not merely false but impossible?


----------



## Brian Bosse (Nov 21, 2006)

Hello T.E.,



> If…everything is necessary, why did God create us with the ability and proclivity to think in terms of a contrast of possibility and necessity…?



There is a distinction that is relative of the perspective of the being. God ordains that tomorrow when I reach into the bag hanging on my door containing only a green ball and a red ball I will grab a green ball. God knows this will necessarily happen. I, on the other hand, am not privy to God’s plan and as such do not know this. However, I do know that there is one green ball and one red ball in the bag. I do know that if I reach in the bag tomorrow and draw out a ball that I will necessarily get a green ball or a red ball. This true. Consider this logical argument:

G(B)→(G(B)∨R(B)) – if it is necessarily the case that Brian will grab a green ball, then it is necessarily the case that Brian will grab a green ball or Brian will grab a red ball. This follows by the logical law of addition. 

To stay consistent with the above illustration, I do not know G(B). However, I do know (G(B)∨R(B)). I know this not because of God’s ordination, but because of logical necessity. That is to say, if there are only two ball(s) in the bag, then it is necessarily the case that when I grab one it will be one of the two ball(s). Based on this, I can validly say this…

(G(B)∨R(B))→◊R(B) – if it is necessarily the case that Brian will grab a green ball or a red ball, then it is _possibly_ the case that Brian will grab a red ball. The basis for this knowledge is the logical necessity involved and not God’s ordination. If I knew that God ordained G(B), then I could not validly conclude ◊R(B) even though I knew there were only two ball(s) and one was red. The whole point here is that based on my epistemological limitations (or, epistemelogical perspective) as a creature, I reason in terms of necessity and possibility even though God ordains every event. As was demonstrated above, this follows logically. 



> Why do our minds work in terms of a distinction that, according to some, is not merely false but impossible?



Our minds work in terms of what we know. The epistemological limitation of not knowing all events ordained by God leaves us rationally thinking in terms of necessity and possibility rather than just necessity. 

I still do not understand what the problem is. Are you struggling with the idea that God ordains every event necessarily? 

Brian


----------



## tewilder (Nov 22, 2006)

Brian Bosse said:


> Hello T.E.,
> 
> 
> 
> ...



You are using "necessity" for logical implication. We already have first order logic to cover that. We don't need modal logic. Since everything that is true is necessary and of course everything that is necessary is true, there is not distinction, and nothing for modal logic to do.


----------



## Brian Bosse (Nov 22, 2006)

Hello T.E.,

If your sole objection is pragmatic, then consider this very practical use. As a practicing presuppositional apologist, I speak in terms of _possible_ worldviews. There is the set of _possible_ worldviews, which contains as one of its elements the Christian worldview. From there I argue that out of this _possible_ set of worldviews only Christianity can provide the _necessary_ preconditions for intelligibility. That is to say, if intelligibility is required, then the Christian worldview is _necessary_. Modal Logic is very helpful with this method of argumentation. 

Brian


----------



## tewilder (Nov 23, 2006)

Brian Bosse said:


> Hello T.E.,
> 
> If your sole objection is pragmatic, then consider this very practical use. As a practicing presuppositional apologist, I speak in terms of _possible_ worldviews. There is the set of _possible_ worldviews, which contains as one of its elements the Christian worldview. From there I argue that out of this _possible_ set of worldviews only Christianity can provide the _necessary_ preconditions for intelligibility. That is to say, if intelligibility is required, then the Christian worldview is _necessary_. Modal Logic is very helpful with this method of argumentation.
> 
> Brian



What you have going is another case of collapse into Predicate Calculus. In your usage "necessity" simply means 
"a theorem of first order predicate calculus", in which case there is no need for modal (second order) logic.


----------



## Brian Bosse (Nov 23, 2006)

T.E.,

I did not use any predicate calculus or for that matter modal logic. All I did was put forth an argument in informal terms using 'necessity' and 'possibility'. Once I have done this, then I can go back and put it into formal terms using modal logic. If you do not want to use modal logic, then fine. Don't use it. Modal logic is a fairly recent system. However, it is very useful in the above apologetic approach. I never said it was necessary. In fact, I have been defending the idea that it is rational. Even now, I do not understand your beef. Are you saying that we can live without modal logic? If so, then I would argue that we can live without first (or second) order predicate calculus, which, too, are fairly recent.

Brian


----------



## tewilder (Nov 25, 2006)

Brian Bosse said:


> T.E.,
> 
> I did not use any predicate calculus or for that matter modal logic.



So? You said "logical necessity", i.e. provable in the predicate calculus. That is how you defined necessity. Who cares if you went on to "use" it.



> All I did was put forth an argument in informal terms using 'necessity' and 'possibility'. Once I have done this, then I can go back and put it into formal terms using modal logic.



Modal logic is second order logic, generally thought to be about possibility and necessity. You have interpreted possibility and necessity as provabiltiy, i.e. first order logic. There is no use left for modal logic. It is pointless.



> If you do not want to use modal logic, then fine. Don't use it. Modal logic is a fairly recent system.



No it isn't. See, for example, Ockham's _Summa Logicae,_ e.g. Part II "On Propositions, section 9 "What is required for the Truth of Modal Propositions".



> However, it is very useful in the above apologetic approach. I never said it was necessary. In fact, I have been defending the idea that it is rational. Even now, I do not understand your beef. Are you saying that we can live without modal logic? If so, then I would argue that we can live without first (or second) order predicate calculus, which, too, are fairly recent.
> 
> Brian



Not it is not useful. It is only confusing as you have already suffered collapse into PC, but you use of modal notations might mislead people to think that you hold to modal distinctions. 

Now, even so, I can think of two other uses for modal logic, but you are not using it for either one.


----------



## Brian Bosse (Nov 25, 2006)

Hello T.E.,

I guess we will just agree to disagree, even though I still am not sure what your beef is.

Brian


----------

