GAH! <-> not just ->
erislover: Free will may be nothing more than a collection of neurons in the prefrontal lobe of the brain that respond to certain inputs. For example, someone reminds you that you didn’t feed the cat as you said you would. You feel guilty; guilt feels bad and you want to feel good, so you do what you believe is necessary to feel good again: You go feed the cat.
Why is mysticism required to understand how this works?
Using words like “forbidden” and “compulsory” seems to confuse things. There is only a way things are, and true statements correspond to that way things are. Everything that occurs had to occur, or else it wouldn’t have occured. If that makes everything that occured “compulsory” by your language, then I agree.
The idea that “everything which is not forbidden is compulsory” is not at all problematic as I see it. Commonly we think of something like a pebble falling off a local cliff or overlook as something that isn’t forbidden, since we know such things tend to occur. It would indeed be the height of folly to suppose that the pebble must fall just because common laws of physics don’t prevent the isolated incidence of it falling. This would be to confuse the common notion of forbidden (i.e. not inconsistent with physical laws) with the causal sense of the word (i.e. lacks sufficient cause.)
Take the pebble on the cliff for example. With our general lack of information about the forces at work on the cliffiside, we are tempted to say that such a thing is not “forbidden”. However, the pebble will only fall if sufficient cause leads to that event. I will gladly say that it is “forbidden” for an event to occur without sufficient cause.
So under that interpretation of “everything which is not forbidden is compulsory”, the interpretation that most fits what I claim about the world, I agree. So if we boil that statement down with some definitions…
- An event is “forbidden” if it lacks sufficient cause, since that lack will prevent it from occuring.
- An event is “compulsory” if it has sufficient cause, since that will compel it to occur.
- An event either has sufficient cause or does not have sufficient cause. (law of excluded middle)
C. All events must be either “forbidden” or “compulsory”
If that’s how you’re reading what I said, then I agree completely. If you care to deny that argument, than show me either…A) an event that occurs without sufficient cause, noting that I make no claims about the materialistic origin of the cause…or B) demonstrate that the attribute of “being caused” cannot be related to an event.
Then, Rex, I think you should be pretty much compelled to accept modal logic, which also doesn’t say how the chess game will be played, it only puts a byunch of boards out and notices a king exists on all of them.
That is, God.
That is,
Though, heh, that should be “4”, no? 
anyway, everything is either forbidden or compulsory allows modal logic to work the way it does here, by saying that
<>G<-> G || ~G
which does not follow the normal use of “possible” in the sense of “Will you make it to the bank today?” ; “It’s possible.”
Either that or it is senseless to speak of the future, which is an interesting notion in itself (since the future “isn’t”).
jab
Well, I’ll invite you right out of this thread and into this one, then, where I eagerly await a description of feeling from a materialist perspective. 
Once again, I hate the hocus pocus arguments and 50 cent words that seem to rise up every time someone tries to sell you a load of horse doody.
Since Lib is taking the high esoteric and academic path with the professional philosophers and whatnot (professional philosopher?) I’ll take the low road an play the brutalist.
You’re palming a card Lib. They game is rigged, and the modal mode just a bit of hinky misdirection, a two dollar parlor trick that even Penn & Teller would be ashamed to pull.
Your definition is false. The God you define isn’t the God everybody else is talking about. In fact I say your God isn’t even a God at all. At the very best he’s a minor league demigod from a minor pantheon. The kind of God Hermes would kick around, the butt-end of all Gods. More likely the God you define is nothing more exciting than a plate of cold beans.
Since when does possible come into the criteria for Godhood?
The way we figure it out here in detention and without the help of no Professional philosophers is that if you can’t do something impossible then you ain’t no God.
Your miserable, little puny philosopher’s God is constrained by the possible. Big whoop. I can blow a quarter out of my nose at 40 mph. I’ll bet your God can’e even do that.
The God of your proof can’t do half the stuff that it was in the Bible. I therfore say that it ain’t God. In fact I know who it is. It’s Fred isn’t it?
All you proved was Fred. I know about him already, and let me tell you. Fred ain’t no big deal.
erislover let me try to explain why what I argued isn’t compatible with modal logic. I use “v” for “or”, that’s how I was taught. I’ll use parentheticals to group to avoid confusion of operating order, and parenthetical notes. This is my first time trying this out, and it’s taken me awhile to work through this, I’m out of practice:
- X -> X (everything that occurs is compulsory)
- ~X -> ~X (everything that does not occur is forbidden)
- X v ~ X (excluded middle)
- X v ~X (from 1 and 2)
- X v ~X (excluded middle)
- ~X <-> ~X (from 4 and 5)
At this point, I’ve concluded that for any statement about the world, that statement is either necessarily true or necessarily not true. I have also equated “not necessarily X” with “necessarily not X”. Now I’ll use some modal logic relations:
- X -> <>X (if X is necessary, then it must also be possible)
- ~X -> ~<>X (if it is necessary that ~X, then X is not possible)
Those are basic concepts of the relation between possible and necessary as I understand you use them. Now, for “possible” to have any use at all in philosophy, there must be at least one X for which X is possible but not necessary…so suppose premise 9:
- (<>X and ~X)
- ~X (from 6)
- ~<>X (from 8)
- <>X and ~<>X (a contradiction)
Since premise 9 leads to contradiction, it cannot be the case, therefore:
- ~(<>X and ~X)
- <>X -> X
- X -> X
- <>X -> X (from 14 and 15)
Premise 13 is merely “for no statement X can X be possible and not necessary.” This flows from my original two premises that represent what I think of the world. Thus, every X that is possible must be necessary. This means that anything that is possible exists. “Possible” as you use it to describe possible worlds means a proposition that could be true, but sometime isn’t. From what I’ve figured in the argument above, that can never happen. So, for someone who adopts my first two premises, possible never describes the situation it purports to. I must conclude it is meaningless. Things that don’t exist cannot be thought of as being possible. Possible worlds don’t exist, so they cannot in fact be thought of as possible. Possibly true, necessarily true, and true all mean the same thing. There is a way the world is, and only discussions referring to that world and how it really is have any meaning.
As an aside, I suppose this ontological argument for God must do something similiar along the way to arrive at <>G -> G. Obviously I disagree with that, since my attempt to work this modal logic above was simply a way of showing that the conclusions such logic leads to appear meaningless to me.
Well, you’ve presented this argument before, I pointed out quite a few places where the argument is not only unsolid but invalid as well. But in the vain hope that you’ll listen this time:
How so?
How do you compare two possible existences to see which is “more” possible"? What if there are two that are equally possible.
The word “possible” is ambiguous.
Oh, and I should have written to followup to 16:
~X -> ~<>X (modus whateverthehell)
That was what I was trying to say at the end anyways.
No duh.
Try this:
*^^^>>>*X~~
You know when I first saw this thread title I thought it was “Are Masturbation and logic incompatible?”
Now I’m wondering if they’re the same thing.
Step 6 does not follow from steps 4 and 5. What you’re claiming is that ((A v B) & (B v C)) -> (A <-> C), which is obviously false: if B is (D v ~D) and C is ~A, then your hypothesis is true and your conclusion is false. Care to try again?
Colibri
In “normal parlance”, survival of the fittest is natural selection, but biologists, when using the term, don’t mean the same thing as armchair science critics who acquired their knowledge of Tennessee v John Scopes from movies like Inherit the Wind.
Here’s an introduction to modal logic, hosted by Stanford University. There, you’ll see that possible and necessary have strict and formal meanings. And certainly, possible does not equal necessary. So, I am using the standard definition of the two words as they are used in formal logic.
Possibility is truth in at least one world. Necessity is truth in all possible worlds.
Ultra
That’s certainly right. In fact, replace God with “Yiznetsin” and it’s equally unremarkable so long as Yiznetsin is defined as the greatest possible existence. That’s why symbological systems are so useful — it is impossible to equivocate since your definitions are always carried forward through your tableaux.
Absolutely. Likewise, the conclusion of an invalid argument may be true even if every axiom is false and not one inference follows from another.
That’s right, except that I wouldn’t say that possibility is undefined; it is merely underived. It’s defined as truth in at least one world.
No. It makes use of strict definitions of both possible and necessary. A statement is possible if it is true in at least one world. A statement is necessary if it is true in all possible worlds. Here are a couple of examples:
“A=A” is a necessary statement.
“Parallel lines do not intersect” is a possible statement.
You are most certainly in error, sir, for two distinct reasons. First, proposition 5 is most definitely an exclusive “or”, for such is the nature of the law of excluded middle. So is proposition 3, “X v ~X”, from which proposition 4 follows straight to form, so it is also exclusive. In which case A v B means A -> ~B, since it is an exclusive “or.” With exclusive “or”, ((A v B) & (B v C)) -> (A <-> C) is in fact true.
Your example makes B a proposition that is always true, that’s OK. What’s not OK is that it defines C in relation to another element of the statement, so it is not a proper substitution. If we are to apply your form to the elements of my argument that you call into question, then B is the element common to both propositions, namely X. So the other two elements, A and C, are ~X and ~X. You then go on to define C in reference to A, for some arbitrary reason, making it ~A. No matter how you assign the letters, you are making a bad substitution. You are handwavingly assigning C a value of ~A, which is not appropriate to my terms. Are you saying that for some legitimate reason ~X is assigned by you a value of ~(~X), or that ~X is assigned a value of ~(~X)?
Let me further illustrate this in case you don’t understand why your substitution is bad. If I say:
A -> B
A
B
…that is a valid argument. You can’t just reply with…
Oh yeah? Well, let B = ~A, then
A -> ~A
“Hahahahaha, I fooled you, try again!!!”
It’s an improper substitution, plain and simple.
Scylla and Jab
God was defined for the tableau as the greatest possible existence (which itself is the definition of necessary existence). I think it is clearly demonstrated on its face that that which is the greatest possible is possible, unless you would care to show how A = not A.
If you mean what you say, then abandon your position; otherwise, show how that which is the greatest possible is not possible.
For noncontradiction, I reckon. You may define God however you wish (and clearly, you do) and develop whatever tableau you like. For this tableau, however, God is defined as necessary existence. And that means that He exists in all possible worlds.
If you think that some entity other than one that exists in all possible worlds merits the designation “God”, then please explain why. And if you think that there is some greater entity than the greatest possible entity, then please describe it.
Once again, I cannot imagine a more accurate definition for God than that entity for which there is none greater. And once again, I wish you would explain what entity might be greater than the greatest one.
PT Barnum sold horse doody using widdle biddy words to people who thought Newton’s laws were hocus pocus.
Do you have another choice?
Said the creationist to the evolutionist. Honestly, Scylla, if you simply said “I don’t understand this stuff”, I could respect your position. But when you say “I don’t understand this stuff, and therefore it is hooey”, I can’t take you seriously.
What is superior to that which is the greatest?
You’ve got the contingency reversed. It seems reasonable to me to assume that God and truth are compatible. Worlds in which statements may be both true and false (A = not A) are not possible.
I see. Well, that would explain right much.
You leave me torn by ambivalence. Should I be delighted that you can form an argument no more compelling than a squint-and-grunt, or should I feel sorry for my materialist friends who must deal with your being on their side?
If you prefer to call the greatest possible existence “Fred”, I have no problem with that. What matters isn’t the word but the meaning that it carries.
Sadly, I believe you.
Okay, Scylla. You can stop staring at me now and eat your checkers.
Are materialism and logic incompatible, or are materialism and possible worlds theory incompatible? I think you asked the wrong question.
No matter how much faith you have in them, possible worlds are not part of all logic. They are a part of modal logic, but modal logic is particularly unsuited to be used to describe the validity of statements such as “god exists.” If you expect anyone to accept this proof, you must first explain why modal logic is the best form of logic to determine the validity of such a statement.
In any case, this proof is both flawed and meaningless.
This thread actually shows the flaws of the proof better than any of the arguments I have seen before. The proof does in fact contradict materialism. It assumes that there are things that are “possible.” The question that comes to my mind is: is modal logic incompatible with materialism? It clearly is. Is that not a point against modal logic, rather than against materialism?
RexDart makes the clear case that everything either is, or is not. There is no possible. If all the causes for anything were known, it would be clear that it was inevitable. If there are no random forces, everything that is, is necessarily. The proof would obviously fail. Presumably the followers of modal logic would attempt to bring up examples of random forces. But can they prove that there are completely random forces at work? Even in that highly unlikely case, could they prove that those things which could have happened, but did not, have any implications on the real world? If not, the proof fails. It is logical to conclude that everything has a cause, until it is proven otherwise.
Eris brings up the question of free will. I have gone over this before, but once again, I am baffled by how people think random forces are necessary for free will. Exactly what is your definition of free will, that it relies on chance? If a decision is based on chance, wouldn’t that mean that it was not based on free will?
As for why the proof is meaningless, you have to go back to the definition. God is necessary existence and he is the greatest possible. Both these terms rely on the concept of “possible”, and therefore in order to even be coherent you would first have to disprove materialism before attempting the proof, but aside from that there are other issues. The concept of “greatest” is similar to concepts such as “eternal.” You cannot speak of something as the “most eternal.” It is dangerous to modify such terms if you wish to make sense. In fact “greatest possible” only makes sense if something is the absolute standard. For example, the greatest possible power can only refer to something that contains all power. The complete scope of existence contains all existing power. Is there any reason to believe there is an entity apart from all of existence that contains all existing power? No. Therefore “god” is indistinguishable from “existence.” So, the conclusion is “existence exists.” Not a conclusion with many religious implications.
RexDart: My substitution most certainly is valid. If you don’t believe so, provide a citation. However, if you’re using “v” to mean exclusive or, then you’re using non-standard notation without telling us, which isn’t nice.
You are correct in that this is true if you’re using an exclusive or, but once again, shame on you for not telling us.
There’s nothing wrong with that substitution. Consider the argument you get by that substitution:
A -> ~A
A
~A
Recall that a valid argument is one in which the conclusion is true if all the hypotheses are true. Since the hypothesis of that definition is false, it is vacuously satisfied, and the argument is valid.
Question: is there a possible world where the greatest possible existence is none at all? If a barren world is possible, then then the proof can be valid but otiose. What counts as a possible world?
It’s close to A and !A, but not. It’s A, but A is uninteresting. It’s also close to Scylla’s ugly anti-intellectual critique. In the other thread I callled the axiom portmanteau and vague. It wasn’t just a grumpy drive-by. What counts as a possible world? What doesn’t? What counts as existence? The fleeting? The known? If in a possible world the greatest possible existence is that which shuns the light for a millisecond in the company of no sentients - or even life forms - does that count?
But, yeah, given I don’t understand what qualifies as a “possible world”; what can qualify as a “God”; nor what “existence” is; the proof looks valid.
That being said, Lib, I do appreciate that you (i) have a serious agenda; and (ii) usefully test some oversure types here.
Smogily,
I know next to nothing about modal logic, but I did want to address a something I found in this thread.
At least one poster suggested that a proof of the divine necessitates that the material world does not exist. I would take issue with this. My religion teaches that the divine is an inherent quality of the physical world, a hidden aspect of it. I do not see how the divine and material would be mutually exclusive.
As regards the OP, I don’t find it surprising at all that two different methods – modal logic and materialism – with two different definitions of “truth” should arrive at two different conclusions. I believe both methods are useful in understanding the world but blind if taken in exclusivity. Truth is best understood through a multiplicity of methods, which requires that one accept that these methods will occasionally contradict.
Fair enough. I admitted it had been awhile since I’d done this sort of formal logic. I figured that an “or” statement founded on the law of excluded middle was obviously exclusive, since ~(A&~A) is always true.
If it’s still valid after that, then you really didn’t defeat my argument with your so-called substitution, did you?
As an aside, I’m curious if an argument in which the premises can never be true could ever be valid. I agree a valid argument is one in which the conclusion is true if all the hypotheses are true, but that can never be tested with the argument above since A -> ~A will never be true for any A.
If an argument form contains three elements labelled A, B, and C, and defines relationships between those elements, it certainly seems like one ought not be able to substitute by defining one of those terms in relation to another term outside the relations already established. A, B, and C represent distinct propositions, if they were meant to be negations of one of the other propositions you’d use that relation in the first place.
Using your methods I can appear to disprove the transitive principle:
A = B
B = C
A = C
Let C = ~A, substitute…
A = ~A
I haven’t actually disproven it, since if A=B then B most certainly cannot ever equal ~A. Since B has already been defined as equal to A, how can you call substituting ~A for B a valid substitution? What I’ve really done above is artificially alter the argument such that one of it’s premises can never be true. It’s the same handwaving trick you used on my argument. I defined three elements in relation to each other, then you just waved your hand and substituted for one of the elements with a negation of another element.
What you really did wasn’t a substitution at all. It was a new line of argument. To take the simple example as above, it’s as if you saw A=B, B=C and then added a new line C=~A.
I haven’t the first bloody clue where I could find a “cite” for this online. If somebody who knows about this sort of thing can pipe up, I’d appreciate it.
Anyways, it’s all moot since with the exclusive “or” my argument is alright anyways, correct?