—t appeared to me that you had not read what you quoted from me, so I responded with a rather bad joke.—
Of course, you could have just not understood what I was saying (which, like any misreading, could be either your fault or mine). But if you suspected so, it would have been more informative (though less funny) to explain what I appeared to have misread.
To restate what I meant in that post: it was essentially, I think there is something strange going on with the usage of “possibly existing” when it is applied to a being that has already been defined as “necessarily existing.”
— I apologize. I ask that you allow me to respond to you in the morning (assuming that I am still allowed to post).—
You can respond to me long after I’m dead, and I wont think ill of you. The response matters to whomever gets to read it.
Indeed, I wont think ill even if you never respond. I’m well used to being the only poster in a thread who has to deal with hundreds of posts clammoring for attention.
I apologize for being flippant at first in the original thread (whether or not I actually was, I can’t remember), but at the very least I didn’t find the arguement as interesting then. Now I do, and you have definately done much to make it an interesting subject well worth lots of thought.
So now, I am working under this assumption that I try to hold when debating with someone: that they are the sort of thinker who has, and will always continue to, look for fatal flaws in this and every arguement, play devil’s advocate every chance they get, and if any are found, will be elated at an incredible discovery, regardless of the conclusion. And, indeed, the primary reason they are arguing for the arguement in this particular case is not ultimately just because they believe it to be true (though they may be quite assured of its truth), but rather that they think that it is well worth defending its truth whenever others reject it unfairly.
Whether this particular arguement is successful or not, I would caution anyone who thinks that it is not important or worth, say, a few lifetimes worth of thought (as many have devoted to it)
Libertarian, I’m still not sure why the argument presents a problem for materialists. (But other than that I think we are on the same page.)
I agree.
We even said, and agreed on, this very thing on page three.
But as I said I’m not sure why this argument “presents a problem for materialists.” As we have agreed, the argument might (or might not) imply that the material universe is God[sup]1[/sup]. I think this meshes quite well with materialism. Just as the argument might (or might not) imply that a Greatest Possible Being (In English) is God[sup]1[/sup]. I think this meshes quite well with many theologies. I can’t really see where it presents a problem to either. (Other than that a few materialists might object, on a superficial level, to using the term God to describe the material universe. :))
[sup]1[/sup] The Greatest Possible Being (In Modal Logic).
(As a side note I just wanted to thank you for the time and effort you’ve put into this thread by sticking with it (much to the detriment of your typing fingers no doubt :)), and you’ve even learned me some new words. :))
One other item about this proof that came to me last night seems illogical, please consider it for a moment, if you can.
The proof states that God, if he exists in any world must exist in all worlds. The axiom states that is it possible for God to exist. The axiom is then said to mean that God does in fact exist in one world of all possible worlds, and by extension, God exists in all worlds.
Can this axiom not be changed? My new axiom states that it is possible for God to not exist. This is not necessarily a direct reversal of the original, but is most certainly a statement as reasonable as the original. For God to not exist in one world must mean that he does not exist in all worlds, because of our definition. There cannot be one world without God unless all worlds are without God.
I am just placing “no God” in the axiom where “God” is now. It does not state that God is forbidden to exist, just that the “no God” state can exist somewhere. If the “no God” state exists somewhere, it must exist everywhere.
An eminently fair question (although I’ve answered it several times already). I’ll try a different approach.
Definitions are recursive statements that identify. Or, as American Heritage puts it, a definition is “A statement conveying fundamental character.” If you identify a pickle as as the greatest possible existence, then I have no quarrel with that except that I have to wrench my mind into an unfamiliar gear and struggle to remind myself that by the sounds “pick” and “le”, you mean Supreme (greatest possible) Being (existence).
God happens to be a more satisfying term to me because it is more familiar as a sound that signifies what it is intended to define. See American Heritage for the entry on Supreme Being. It says, simply, “God”.
Whoa, Eris! I’m glad you reminded me. I’ll go back and pick up your post. (I know you meant no harm, my friend. :)) I just hope that I can catch up with these today because next week I’ll be out of the loop. (I picked up a nice fat contract and have to begin work on it!)
(I’m didacting some of your post in deferential respect for what I know your intentions to be.)
Yes, is equivalent to ~<>~. But ~<> isn’t. The reason it has to be compatible is that we started by describing (defining) what we’re talking about. If we proceed by talking about things that are not compatible with what we said we would be talking about, then we run the (practically certain) risk of developing an invalid proof.
You’re certainly free to put that into a proof if you wish; it’s just that it doesn’t fit here.
I make no bones about the fact that the proof sets out from the get-go to prove God’s existence. Please understand that, when Anselm first pondered the notion that “God is that for which no greater can be conceived”, his intention clearly wasn’t to drop a random postulate and start drawing inferences to see what would happen.
I think that it’s possible that some people (like DrMatrix, for example) are confusing the assumption of a result with the desire for a result. Sure, it’s a brazen attempt to prove God’s existence, but so what? Most deductive (and inductive, for that matter) exercises work exactly the same way. We have in our minds, before we begin, a hypothesis. We think to ourselves, ‘Here’s what I suspect, now let me see if it’s true’.
If we’re honest, we will not break the rules nor invoke any suspicious elements into our endeavor. But neither are we kidding ourselves into believing that we don’t have a hoped for goal in mind. There are a few rules that concern negations (precious few, but they are there nonetheless). If it piques a man’s interest to see whether he can prove that God does not exist, then I tell him to proceed.
But <>~G won’t even help him in that regard because it does not contradict <>G. It does, however, fail to convey in any sensible manner that which is defined as a means to carry the argument forward. I’ve flirted with it. Tisthammer has flirted with it. And I reckon that most logicians have flirted with it. But there doesn’t seem to be any valid way to carry forward to a conclusion of ~G except by beginning with a definition of God as ~G. And for my money, that would be the definition that would open itself up to cries of the greatest possible spoon and whatnot.
The definition is this: G = G. The definition is a recursive statement intended to identify on the right what we are talking about on the left.
The axiom is this: <>G. This is intended to be a starting point on which most reasonable people (including all but hard atheists) might reasonably be expected to agree.
The first inference is this: G -> G. This is intended to be a wiff (a well formed formula) that expresses the definition as an implication, something like this: “When we speak of G, we mean G; so if G is true, then G is true as well.”
The quote in question is this: “that God exists — having been defined as necessary existence — in at least one world”.
The problem is that, incredible as it may seem, necessary existence does not imply actual existence (though it does imply possible existence). Put in plain language, the assertion that something is true in every possible world does not make it actually true in any world. It could be a lie. If necessary existence directly implied actual existence, then I could say “All crows are white” and use that to prove that the crow in your backyard is white. Maybe it is and maybe it ain’t, but in order to prove that your crow is white, I’m going to have to examine not just necessity, but possibility.
Absolutely. When all is said and done, at the end of the day, I cannot prove that God exists without many underlying assumptions, not the least of which is that He does exist. Even defining Him as G presumes His existence in that sense.
But wait, that happens to be true of everything under the sun. Logic itself is a tautology, presuming its own truth. And you will recall the early days when I insisted (and still do) that it is impossible for you, me, or any man to prove his own existence! Why? Because before you can do anything at all, including prove your own existence, you must first exist! That makes your existence axiomatic. And because your conclusion — that you exist — is the same as your axiom — that you exist — your argument is circulus in demonstrandum (circular). Logic itself fails by one of its own fallacies.
But just as materialists accept that their senses faithfully represent the world even though their senses are themselves a part of that world (and therefore tautological), and just as theists accept that their experience faithfully represents the God they’ve encountered even though their experience is itself a part of their walk of faith (and therefore tautological), so does the logician, the scientist, the mathematician — anyone who conducts inquiry or investigation by means of reason — close the curtain to hide that man who is pulling the levers: Mr. Tautology.
I can understand why Kitarak said that he believes only tautologies (even though I tease him about it). In the end, there’s nothing there but what’s there, whatever that is. But this whole construct of logic, of science, of any of man’s noble endeavors, has as its foundation a house of cards, a mirror, and some smoke.
Nothing really exists but truth. And truth is always a tautology.
There is no axiom that God exists, Eris. (Other than the same underlying, unspoken one mentioned above that also presumes that you exist as well.) Note that <>G (the axiom) does not equal G (the statement “God exists”).
Lib would the following be valid ~G = ~G ? I think that is what Eris is getting at. If we assume God doesn’t exist, he must not exist in all possible worlds, this is consistent with your original definition of necessary existance, is it not? God being an all or nothing type of guy, if he does exist, he’s everywhere, if he doesn’t exist, he is nowhere, there is nothing in between.
If we have an axiom that it is possible for God to not exist, <>~G, then we can state that there is in fact at least one world without God. If there is one world without God, then all must be without God.
Whew. I suppose the third time is a charm. I think I know now what you meant to say before.
But as I have said (more times than three, I think), we are not talking about cardinality here; we are talking about ordinality. We’re not talking about objects of existence; we are talking about attributes of existence. If you want to get into an argument about whether or not existence is predicated, that’s fine, but it won’t apply here in any case, because we’re not talking about predicative existence.
I’m not the one who has raised examples of spoons and chessboards and such as examples of things that might exist necessarily. In fact, I have waged a unilateral campaign to strike them from the discussion. They aren’t relevant. I’ve given innumerable (not literally, of course, but it seems like it) examples of what we’re talking about and what we’re not talking about.
One example that I used was that this is not a matter of God, Who knows four billion and one things, versus Cecil Adams, who knows four billion things, and therefore God knows more than Cecil. I’ve spelled this out forty ways from Sunday.
All we are saying is that God knows all that it is possible to know. It isn’t “how many”; it’s “how far”. It is to the extent of possibility. And before you ask, I’ve already discussed (I don’t know how many times), why, for example, I don’t think it’s reasonable to say that Cecil (or any other earthly entity) knows all that can be known. So, if you have questions in that regard, please do me the kindness of looking for those answers. They won’t change from me just because you bring them up again.
I’m sure that the term “maximum” and its variants has likely been used in informal senses in order to convey an ordinality. But you shouldn’t construe it to mean anything like “infinite”.
I know that I teased you, but you know, having read my posts, that I agree with you. God, of course, is the ultimate tautology. He underlies all truth. Everything, in fact, proves His existence. But that’s a matter far removed from any discussion of Dougherty’s proof.
Well, that’s fine, I reckon, except that in a discussion of evolution, it seems left-fieldish to introduce the topic of intelligent design as a different way of looking at things. Maybe in a broader discussion of origins, but not in a discussion specifically about tenet’s of Darwin’s theory.
I don’t think you can use set theory (with which I am only minimally familiar) to discredit modal logic. I think that if you can, then you should do so and collect your nobel prize. My faith in God certainly doesn’t hinge on this proof. I’ve seen specious proofs before. My faith comes from my own experience. If this argument ever should fall, my faith won’t fall with it, and even if every materialist on earth should declare its soundness, my faith would not increase one iota.
I don’t think that God exists because of a modus ponens. I think that God exists because I’ve experienced Him.
Yes, I have, Kitarak. In fact, I’ve written most of it (or at least a substantial portion). I’m sorry for my testiness, but when I announce that my favorite color is brown, and then twenty people ask me in succession what my favorite color is, I just begin to suspect that I am some kind of invisible entity.
Sometimes it really doesn’t seem like some people (maybe me, maybe you, maybe others) aren’t really looking for any answers, but are just looking to be counted as present. No one is satisfied when I consolidate practically identical protests or comments and then respond, so I end up answering the same questions over and over. Soon, that will cease anyway, and people can have their last words, and presume my nonresponse as victory, because I now have some work to do (hurray!). But I will be absolutely knocked-off-my-feet amazed if anyone raises anything new that hasn’t been covered already. (Other than weird stuff like Phoenix’s cherry picked “syllogism” about Tisthammer proving Brouer’s Theorem.)
Fair enough. As the Stanford Encyclopedia of Philosophy says, “The system K is too weak to provide an adequate account of necessity. The following axiom is not provable in K, but it is clearly desirable. (M) A -> A.” As I explained to Eris, there is no direct jump from necessary existence to actual existence.
Well, heavens, man! You could have saved yourself an awful lot of trouble by merely noticing that I had already said the exact same thing! Repeatedly, in fact!
Ack! What could possibly be more interesting than truth? Truth is all that exists. No, really. Not in the sense of a nod over a cup of cappuccino between two philosophy nerds in a cafeteria at Princeton. Truth. Is. All. That. Exists.
That doesn’t make it trivial. That makes it perfect. Boundless. Wonderful. Profound and simple all at the same time. “Thank you, Father, for hiding these truths from the wise and learned, and revealing them to the meek and simple minded.” — Jesus
(Stepping way outside the topic and into a metaphysical dance with myself…)
God is the singularity of truth from which all existence, all knowledge, all power — all universes of calculus, of modalities, of sets both infinite and finite emerge. That He has chosen to be morally good, to love, to forgive, to share eternity is for me more significant than anything else that I can imagine.
To each his own, I reckon.
The definition was separated from the proof for a reason, just as Euclid separated his 23 definitions from his Postulates. All they do is tell us what it is we’re talking about. They are all insufficient. They all invoke terms that are themselves undefined. That’s just the nature of the beast, and we all have to live with it. Mathematicians included.
Let me just catch this quickly that I saw on preview since it’s an easy one (and thankfully new):
Cheesesteak
No. Definitely not. The left-hand side means “God does not exist in actuality.” The right-hand side means “It is necessary that God does not exist (in any possible world).”
Whew. I suppose the third time is a charm. I think I know now what you meant to say before.
But as I have said (more times than three, I think), we are not talking about cardinality here; we are talking about ordinality. We’re not talking about objects of existence; we are talking about attributes of existence. If you want to get into an argument about whether or not existence is predicated, that’s fine, but it won’t apply here in any case, because we’re not talking about predicative existence.
I’m not the one who has raised examples of spoons and chessboards and such as examples of things that might exist necessarily. In fact, I have waged a unilateral campaign to strike them from the discussion. They aren’t relevant. I’ve given innumerable (not literally, of course, but it seems like it) examples of what we’re talking about and what we’re not talking about.
One example that I used was that this is not a matter of God, Who knows four billion and one things, versus Cecil Adams, who knows four billion things, and therefore God knows more than Cecil. I’ve spelled this out forty ways from Sunday.
All we are saying is that God knows all that it is possible to know. It isn’t “how many”; it’s “how far”. It is to the extent of possibility. And before you ask, I’ve already discussed (I don’t know how many times), why, for example, I don’t think it’s reasonable to say that Cecil (or any other earthly entity) knows all that can be known. So, if you have questions in that regard, please do me the kindness of looking for those answers. They won’t change from me just because you bring them up again.
I’m sure that the term “maximum” and its variants has likely been used in informal senses in order to convey an ordinality. But you shouldn’t construe it to mean anything like “infinite”.
I know that I teased you, but you know, having read my posts, that I agree with you. God, of course, is the ultimate tautology. He underlies all truth. Everything, in fact, proves His existence. But that’s a matter far removed from any discussion of Dougherty’s proof.
Well, that’s fine, I reckon, except that in a discussion of evolution, it seems left-fieldish to introduce the topic of intelligent design as a different way of looking at things. Maybe in a broader discussion of origins, but not in a discussion specifically about tenet’s of Darwin’s theory.
I don’t think you can use set theory (with which I am only minimally familiar) to discredit modal logic. I think that if you can, then you should do so and collect your nobel prize. My faith in God certainly doesn’t hinge on this proof. I’ve seen specious proofs before. My faith comes from my own experience. If this argument ever should fall, my faith won’t fall with it, and even if every materialist on earth should declare its soundness, my faith would not increase one iota.
I don’t think that God exists because of a modus ponens. I think that God exists because I’ve experienced Him.
Yes, I have, Kitarak. In fact, I’ve written most of it (or at least a substantial portion). I’m sorry for my testiness, but when I announce that my favorite color is brown, and then twenty people ask me in succession what my favorite color is, I just begin to suspect that I am some kind of invisible entity.
Sometimes it really doesn’t seem like some people (maybe me, maybe you, maybe others) aren’t really looking for any answers, but are just looking to be counted as present. No one is satisfied when I consolidate practically identical protests or comments and then respond, so I end up answering the same questions over and over. Soon, that will cease anyway, and people can have their last words, and presume my nonresponse as victory, because I now have some work to do (hurray!). But I will be absolutely knocked-off-my-feet amazed if anyone raises anything new that hasn’t been covered already. (Other than weird stuff like Phoenix’s cherry picked “syllogism” about Tisthammer proving Brouer’s Theorem.)
Fair enough. As the Stanford Encyclopedia of Philosophy says, “The system K is too weak to provide an adequate account of necessity. The following axiom is not provable in K, but it is clearly desirable. (M) A -> A.” As I explained to Eris, there is no direct jump from necessary existence to actual existence.
Well, heavens, man! You could have saved yourself an awful lot of trouble by merely noticing that I had already said the exact same thing! Repeatedly, in fact!
Ack! What could possibly be more interesting than truth? Truth is all that exists. No, really. Not in the sense of a nod over a cup of cappuccino between two philosophy nerds in a cafeteria at Princeton. Truth. Is. All. That. Exists.
That doesn’t make it trivial. That makes it perfect. Boundless. Wonderful. Profound and simple all at the same time. “Thank you, Father, for hiding these truths from the wise and learned, and revealing them to the meek and simple minded.” — Jesus
(Stepping way outside the topic and into a metaphysical dance with myself…)
God is the singularity of truth from which all existence, all knowledge, all power — all universes of calculus, of modalities, of sets both infinite and finite emerge. That He has chosen to be morally good, to love, to forgive, to share eternity is for me more significant than anything else that I can imagine.
To each his own, I reckon.
The definition was separated from the proof for a reason, just as Euclid separated his 23 definitions from his Postulates. All they do is tell us what it is we’re talking about. They are all insufficient. They all invoke terms that are themselves undefined. That’s just the nature of the beast, and we all have to live with it. Mathematicians included.
Let me just catch this quickly that I saw on preview since it’s an easy one (and thankfully new):
Cheesesteak
No. Definitely not. The left-hand side means “God does not exist in actuality.” The right-hand side means “It is necessary that God does not exist (in any possible world).”
Mmm… We seem to disagree slightly as to what a tautology means. I merely meant a tautological statement of symbolic logic (or predicate logic. Any type of formal logic you choose), so I don’tsee how logic itself is a tautology.
Anyway, you say “Nothing really exists but truth. And truth is always a tautology.”
The thing is, it seems to me that a tautology can’t really be an object (or being) as such (unless our definitions are wildly different). So, if only tautologies exist, how can you really say that god exists? (Unless you want to take my route and define yourself to be god. For the record that argument wasn’t entirely serious in case you hadn’t guessed.)
[…shaking head in disbelief…] That is not the definition.
Night, I don’t know what to say. We’re certainly not clear on the definition, so now I have to decide whether the rest of your post applies or not, and frankly that’s not fair.
I think it would be fair for you to go back and see what the definition is and reformulate your post. If you don’t, then don’t bother. I’m sorry, but gah.
Would you honor a respectful request that you wait until I get caught up here? I’m debating like twelve people at once. Presently, I’m working on Night’s second post in which he noticed what the definition was, so now I think he deserves a response. Thanks in advance.
Criminey. G -> G is the first inference. Please stop assuming things.
Mercy.
Why I bother repeating this is beyond me (why should I think it will be seen this time?): Contradictions prove anything. Tautologies are proved by anythng. It’s common knowledge.
Okay, I just want to stop here and ask a question of everybody. How does something like this happen? I had already stated that contradictions prove anything. In fact, A or Not A -> X where X is any arbitrary element.
What I want to know before I spend the rest of this afternoon and possibly weekend responding to people is this: why is it that when I typed it, it was so unimportant as to not even be remembered, but now that Kitarak has typed it, it is suddenly “interesting”.
I just want to know whether there is one single person here who is reading my posts. If there is, please identify yourself and I’ll address my responses to you. If there isn’t, I can spend my time preparing for my work.
Actually, I thought the argument was quite valid in Tishammer’s presentation. He felt it wasn’t because it provided a contradiction; specifically, a line in the proof would read, “The greatest possible being cannot possibly exist.” That is only a contradiction if you’ve assumed God exists. If you assume God exists, you can’t prove God exists (or if you do, you’ve said nothing).
I honestly have no problem with the proof. It is easy to follow. I have a problem with the meaning behind the definition and the axiom. They don’t seem to mesh well with the symbols.
Well, no, it doesn’t. but <>G does assert that, in possible worlds, at least one world has “G” as an element. That is, by any means, an assertion that God exists. We’ve not even demonstrated that God is possible, we assume he is by trying to impose English “possible” onto the modal symbol “<>”.
“<>G” means that we can construct at least one logical world which contains “G”. As an assumption I think that stinks. It has all the feel of something that should be proved. If you can’t prove it, you must accept it or reject it axiomatically. I see no way that rejectiong the axiom (which doesn’t mean accepting the opposite) is contradictory to anything. At least, not yet.
But that isn’t the sense that is sticking in my craw. The possibility of G in modal logic says a lot. It is trivial for me to say that it is possible I will go to the bank today as I’ve been to the bank before. But consider the proposition that it is possible for man to fly into Jupiter’s atmosphere. We don’t know that we can at all. It seems possible, in some respects, but before we do anything about it we would prove that possibility. Because ew don’t know it is possible.
It seems possible that God can exist. But before I would acknowledge use of that possibility, I would like it to be demonstrated. Can you see why I would like that? Much of the problem is that I don’t know that God is possible. So I can’t swallow <>G or ~<>G. I can entertain the thought, yes. In entertaining the thought, you’ve proved that whatever God can be described as having necessary existence and is possible must exist.
No doubt in my mind.
Well, you know we agree here. This is my problem with all philosophies in general: they require we accept a lot that can’t be demonstrated but seems like it should be. This is why I can’t criticize you for believing in God, and I can’t criticize (for example) Colibri for believing in the Big Bang (as he understands it): because it meets your own (self-defined and/or self-accepted) standard of proof. I can’t say even atheists have faith. I never have and I highly doubt I ever will. That just isn’t how I understand the use of that word in a metaphysical context. But I think that you and I are right (by my standards ;)) that the the reasoning is similar enough to not warrant the dogmatism we seem to see in people’s different metaphysical outlooks.
Am I right there?
Back on the previous track…
I think you’re wrong there. <>G means that we can construct a world where G holds. That’s how I understand modal logic’s symbol “<>”. Am I wrong there?
Thanks for looking past my unwarranted hostility before. It really was uncalled for.
Ok, I get that. On the other hand, if you’re going from ‘greatest possible existence’ to ‘greatest possible knowledge’ (for example), I’d like to know how you express greatest possible knowledge modally. (ok, maybe knowledge isn’t a good example. How about love?). That seems far more of an order than of a modal statement.
Actually I still don’t see where that follows… You’ve defined god as maximal possible existance. i.e. G => ~<>~G. This doesn’t say anything about other attributes Se might posess.
What part of this appears in your proof? You’ve proved the existence of something, which you’ve called god, with the property that G=>G. That’s fine, I accept that it’s a valid proof. Probably even sound. However, you have shown that neccesary existence exists, yes? So, let T be some statement for which T is true. Then T=>T is true and <>T is true. So there’s no reason to suppose ~(T=G). Hence your definiton of god seems rather weak.
Incidentally, what do you mean by the ‘ultimate tautology’?
That isn’t a fair assessment. Formal logic and set theory are often used to discuss the same problem in different ways.
No nobel prize for mathematics. Nor did I claim to have discredited modal logic. It was merely intended as a demonstration (one I admit didn’t work very well) as to why <>G was by no means self-evident.
As it should be. Faith is just that - Belief without proof. There are some things that can’t be proved logically, hence the need for axioms. My point has never been that god doesn’t exist. I don’t believe he does, you do. That doesn’t mean either of us have to be wrong. (It’s great not believing in an objective reality. :)). My objection was to trying to prove the existence of god.
Well, ok. That was poorly phrased. What I meant was that a tautology of statement calculus, in the sense of something you can write out purely with the symbols A, ~ and => doesn’t make a very impressive deity (no matter how you interpret A).
Well, you see here’s the thing. I still don’t see how you’re making the leap from “god as a tautology” to “god as an entity”
Well, there’s a statement we can both agree is true.
Well, yes. But my complaint wasn’t about undefined terms, it was about an incorrect definition. As I showed, if you allow definitions of the form A=BA (where B is a non-zero string) then you need a heavy restriction on what you’re allowed to use for B if you don’t want it to cause a contradiction. Even with those restrictions it’s not standard logic.
G=G=G=G=…
You can’t write G as a finite sentence, and you’re not allowed to deal with an infinite sentence in standard logical systems.
Look carefully - Av!A isn’t a contradiction, it’s a tautology (v meaning OR in this case). That proof was intended to show that B was a tautology.
Take your time replying to this, I didn’t see your request until I finished writing this post, so I figure I may as well post it.
Also, please tell Night that you did not use modal logic, but rather ordinary first order logic when you reiterated my comment about contradictions (though yours was significant and mine wasn’t).
Eris
Bear with me. I’m undergoing a crisis of conscience here. I’m trying to determine whether what I say is worth anything at all.
I’ll try a different approach.
Repeatedly, in fact!
For the record that argument wasn’t entirely serious in case you hadn’t guessed.)