As a plain language person I get a kick out of these discussions. You and Banno et al are obviously very smart/knowledgeable people. That said, I cannot figure out what you are saying.

P1. We know shit.
P2 We do not know shit.
P3 It is possible to know shit.
P4 It is not possible to know shit — Metaphysician Undercover

If we know shit at time t, then clearly at some time prior to time t it must have been possible to know said shit - otherwise there's no way we could know said shit at time t. This is the plain language interpretation.

So I'm trying to figure out how P1 would not automatically imply P3 at time t. Are you saying that prior to time t we were somehow able to figure out the shit, but that at time t the situation has changed and we whatever means/mechanism we used to determine the shit prior to t is no longer applicable - and thus P1 no longer automatically implies P3?

Or (more likely) I am totally not getting what you're saying.

BTW -- If possible - a plain language response please. :smile:

Look at the temporality of your statements; "it might have been that we did not know stuff", refers to past time. — Metaphysician Undercover

No, it doesn't. It might have been the case now that we didn't know stuff. In some other posibel world we might not have known stuff. Tensed logic, if needed, is constructed separately to modal logic. But your not seeing this is yet another example of your eccentricity.

So I'm trying to figure out how P1 would not automatically imply P3 at time t. — EricH

Yep. That we know p implies that it is possible to know p.



The technicalities are to a large extent unavoidable. In plain language, we might replace "accessibility" with "the worlds about which we can talk" and call the possible world we are in, the actaul world. Then:

The inference p → possibly p is valid only in modal systems where each world counts itself as possible, that is, where we can talk about the actual world. In Kripke semantics, “possibly p” means that p is true in at least one world about which we can talk. If you drop reflexivity, then we can't talk about the actual world, and so p may be true in the actual world but not in any world about which we can talk. So the inference fails. Since Meta denies p → ◇p, his view amounts to saying that the actual world is not among the worlds about which we can talk. But in p → ◇p, the world where p is true is simply this world.

The tense is not usually considered in modal logic. So we can for example talk about the possibility that you did not write the post to which I am replying, by talking about a possible world in which that was so. That's not the actual world, of course, but it's still a possible world.

Meta's confusion might be the result of thinking of accessible worlds as “counterfactual” only, never including the actual world. This seems likely. But for the rest of us, the actual world is considered to be one of the possible worlds.

If we know shit at time t, then clearly at some time prior to time t it must have been possible to know said shit - otherwise there's no way we could know said shit at time t. This is the plain language interpretation. — EricH

That is not the issue. The question is whether at the same time, "We know shit", and "It is possible that we know shit", could both be judge to be true.

So I'm trying to figure out how P1 would not automatically imply P3 at time t. Are you saying that prior to time t we were somehow able to figure out the shit, but that at time t the situation has changed and we whatever means/mechanism we used to determine the shit prior to t is no longer applicable - and thus P1 no longer automatically implies P3? — EricH

The issue is if, when you judge that p is true, you can also judge that it is possible that p is true. I think that this is dishonesty and contradiction because "it is possible that p is true" contradicts "p is true". This is because "p is true" means that it is not possible that p is false, whereas "it is possible that p is true" means that it is possible that p is false. Therefore contradiction.

No, it doesn't. It might have been the case now that we didn't know stuff. In some other posibel world we might not have known stuff. Tensed logic, if needed, is constructed separately to modal logic. But your not seeing this is yet another example of your eccentricity. — Banno

For God's sake Banno, what are you talking about? "Did" is the past tense of do. "Did not know" refers to the past. It does not refer to the present, which would be "does not know".

Are you suggesting that the past tense "did" can refer to the present, but in another world? So that "we did not know" doesn't refer to us in the past, but it refers to us at the present, but in another world? So right now, we know shit, but in another world there's another us that does not know the same shit, right now. And somehow it seems reasonable to you to say that this other "we", at the present time "did" not know shit right now, because the usage of the past tense creates the illusion of a temporal separation between one thing referred to with "we" and the other as if it's a temporal extension of one thing referred to with "we". But the illusion of the temporal separation only really helps to veil the absurdity of two versions of 'we" existing at the very same time. Why not just say what you mean, there's one "we" which knows, and another "we" which does not know.

In my last post I warned you about using ambiguity. See here, "we" refers to two distinct groups of people, one which knows stuff, and the other which does not know stuff, both at the same time. Can you see that you are intentionally proposing ambiguity? That fills the criteria of sophistry.

"My eccentricity"? Is that meant as a joke? You are the one talking about the 'we" which know stuff at the present time, and another "we" which does not know the same stuff at the same time. And to cover up the absurdity of this you say that the one "we" does know stuff right now, and the other "we" did not know the same stuff right now. Don't you admit that that is very strange "stuff" which you are on about?

Please Banno, try to provide something more reasonable.

The question is whether at the same time, "We know shit", and "It is possible that we know shit", could both be judge to be true. — Metaphysician Undercover

And the answer, overwhelmingly, is "yes". If we know something then by that very fact it is possible for us to know that thing.

This is because "p is true" means that it is not possible that p is false — Metaphysician Undercover

No — that conflates truth with necessity. “p is true” does not mean “p cannot be false.” It means only that p is not false in the actual world. Something can be true without being necessary, and false without being impossible.

It is true that you read this post. It is also possible that you might not have read it.

'Did' marks what happened, not what had to happen. Saying 'Jill did push Jack' tells us what actually happened, not that her pushing him was necessary, inevitable, or impossible to be otherwise. Confusing tense with modality is exactly the same mistake as treating 'true' as meaning 'cannot be false.'

"My eccentricity"? Is that meant as a joke? — Metaphysician Undercover

Unfortunately, no. Your ignorance of modal logic stands alongside your denial of instantaneous velocity and insistence that 0.9... ≠ 1.

And the answer, overwhelmingly, is "yes". If we know something then by that very fact it is possibel for us to know that thing. — Banno

You have not yet defined "possible" to support this, as I asked. What you are saying here is that "it is possible that we know X" is implied by "we know X". I've already explained to you over and over, why this is incoherent. The two actually contradict each other because "it is possible that we know X" means that it could be the case that we do not know X, while "we know X" means that it could not be the case that we do not know X.

I've shown you the logic. Continuing to assert something completely illogical is pointless. You need to back up your claims, show how you understand the meaning of "possible" in such a way which allows what you assert to somehow be coherent.

No — that conflates truth with necessity. “p is true” does not mean “p cannot be false.” It means only that p is not false in the actual world. Something can be true without being necessary, and false without being impossible. — Banno

Your mention of necessity is a distraction of sophistry. If p is true it very clearly does mean that p cannot be false. Notice "is" and "be" imply the present time. If p is true, p cannot be false, because that would mean that p is true and false at the same time.

Furthermore, truth and falsity are determined by the actual world, as correspondence. I'm very surprised that you, a self-proclaimed realist would suggest otherwise. If truth is not determined by the actual world, realism has no standing.

But that issue is which I told you about yesterday, your tendency to say one thing, then argue principles which explicitly undermine what you claim. It's a sort of hypocrisy on your part.

It is true that you read this post. It is also possible that you might not have read it. — Banno

What? How does that make sense? If it is true that I read this post, how is it possible that I did not read it?

'Did' marks what happened, not what had to happen. Saying 'Jill did push Jack' tells us what actually happened, not that her pushing him was necessary, inevitable, or impossible to be otherwise. Confusing tense with modality is exactly the same mistake as treating 'true' as meaning 'cannot be false.' — Banno

I agree, "did" marks what actually happened, and this is the truth. As it is the truth, it is impossible to be otherwise. If Jill did push Jack, then that is the truth, and it is impossible to be otherwise. True does mean, precisely and exactly, "cannot be false". If what is true could be false we would have contradiction. If you really believe otherwise, you have some explaining to do.

And I don't know how "modality" is related here. You haven't provided any definitions or principles of relations. All you have done so far is made absurd assertions.

Unfortunately, no. Your ignorance of modal logic stands alongside your denial of instantaneous velocity and insistence that 0.9... ≠ 1. — Banno

You keep bringing up "modal logic" but you have done nothing to show how this is relevant. We have been talking about what it means to know p, not to know p, and the possibility of knowing p. That is what we are talking about, what these propositions mean. If you want to apply modal logic, then you need to provide some principles, definitions, and structure. To simply keep on asserting that what I say is contrary to modal logic is pointless if you cannot prove your claims with reference to some principles or definitions.

You have not yet defined "possible" to support this, as I asked. — Metaphysician Undercover

Yeah, I did, you missed it. It's the standard Kripkeian definition:

In Kripke semantics, “possibly p” means that p is true in at least one world about which we can talk. — Banno

All the stuff I've said here is straight forward possible world semantics and standard modal logic. Folk can check it by feeding it in to the AI of their choice. It'll also point out the errors in your posts.

"we know X" means that it could not be the case that we do not know X. — Metaphysician Undercover

Nuh, it doesn't. We know that Branson's missus has died. But it could be the case that we did not know she'd passed on. They might not have made it public, if they had wanted. Or we might have missed the news that day.

What? How does that make sense? If it is true that I read this post, how is it possible that I did not read it? — Metaphysician Undercover

Here's the problem, then - your incapacity to understand a simple situation; or is this the doubling-down I spoke of earlier? We can happily consider what might have been the case had you not read that post. I would not be writing this, for starters. That does make sense.

You keep bringing up "modal logic" but you have done nothing to show how this is relevant. — Metaphysician Undercover

:lol: What to make of that. Modal logic not relevant to possibility and necessity.

Again, I'm here for the post count. So far as I can see, you have not added anything new for a day or two. But keep going.

Working backwards, we got to arguing about modality after I introduced Fitch's paradox. That was introduced because it deals with the logic of unknown truths. And that relates directly to the question in the title: How do we know there isn’t anything beyond our reality?

I'll go back to my original answer:

"Beyond reality" is not a region; it is a grammatical error. — Banno

to which was added:

The set of true sentences is never complete — Banno

And then to

...the way the issue is phrased. As "there is stuff beyond our reality" when it should be "there is stuff that is true but unknown" — Banno

Hence to Fitch, in which it is shown:

Anti-realism says: every truth must be knowable.
But you also say: there are truths we don’t and maybe can’t know.
Fitch shows you can’t have both.
If there are unknown truths, then not every truth is knowable, which just is the denial of anti-realism. — Banno

The way that antirealism usually avoids omniscience is by rejecting classical logic. That for instance is the approach in Kripke's theory of truth, which has some merit.

In effect, in talking about the medium-size goods around us, we have a choice between using classical logic and accepting that there are truths we don't know on the one hand; and supposing that there are no such unknown truths and rejecting classical logic on the other.

Ether will do, but the former seems more intuitive, less sophistic and simpler.

Yeah, I did, you missed it. It's the standard Kripkeian definition:
In Kripke semantics, “possibly p” means that p is true in at least one world about which we can talk.
— Banno — Banno

From the perspective of truth by correspondence, these appears to be incoherent. How can we talk about things being true in more than one world, when "true" is determined by what corresponds with "the world"? I thought you were realist. No? Are you saying that there is a whole bunch of contradictory truths depending on which world we are talking about?

Regardless, I'll accept this definition as a working platform. But I'll warn you that it will be very hard to support any type of realism which could be consistent with this definition. So a "world" is a product of the imagination, and "true" means consistent with that specific product. This is a reflection of the basic idealist assumption covered in the thread called "The Mind Created World". The difficulty with this approach is to find principles which would provide "correctness". that is because my proposed world produced from my experience may differ from your proposed world produced from your experience. Each is " a world about which we can talk".

We cannot us "true", to talk of the "true world", or "real world", in the sense of correspondence, because "true" is already used in the sense of coherence, as consistent with the proposed possible world. Furthermore, we cannot refer to an independent "actual world", because all we have is the different proposals from different people, based on their experiences. By what principles would we say that one person's experience represents "the actual world", over another's, when they contradict?

We know that Branson's missus has died. But it could be the case that we did not know she'd passed on. — Banno

You are mixing up tenses and not properly representing what I said. I said "we know X" means that it could not be the case "that we do not know X". You have replaced "do not" with "did not". Sure it is possible that we did not know what we do know now, but that's not what I'm talking about. If we know X right now, it is absolutely impossible that we do not know X right now. Of course if we allow different imaginary worlds, we could have one of each, but those two different cases would not be in the same world.

Here's the problem, then - your incapacity to understand a simple situation; or is this the doubling-down I spoke of earlier? We can happily consider what might have been the case had you not read that post. I would not be writing this, for starters. That does make sense. — Banno

Your claim here is incorrect. What you insinuate is contrary to your definition of "possibly". Notice, "possibly" refers to what is true "in at least one world". It does not provide the principles to cross from one world to another. In one world I read the post. In another world I did not read the post. "True" refers to consistency within the referred to world. Therefore if it is true that I read this post, (meaning in that world where it is true) it is not possible that I did not read it. So your claim that what I said was wrong is incorrect. Your incorrectness is the reason for my doubling down.

You seem to misunderstand "true" in the context of your proposed modal logic. Notice in your definition of "possibly", "true" is relative to the specified world. Therefore if it is true that I read the post, it cannot be the case that I did not. "True" indicates what is the case within a specified world. You can go ahead and talk about other worlds, in which I did not read the post, but in those worlds it is not true that I read the post.

What to make of that. Modal logic not relevant to possibility and necessity. — Banno

The words "possibility" and "necessity" were being used long before modal logic was invented, so it is clear that those words can be used in ways not at all related to modal logic. If you want to limit use specifically to modal logic, then to avoid ambiguity we need principles or definitions. So, if you want to bring a specific form of modal logic to bear on this discussion, you need to provide some principles or definitions, as you did with "possibility" above.

However, you need to respect the consequences of these principles. Notice for instance what becomes of "true" under your definition of "possibly". "True" becomes relative to the specified world, it is not absolute, or relative to any sort of supposed independent actual world. If you use "true" in a number of different ways you likely equivocate.

The way that antirealism usually avoids omniscience is by rejecting classical logic. That for instance is the approach in Kripke's theory of truth, which has some merit.

In effect, in talking about the medium-size goods around us, we have a choice between using classical logic and accepting that there are truths we don't know on the one hand; and supposing that there are no such unknown truths and rejecting classical logic on the other.

Ether will do, but the former seems more intuitive, less sophistic and simpler. — Banno

In the way that "true" is used in your definition of "possibly", how does "truths we don't know" say anything meaningful? Since truth is relative to the specified world, and "true" means what is consistent with that world, and we can imagine any type of world, than anything, and everything is true. How does "truths we don't know" say anything meaningful, when everything and anything is a truth?

There's that old adage about not wrestling with a pig.

The definition provided is not mine; it is the standard definition in modal logic. It has nothing to do with correspondence, since truth in such systems is model-theoretical.

In modal logic:
“◊p” means “p is true in at least one accessible world”
This does not claim that there are multiple concrete universes out there and that truth “corresponds” to each. It is a semantic model, a mathematical structure used to evaluate formulas. Model-theoretic “worlds” are not metaphysical worlds. They are semantic devices, exactly like the points on a truth table are not little universes.

You simply have a very poor understanding of the topic at hand, Meta.

It does not provide the principles to cross from one world to another. — Metaphysician Undercover

Yeah, it does. That's exactly what the accessibility relation is for.

Frankly, your attempts to show that modal logic, and possible world semantics, which are accepted fields of study in mathematical logic, are somehow inconsistent, is just a bit sad.

In the way that "true" is used in your definition of "possibly", how does "truths we don't know" say anything meaningful? Since truth is relative to the specified world, and "true" means what is consistent with that world, and we can imagine any type of world, than anything, and everything is true. How does "truths we don't know" say anything meaningful, when everything and anything is a truth? — Metaphysician Undercover

You are here confusing "true in a model" with "true in reality".

Again, a bit sad.

The definition provided is not mine; it is the standard definition in modal logic. It has nothing to do with correspondence, since truth in such systems is model-theoretical. — Banno

That's right. It's exactly what I pointed out in my post.

This does not claim that there are multiple concrete universes out there and that truth “corresponds” to each. It is a semantic model, a mathematical structure used to evaluate formulas. Model-theoretic “worlds” are not metaphysical worlds. They are semantic devices, exactly like the points on a truth table are not little universes. — Banno

I don't care what you call it, a "semantic model" if you want. However, if you choose to use "true" in that way, we must adhere to that for the purpose of our discussion here, so that we do not equivocate. That is the reason why I asked you to provide some principles or definitions, so that we have something concrete to go by.

That's exactly what the accessibility relation is for. — Banno

Well give me the "accessibility relation" then. I don't think it's going to change the meaning of "true".

Frankly, your attempts to show that modal logic, and possible world semantics, which are accepted fields of study in mathematical logic, are somehow inconsistent, is just a bit sad. — Banno

I am not trying to show inconsistency in modal logic, I am trying to show incorrectness in your presentation of it. And, in case you didn't notice, that is what I did in my last post.

You are here confusing "true in a model" with "true in reality".

Again, a bit sad. — Banno

Ha ha, I'm staying consistent with "true in a model". From here, there is no such thing as "true in reality", because that would be equivocation. That's the problem, your realistic tendencies make you want a "true in reality", while you argue modalities. That is your inconsistency, your incorrectness, which I am trying to help you to understand.

Are you ready to proceed with the "accessibility relation" now?

That is the reason why I asked you to provide some principles or definitions, so that we have something concrete to go by. — Metaphysician Undercover

Here you go: Boxes and Diamonds: An Open Introduction To Modal Logic. Sections 1.5 and 1.6 cover truth at a world and truth as a model. There's a couple of sections on accessibility relations, but you might find 15.5, "Accessibility Relations and Epistemic Principles", most useful.

I am not trying to show inconsistency in modal logic, I am trying to show incorrectness in your presentation of it. — Metaphysician Undercover

I've over-simplified much of the logic, and I'm sure that Tones or one of the other mathematicians hereabouts could have a field day with some of my phrasing. But I do not think that anything I have said here is at odds with standard, accepted modal logic. What you have said, on the other hand, is.

But you are welcome to try and show otherwise.

Here you go: Boxes and Diamonds: An Open Introduction To Modal Logic. Sections 1.5 and 1.6 cover truth at a world and truth as a model. There's a couple of sections on accessibility relations, but you might find 15.5, "Accessibility Relations and Epistemic Principles", most useful. — Banno

OK, so truth is defined as within the model, so we haven't gotten to anything to support the assumption of a real, or actual world, or truth by correspondence to the actual world. How do you claim to be realist if you believe in the principles of modal logic? How do you assume to make modal logic consistent with realism?

How do you assume to make modal logic consistent with realism? — Metaphysician Undercover

Odd. Can you explain how you think it isn't?

You do understand that the model theoretical account is extensional...? I guess not.

Can you explain how you think it isn't? — Banno

I did that already.

https://thephilosophyforum.com/discussion/comment/1027665

Truth is determined by the model,, The model is a product, imaginary. Unless you are assuming something like model-dependent realism, (which isn't actually realism, it just has that word in the name), there is no place for a real, independent world.

The model is a product, imaginary. — Metaphysician Undercover

A model is not an “imaginary world” we’re claiming to be real; it’s a mathematical structure used to interpret a language. The whole point of model-theoretic semantics is precisely not to replace the actual world, but to give us a rigorous way to talk about it.

But your "rigorous way to talk about it" assigns truth to the talk not the actual world, and it provides no principles to even support the reality of an actual world. Look at the definition of "possibly" you gave me:

In Kripke semantics, “possibly p” means that p is true in at least one world about which we can talk. — Banno

Clearly these are "imaginary worlds". Consider that I may produce a world based on my experience, and you may produce a world based on your experience. Despite each of us claiming that mine is the actual world, based on my experience, they are both imaginary worlds derived from our memories and other parts of our minds, and there may very well be contradiction between us. So we may establish modalities, and ways to cross reference between your world, my world, and numerous others, to produce "a model". This model which is produced is just another imaginary world though.

You say "The whole point of model-theoretic semantics is precisely not to replace the actual world, but to give us a rigorous way to talk about it", but that is not correct. It gives us a rigorous way to talk about our experiences, compare them, apply logic, and seek consistencies and inconsistencies. It does not give us a way to talk about the actual world, nor do the principles of modal logic claim we talk about the actual world. That's why it leads to ontologies like model-dependent realism. It provides principles to talk about possible worlds, and produce conclusions concerning these possible worlds, and then we might stipulate some principles whereby we'd choose the best possible world (the one we think could qualify as the actual world), but it is not working with descriptions of the actual world. Nor does it claim to be. It cannot, or the possible worlds structure would be negated.

Notice the inversion. Modal logic does not provide a way to talk about the actual world. It provides a way to talk about possible worlds. Then, through principles, and logical proceedings, it stipulates "the actual world". So instead of the classic approach, talking about the actual world (propositions judged for truth and falsity), and proceeding logically from there to determine what is possible within that actual world, modal logic talks about possible worlds, and proceeds to make a logical determination about the actual world. That is not a matter of giving us a rigorous way to talk about the actual world. It is a way to make logical conclusions about the actual world. The descriptions, therefore what we are talking about is possible worlds, not the actual world. Therefore, a rigorous way to talk about the actual world is what is really missing here.

But your "rigorous way to talk about it" assigns truth to the talk not the actual world, and it provides no principles to even support the reality of an actual world. — Metaphysician Undercover

That's pretty hopelessly confused. As is the rest of that post.

The best way to think of possible worlds is not as imagined, but as stipulated. We can consider the possible world in which we did not know Bransons wife had died, and consider the consequences thereof - such as that I would not be using it in this example. That's quite sensible.

And, to add to your confusion, we make such stipulations in the actual word... As indeed, I just did.

The difference with the actual world is that it is not stipulated. It's already there.

You continue to muddle semantics and ontology, and blame logic for your own muddle.

The best way to think of possible worlds is not as imagined, but as stipulated. — Banno

Sure, "stipulated". But I don't see how this change of words makes any significant difference. A stipulated world is nothing other than a special type of imagined world, one put to words, and proposed for agreement. But I'll use your word if you think it adds some significance.

We can consider the possible world in which we did not know Bransons wife had died, and consider the consequences thereof - such as that I would not be using it in this example. That's quite sensible. — Banno

So you are suggesting two distinct stipulated worlds, one in which Branson's wife died and one in which Branson's wife did not. I have no problem with this, those are two possible worlds.

The question is how do we get to an actual world?

And, to add to your confusion, we make such stipulations in the actual word... As indeed, I just did. — Banno

Yes, that definitely confuses me. The way you phrase that, "to add to your confusion", creates the appearance that you are doing this intentionally. Why would you strive to confuse rather than to clarify?

You are stipulating that we make such stipulations in the actual world. But that stipulation you make, just produces another stipulated world. Just because you stipulate that we make stipulations in the actual world, doesn't give that stipulated world any special status as anything other than another stipulated world, just like all the rest of the stipulated worlds. I could stipulate that there is another world, "the real world", within which you make the stipulation that we make such stipulations in the actual world. Then someone might stipulate that there is a "physical world" within which I made the stipulation about the real world. And someone could stipulate an "existing world" within which the stipulation about the physical world was made. As long as people could keep coming up with new terms, we'd approach an infinite regress. All the while, we'd only be dealing with stipulated worlds, which are just a special type of imaginary world.

The difference with the actual world is that it is not stipulated. It's already there. — Banno

I don't understand this at all. How could that even be a "world", what's already there? Very clearly, a world is what is stipulated. If there is anything which has not been stipulated, then this is very obviously categorically distinct from what "a world" is. We cannot now use "world" to refer to something "not stipulated", when "a world" very clearly refers to what is stipulated. I agree that there is much more to reality than what is stipulated, but if worlds are what is stipulated, we sure as heck cannot talk about what is not stipulated as if it is a world. That would be extremely confusing.

That's pretty hopelessly confused. — Banno

Now I think I understand very clearly why I am hopelessly confused. You use the word "world" in an extremely confusing way. You suppose worlds which are stipulated, and also a world, or perhaps a multitude of worlds (I really can't know, because everything you say about this "world" would just be stipulated, therefore a stipulated world) which is/are not stipulated. How could we even know that there is such a world, or worlds?

Can you see the inherent contradiction here, which is confusing me immensely? You are stipulating that there is an actual world, which is not stipulated, but is already there. If we remove this stipulation, of an actual, not stipulated world, which is already there, because it is self-contradicting, a stipulated not stipulated world, how can we know, or even say, anything about this supposed contradictory world, because that would be to make the contradiction of stipulating the not stipulated?

What I suggest to you Banno, is that it is actually you who misunderstands modal logic. In modal logic there cannot be any such thing as the actual, not stipulated world, which is already there. This realist assumption contradicts the very principles of modal logic. This is why we have ontologies like model-dependent realism, which the adherents recognize is not consistent with traditional realism, but they give it that name anyway, to create the illusion of consistency. And, you either get deceived by this illusion, or grasp it, and propagate it in intentional deception, by insisting that modal logic is consistent with realism.