1. it is raining
2. it is not raining

If I entertain 1 I will find that if I were to believe it true I would not be wrong about it raining. Therefore, if I can be wrong about it raining 1 must be false and so 2 must be true. — Michael

This (and the other) are not examples of the same sort because the neither the assumption that it's raining, nor the assumption that God exists have any bearing on knowledge.

The assumption that only my mind exists has a bearing on knowledge (I must know everything there is to know if all that exists is my own mind). It is that assumption which changes the options. Neither rain, nor god do that.

See here but add in:

I believe that something other than my mind does not exist
I am wrong if something other than my mind exists
Therefore either something other than my mind exists or I cannot be wrong

The conclusion doesn't follow for exactly the reason I explained in that post. "I cannot be wrong" doesn't follow from "I am not wrong".

The conclusion doesn't follow for exactly the reason I explained in that post. "I cannot be wrong" doesn't follow from "I am not wrong". — Michael

The conclusion "I cannot be wrong" doesn't follow from "I'm not wrong" in my argument either. It follows from the logical consequence of all that exists being in one's mind. If all that exists is in one's mind one cannot be wrong about anything.

If all that exists is in one's mind one cannot be wrong about anything. — Isaac

I believe that something other than my mind does not exist
I am wrong if something other than my mind exists
Therefore either something other than my mind exists or I cannot be wrong

The conclusion doesn't follow.

I believe that something other than my mind does not exist
I am wrong if something other than my mind exists
Therefore either something other than my mind exists or I cannot be wrong

The conclusion doesn't follow. — Michael

It does.

1. I believe that something other than my mind does not exist

2. I am wrong if something other than my mind exists

If 1. is the case I cannot be wrong about anything (else).

What is the case is either 1 or 2

Therefore what is the case is either something other than my mind exists (2) or I cannot be wrong (implication of 1)

It does. — Isaac

It doesn't, and I explained why. I'll simplify the logic for you:

Bp ≔ I believe p
W ≔ I am wrong about p

1. Bp
2. ¬p ↔ W
3. ¬p ∨ ¬◇W

The conclusion doesn't follow. The actual conclusion is:

¬p ∨ ¬W

It doesn't matter what you substitute for p. It could be "it is raining" or it could be "God is a man" or it could be "only my mind exists". The rules of inference don't change.

You're ignoring what p implies. Why?

You're ignoring what p implies. Why? — Isaac

It doesn't imply what you're saying. You can't get from "only my mind exists" to "I cannot be wrong".

It doesn't imply what you're saying. You can't get from "only my mind exists" to "I cannot be wrong". — Michael

Of course you can. If only your mind exists then you must know everything, therefore you cannot be wrong about anything.

If only your mind exists then you must know everything — Isaac

No. If only your mind exists then you know of everything that exists. But it doesn't follow that you know that no other stuff exists.

Remember the examples of the coins. If only 10 coins exist and if I know that 10 coins exist then I know of all the coins that exist. But it doesn't follow that I know that there aren't more coins.

p ≔ only my mind exists
Bp ≔ I believe that p

1. Bp (premise)
2. ¬□p (premise)
3. Bp ∧ ◇¬p (from 1 and 2)

3 is just what it means to possibly be wrong.

If only your mind exists then you know of everything that exists. But it doesn't follow that you know that no other stuff exists. — Michael

I know I said I'd drop this issue, but this caught my eye.

(1) If it exists, I know of it.

Now assume that something I don't know of exists. Then I know of it, by (1), and yet don't know of it, by assumption, a contradiction. Hence I cannot fail to know of anything that exists, and I can be confident that there are no entities unknown to me.

Maybe I'm missing something.

See the example with the coins.

1. John knows that 10 coins exist
2. Only 10 coins exist
3. Therefore, John knows of every coin that exists

However, John doesn't know that only 10 coins exist. This is where Isaac gets it wrong.

I think the coins are a different scenario. It's possible that the inference I actually challenged was not your considered position.

To me the issue looks like semantics, what we mean by our terms.

You can't get from "only my mind exists" to "I cannot be wrong". — Michael

If only your mind exists then you must know everything, therefore you cannot be wrong about anything. — Isaac

I prefer understanding 'mind' in a way that agrees with @Isaac. But this isn't math, we don't have a formal definition, and so we basically have to make a case for this or that understanding. In that spirit, I hope to at least shift gears from trying prove there is a Correct choice here to untangling our individual preferences and presuppositions.

We can imagine a person mistaking a dreamscape for public reality. The dreamself bangs on a door, sure that the princess needs rescuing on the other side. Can he be wrong ? If he can, we seem to be making the dreamscape an 'other' to the dreamself, about which he can be wrong. To me, this would make it a kind of world. But the dreamself has a mind that is 'in' this world as a mere part of it. Can the dreamself say 'this is all just my mind' ? It gets messy, because there are two minds here. The one that's basically what Wittgenstein calls the limit of the world and also the conventional one which does not know what's on the other side of the door.

I think the coins are a different scenario. — Pie

The logic is the same, regardless of what X is.

1. John knows that his mental phenomena exist
2. Only John's mental phenomena exist
3. Therefore, John knows of everything that exists

However, John doesn't know that only his mental phenomena exist. 3 doesn't entail that John knows 2, just as it didn't with the coins.

However, John doesn't know that only his mental phenomena exist. 3 doesn't entail that John know 2. — Michael

OK. John doesn't know that he knows of everything that exists. I'll add that to my computations.

OK. John doesn't know that he knows of everything that exists. I'll add that to my computations. — Pie

And I'll add, knowledge isn't just knowledge of what does or doesn't exist, so even if it could be shown that the solipsist knows everything about what does or doesn't exist it doesn't then follow that the solipsist knows everything.

Whether or not Hitler would have been executed had he not killed himself has nothing to do with what does or doesn't exist. Whether or not I will be sad tomorrow has nothing to do with what does or doesn't exist. Whether or not the Reimann hypothesis is correct has nothing to do with what does or doesn't exist.

So even if the solipsist cannot be wrong about what does or doesn't exist, he can still be wrong about counterfactuals, predictions, and maths. The truth and falsity of these things does not depend on the existence of something other than one's mind. This is where some are conflating two different senses of "mind-independence".

But could that-which-exists not be understood as including tendencies and relationships ? What of the conception of an entity as essentially relational ? An electron 'is' what it might do with what other entities might do and so on.

'Exists' seem to be quite an open concept.

But could that-which-exists be understood as including tendencies and relationships ? What of the conception of an entity as essentially relational ? An electron 'is' what it might do with what other entities might do and so on. — Pie

I have no idea what it means to say that a counterfactual scenario exists. I suppose that I could understand what it means for the future to exist (i.e. eternalism), but I don't think eternalism is required for me to be wrong about the future. And I don't think mathematical realism (or a bunch of other mathematicians) is required for me to get maths wrong.

How do you feel about Hamlet ? Or Charlie Brown ?

I feel no loyalty to any definition of the real. I don't take a vision of elementary particles 'behind' things as the really real, for instance. Sidewalks and promises and electrons and Snoopy and even sensations and thoughts exist.

How do you feel about Hamlet ? Or Charlie Brown ? — Pie

They don't exist, but books about them do.

They don't exist, but books about them do. — Michael

That might explain some of our talking past one another. To me, electrons and marriages are just characters in a story too.

We call some stories true.

And I don't think mathematical realism (or a bunch of other mathematicians) is required for me to get maths wrong. — Michael

Nor I.

But I speculate that it doesn't make much sense to get math wrong if you are the only being.

I suppose we must allow the edge case of the sole survivor finding the zeros of polynomials, but this is just the guy in the woods writing poetry.

But I speculate that it doesn't make much sense to get math wrong if you are the only being. — Pie

I would say that pi is irrational even if I'm the last man alive and even if I believe otherwise.

I would say that pi is irrational even if I'm the last man alive and even if I believe otherwise. — Michael

I understand why one would. But if no one else had ever existed, it'd be hard to find a meaning for 'pi.'
Of course there'd be no language in the first place.

But if no one else had ever existed, it's hard to find a meaning for 'pi.' — Pie

Someone coined the term "pi". He was quite capable of coining it without assistance.

I learned what $\pi$ was in the context of an axiomatic system, as intimately related to the first positive zero of a famous trigonometric function. Its existence is proven within a complex system, developed over centuries. Is math still math if I make it all up myself ?

Someone coined the term "pi". He was quite capable of coining it without assistance. — Michael

So for you it preexisted us...and you are not a platonist ?

My take is that the 'I' is logically/semantically an appendage of the 'we.' The self that speaks and thinks is fundamentally tribal, social, other-directed, and self-transcending. But I don't expect to be believed without justification. I'm just abbreviating my position, for context.

So for you it preexisted us...and you are not a platonist ? — Pie

I think that the truth of "God does not exist" is mind-independent. And I think that "God does not exist" is true. But I don't think that God's non-existence "exists" as some Platonic fact.

And the same with maths.

But leaving maths aside, even if the solipsist knows that only his mental phenomena exists he doesn't know what his mental phenomena will be tomorrow, and so he doesn't know everything.