Here's my proof:

Let G be the claim that Goldbachs Conjecture is true.
Furthermore, we add as a premise that G is not proven, and also ~G is not proven.
Let P be the claim that an unproven truth is true.
G is true or it's not true
G v ~G (law of excluded middle)
G -> P (because G is unproven, if it's true, P must be true)
~G -> P (because ~G is unproven, if it's true, P must be true)
assume ~P
....... ~P implies ~G (by applying contraposition to G -> P)
....... ~G
....... ~P implies G (by applying contraposition to ~G -> P)
....... G
....... G ^ ~G is a contradiction, so we can conclude that
P



There's my proof that there's an unproven truth.

How about this: Goldbachs Conjecture

We've got two claims here: GC is true, or GC is false.

One of those two claims is an unproven truth. The other one is unproven and false.

so you won't be able to prove it if I can't name one?

what process do you think shifting sand is implementing that's conscious?

No, I don't think there are unprooven truths. — SpaceDweller

Can you prove it? Can you prove there aren't any?

oh well then, in principle... MAYBE

Though I'm partial to the idea that, rather than dominos being conscious, or a computer being conscious, or a brain made of neurons being conscious, what if it's the *process* that's conscious? The process is substrate independent, maybe THAT'S the thing that's conscious, and not the thing the process is implemented on.

I believe someone linked to process philosophy earlier in the thread.

have fun

but the context is that for something to be true you need proof. — SpaceDweller

How in the world do you figure that?

You don't think there are any unproven truths?

I think if it can't, it's because what other people have mentioned - the dominos fall and don't pick themselves back up. Consciousness might require a certain level of recursion, and Dominos, becaus they fall and stay down, are kinda hampered in their ability to implement recursive algorithms.

I think computers - or even neurons - are basically fancy dominos without that limitation.

From what truth table? Would you mind posting the table here?

So the proof that you posted here then:

https://thephilosophyforum.com/discussion/comment/889798

That's not based on logical laws, that's... what, then? Just some of your own personal reasonings based on your own personal relevant inferences?

and yes there is mention of proof in the article but you're reluctant to study it — SpaceDweller

Does the article say "proof" and "truth" are synonyms? Because that's what you're saying.

We have already been over this before and I replied to you that this is not how epistemology works — SpaceDweller

I COMPLETELY AGREE that it's not how epistemology works. That's why I don't say things like "beliefs are justified iff they're true".

for example?

There is no hard coded laws here. — Corvus

I think classical logic very much has hard coded laws. Basic logic very much has hard coded laws. Logical proofs are a sequence of steps using hard coded logical laws.

I hope this helps you to understand my stance? — SpaceDweller

No, unfortunately it doesn't. Your use of various terms in this conversation has seemed wildly and irreconcilably inconsitsent to me. First you say, if a belief is true then it's justified. Then you say my belief in something was not justified - even though it was true.

Yesterday, before I went home, I believed my house was still there and was still going to be there when I got home - you said this was unjustified, but I went home and it turned out to be true! So if it was true, how could it be unjustified, if you think all true beliefs are justified?

This starts out sounding like a 'yes' but ends up sounding like a 'no'.

What's an example where (A implies B) is true, but (~B implies ~A) is not true?

When did PROOF become the T condition? T stands for "true", not "proof".

Do you think JTB stands for "Justified Proved Belief"?

Anyway "certain" or "proof" is same thing here. you have no proof that your house will be there in the future. — SpaceDweller

But if it's true, then it's justified, right? That's what you were saying yesterday.

If you believe something that's true, then it's justified.
— flannel jesus
Yes.
— SpaceDweller

Sure, if the truth table says so, then it must be it — Corvus

So do you agree that, if one accepts a statement (A -> B), then according to classical logic one must always accept the contraposition, (~B -> ~A)?

If you believe something that's true, then it's justified.
— flannel jesus
Yes. — SpaceDweller

You said it yourself here. If it's true, then I'm justified.

Thus your belief is not justified because what you believe is not true for certain. — SpaceDweller

But that's not what you said before. You said before that a belief is justified if it's true. If I believe it, and it's true, then it's justified, regardless of if I'm certain - that's the implication of your wording.

If it's raining, then the ground is wet.
The ground is not wet, so it's not raining.

This doesn't seem like it depends on anything to me - if the first `if-then` is true, then the second `if-then` is true. In classical logic, given a statement of implication, contraposition is taken to be always true, not "it depends".

In classical logic, A -> B being true always means ~B -> ~A is also true.

They have the same truth tables as each other.

Do you have an example for this?

An example where a implies b, but it's not true that not b implies not a.

yeah, physicists can believe in just about anything - the only thing they're almost guaranteed to believe in is the efficacy of learning about the world through observation and experiment.

if it depends, I would love to see some examples. I would love to see an example from you where the answer is "yes" and an example from you where the answer is "no".

An example where a implies b, and not b implies not a,

and an example where a implies b, but it's not true that not b implies not a.

I'm especially interested in the second example. The first example is very agreeable. The second is much more tricky, I think.

Yes, it is correct. — Corvus

Awesome, and this one?

And is the same thing true about the contrapositive? For every (a implies b) it's always true that (not b implies not a), correct? Even if it's not always useful to bring it up, it's always true?

I need clear, unambiguous answers. Preferably Yes or No.

One thing at a time

So do you think any time you have (a implies b) , it's always true that (not a implies not b), you just don't always need to bring that up. Is that what you're saying?

I think I misread this before. You're saying you "don't have to apply it", but you always can right? You CAN always apply it, because it's always true, you're just saying there's not always a contextual need to apply it, is that right?

So any time you have (a implies b) , it's always true that (not a implies not b), you just don't always need to bring that up. Is that what you're saying?

And is the same thing true about the contrapositive? For every (a implies b) it's always true that (not b implies not a), correct? Even if it's not always useful to bring it up, it's always true?

. Ignore this, see next post

there's more than one flavour of random. That's why I'm comparing it to a seeded random generator, and bringing up chaos - chaotic deterministic systems can be "effectively random" even if they're not actually genuinely random

What's the assumption? Specifically.

Does (a implies b) always lead to (not a implies not b), or only sometimes?

wait you edited this response, we have to go back. We need clarity on this conversation or nothing will work.

It either always applies, or it doesn't always apply. When you say you think I'm right, that means it always applies. But then you say it depends on the case. It either always applies, or it depends on the case, it can't be both.

do you have examples where it doesn't apply?

Examples of a implies b where is not true that not b implies not a

Do you also agree with the contrapositive rule, which states that if (a implies b), then (not b implies not a)?

That sounds like you're confirming that yes, it's always applicable any time you have (a implies b), am I interpreting that correctly?

Would you mind explicitly stating if every (a implies b) also leads to (not a implies not b), or can you only do that for specific (a implies b) statements?

Are there any exceptions?

if you agree with corvus, I wouldn't mind talking to you about why.

If you disagree, it would be appreciated if you expressed briefly why but, ideally, exited the thread after that to avoid too many overlapping debates and confusion.

If corvus has other preferences, I welcome him to express them and hopefully they can be accommodated.

they're random in one sense and not in another. They're not RANDOM random, but they're distributed as if they were random and unpredictable ahead of time like they would be if they were random.

Pi is effectively a seeded random number generator. A deterministic-yet-chaotic generator of digits.

Sure, knowledge is a rigorously arrived at belief in JTB theories of truth. — Bylaw

Equally rigourously if you drop the T though. The rigor is all in the J - the J is where all our confidence in the T comes from.

If it's rigor we're looking for, then we should place a threshold on the minimum amount of J before we call it "knowledge". Which is probably what we do anyway, given we don't have access to a universal dictionary of objective truths.

And then we just have beliefs with varying levels of justification, and the ones with the most justification we call "knowledge" - and some of that knowledge is probably wrong.