Pippen

Hi Tim, I add "If S is consistent then G (is not provable)" to S as an axiom. It then becomes clear why we can't prove the consistency of S within S b...

Both impossible if p & ~p becomes true because then we couldn't talk/think straight/meaningfully. More and more it seems that the main difference betw...

I can't, you are right. My line of thinking goes like this: Imagine tomorrow the proposition "p & ~p" becomes somehow true! At that point our logic wo...

But we assume there's only one world, therefore just one roll of your million-sided die which we assume as random. And if you roll there a 566, what w...

Not really. It just means trivialism, i.e. everything becomes true, but I can still talk and be understood on an ostensive level. That sounds enough m...

@EEE: I don't care about the creator at all. My argument only is that because of statistical reasons it is very probable that we were created non-rand...

But your answer implies that it could happen and so we'd need to adjust our logic and math, but that means the problem of induction also applies to lo...

Again: Why is it impossible that we wake up tomorrow in a world where one tiny particle has the property to be and not to be (which would make the who...

Let me re-emphasize my thought-experiment: Suppose the world changes overnight so that it becomes impossible to model an implication (per se and of co...

Why? P, P -> Q | Q is just right because it follow from some rules. But these rules can change overnight, can they? So MP could be true today but fals...

But from your (3) it also follows that you can't control your very argument, so how can you believe in it? That's exactly my problem.

Just that we not forget it: the question is if one can hold determinism rationally because it seems in case one holds determinism, i.e. thinks determi...

No, I choose to believe in non-contradiction, because it compares better to the alternative (contradictions). Without an alternative you can't compare...

Actually we do, because we choose our rules of logic out of many possible alternatives, because they work better than others and because they persuade...

Here's a better version of my proof of nihil ex nihilo: 1. We postulate the empty set as an universe (= representation of nothingness). 2. We assume s...

@terrapin station: Ok, let's assume only ? + time. Still it's (logically) impossible for a thing to exist from these premises.

@fooloso4: We just can reason within our intellectual scope, i.e. logic and meaningful concepts. My proof wants to show that within our scope it's imp...

No. If we assume only ? then nothing else matters, not even time. No thing can come out of this assumption, no matter how one twists it.

1. Let's postulate only ? (Nothingness). 2. Let's assume some t, but that's contradicting 1., so it's impossible. 3. Conclusion: If only ? then nothin...

1. Let me present you a more simple version of my argument "nothing can come from nothing" which renders a creatio ex nihilo impossible, an argument w...

Definitely appreciate your input. 1) By definition my set contains only things that exist (non-contradictory). That excludes Russell's set. No Russell...

Russell's paradox is no problem since I don't talk about the set of everything, but the set of everything that exists. That's a huge difference. Obvio...

How do you prove G to be true in T? You can't for then you'd prove G and contradict to its content. So G is true or false in T but we cannot know it (...

First of all I disagree with Srap that you can't have a predicate "is true/false" in PL. I think you can have, but sometimes it leads to inconsistenci...

@srap: Why can't I have "is a statement" and "is false" in predicate logic? @Meta: Your formulation in propositional logic is too simple, you can't ex...

That's my point. The problem is this: To prove that (S) "All sentences are false" is not a wff, I have to assume that S = S' with (S') "All sentences ...

Yes, that's my point. Now, a conjunction of the form " & P" is neither a conjunction nor a proposition at all, because a conjunction is formally defin...

@Michael: It may not be true, but it wouldn't be false either. It would hang in the middle between the two values.

Yeah, but that statement wouldn't be false either! And it's a huge difference if a statement is false or not false (no matter if it's true or not besi...

I assume a set of all statements as the domain. Then indeed ?x(Sx?Fx) means: everything is a statement and everything is false. But that's exactly wha...

Ok, but why is my formulation of "All statements are false" as ?x(Sx?Fx) impossible and only ?x(Sx?Fx) the correct formulation? Is there any reason? B...

Here is what I found out so far: The logicians formulate "All (S)tatements are (F)alse" as follows: All x: (Sx -> Fx). If you do that you can indeed p...

Not in classical logic. Not having a truth value is not a third option there. I think 2. of my proof is dubious, maybe nagase will check that out.

@Michael: We are dealing just in the scope of classical (two-valued) logic and there a statement like "This statement is false" is just without a trut...

You are right with the reference, but if the part "...this statement is false" is false then it'd be true (and vice versa false if it's true), isn't i...

Why? 1. We assume (A) "All statements are false" has a truth value. 2. Since we can always go from "All x are y" (x may stand for 1,2,3 here) to for i...

Yes, but maybe this proof makes everything clearer:. If "All statements are false" would have a truth value and therefore would be a statement, it'd f...

But I say that "All statements are false" has no truth value and therefore can't be false. And my proof is simple: We know that (S') "All statements, ...

But if (S) "All statements are false" is illogical - like I want to prove - then it can't be false (and therefore it's negation be true) like the majo...

~p -> p is not equivalent to ~p & p, that's my point. Now if creatio ex nihilo is modeled as: ~p & ~p -> q then it's logically possible. Is there any ...

No. It's an implication, not a conjunction. So your model would look like this: ~p & ~p -> p(t>0). Correct? Well, this would be inconsistent too, beca...

How would your model of a creation out of nothing look like if you don't accept mine?

I disagree, because I interpret the implication arrow (->) as "then", a consequence in a formal, non-physical way. So ~p -> p means "if there exists n...

@bluebanana: Let's clearfy things. 1. Let p = "There exists at least one thing", so ~p = "There exists no thing at all". 2. Let creatio ex nihilo = ~p...

@Srap: We agree. The set of premises ~p and ~p -> p is inconsistent, but I ask you: isn't this set of premises modeling what we think should be going ...

@Sophicat: ~p -> p is not a contradiction! And IMO I can interpret the implication "->" as a kind of "follows from". But even if I do not: If I have ~...

A lot is not so good here, but anything is better than nothing. 1. Citations should be in grey body to distinguish them better from the answer. 2. We ...

If p stands for "something exists", ~p stand for "nothing exists" and ~p -> p for "something follows from nothing" then I can prove that ~p and ~p -> ...

@madfool: My claim is that we can prove from logic that nothing must come from nothing. Yes, I use propositional logic in an odd way for my variables ...

@srap: I don't understand what you mean. The creatio ex nihilo is modeled by me as "~p & (~p -> p)" and that is logically impossible which means nothi...