I wonder, who doubts the existence of the universe? — Banno
The Boltzmann brain argument suggests that it is more likely for a single brain to spontaneously and briefly form in a void (complete with a false memory of having existed in our universe) than it is for the universe to have come about in the way modern science thinks it actually did.
...and in what did said brain appear? — Banno
I take your point that the atoms had to be there already — fishfry
I wonder, who doubts the existence of the universe? — Banno
Don't you mean prove to their own satisfaction?Any rational person ought to doubt of everything he or she cannot prove. — Alexandre Harvey-Tremblay
But here's a question I think fair even if I don't read your OP - and if the answer is in it, then you can just point me back to it. How does mathematics prove anything about anything that is not mathematics? Key word being prove. — tim wood
How does mathematics prove anything about anything that is not mathematics? Key word being prove. — tim wood
(In fact, he doubted mathematics a priori) — Gregory
Any rational person ought to doubt everything he or she cannot prove. — Alexandre Harvey-Tremblay
The only thing you can prove is that man's intelligence is incapable of accessing Reality in any substantial way. — synthesis
I fact, I have shown that man's intelligence is incapable of [departing] reality (necessary coupling to the universe). The exact opposite of what you claim. — Alexandre Harvey-Tremblay
Define universal facts.
1. Show that universal facts are true for all possible world.
2. Show that universal facts are computationally universal.
3. Define reality as a subset of universal facts.
4. Define a transformation of reality as bijection of the powerset of universal facts onto itself.
5. Show that the maximally informative (e.g. entropy maximization of a probability measure) interpretation of a transformation of reality, is bounded to a mathematical structure isomorphic to the universe.
How does mathematics prove anything about anything that is not mathematics? Key word being prove.
— tim wood
6. Easy; The existence of such a proof precludes the possibility that the universe is not. — Alexandre Harvey-Tremblay
I leave the math to you. But for its utility in 6), one might say that for all and any X, if X exists then the universe (i.e., that which contains X) exists — tim wood
1) A fact is a proposition, as such never in itself true. Or, to say that a fact is true is a syntactical statement which in itself says nothing about the world. Of course this is not ordinary usage, but then the context is not ordinary. — tim wood
If we use the tools of algorithmic information theory, we can write definitions that have no exploits whatsoever: A universal Turing machine which takes a Turing machine $TM$ and a sentence $p$ as inputs, will halt iff $p$ halts on $TM$. Thus the fact that $p$ halts on $TM$ is indeed a fact because it is verifiable on all universal Turing machine. Note the improvement provided by algorithmic information theory in terms of elegance, clarity, loop-hole elimination and language-dependance elimination (no need for any specific symbols such as $\vdash,\implies, etc$... just a sentence $p$ that may in principle use any symbol). The possible facts of reality are then simply the set of all pairs $(TM,p)$ which halts on all universal Turing machines... yielding a completely indubitable definition of reality consistent with the original intent of the philosophical definition of reality in terms of facts, but now formally defined.
Let $(\operatorname{TM},p)$ be a pair comprising two sentences of a language $\mathbb{L}$. The first sentence, $\operatorname{TM}$, is called the protocol. The second sentence, $p$, is called the hypothesis. Let $\operatorname{UTM}$ be a universal Turing machine. If $\operatorname{UTM}(\operatorname{TM},p)$ halts then the pair $(\operatorname{TM},p)$ is a (successful) experiment. In this case, we say that the protocol verifies the hypothesis.
An experiment, so defined, is formally reproducible. I can transmit, via fax or other telecommunication medium, the pair $(\operatorname{TM},p)$ to another experimentalist, and I would know with absolute certainty that he or she has everything required to reproduce the experiment to perfection. Indeed, for the protocol $\operatorname{TM}$ to be a Turing machine, the protocol must specify all steps of the experiment including the complete inner workings of any instrumentation used for the experiment. The protocol must be described as an effective method equivalent to an abstract computer program. Should the protocol fail to verify the hypothesis, the entire experiment (that is the group comprising the hypothesis, the protocol and including its complete description of all instrumentation) is rejected.
The set of all experiments are the programs that halt. The set includes all provable mathematical statements and it is universal in the computer theoretic sense. The set of all experiments is the same as the set of all universal facts, and thus, necessarily, can be used to constitute a complete description of reality for the same reasons as those described in the first perspective.
Any rational person ought to doubt of everything he or she cannot prove. — Alexandre Harvey-Tremblay
That may be, but said universe follows the laws of physics only if you do it my way. — Alexandre Harvey-Tremblay
a thing that is known or proved to be true. — Alexandre Harvey-Tremblay
The possible facts of reality are then simply the set of all pairs $(TM,p)$ which halts on all universal Turing machines... yielding a completely indubitable definition of reality consistent with the original intent of the philosophical definition of reality in terms of facts, but now formally defined.
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