A wild theist platonist appears, to ask about the path

Hang

I recognize the title could be more informative. At the same time I believe it says what is important.
I believe in a deity, I believe in mathematical entities in the same way.

The community of LessWrong (from whenceforth: LessWrong) is deeply interesting to me, appearing as a semi-organized atheist, reductionist community.
LessWrong seems very interested in promoting rationality, which I applaud. The effort does seem scattered, though, and this is the reason I post.

One has Eliezer's website with some interesting posts. The same of this community. The community links to some posts when you are coming for the first time into it, and you also have a filter for top posts. One has the blog. And recently, the center for modern rationality (in the same page as harrypoter fanfiction about rationality).

The point being there is no defined roadmap to go from AIC (average irrational chump to make an analogy to Game - which also seems to come up around quite a bit) to RA (again, rationality artist).

I write this post as to maybe generate a discussion on how the efforts could be concentrated and a new direction taken.

Should the creation of the Center for Modern Rationality envision this same concentration, this post may and should be disregard.
If it does not, then I leave it to your consideration.

Hang.

I included the qualification "the formal systems that you're thinking of". Were you thinking of that formal system when you wrote (quote)

I wasn't, but I rather strongly opine that the word 'exists' should not be applied to a state that can change with the vagaries of what formal system I happen to be thinking of. At an absolute minimum, it should be qualified along the lines of "X exists within formal system Y" or "The existence of X is a theorem of formal system Y". At which point I can return to my original question: What is the formal system of which "God exists" is a theorem or axiom? I also note that "Given axioms X, God exists" is somehow a rather less impressive claims than a floating "God exists". Yet it's so much more specific and satisfactory.

To answer your original question, the platonist need only point to a particular formal system (e.g., PA), and say that the nonexistence of the number 2 would mean that there would be no proof of 2's existence in that particular system.

This is at least an answer to the question, "What is meant by 'exist'?"; it gives us a definite procedure for deciding what does and doesn't exist. But I opine that it's not a very satisfactory one. Why that formal system and not some other one?

But it is not even known whether the TPC is decidable in any of the standard formal systems. Suppose that the TPC were proved undecidable in, say, ZFC. Would the question really then lose all meaning? Consider a physical computer that brute-force factors one odd number after the next, and prints every consecutive pair of odd numbers that have no nontrivial factorizations. Would it really become meaningless to ask whether there is a bound on how many entries the computer would print, regardless of how many physical resources it were given?

I don't think so, but I'm not sure I understand the relevance, but what I'm objecting to is the word 'exists'. Suppose you established that the computer was going to print these two numbers and then stop. That is an experimental prediction which we can test. (Updating our belief in the proposition upwards with every second that the computer prints nothing more.) I still don't see the value in asserting on these grounds that something exists. Why not stick with what is observable, namely that the computer halts, or doesn't halt?

If you want to say that 'exists' is a short form of "the computer halts", fine; but it does not seem to me that this is what platonists usually intend to say. And, to return to the original problem, it is still completely unclear what "God exists" is shorthand for.

I don't think so, but I'm not sure I understand the relevance, but what I'm objecting to is the word 'exists'.

Why not stick with what is observable, namely that the computer halts, or doesn't halt?

This is a universal counterargument against saying that anything besides what we are currently observing exists.

1Tyrrell_McAllister14y

The platonist certainly agrees. The test I described would only work for "accurate" maps of the territory. The platonist would consider PA to be an accurate (but incomplete) map of the actual natural numbers, while the formal system you described is not. [...] Actually, I was a little sloppy, there. When speaking on behalf of the platonist, I shouldn't have written "would mean", but rather "would imply". The point is that I wasn't defining what "the number 2 exists" means, but rather describing what the world would be like if the number 2 didn't exist. At any rate, I don't mean to be giving a "definite procedure". For the platonist, PA is an accurate, but incomplete, map. Consider that there probably exist physical things of which we will never find any empirical trace. Similarly, the platonist expects that there exist mathematical objects that remain entirely unmapped by our formal systems or intuitions. [...] If you would be willing, on these grounds, to assert with some confidence that the computer will never print any more pairs, why would you demure from asserting, on these same grounds, and with this same confidence, "A largest pair of twin primes exists, and this most-recently printed pair is it."? [...] (Just to clarify: The program I described never halts, even if the TPC is true. The program continues to run; it continues to brute-force factor progressively larger odd integers. It just never prints anything further to its output tape beyond a certain point.)

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A wild theist platonist appears, to ask about the path

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A wild theist platonist appears, to ask about the path

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