prase comments on A Sketch of an Anti-Realist Metaethics - Less Wrong

16 Post author: Jack 22 August 2011 05:32AM

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Comment author: prase 22 August 2011 11:36:52AM 0 points [-]

x(x {is an element of} IM) & (x = M)

Shouldn't x be a subset of IM rather than an element?

Also, do you somewhere define what the ideal map is?

Comment author: Jack 22 August 2011 11:47:24AM 0 points [-]

To the first, I just changed it. To the second, I was attempting to do that in the first section, though obviously not formally. What I mean by it is the map that corresponds to the territory at the ideal limit Einstein is talking about.

Comment author: prase 22 August 2011 01:09:33PM 0 points [-]

What I mean by it is the map that corresponds to the territory at the ideal limit Einstein is talking about.

Well, yes, but, is IM set of sentences compatible with experimental results, or set of sentences whose negation is incompatible with the results? What about sentences speaking about abstract concepts, not directly refering to experimental results?

Comment author: Jack 22 August 2011 06:35:06PM 0 points [-]

This depends on your philosophy of science and what science ultimately decides exists. The exact answer doesn't really matter for the purposes of the post and it's a huge question that I probably can answer adequately in a comment. Basically, it's what would be in a universal theory of science. I'm not constraining it to eliminative reductionism- i.e. I have no problem including truths of economics and biology in IM in addition to truths about physics. Certainly the conjunction of 'sentences compatible with experimental results' and 'sentences whose negation is incompatible with experimental results' is too broad (are those sets different?). We would want to trim that set with criteria like generality and parsimony.

Comment author: prase 22 August 2011 07:21:37PM 0 points [-]

My concern was mainly with propositions which aren't tied to observation, albeit being true in some sense. Mathematical truths are one example, moral truths may be another. The language is presumably able to express any fact about the territory, but there is no clear reason that any expression of language represents a fact about the territory. The language may be broader. Therefore,

Now it might seem that [...] moral realism must be true (where else but the territory could morality be?)

seems a bit unwarranted. Morality could be only in the map.

Comment author: Jack 22 August 2011 07:25:48PM 1 point [-]

Now I'm confused. Beliefs that don't correspond to the territory are what we call "wrong".

Comment author: prase 22 August 2011 07:51:15PM 0 points [-]

Is "this sentence is true" a wrong belief?

Comment author: Jack 22 August 2011 08:09:11PM *  2 points [-]

Its a classic problem case. I think its semantic function calls itself and so it is meaningless. See here.

Comment author: lessdazed 22 August 2011 09:41:40PM 0 points [-]

I understand why people might think this was a snarky and downvote worthy comment with an obvious answer, but I greatly appreciated this comment and upvoted it. That is to say, it fits a pattern for questions the answers of which are obvious to others, though the answer was not obvious to me.

What's worse, at first thought, within five seconds of thinking about it, the answer seemed obvious to me until I thought about it a bit more. Even though I have tentatively settled upon an answer basically the same as the one I thought up in the first five seconds, I believe that that first thought was insufficiently founded, grounded, and justified until I thought about it.

Comment author: prase 23 August 2011 08:48:30AM 1 point [-]

Just to clarify, I wanted to point out that sentences are not the same category as beliefs (which in local parlance are anticipations of observations). There can be gramatically correct sentences which don't constrain anticipations at all, and not only the self-referential cases. All mathematical statements somehow fall in this category, just imagine, what observations one anticipates because believing "the empty set is an empty set". (The thing is a little complicated with mathematical statements because, at least for the more complicated theorems, believing in them causes the anticipation of being able to derive them using valid inference rules.) Mathematical statements are sometimes (often) useful for deriving propositions about the external world, but themselves don't refer to it. Without further analysing morality, it seems plausible that morality defined as system of propositions works similarly to math (whatever standards of morality are chosen).

The question is, whether this should be included into the ideal map. To peruse the analogy with customary geographic maps, mathematical statements would refer to descriptions of regularities about the map, such as "if three contour lines make nested closed circles, the middle one corresponds to height between the heights of the outermost one and the innermost one". Such facts aren't needed to read the map and are not written there.

If my remark seemed snarky, I apologise.

Comment author: Vladimir_Nesov 23 August 2011 09:01:07AM *  1 point [-]

Mathematical statements are sometimes (often) useful for deriving propositions about the external world, but themselves don't refer to it.

What's the distinction between the two? (Useful for deriving propositions about smth vs. referring.)

Comment author: Vladimir_Nesov 23 August 2011 08:54:57AM *  0 points [-]

There can be gramatically correct sentences which don't constrain anticipations at all, and not only the self-referential cases. All mathematical statements somehow fall in this category, just imagine, what observations one anticipates because believing "the empty set is an empty set".

If you build an inference system that outputs statements it proves, or lights up a green (red) light when it proves (disproves) some statement, then your anticipations about what happens should be controlled by the mathematical facts that the inference system reasons about. (More easily, you may find that mathematicians agree with correct statements and disagree with incorrect ones, and you can predict agreement/disagreement from knowledge about correctness.)