Silas: I agree that if arithmetic is a human invention, then my counterexample goes away.
If I’ve read you correctly, you believe that arithmetic is a human invention, and therefore reject the counterexample.
On that reading, a key locus of our disagreement is whether arithmetic is a human invention. I think the answer is clearly no, for reasons I’ve written about so extensively that I’d rather not rehash them here.
I’m not sure, though, that I’ve read you correctly, because you occasionally say things like “The Map Is Not The Territory” which seems to presuppose some sort of platonic Territory. But maybe I just don’t understand what you meant by this phrase.
[Incidentally, it occurs to me that perhaps you are misreading my use of the word “model”. I am using this word in the technical sense that it’s used by logicians, not in any of its everyday senses.]
Less confusing than saying “belief and reality”, “map and territory” reminds us that a map of Texas is not the same thing as Texas itself. Saying “map” also dispenses with possible meanings of “belief” apart from “representations of some part of reality”.
Since our predictions don’t always come true, we need different words to describe the thingy that generates our predictions and the thingy that generates our experimental results. The first thingy is called “belief”, the second thingy “reality”.
I agree that if arithmetic is a human invention, then my counterexample goes away.
Then you agree that your “counterexample” amounts to an assumption. If a Platonic realm exists (in some appropriate sense), and if Dawkins was haphazardly including that sense in the universe he is talking about when he describes complexity arising, then he wrong that complexity always comes from simplicity.
If you assume Dawkins is wrong, he’s wrong. Was that supposed to be insightful?
On that reading, a key locus of our disagreement is whether arithmetic is a human invention. I think the answer is clearly no, for reasons I’ve written about so extensively that I’d rather not rehash them here.
It’s a false dispute, though. When you clarify the substance of what these terms mean, there are meanings for which we agree, and meanings for which we don’t. The only error is to refuse to “cash out” the meaning of “arithmetic” into well-defined predictions, but instead keep it boxed up into one ambiguous term, which you do here, and which you did for complexity. (And it’s kind of strange to speak for hundreds of pages about complexity, and then claim insights on it, without stating your definition anywhere.)
One way we’d agree, for example, is if we take your statements about the Platonic realm to be counterfactual claims about phenomena isomorphic to certain mathematic formalisms (as I said at the beginning of the thread).
[Incidentally, it occurs to me that perhaps you are misreading my use of the word “model”. I am using this word in the technical sense that it’s used by logicians, not in any of its everyday senses.]
The definitions aren’t incredibly different, which is why we have the same term for both of them. If you spell out that definition more explicitly, the same problems arise, or different ones will pop up.
(By the way, this doesn’t surprise me. This is the fourth time you’ve had to define a term within a definition you gave in order to avoid being wrong. It doesn’t mean you changed that “subdefinition”. But genuine insights about the world don’t look this contorted, where you have to keep saying, “No, I really meant this when I was saying what I meant by that.”)
The only error is to refuse to “cash out” the meaning of “arithmetic” into well-defined >predictions, but instead keep it boxed up into one ambiguous term,
Silas: This is really quite frustrating. I keep telling you exactly what I mean by arithmetic (the standard model of the natural numbers); I keep using the word to mean this and only this, and you keep claiming that my use of the word is either ambiguous or inconsistent. It makes it hard to imagine that you’re actually reading before you’re responding, and it makes it very difficult to carry on a dialogue. So for that reason, I think I’ll stop here.
When I saw this in the comment feed, I thought “Wow, Steve Landsburg on Less Wrong!” Then I saw that he was basically just arguing with one person.
While I think you’re not correct in this debate, I hope you’ll continue to post here. Your books have been a source of much entertainment and joy for me.
Bo102010: Thanks for the kind words. I’m not sure what the community standards are here, but I hope its not inappopriate to mention that I post to my own blog almost every weekday, and of course I’ll be glad to have you visit.
I can second that. Though, for a lack of education, I cannot tell who’s right in this debate, I don’t think anybody is for that it is just pure metaphysical musing about the nature of reality. But so far I really enjoyed reading your book. I also hope you’ll participate in other discussions here at lesswrong.com. It’s my favorite place.
Sorry for possible bad publicity, I committed the mistake to quick-share something which I’ve just read and found intriguing. Without the ability to portray it adequately. Especially on this forum which is rather about rationality as practical tool to attain your goals and not pure philosophy detached from evidence and prediction.
I also subscribed to your blog.
P.S.
Send you a message, you can find it in your inbox.
Are you reading my replies? Saying that arithmetic is “the standard model of the natural numbers” does not
“cash out” the meaning of “arithmetic” into well-defined predictions
For one thing, it doesn’t give me predictions (i.e. constraints on expectations) that we check to see who’s right.
For another, it’s not well-defined—it doesn’t tell me how I would know (as is necessary for the area of dispute) if arithmetic “exists” at this or that time. (And, of course, as you found out, it requires further specification of what counts as a model...)
(ETA: See Eliezer_Yudkowsky’s great posts on how to dissolve a question and get beyond there being One Right Answer to e.g. the vague question about a tree falling in the forest when no one’s around.)
So if you don’t see how that doesn’t count as cashing out the term and identifying the real disagreement, then I agree further discussion is pointless.
But truth be told, you’re not going to “stop there”. You going to continue on, promoting your “deep” insights, wherever you can, to people who don’t know any better, instead of doing the real epistemic labor achieving insights on the world.
Silas: I agree that if arithmetic is a human invention, then my counterexample goes away.
If I’ve read you correctly, you believe that arithmetic is a human invention, and therefore reject the counterexample.
On that reading, a key locus of our disagreement is whether arithmetic is a human invention. I think the answer is clearly no, for reasons I’ve written about so extensively that I’d rather not rehash them here.
I’m not sure, though, that I’ve read you correctly, because you occasionally say things like “The Map Is Not The Territory” which seems to presuppose some sort of platonic Territory. But maybe I just don’t understand what you meant by this phrase.
[Incidentally, it occurs to me that perhaps you are misreading my use of the word “model”. I am using this word in the technical sense that it’s used by logicians, not in any of its everyday senses.]
Map and territory
More: Map and Territory (sequence)
Then you agree that your “counterexample” amounts to an assumption. If a Platonic realm exists (in some appropriate sense), and if Dawkins was haphazardly including that sense in the universe he is talking about when he describes complexity arising, then he wrong that complexity always comes from simplicity.
If you assume Dawkins is wrong, he’s wrong. Was that supposed to be insightful?
It’s a false dispute, though. When you clarify the substance of what these terms mean, there are meanings for which we agree, and meanings for which we don’t. The only error is to refuse to “cash out” the meaning of “arithmetic” into well-defined predictions, but instead keep it boxed up into one ambiguous term, which you do here, and which you did for complexity. (And it’s kind of strange to speak for hundreds of pages about complexity, and then claim insights on it, without stating your definition anywhere.)
One way we’d agree, for example, is if we take your statements about the Platonic realm to be counterfactual claims about phenomena isomorphic to certain mathematic formalisms (as I said at the beginning of the thread).
The definitions aren’t incredibly different, which is why we have the same term for both of them. If you spell out that definition more explicitly, the same problems arise, or different ones will pop up.
(By the way, this doesn’t surprise me. This is the fourth time you’ve had to define a term within a definition you gave in order to avoid being wrong. It doesn’t mean you changed that “subdefinition”. But genuine insights about the world don’t look this contorted, where you have to keep saying, “No, I really meant this when I was saying what I meant by that.”)
Silas: This is really quite frustrating. I keep telling you exactly what I mean by arithmetic (the standard model of the natural numbers); I keep using the word to mean this and only this, and you keep claiming that my use of the word is either ambiguous or inconsistent. It makes it hard to imagine that you’re actually reading before you’re responding, and it makes it very difficult to carry on a dialogue. So for that reason, I think I’ll stop here.
When I saw this in the comment feed, I thought “Wow, Steve Landsburg on Less Wrong!” Then I saw that he was basically just arguing with one person.
While I think you’re not correct in this debate, I hope you’ll continue to post here. Your books have been a source of much entertainment and joy for me.
Bo102010: Thanks for the kind words. I’m not sure what the community standards are here, but I hope its not inappopriate to mention that I post to my own blog almost every weekday, and of course I’ll be glad to have you visit.
I can second that. Though, for a lack of education, I cannot tell who’s right in this debate, I don’t think anybody is for that it is just pure metaphysical musing about the nature of reality. But so far I really enjoyed reading your book. I also hope you’ll participate in other discussions here at lesswrong.com. It’s my favorite place.
Sorry for possible bad publicity, I committed the mistake to quick-share something which I’ve just read and found intriguing. Without the ability to portray it adequately. Especially on this forum which is rather about rationality as practical tool to attain your goals and not pure philosophy detached from evidence and prediction.
I also subscribed to your blog.
P.S. Send you a message, you can find it in your inbox.
Are you reading my replies? Saying that arithmetic is “the standard model of the natural numbers” does not
For one thing, it doesn’t give me predictions (i.e. constraints on expectations) that we check to see who’s right.
For another, it’s not well-defined—it doesn’t tell me how I would know (as is necessary for the area of dispute) if arithmetic “exists” at this or that time. (And, of course, as you found out, it requires further specification of what counts as a model...)
(ETA: See Eliezer_Yudkowsky’s great posts on how to dissolve a question and get beyond there being One Right Answer to e.g. the vague question about a tree falling in the forest when no one’s around.)
So if you don’t see how that doesn’t count as cashing out the term and identifying the real disagreement, then I agree further discussion is pointless.
But truth be told, you’re not going to “stop there”. You going to continue on, promoting your “deep” insights, wherever you can, to people who don’t know any better, instead of doing the real epistemic labor achieving insights on the world.