tag:blogger.com,1999:blog-5592542.post1090357761736000844..comments2024-03-18T17:28:44.693-07:00Comments on Rondam Ramblings: The last word (I hope!) on Fitch's paradoxRonhttp://www.blogger.com/profile/11752242624438232184noreply@blogger.comBlogger33125tag:blogger.com,1999:blog-5592542.post-11308410826408333962018-10-12T15:52:53.274-07:002018-10-12T15:52:53.274-07:00@Luke:
It also seems predicated upon LKp → p
LKp ...@Luke:<br /><i>It also seems predicated upon LKp → p</i><br /><br />LKp → p is not a premise of Fitch's Paradox. What is a premise of Fitch's Paradox is p -> LKp. I trust you are aware that the latter is not logically equivalent to the former. :-)Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-64618220011909508562018-10-12T13:23:30.285-07:002018-10-12T13:23:30.285-07:00> Given that I offered a candidate definition, ...> Given that I offered a candidate definition, why exactly did you write "even if you are too lazy and/or incompetent to actually come up with an acceptable definition"?<br /><br />Because the "candidate definition" you offered was:<br /><br />> can be computed within the next 200 years, barring civilization collapse<br /><br />This makes reference to TIME. But Fitch&#Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-32694912593834360992018-10-12T13:04:28.523-07:002018-10-12T13:04:28.523-07:00@Luke:
you and Ron portray yourselves as [vastly?]...@Luke:<br /><i>you and Ron portray yourselves as [vastly?] smarter than I am.</i><br /><br />You need to stop worrying about who is smarter and start concentrating on the actual subject of discussion. Perhaps Ron and I seem smarter to you because we are better at doing that. I can't speak for Ron, but thoughts about which of us is smarter, you or me, have not even crossed my mind. I have no Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-2618339167178660262018-10-12T12:08:42.624-07:002018-10-12T12:08:42.624-07:00@Ron:
> And how exactly are you going to deter...@Ron:<br /><br />> And how exactly are you going to determine how many steps are required?<br /><br />I <a href="http://blog.rongarret.info/2018/08/fitchs-paradox.html#c5473170804907763910" rel="nofollow">already linked</a> you the 1989 paper <a href="https://www.sciencedirect.com/science/article/pii/0168007289900122" rel="nofollow">On the number of steps in proofs</a>.<br /><br />> And whyLukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-17243810318969575342018-10-12T11:58:14.592-07:002018-10-12T11:58:14.592-07:00@Peter Donis:
> Which requires you to have a s...@Peter Donis:<br /><br />> Which requires you to have a semantic model of the computer that's doing the steps. (And yes, that makes the number of steps model-dependent.)<br /><br />Ok, so what about counting the number of steps required in the smallest currently known proof? There are 11 steps in <a href="https://en.wikipedia.org/wiki/Fitch%27s_paradox_of_knowability#Proof" rel="nofollow">Lukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-39635409898941935052018-10-12T07:47:43.375-07:002018-10-12T07:47:43.375-07:00> that doesn't stop people like Ron from t...> that doesn't stop people like Ron from thinking you really can use Kolmogorov complexity in discussions like this.<br /><br />That depends on what you want to use it *for*. If you want to use it as a theoretical construct to illustrate an abstract point, then sure. If you want to use it in a context that would require you to actually know its numerical value, then no.<br /><br />For Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-75824682935360595742018-10-10T17:03:47.703-07:002018-10-10T17:03:47.703-07:00that premise indicates that if I know something at...<i>that premise indicates that if I know something at the aggregate/high-level, then necessarily I know the component pieces. It means I can judge from appearance to constitution.</i><br /><br />That's not what I get from K(p & q) → (Kp & Kq). Let me translate back into plain English to explain why:<br /><br />K(p & q) → (Kp & Kq): I know that object I see out there is a red Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-34370398503831329462018-10-10T16:56:56.313-07:002018-10-10T16:56:56.313-07:00That's not what I get from (B) K(p & q) → ...<i>That's not what I get from (B) K(p & q) → (Kp & Kq).</i><br /><br />See, this is why Ron gets so frustrated with you. You're completely ignoring my response to what you said in your last post, and responding to something I didn't even say. *You* are the one who brought up seeing an object that could be a real barn or could be a facade, not me. If that is irrelevant to K(p &Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-41567924237081163792018-10-10T16:54:28.009-07:002018-10-10T16:54:28.009-07:00How about # of steps required?
Which requires you...<i>How about # of steps required?</i><br /><br />Which requires you to have a semantic model of the computer that's doing the steps. (And yes, that makes the number of steps model-dependent.)<br />Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-18407505167694096942018-10-10T16:52:48.241-07:002018-10-10T16:52:48.241-07:00where do the inconsistencies become measurable—tha...<i>where do the inconsistencies become measurable—that is, rise above the noise floor?</i><br /><br />We don't know. All we know is that this doesn't happen in any domain that's accessible to our current experiments; everywhere we can actually measure, there is no problem.Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-27574942956564991062018-10-10T10:50:29.556-07:002018-10-10T10:50:29.556-07:00@Peter Donis:
> It's correct even more gen...@Peter Donis:<br /><br />> It's correct even more generally than that: the GR and QFT we use today are inconsistent with each other, so at least one of them can't be exactly right, and at least one of them will have to change, even if we didn't know about the black hole information paradox.<br /><br />But where do the inconsistencies become measurable—that is, rise above the noise Lukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-16050773236023803212018-10-09T13:31:58.280-07:002018-10-09T13:31:58.280-07:00@Luke:
If you see a barn while on the highway, you...@Luke:<br /><i>If you see a barn while on the highway, you don't know whether it's a façade or a real barn. So, reject (B) K(p & q) → (Kp & Kq).</i><br /><br />I don't see the connection here either. If you see an object and you don't know whether it's a facade or a real barn, the proposition that describes your state of knowledge (assuming those are the only two Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-12218572927971779492018-10-09T13:29:19.890-07:002018-10-09T13:29:19.890-07:00@Luke:
My real point is that the GR and QFT we kno...@Luke:<br /><i>My real point is that the GR and QFT we know and love and use in all our GPS devices today won't both remain unscathed in resolving the black hole information paradox. Is that correct?</i><br /><br />It's correct even more generally than that: the GR and QFT we use today are inconsistent with each other, so at least one of them can't be exactly right, and at least one Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-21725816331218322172018-10-06T09:55:05.351-07:002018-10-06T09:55:05.351-07:00@Peter Donis:
> We don't know. It's po...@Peter Donis:<br /><br />> We don't know. It's possible that a resolution to the black hole information paradox will be found that doesn't change anything at the event horizon, only near the singularity. If that's the case, then our current experimentally tested QFTs will work just fine at the horizon.<br /><br />My real point is that the GR and QFT we know and love and use in Lukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-19277974682998283102018-09-29T12:43:13.943-07:002018-09-29T12:43:13.943-07:00if the experimentally-tested QFTs fail to resolve ...<i>if the experimentally-tested QFTs fail to resolve the black hole information paradox, then they appear to be poor models around black hole event horizons—or am I in error?</i><br /><br />We don't know. It's possible that a resolution to the black hole information paradox will be found that doesn't change anything at the event horizon, only near the singularity. If that's the Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-68134622063868805062018-09-29T10:19:09.427-07:002018-09-29T10:19:09.427-07:00@Peter Donis:
> As a side note: that's act...@Peter Donis:<br /><br />> As a side note: that's actually not the case for all QFTs. It's only the case for certain hypothetical QFTs that are supposed to "solve" the black hole information paradox by making quantum effects non-negligible near the horizon. But nobody has ever experimentally tested any such QFT. All of the QFTs that have been experimentally tested--which Lukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-20011190834609318672018-09-28T22:41:37.283-07:002018-09-28T22:41:37.283-07:00@me:
To say that it is true in all possible worlds...@me:<br /><i>To say that it is true in all possible worlds? First, that would be "necessarily true", not just "true"; and second, KTP can't be true in all possible worlds because TP itself is not true in all possible worlds.</i><br /><br />To clarify, by "KTP" I mean the proposition "TP is known". Or, to rephrase the sentences quoted above: "To sayPeter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-70906923107847624752018-09-28T22:39:29.986-07:002018-09-28T22:39:29.986-07:00Why shouldn't we expect a distinction between ...<i>Why shouldn't we expect a distinction between actual and possible knowledge to be capturable by formal logic?</i><br /><br />First consider what "possible" means for a simple proposition that doesn't involve knowledge: for example, "Donald Trump is President of the United States". Call this proposition TP. In possible world semantics, TP is "possible" if Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-58913524747510898222018-09-28T22:30:35.993-07:002018-09-28T22:30:35.993-07:00The contradiction with GR and QFT just means they ...<i>The contradiction with GR and QFT just means they cannot possibly both be sound near the event horizons of black holes.</i><br /><br />As a side note: that's actually not the case for all QFTs. It's only the case for certain hypothetical QFTs that are supposed to "solve" the black hole information paradox by making quantum effects non-negligible near the horizon. But nobody Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-47763173721776106102018-09-28T22:23:59.307-07:002018-09-28T22:23:59.307-07:00@Peter Donis:
> I thought his posts in previou...@Peter Donis:<br /><br />> I thought his posts in previous threads were pretty clear.<br /><br />Care to pick one out which you think unambiguously shows that Ron believes <a href="#c2865384276063344468" rel="nofollow">"Fitch's paradox basically collapses this distinction"</a>? There's some subtlety here, because the less of a good match there is between <b>K</b> and <b>L</b>Lukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-90888277804636221932018-09-28T19:51:21.636-07:002018-09-28T19:51:21.636-07:00@Luke:
I am not at all convinced that Ron agrees.
...@Luke:<br /><i>I am not at all convinced that Ron agrees.</i><br /><br />I thought his posts in previous threads were pretty clear. But in any case, I agree.<br /><br /><i>I too am inclined to think that there is a meaningful distinction between actual and possible knowledge. But if one cannot be constructed with formal logic, then I don't think one should assume or presuppose that in fact Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-54321862424764192072018-09-28T16:44:23.170-07:002018-09-28T16:44:23.170-07:00@Peter Donis:
> The fact that Fitch's para...@Peter Donis:<br /><br />> The fact that Fitch's paradox basically collapses this distinction was, I thought, a key thing that came out of previous threads on this topic.<br /><br />I am not at all convinced that Ron agrees. He seems to jump back and forth between formal/abstract-land and empirical-land at the drop of a hat. It makes it very hard for me to see what his position is. But Lukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-28653842760633444682018-09-28T12:28:09.612-07:002018-09-28T12:28:09.612-07:00@Ron has bowed out but I'll give a try at a co...@Ron has bowed out but I'll give a try at a couple of points that strike me:<br /><br /><i>are you presupposing that there is a meaningful distinction between 'actual knowledge' and 'possible knowledge'? Fitch can be seen as basically collapsing any real distinction.</i><br /><br />The fact that Fitch's paradox basically collapses this distinction was, I thought, a key Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-72458566321855776752018-09-28T11:32:17.930-07:002018-09-28T11:32:17.930-07:00@Ron:
> > Something can be unsound and yet ...@Ron:<br /><br />> > Something can be unsound and yet a very good model<br /><br />> … Since you are obviously not bothering to read what I write<br /><br />Says the person who wrote:<br /><br />> <a href="#c2848852391924742699" rel="nofollow">Ron</a>: Please go back and carefully re-read that sentence, its containing paragraph, and the paragraph that follows. Pay particular attentionLukehttps://www.blogger.com/profile/18395549142176242491noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-61261579884672964742018-09-28T10:57:54.493-07:002018-09-28T10:57:54.493-07:00> Are you making a sharp distinction between so...> Are you making a sharp distinction between soundness and validity?<br /><br />In the case of a reductio proof (which my proof is) these are synonyms.<br /><br />In the case of Fitch, I should have said that his argument is valid rather than sound.<br /><br />> Something can be unsound and yet a very good model<br /><br />Yes, that is exactly what I said:<br /><br />"The fact that Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.com