tag:blogger.com,1999:blog-7068528325708136131.post1710488866796451413..comments2024-03-01T21:25:21.218-08:00Comments on Structural insight: Sapience and the limits of formal reasoningJohn Shutthttp://www.blogger.com/profile/00041398073010099077noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-7068528325708136131.post-74113599679352595612020-08-12T09:04:14.387-07:002020-08-12T09:04:14.387-07:00With fewer hostile assumptions this time (feel fre...With fewer hostile assumptions this time (feel free to delete prior):<br /><br />Turing machines don't exist, only finite approximations of them exist. Sapiences do exist, at least insofar as we consider humans to be sapient.<br /><br />Any finite system can only reach a subset of mathematical truths. It is quite feasible to model an axiomatic system that can exhaustively explore all possible conclusions reachable by any finite system. The incompleteness theorems don't apply to the question of truths reachable within finite systems.<br /><br />To be more powerful than formal systems (where 'power' is the narrow measure of access to 'truth'), a sapience must *first* be more powerful than finite systems. However, there is no evidence that sapiences need or have access to infinite anything.<br /><br />Of course, in practice, even sixty binary decisions is beyond the technological limits of exhaustive checking.<br /><br />Sapience could arguably provide more *efficient* access to truths, or at least a subset of them, via intuiting leaps of logic, developing hypotheses, working backwards to grounded arguments. They might prune searches they view as unproductive. Of course, there may also be biases and errors that cause a sapience to miss valid truths, to ignore subtle but essential distinctions between two similar arguments, to overreach then fail to correct. <br /><br />Based on human history, at least, it seems that the vast majority of sapient thinking falls into error long before it reaches 'truth'. Those rigorous, structured methods - such as formal logics and falsifiable sciences - have greatly augmented our ability, but arguably don't need sapiences.<br /><br />For example, in theory, we could automate our labs, automate hypothesis generation based on data, and automate production of new labs to potentially falsify hypotheses. Automating search for mathematical constructs that can predict observed properties would be part of hypothesis generation. <br /><br />Some machine-learning with informal reasoning might augment the system, e.g. to automate generation of hypotheses that are more likely to survive testing, and adversarial generation of experiments that are more likely to falsify hypotheses. No need for an general AI that could comprehend natural language or form political opinions or have a sense of self and self-interest.<br /><br />With these issues in mind, I'm not positively inclined to an assumption that sapiences are inherently powerful in pursuit of truth. <br /><br />Today, our sapient minds are certainly among the most powerful tools we have for pursuit of truth. Despite the flaws of bias and intuition, the tedium of running experiments to falsify hypotheses, the challenges of recognizing useful patterns in data. But this speaks as much of the current limitations of our tech as it does the strength of our minds.dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-66659464753888312052020-08-11T11:44:49.226-07:002020-08-11T11:44:49.226-07:00The abusive atmosphere has been your doing, and yo...The abusive atmosphere has been your doing, and you suggest <i>I</i> should do something about it by writing a post that I've not only already written, but that I explicitly mentioned in the first sentence of this post and provided an explicit link to. You are de facto trolling me. This discussion is closed.John Shutthttps://www.blogger.com/profile/00041398073010099077noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-14023470083640268912020-08-11T09:36:23.037-07:002020-08-11T09:36:23.037-07:00Change the context if that suits your preferences....Change the context if that suits your preferences. You can always write a fresh blog post. <br /><br />You've written a few sentences on the subject of what sapience means to you across many blog posts, albeit usually entangled with the local context and other concepts. <br /><br />If you could distill it down to the features you consider most critical - for example, adaptiveness to unexpected problems is a recurring theme, but should not be the whole of sapience (or we'd just use 'adaptiveness') - in a manner that we can begin to measure sapience, that would be quite useful.dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-37906027204008458602020-08-11T05:36:09.469-07:002020-08-11T05:36:09.469-07:00Your last remark, about interesting questions, wou...Your last remark, about interesting questions, would almost be tempting to respond to (despite its somewhat immature wording) if not that it's embedded in a context of abuse and ignoring what I've actually written on the subject.John Shutthttps://www.blogger.com/profile/00041398073010099077noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-6918453700805526512020-08-10T10:09:06.654-07:002020-08-10T10:09:06.654-07:00Also, whether sapience has potential to be more po...Also, whether sapience has potential to be more powerful than formalism is a very silly question to "start with". <br /><br />More interesting and salient starter questions, to me, are "how do I know whether I'm sapient"? and "how do I know whether someone/something else is sapient"?<br /><br />And to demonstrate a need for 'more powerful than formalism', first you'll need to show that your definition of sapience objectively discriminates against formal systems.dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-2493117948474688012020-08-10T07:05:47.447-07:002020-08-10T07:05:47.447-07:00I'm criticizing introduction of variable x bec...I'm criticizing introduction of variable x because the NEED for x hasn't been demonstrated. Occam's Razor. I'd make similar criticism if x were well defined, e.g. number of aliens beaming thoughts to me.<br /><br />Unfortunately, we can't even begin to demonstrate necessity without an objective definition of sapience that can be effectively and falsifiably be applied to humans, squirrels, neural nets, and other things that can be said to 'think' in some manner. <br /><br />Your approach to studying sapience seems much more philosophical than scientific. Sapience, if it exists in this world, should be robust enough to survive scientific scrutiny.dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-77101582749331308692020-08-09T21:07:47.508-07:002020-08-09T21:07:47.508-07:00You're criticizing me for not making your mist...You're criticizing me for not making your mistake; in essence your complaint is tantamount to ridiculing an algebraic equation in variable x on grounds that it's obviously invalid because the value of x hasn't been defined. I've been seriously exploring really interesting questions here, starting with whether it's even possible for sapience to be more powerful than formalism, and whether there is any evidence that it is; the difference is, you've chosen to refuse to ask those questions.John Shutthttps://www.blogger.com/profile/00041398073010099077noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-20878603241049614292020-08-07T15:23:33.554-07:002020-08-07T15:23:33.554-07:00I think sapience is very poorly defined. Even the ...I think sapience is very poorly defined. Even the words used when people attempt to define it - wisdom, discernment, intuitive knowing, transcendent knowledge - are, transitively, poorly defined. If sapience isn't well defined, how do we know humans have it? How can we know that a simple neural network that mastered surviving within the Asteroids game does not have sapience? Is sapience necessarily scoped to the human world, or to the world we evolved in?<br /><br />People refusing to define terms, while claiming they have it and others do not, starts to sound more like self-congratulatory tribal affiliations than a useful argument. And I have the impression all of humanity - or at least those elite enough to use the word - has been collectively patting itself on the back for sapience, while often refusing to seek any objective definition for it, perhaps because definition would threaten human supremacy. <br /><br />I am interested in exploring mental phenomena we associate with 'sapience'. But I would dismiss an arbitrary claim, without objective measures, that humans are sapient and squirrels/slime molds/neural nets are not.<br /><br />You try to not jump to conclusions. But haven't you already jumped to "humans are sapient"? Did you objectively define sapience before making this judgement?<br /><br />Regarding you introducing 'unknown' variables for informal reasoning: Don't multiply entities beyond necessity.<br /><br />If you want to "tease out what sapience might have that formalism doesn't", the best way to do that is to clearly define sapience - i.e. to give these properties of sapience some names and clear descriptions, then compare to formal systems and neural networks, etc.. If you need a hidden variable, leave it at the end of your definition for sapience - room for expansion after you take offense at a neural network exhibiting everything you attributed to sapience so far. At least that will be productive for all parties interested in sapience.<br /><br />E.g. do neural networks have intuitive knowledge? Define this. How about: when a lot of little clues contribute to a valid judgement about the world, without an obvious primary source? Well, neural nets certainly have that, e.g. when lots of weak signals add up to a trigger.<br /><br />When we have a lot of good definitions, we can do a lot of good with them. Trying to keep sapience all mysterious and undefined is good for only one thing: protecting the tribal affiliation, i.e. human supremacy.dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-37423849960274609332020-08-07T12:46:25.802-07:002020-08-07T12:46:25.802-07:00"But it seems you don't clearly grasp tha..."But it seems you don't clearly grasp that so-called 'informal' reasoning is technically a way to say 'computational/mechanical' reasoning, [...]"<br /><br />This is a key point you're missing. (I did discuss it carefully in the earlier post on sapience and non-sapience, which I carefully cited at the top of this post, but idk if the earlier post would work any better for you, so, fine, we're discussing it here.) I don't call it "informal" because of some failure to realize that I should start by assuming sapience is reducible to formalism. I call it "informal" because I've realized I shouldn't start by assuming that. I'm not thinking about this less clearly; I'm thinking about it more cautiously. This is an intense exercise in <i>not jumping to a conclusion</i>. It's relatively easy to set up an equation with an unknown in it, and not assume what the value of that unknown (although one can still mess up, e.g. by failing to notice that one has implicitly assumed it's non-zero, or the like). It's much, much more difficult to reason without making assumptions about one's own reasoning. One has to carefully, patiently consider the implications of the non-assumption, and this is where the misanthropy thing comes in: because you're evidently so eager to dismiss sapience (which is not necessarily a human trait, btw), it seems you can't exercise the needed patience in teasing out what sapience might have that formalism doesn't. Indeed, my previous and current posts have only made a start on that exploration.<br /><br />Regarding the state of US and world politics right now... I'm not without sympathy; I'm concerned atm with allowing it to interfere with clear thinking. I've recently been reading E.T. Bell's <i>Men of Mathematics</i> (written in the 1930s, between WWI and WWII); Bell has various remarks on the French Revolution from mathematicians' perspectives. From his chapter on Lagrange: "[...] the revolting cruelties sickened him and all but destroyed what little faith he had left in human nature and common sense. [...] Although practically the whole of Lagrange's working life had been spent under the patronage of royalty his sympathies were not with the royalists. Nor were they with the revolutionists. He stood squarely and unequivocally on the middle ground of civilization which both sides had ruthlessly invaded." Kind of puts a different spin on describing a politician as a "centrist".John Shutthttps://www.blogger.com/profile/00041398073010099077noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-15656236052793009322020-08-07T06:38:50.072-07:002020-08-07T06:38:50.072-07:00You clearly understand some implication of Gödel&#...You clearly understand some implication of Gödel's theorems. <br /><br />"question of whether there is a notion of objective mathematical truth beyond the power of all these formal systems, the evident answer is, not formally"<br /><br />But it seems you don't clearly grasp that so-called "informal" reasoning is technically a way to say "computational/mechanical" reasoning, and thus still falls within the same limitations of seeking mathematical truths as the weakest formal system that can simulate the mechanics.<br /><br />Thus, to you, it looks like I'm confusing computation and logic. To me, it seems you're failing to account for the relevance of computation to an entire half of your argument. When you claim informal reasoning might be superior, you're essentially waving your hands to claim about potential for some mysterious mechanics that cannot be simulated by any formal system.<br /><br />Also, if I'm feeling misanthropy, you can blame the state of US and world politics right now. Do avoid the fundamental attribution error. I've still got a sputtering flame of optimism for humanity sheltered deep in my heart.dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-69641007432529915212020-08-06T19:07:20.604-07:002020-08-06T19:07:20.604-07:00Evidently you didn't understand the post. No ...Evidently you didn't understand the post. No doubt there's a better way to explain my point, but, tbh, the available evidence suggests it wouldn't help in your case. Over time I've observed in general you have trouble self-diagnosing errors in your own thinking, and specifically in this area you fail to think carefully because of, evidently, fundamental misanthropy.John Shutthttps://www.blogger.com/profile/00041398073010099077noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-18574018781218181722020-08-06T13:17:04.713-07:002020-08-06T13:17:04.713-07:00In practice, all logics are bounded by finite comp...In practice, all logics are bounded by finite computation - finite representations and traces. And under these constraints, informal reasoning is certainly not more powerful than formal reasoning. <br /><br />Indeed, formal logics can reason informally about themselves. For example, we could represent a huge neural-network proof-assistant for a logic, within that logic. The neural network might be better at constructing proofs than any human expert, yet be entirely opaque regarding the concepts and intuitions developed while training. <br /><br />Unless you allow for a hidden, mysterious variable that would require *infinite* representation of informal reasoning within a formal system, there isn't even a small possibility for informal reasoning to be more powerful.dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-3887049033377068652020-07-22T22:18:33.558-07:002020-07-22T22:18:33.558-07:00Inconsistency as such is logical, rather than comp...Inconsistency as such is logical, rather than computational. (I note your introduction of the spurious concepts of soul and oracle. These suggest to me that your expectations have replaced what I'm saying with something quite different, and you've then responded to the replacement.)John Shutthttps://www.blogger.com/profile/00041398073010099077noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-6713887073554731752020-07-21T15:30:20.437-07:002020-07-21T15:30:20.437-07:00Re Truth: "That last goal was decisively nixe...Re Truth: "That last goal was decisively nixed by Gödel's Theorem(s) in 1931."<br /><br />Unless you're a finitist. ;)<br /><br />Re: "a sapient mind that emerges by some combination of its constituent parts and so seemingly ought to be no more powerful than those parts, but... is."<br /><br />All minds we call sapient today are finite and inconsistent. They cannot model or represent all natural numbers. Gödel's Incompleteness Theorems don't seem to be applicable.<br /><br />Of course, this is a 'finite' in context of very large numbers - tens of billions of nodes, hundreds of billions of connections, fractional transmissions, non-uniform organization. A single human brain is orders of magnitude larger, more sophisticated, and buggier than any formal system or program ever developed by humans. <br /><br />Brains aren't the same as minds or sapience, e.g. in context of external memory. But so far every being we consider sapient has a rather hefty brain.<br /><br />Re: "Church-Turing thesis"<br /><br />On one hand, Turing complete computation models are inconsistent. On another, all physically realizable computations are bounded by space, time, matter, and energy and are thus not Turing complete. <br /><br />Sapience is a condition we observe to exist within a finite system. There is no evidence of a 'soul' or mysterious something providing energy or computation or useful oracular input. All this stretching for infinite causes might be appealing to a spiritual philosophy that places humans on pedestals. But Occam's razor says: YAGNI.<br />dmbarbourhttps://www.blogger.com/profile/12370605342201490009noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-91892371821512721272018-07-08T03:14:34.250-07:002018-07-08T03:14:34.250-07:00If you are concerned with modifying PA, you can av...If you are concerned with modifying PA, you can avoid doing this altogether (see Feferman's op. cit. for details). In PA take Con—the usual formula expressing consistency. PA cannot prove Con. It is possible to build another formula Con', such that Con' also expresses PA consistency and PA proves Con'. Con and Con' equivalence can be proved at the meta-level, but PA cannot prove their equivalence.nikitahttps://www.blogger.com/profile/09403336533089968821noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-43127716090629311242018-07-06T09:26:13.338-07:002018-07-06T09:26:13.338-07:00PA1 has exactly the same theorems as PA, so their ...PA1 has exactly the same theorems as PA, so their formal "triviality" is the same.nikitahttps://www.blogger.com/profile/09403336533089968821noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-69367313251037548932018-07-06T06:41:06.463-07:002018-07-06T06:41:06.463-07:00I did qualify that the formal axiomatic system mus...I did qualify that the formal axiomatic system must be "sufficiently nontrivial".John Shutthttps://www.blogger.com/profile/00041398073010099077noreply@blogger.comtag:blogger.com,1999:blog-7068528325708136131.post-59537280256619695452018-06-07T10:03:22.826-07:002018-06-07T10:03:22.826-07:00> Gödel proved, in essence, that any sufficient...> Gödel proved, in essence, that any sufficiently nontrivial formal <br />> axiomatic system, if it doesn't prove anything false, cannot prove <br />> itself to be self-consistent.<br /><br />This statement, while often repeated, is not entirely correct. For Godel's second theorem to be applicable, the formal system must satisfy a number of technical properties ("Hilbert–Bernays provability conditions"). It is relatively easy to construct a formal system essentially equivalent to PA and that trivially proves its own consistency. This is done in Hilbert-Bernays opus. A more self-contained treatment is in Feferman's Arithmetization of metamathematics in a general setting. One way (very roughly) is to build a system PA1, with the same terms, formulae, inference rules, etc. as PA and define provability in PA1 as following: "P is a proof of S in PA1 iff: (i) P is a proof of S in PA and (ii) there is no shorter proof of 'not S' in PA".<br /><br /><br /><br />nikitahttps://www.blogger.com/profile/09403336533089968821noreply@blogger.com