{"id":393,"date":"2007-02-18T20:39:00","date_gmt":"2007-02-18T20:39:00","guid":{"rendered":"http:\/\/jimgworld.com\/blog1\/2007\/02\/18\/393\/"},"modified":"2007-02-18T20:39:00","modified_gmt":"2007-02-18T20:39:00","slug":"393","status":"publish","type":"post","link":"https:\/\/jimgworld.com\/blog1\/?p=393","title":{"rendered":""},"content":{"rendered":"

Waiting On Godel:<\/span> I\u2019ve been reading and thinking about the nature of human consciousness<\/span> lately. I\u2019ve found out that anyone seriously interested in the subject must sooner or later face the question of Godel\u2019s Incompleteness Theorem<\/span>. Godel was a mathematician from the early part of the 20th Century. He was one of those brilliant guys who wondered what was behind mathematics. They call it \u201cmeta-mathematics\u201d: it asks, what are the most basic ground rules behind the world of math. Whatever they are, they should be expressible as a system of axioms and associated rules. An \u201caxiom plus rules\u201d system should be compact and yet powerful, such that when you \u201cunfold\u201d it, it explains everything about how we do math. And if you take it further, it can explain all of logic, and ultimately, all of rational thinking in general. And maybe even all of our not-so-rational thinking too. Maybe it can explain everything about how our brains and minds work.<\/p>\n

But maybe not. Godel showed that for any system of axioms and rules, no matter how powerful and brilliant, you can formulate a clever proposition that trips the whole system up. Such a proposition is usually self-referential; something like \u201cI will never say that I am true\u201d. Is that proposition true or false? If true, there\u2019s a problem, since you then say that \u201cI am true\u201d, right after saying that \u201cI am false\u201d. If false, then \u201cI\u201d will say that I am true; but didn\u2019t we just say that I is false? There\u2019s a contradiction either way you cut it. In contradictions, the rules of logic tell you to do nothing; no answer is given; you tilt. But if so, then . . . . . well, then the proposition was right, wasn\u2019t it<\/span>? Even though the system for answering it (based on axioms and rules) couldn\u2019t give an answer. (You had to \u201clook above\u201d the system of axioms and rules to see the ultimate outcome.)<\/p>\n

Ultimately, Godel proves that we can never know if a \u201ccomputational system\u201d gives fully consistent and valid results in all instances, even if that system is in fact fully consistent \u2013 unless we can somehow get outside of it, use a bigger paradigm. This all sounds like a lot of mental masturbation, until you realize that the brain is probably a system that is ultimately reducible to axioms and rules. The interactions of atoms and molecules within the brain is complex, but ultimately is predictable. Ultimately there are only so many ways that any two atoms can interact. As for molecules, there are a lot more ways of interaction, but ultimately it\u2019s a finite set. Our brain is the stage for a hugely complex set of molecular interactions. There may be billions or trillions of interaction pathways; but ultimately it is finite. It could ultimately be reduced to a set of axioms and rules, although an incredibly huge set, something beyond human comprehension. <\/p>\n

So, our brain is felt by many scholars to ultimately be governed by a set (however huge and complex) of axioms and rules. If so, then Godel\u2019s theories kick in. We cannot know for sure that our brains work according to a \u201csound\u201d set of rules (fully consistent, no contradictory results), even if it does. At some point, our minds (the conscious workings of our brain) are going to tilt for us; they\u2019re not going to be able to figure something out; not because we didn\u2019t have our coffee this morning, but because of an inherent limitation in the brain\u2019s algorithm\u201d (the set of axioms and rules laid out by nature). If it\u2019s a \u201cperformance\u201d problem (our minds are just not up to it at the time), then eventually things will click for someone, and a good, solid answer will appear in lieu of the inconsistency that Godel talks about. But if it\u2019s something inherent, if it\u2019s a question from the outer limits, then the problem will go on and on, really getting philosophers and anyone else interested really ticked off.<\/p>\n

I myself can\u2019t help but wonder if the whole question of consciousness and \u201cdo I really exist, or am I just an illusion created by the workings of my body<\/span>\u201d (really the same question) are in fact Godelian questions. Human beings have been working on this issue for a long, long time now. No one yet has been able to crack it. Back in the late 1980s, scientists and philosophers and psychologists and computer people got interested in human consciousness once again, after a few decades of just ignoring the topic (in favor of stimulus-response behavioralism; i.e., just study what people do, don\u2019t worry what does or doesn\u2019t go on in their heads). Go back a hundred years or so, however, and people did talk about consciousness (most notably philosopher-psychologist William James). Go back many, many centuries to the days of Plato and Aristotle, and ditto. <\/p>\n

Well, our modern minds and computers have been going at it full tilt now for about 20 years, and nothing much has been accomplished, in terms of an accepted, unquestionable theory regarding human consciousness. Some of the great minds say that human consciousness isn\u2019t anything more than the physical workings of the brain. According to them, we THINK that there\u2019s something more; it certainly FEELS like there\u2019s a \u201clittle man\u201d (or woman) in our heads who is ultimately the conscious being behind our existence. But these scientists say that this represents a mistake on every level (it certainly is on the immediate physical level; surgeons have cut working brains open, and there are no \u201clittle people\u201d or ghosts roaming around inside the skull). From the Godel viewpoint, these great minds may be saying that this is just the result of lazy, superstitious thinking encouraged by ancient religious myths (i.e., it\u2019s a question of poor mental performance). But they might also be implying that something is ultimately unsound with the program behind our mental workings, and that\u2019s what causes the unenlightened masses to feel that we all have an \u201cinner identity\u201d. Let\u2019s call that possibility number one.<\/span> Something in the process of evolution came out a little quirky, making our minds crank out bogus results with regard to mental ontology.<\/p>\n

Possibility number two<\/span>, according to Godel, is that the background system works just fine, but we humans, who are trapped within the overall system (can\u2019t see the \u2018bigger picture\u2019), will at some point perceive an unresolvable paradox, nonetheless. Godel hints that the paradox will have something to do with a self-referential proposition. Well, the question of whether we really exist looks to me a lot like the ultimate self-referential question. We only know things through our consciousness. Our conscious mind is \u201cthe observer<\/span>\u201d, the most sacred entity<\/span> in empirical science. How can you observe the observer? How can you get a frame of reference to put it into? <\/p>\n

As philosopher John Searle and others say, if \u201cconsciousness\u201d really does exist, it\u2019s not a question of God doing something outside the boundaries of our physics (by the way: Searle, like most consciousness researchers, proclaims himself to be an atheist; it’s quite the fashion). It\u2019s most likely something within our physics, but something that we just don\u2019t know yet; just as scientists in the 1800\u2019s didn\u2019t know about quarks and anti-protons and E = M x (C squared). Some people think it will ultimately be knowable (if it does indeed exist; if the cynical philosophers like Daniel Dennett are wrong about \u201cpossibility one<\/span>\u201d). And some others don\u2019t. If the Godel \u201cgrey zone\u201d is at work here, and we can\u2019t figure out a way to \u201csee behind the seeing eye of consciousness\u201d, the
\nn maybe it will forever remain a frustrating mystery.<\/p>\n

Well then, if there is a God, and that\u2019s the way that such a God works . . . . . hey, then who am I to complain, so long as I get to enjoy the experience of having human consciousness? That would all be nice \u2013 but Godel would say \u201csorry, can\u2019t take you there; the possibility of an unsound mind algorithm causing the delusion that consciousness has its own \u2018being\u2019 is just as strong\u201d. So, we remain on the fence, despite some interesting thought experiments.<\/p>\n","protected":false},"excerpt":{"rendered":"

Waiting On Godel: I\u2019ve been reading and thinking about the nature of human consciousness lately. I\u2019ve found out that anyone seriously interested in the subject must sooner or later face the question of Godel\u2019s Incompleteness Theorem. Godel was a mathematician from the early part of the 20th Century. He was one of those brilliant guys […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/posts\/393"}],"collection":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=393"}],"version-history":[{"count":0,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=\/wp\/v2\/posts\/393\/revisions"}],"wp:attachment":[{"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=393"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=393"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jimgworld.com\/blog1\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}