(C) Daily Kos This story was originally published by Daily Kos and is unaltered. . . . . . . . . . . Atheism v Religion - We all have Faith in Something [1] ['This Content Is Not Subject To Review Daily Kos Staff Prior To Publication.', 'Backgroundurl Avatar_Large', 'Nickname', 'Joined', 'Created_At', 'Story Count', 'N_Stories', 'Comment Count', 'N_Comments', 'Popular Tags'] Date: 2023-02-18 wrote a very nice open-minded diary on this subject. And I started to write a comment from a more math/science point of view, but it got so long I decided it needed to be a diary in its own right. When it comes to religion (vs science or rationalism), I call myself agnostic — which is in some sense a cop-out. I have spent so much of my life being trained (or perhaps even groomed) to believe only what I can see with my own eyes, prove for myself, or what I know to have been proven by (trustworthy) others. After all, how can I (or anyone) believe wholly (pun intended) in something unproved? But I know that is really a copout. We all believe in so many things (often just subliminally) we can’t prove. Your/my “reality” might be purely subjective. There is no way to know from inside a dream whether it is just a dream. I believe in things that relate to others as well — like love and empathy with my family and friends. I believe that tomorrow is going to happen and that it matters (and I matter in it). I believe in hope, even when that is perhaps unrealistic. I believe that many kinds of animals (and perhaps even trees) have consciousness. I believe that there is some higher order Majesty by which the big discoveries of pure mathematics (for example group theory in the 1850’s) turn out to be the foundation for deep science about the real world that isn’t discovered till much later (the theory of subatomic particles is all based on group theory). And I was once a mathematician, so this Faith led me to believe my research work was worthwhile, not just a game. And that’s just scratching the surface. So many things we take on faith. Therefore, why is it so hard to accept that Christianity or Judaism or Islam or Animism or Atheism can be taken of faith the same way. Let’s explore this further: One thing I do know as a rational fact — Science cannot now and never will be able to answer all questions about our existence (even though it answers so many). This is a simple provable fact (which most people don’t realize). Mathematicians (See Godel’s theorems) have proven that in any logical system: (a) there must be axioms first, that is things you believe are true without proof (for example that two points can be connected by one and only one straight line, something we think we know by experience, but can’t prove) because before you can begin to reason you must have as a raw material for your thoughts some kind of axiomatic system to work with; (b) no (finite) set of axioms is complete, in the sense that there will always be rational questions you can pose, which cannot be answered either to be proved or disproved using those axioms — in other words to answer this unanswerable question, you’d have to pose a new axiom that is independent of your old ones — which is to say a new belief to explain what otherwise can’t be explained; and (c) you can never use the axioms of your belief system (even if your belief system is “science” to prove that those same axioms are logically consistent (in other words some day we may discover a paradox (even in mathematics) that blows away the whole system of thinking — Of course, we BELIEVE that will never happen.) And so even mathematics is, at bottom, a belief system. I’ll give one known example in mathematics that most of us should be able to follow: The so-called rational numbers — which is to say all fractions, defined as being any number composed of an integer in the numerator and an integer in the denominator, whether positive or negative. If you think of a number line and you put your pencil down on that number line, you will find rational numbers nearby and all over the place, within the smallest possible distance from your pencil point that you could think of (and even closer than that too). Mathematicians describe this ubiquitousness of rational numbers by saying they are “dense” in the number line. However, most numbers are not rational. For example, the square root of 2 (or 3 or 5 or 6 or 7 or 8 or 10 etc) are not rational. Pi is not rational. And so many more. Now the set of what mathematicians call the real numbers is best described visually as all the numbers on the number line whether rational or not. It has been proven, quite remarkably at first glance though the proof is elegant but quite simple, that the rational numbers can be reordered to have a first and second and third and fourth (etc), meaning you can count through all of them one at a time, just like you can count through the positive integers — 1,2,3,4 etc. Mathematicians call these type of sets “countable”, meaning in one-to-one correspondence with the integers. There are infinitely many in the set, but they are “countably infinite” A more remarkable and difficult theorem is the proof that those pesky “real numbers” — that is the entire number line — is not countable, which is to say there is no scheme possible that can put them in one to one correspondence with the integers. In other words there is no way to order them so that there is a first, second, third, fourth etc real number. A more visual way to say the same thing is that if I put that hypothetical pencil down at random on the number line, the chances are 0% that I actually land on a rational number, even though there would be infinitely many rational numbers right next door. The rational numbers are everywhere dense in the number line, but still they make a very thin soup. Thus the real numbers represent a second and higher level of infinity than the countable numbers. It has indeed been proven that there is not just one but two levels of infinity. This has all been known since the 1930’s (Godel). So here’s the next “obvious” question. Are there any other levels of infinity beside those two? And the answer is -— drum roll please — That question is undecidable. It has been proven that you can neither prove it true (more levels) or false (no other levels) using the established axioms of mathematics. In other words, it is your choice whether to BELIEVE in still higher levels of infinity (I guess that would make you a person of FAITH) or to deny any higher levels of infinity (which would be analogous to being an ATHEIST). Your choice. Mathematicians are generally atheists on this question. But some have experimented with inventing new axioms to create higher levels of infinity (though I don’t know anything about this). BTW — THIS IS A GREAT STATEMENT ABOUT FREE WILL AS WELL. THERE ARE NO PURELY LOGICAL, DETERMINISTIC, AND SELF-CONTAINED SYSTEMS — NOT EVEN MATHEMATICS. Our knowledge is now and always will be open ended. And there will always be questions that you will have to decide whether to believe in or not believe in based upon your (human and sensory) experiences rather than your logic. Will you be a skeptical realist or a faith-based experimenter? Your choice!! Finally, I think no one is really all one way or the other, no matter what you tell yourself about being a person of faith or an atheist. We all sit comfortably on a continuum (for mathematicians in the crowd, that was a pun too) between the two. That’s why I call myself an agnostic. It’s not really a cop-out after all. It’s my radical assertion of FREE WILL. [END] --- [1] Url: https://www.dailykos.com/stories/2023/2/18/2153701/-Atheism-v-Religion-We-all-have-Faith-in-Something Published and (C) by Daily Kos Content appears here under this condition or license: Site content may be used for any purpose without permission unless otherwise specified. via Magical.Fish Gopher News Feeds: gopher://magical.fish/1/feeds/news/dailykos/