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Message: <blockquote data-quote="NotAYakk" data-source="post: 8167346" data-attributes="member: 72555">I can do logic on things when I don't require the actual and absolute values of variables.You draw different conclusions based on that fact than you could with the actual and absolute values of variables.[spoiler]To digress...Hell -- <a href="https://www.springer.com/gp/book/9783642649059" target="_blank">Constructive Analysis | E. Bishop | Springer</a> -- here is a branch of mathematics where we do away with the law of excluded middle and a few other axioms, and we get a pretty good argument that all provable theorems also produce what they claim exists.Due to the restrictions on the operations we are allowed to do, there are things you cannot prove in this branch that you could prove in more classical analysis, like the intermediate value theorem.In classical analysis, if you have a continuous function defined on a closed interval such that it is less than 0 at the start, and greater than 0 at the end, we can prove that there is a point in the middle where its value is 0.In the above constructive analysis we cannot prove it; instead, we can prove that for any non-zero window of precision we want, we can find an value between the start and the end that maps at least that close to 0.Here we have a version of formal analysis that embraces and accepts imprecision and the limits of our ability to reason about infinities concretely.  Now, while it is a "fun" read, it turns out some mad science physicist types have gone off and used it to form an alternative construction of relativistic models of the big bang and generated an irreversible arrow of time from it, which is neat; basically, there isn't enough room in the universe early on for the arrow of time to go backwards into it.  Pop sci version: <a href="https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/" target="_blank">Does Time Really Flow? New Clues Come From a Century-Old Approach to Math.</a>[/spoiler]In any case, yes, Spock isn't what I'm talking about.It is possible to do logical rational reasoning based off incomplete and error prone data.  It is just hard.Formal logic is insanely easier; the difference is that formal logic there is some hope of spotting errors.  Because of that, they actually attempt to avoid errors.  And people working in relatively formal logic still use heuristics rather than actually provably correct steps, except as an academic exercise by logicians (and occassionally such exercises find errors in arguments).In comparison, in everyday reasoning, errors in deduction are basically impossible to eliminate; beyond that, the raw amount of state it takes to reason about a non-trivial conjecture is so ridiculously huge that if you think you are reasoning without pencil and paper, you aren't; you are (again) applying heuristics.  If it is an area of expertise, you are probably using heuristics to reduce the complexity of the problem down to what your experience has told you are relevant details; if it isn't, you are using heuristics to reduce the complexity of the problem down to irrelevant details.Naw, Fermat's Last Theorem is easy to have a reasonable conclusion about.  It remains a bunch of symbols on the page.It is plausible to actually check and have expertise in knowing if the proof of Fermat's Last Theorem is valid, and for that expertise in turn to be objectively and clearly checked. I mean, I haven't done that, but I think I know how hard it is to find out if someone is blathering nonsense about mathematics (my technique involves a ladder of trust basically).[spoiler]On the subject of vaccination; hell, on the subject of "does the sun come up tomorrow" -- that is so insanely hard to have expertise on it isn't funny, compared to formal mathematics.Math is only hard because it is so easy, we have built insane constructs on it, and those insane constructs keep on seeming to generate interesting truths.So we don't even try. We hand wave heuristics around. Some more hand wavey than others.I use a heuristic that people who are expert epidemiologists probably aren't clueless about epidemiology.  Also, that there are going to be better statisticians than me looking at the papers involved.   When I run into statistical claims in popular media about anti virus effectiveness, I do napkin math to see if they are plausible; if I find a mistake, I'll iterate on the assumption that the communication was fuzzy.Does that work?  I don't know.  I haven't build a model of if my napkin math is worth the credibility I put in it (I probably lack the expertise to know if I'm a statistical idiot, most people do; heuristically, I have evidence I am not, but again... I know I have been an idiot about subjects I didn't think I was an idiot on in the past, so why presume I'm not an idiot today?)Down that infinite regress, I just drop it (unless I feel bored).  Why?  Heuristics.  I wasted time on that kind of iteration before.[/spoiler]</blockquote>

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