ydoaPs

I'm currently reading, among other things, Susskind's second volume of The Theoretical Minimum. This one is about QM. Fun fact: my current Uni president tried to censor Zinn from Indiana when he was governor.

Not at all. That's actually a quite remarkable straw man. Considering how you've not actually addressed any of my arguments (for this rather non-controversial position, fyi) and your blatant flamebait, it's not surprised that you would misrepresent me as such. If you take a system and derive from that system a contradiction, the system is necessarily false. There is no set of circumstances in which naive set theory can be consistent. Yet, it can be easily imagined. It is in fact the way humans naturally approach sets, which is why it's called 'naive'. Bayes is irrelevant here and exactly for the reasons I've stated which you've never addressed. Stop trying to take the thread off-topic with your poor understanding of Bayesian epistemology. That's because you cannot know something which is false. Bayes cannot give you any information about what is not the case, but could be. You have no epistemic access to non-actual worlds, so there is absolutely no observation which can be used as evidence for the Bayesian machine when we're talking about the contingently false. Bayes can only tell you what most likely is, not what most likely isn't, but could be or what most likely must be. It sure does. P(f|m)=0 where f: 'ydoaPs is female' and m: 'ydoaPs' is male. Just, fyi, Bayes is what I do. You're wrong and you've been told several times why. You've addressed your mistakes precisely 0 times. Bayes is irrelevant to the topic, so stop. Priors are still based on experience. Things which are known a priori aren't. That's the whole point of Bayes: it updates the probability with new information giving you a new prior.

You're wrong on several levels here. First, 'a priori' is not the same as 'prior probability'. Second, you sure can have your prior and your posterior be exactly the same and there are several ways this can happen. For example, if the likelihood is the same for every one of the hypotheses or when your prior is 1 or 0. And, most importantly, your claim (I'll call 'x') is falsified by the OP (I'll call 'o'), so P(x|o)=0. You are absolutely wrong and it has been proved beyond a shadow of a doubt. Furthermore, none of your waving of Bayes addresses this issue. Yes, I know with 'absolute truth' (whatever that is) that Russell's paradox shows naive set theory to be inconsistent.

Sure, I can point out any number of toy systems logicians have made up that have absolutely no extensional semantics. Or would you rather me construct one of my own?

It is not the case that anything which is proven through deduction (I'm not sure what you even are attempting to mean by 'exists through logical deduction') must necessarily exist. A proof is only as good as its premises. If it has false premises, then the conclusion need not be true. You've also made a very common very bad mistake for lay people in the second sentence. A representation is not the same as the thing it represents. When my niece takes out a crayon and construction paper then draws my house, the resultant drawing is not my house. I do not live in the drawing. Rather, I live in my house. I've taken the liberty of snipping the trolling flamebait out of the quote box. Have you ever gone golfing? A golfer often fails to sink her put. She knows deep down, however, that she could have sunk her put. That's a subjunctive. Bayesian reasoning is of no use when it comes to the modal and the subjunctive, because it only applies to the actual world. You can't get evidence from worlds which never happened. Bayes can only tell you what probably is; it can't tell you what probably could be, but isn't. So, keep your off-topic rants out of other threads. If you want a thread about how Bayesian epistemology is great, I'll join you, but this is not that thread. Since we're talking about whether or not things are possible rather than whether or not we know that something is the case, Bayes need not apply.

If you'd bother to read the OP, you'd know that I made the distinction between what is actually possible and your (actually rather common among lay people) confusion of what is possible with what you don't know to be impossible. Not knowing something to be false does not mean that that is a way the world could actually be. Consider Goldbach's Conjecture: every even number greater than or equal to 4 is the sum of two primes. This is either true or false, but we don't yet know which. However, it would be erroneous to thus conclude that it is possible to be true or possible to be false. As a mathematical theorem (or the denial of a mathematical theorem) it is either necessarily true or necessarily false. If it is true, there is no way the world could be such that it would have been false. If it is false, there is no way that the world could be such that it is true. Epistemic possibility simply isn't in the same game as metaphysical possibility. Epistemic possibility is merely a measure of uncertainty. It's about beliefs, not the real world out there. Metaphysical possibility is about the real world out there. It's about how the world actually is, how it must be, and how it could have been but isn't. As I said, this is a subset of logical possibility (epistemic 'possibility' isn't), so my example of Russell's paradox is in fact a decisive counterexample to the claim that whatever is imaginable is a way the world could actually be. As for your weaker claim that whatever is imaginable is epistemically possible, that was also shown to be false by the OP example. See, I know for a fact that naive set theory is necessarily false. Yet I can still imagine it. I'd wager you can too. But that's even a way stronger example than needed. The mere existence of fiction disproves this claim. He can't even get that far. It's just a blatant fact that a hypothesis is in fact not held true until falsified. Since there is more than one mutually exclusive competing hypothesis at any one time, that would entail that kristalris thinks that science is founded on believing contradictions until we conclusively falsify every possible (metaphysically possible, that is) option. Knowingly believing contradictions isn't rational. With kristalris's absurd and unsupported claim that hypotheses are held to be true until shown to be otherwise, he claims that science is foundationally irrational.

You made no argument. You made assertions. Your assertions are falsified by the counter-example in the OP. It is simply not the case that anything you imagine is possible. Yes. It is an example of something which is incredibly intuitive and imaginable, but impossible. That means it falsifies the claim "Anything I can imagine is possible".

Not only is that false, but has conclusively been shown to be false. Your hypothesis has been falsified. hint: we don't use naive set theory anymore

I wasn't specifically talking about any one person, but if the shoe fits, wear it.

Did you only read the title?

How do you deal with the content of the OP? How is something blatantly inconsistent any less 'illogical' than a square circle? A contradiction is a contradiction.

That's actually something which could in principle have an exact formula, but would be far too unwieldy for practical use. There are just too many variables. You would have to have terms for humidity of the air, how moist the mixture already was, how dense the mixture is, etc. That there are formulas that give approximate answers defeats your point.

Why?

There's a difference between Reductio Ad Absurdum and Indirect Proof. The former shows an absurd result while the latter shows an impossible result. Russel's Paradox (there's a reason I named the set 'R' ) is a case of the later and it acts as a counterexample to the general principle. This principle actually has a name. Despite having been used as early as Descartes, it has come to be called 'Hume's Law'. Indeed. This sort of thinking is one of the foundations of crackpottery. They sincerely think that since they can imagine their perpetual motion device working that it simply must work. Just think of how many times you've heard people proclaim that they don't need math because they "understand" reality with their idea.

The title is a common view among crackpots. They often think that the ability to imagine something means that the universe might actually be that way or could have been that way were things differently. To use philosophy words, they often think that conceivability means epistemic or metaphysical possibility. But, the question is, is that true? To find that out, we need to find something that is conceivable but is impossible. For the first sense of possibility, (how things might actually be), that is incredibly easy. All we have to do is find something that is conceivable but not the case. Have you ever been wrong about something? If you have, you've shown that conceivability does not mean epistemic possibility. The second one is a bit harder, since there's disagreement on the exact requirements of what makes something metaphysically possible, but we do know that for something to be metaphysically possible, it must also be logically possible. That is, were things different, an accurate description of the universe still wouldn't entail a contradiction. So, we can knock this out by finding something which is conceivable, yet logically impossible. Can we imagine things which are contradictions? You might be tempted to say "No one can imagine a square circle!". But I'd like to talk about one which almost everyone intuitively conceives. People intuitively like to group things. It's how we make sense of the world. We have apples, chairs, etc. All you have to do is put things together and you have a group. In mathematics, we call these kind of groupings 'sets'. The things in these groups are called "members". Any group of members of a set is called a "subset". This does mean that all sets are subsets of themselves, but that's not of interest to us here. What we're interested in is the idea that you can group whatever you want into a set. You can make sets of sets. You can take your set of cats and your set of dogs and put them together into a new set! So, let's take a look at a specific set: the set of all sets which are not members of themselves. The set of all cats is not a member of the set of all cats-it's a set of cats, not of sets! So, it goes in! Likewise, any set consisting of no sets will go in this set of all sets which are not members of themselves. So, we pose a question: Is this set of all sets which are not members of themselves (from here on out, we'll call it 'R') a member of itself? If R is a member of R, then it fails to meet the requirements to be in R, so it isn't a member of R. That's a contradiction, so that's no good. That means R must not be a member of itself. But what happens if R is a member of itself? If R is a member of itself, it meets the requirement to be in R. Since R is the set of ALL sets meeting this requirements, it goes in. Again we have R both being a member of itself and not being a member of itself. So, either way, we get a contradiction. This means something is logically impossible. But we got this result simply from the definitions of sets and members and from the very conceivable idea that you can group whatever you want together. This is a situation in which something is conceivable, but logically impossible. This means it is not the case that whatever you can imagine is possible. Crackpots, take note: the fact that you can imagine something in no way implies that it is possible. It doesn't matter how clear your perpetual motion device/unified theory/God/electric universe is, imagining it doesn't cut the mustard. This is one of the reasons you NEED the math.

Yeah, any system strong enough to do both addition and multiplication of natural numbers (which we can do with any reasonable form of set theory) will be incomplete xor inconsistent. You can't prove which one in that system, but that doesn't mean you can't prove which one.

I don't know of any result of Gödel's that would give that implication. Certainly nothing in Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.

Without a consistency and completeness proofs, why should we care about any result you get? If the system is inconsistent, you can prove anything and everything.

You'd be better off reading modern introductions. They are outdated and more difficult than necessary. For example, hardly anyone (even relatively experienced grad students) really "gets" Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I the first time through. I suspect it's vacuous name dropping.

It looks like an odd way to try to do modal logic. Have you tried proving consitency and completeness?

arjundeepakshriram has been banned as a particularly unclever sockpuppet of Arjun Deepak Shriram.

He in no uncertain terms completely failed to overcome the Quine-Duhem thesis. You cannot pull theories apart like that. It doesn't work. That's talking about simple existential statements. Of course you can verify simple existential statements, but that's stamp collecting, not science. The Logic of Scientific Discovery was about theoretical statements rather than simple existential statements. He spends a great portion of the book railing against verification/induction. For example, that's how he starts out the very first chapter. AND he goes so far as to dedicate a whole chapter (and a few additional appendices, if you have the right edition) in a failed attempt to attack probability as a method for validating confirmation. On the contrary to your assertion, it is the Popper apologists who mischaracterize his views by quotemining him and forcing the quotes into contexts where they don't belong.

Przemyslaw.Gruchala has been banned for abusive behaviour and persistent thread hijacking.

Anders Hoveland has been banned for plagiarism, copyright infringement, soap-boxing, trolling, and racism/sexism.

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