That’s actually a fair point, although I’m not sure how much it takes away from the value of the metaphor.It looks to me it can be easily circumvented while mantaining the general idea.
lubinas
Yup, hadn’t read that. Definitely relevant. Thanks!
By the pigeonhole principle (you can’t fit 3 pigeons into 2 pigeonholes) there must be some joint probability distributions which cannot be represented in the first causal structure
Although this is a valid interpretation of the Pigeonhole Principle (PP) for some particular one-to-one cases, I think it misses the main point of it as relates to this particular example. You absolutely can fit 3 Pigeons into 2 Pigeonholes, and the standard (to my knowledge) intended takeaway from the PP is that you are gonna have to, if you want your pigeons holed. There might just not be a cute way to do it.
The idea being that in finite sets and with there is no injective from to (you could see this as losing information); but you absolutely can send things from to , you just have to be aware that at least two originally (in ) different elements are going to be mapped onto the same element in . This is an issue of losing uniqueness in the representation, not impossibility of the representation itself. It is even useful sometimes.
A priori, it looks possible for a function to exist by which two different joint distributions would be mapped into the same causal structure in some nice, natural or meaningful way, in the sense that only related-in-some-cute-way joined distributions would share the same representation. If there are no such natural functions, there are definitely ugly ones. You can always cram all your pigeons in the first pigeonhole. They are all represented!
On the other hand, the full joint probability distribution would have 3 degrees of freedom—a free choice of (earthquake&recession), a choice of p(earthquake&¬recession), a choice of p(¬earthquake&recession), and then a constrained p(¬earthquake&¬recession) which must be equal to 1 minus the sum of the other three, so that all four probabilities sum to 1.0.
If you get to infinite stuff, it gets worse. You actually can inject into (or in this case —three degrees of freedom— into — two degrees —), meaning that not only can you represent every 3D vector in 2D (wich we do all the time), but there are particular representations that wont be lossy, with every 3D object being uniquely represented. You won’t lose that information! (the operative term here being that. You are most definitely losing something).
If you substitute and for and , to account for the fact that you are working in probabilities, this is still true.
So, assuming there are infinitely many things to account for in the Universe, you would be able to represent the joint distribution as causal diagrams uniquely. If there aren’t, you may be able to group them following “nice” relationships. If you can’t do that, you can always cram them willy neely. There is no need for a joint distribution to not be represented. I’m not sure how this affects the following
This means the first causal structure is falsifiable; there’s survey data we can get which would lead us to reject it as a hypothesis
Seemed weird to me that this hasn’t been pointed out (after a rather superficial look at the comments), so I’m pretty sure that either I’m missing something and there are already 2-3 similarly wrong, refuted comments on this , or this has actually been talked about already and I just haven’t seen it.
Edit: Just realized, in
If you substitute and for and , to account for the fact that you are working in probabilities, this is still true.
should be the 1-norm unit balls from and , and , so all the components sum up to 1, instead of the . Pretty sure the injection still holds.
There is a big leap between there are no X, so Y and there are no useful X (useful meaning local homeomorphisms), so Y, though. Also, local homeomorphism seem too strong a standard to set. But sure, I kind of agree on this. So let’s forget about injection. Orthogonal projections seem to be very useful under many standards, albeit lossy. I’m not confident that there are no akin, useful equivalence classes in A (joint probability distributions) that can be nicely map to B (causal diagrams). Either way, the conclusion
This means the first causal structure is falsifiable; there’s survey data we can get which would lead us to reject it as a hypothesis
can’t be entailed from the above alone.
Note: my model of this is just balls in , so elements might not hold the same accidental properties as the ones in A and B, (if so, please explain :) ) but my underlying issue is with the actual structure of the argument.
The fallacy of Proving Too Much is when you challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions. For example, if someone says “You can’t be an atheist, because it’s impossible to disprove the existence of God”, you can answer “That argument proves too much. If we accept it, we must also accept that you can’t disbelieve in Bigfoot, since it’s impossible to disprove his existence as well.”
Wow, I’ve been looking for a name for this thing for sooo long. Thanks so much. The phrasing here is a bit ambiguous, and can lead to confusion I think.
From the whole of the text, it seems that Scott’s view on this is that of the Wiki page, that the fallacy is committed when someone claims a conclusion that is a special case in some category of which there are obviously false instances that would be true if the reasoning was valid. Something like
A) You can (validly) argue that someone else is committing the Proving Too Much fallacy when their argument, were it valid, in addition to proving its intended conclusion, would also prove obviously false conclusions
But
The fallacy of Proving Too Much is when you challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions
Can also read (my first understanding of it) as:
B) You commit the Proving Too Much fallacy when you (invalidly) challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions.
I’m leaning towards A, but would appreciate more info on this. Again, I found this extremely useful.
The preceding sentence gives an intensional definition of “extensional definition”, which makes it an extensional example of “intensional definition”.
This is really elegant. Worth taking a beat to digest
Yeah, that might be me not factoring my own environment out of it as much as I thought. In my case, there has been a lot of recrimination about failure of character, about taking something from everyone else without enough consideration as to how it would cause them harm, implicitly stating that an offense has been incurred. Its not the main reaction, but definitely more common than I would have expected. As to
I’m not sure this can be discussed rationally online, without a LOT of context and trust that’s impossible in an open forum.
it might very well be the case, but sufficient context and trust has been reached to meaningfully engage other taboo topics already. I’m not sure It can be reached here, but cant confidently discard it either.
Lastly, the murder-victim approach I used is just a possible explanation for something I consider a discrepancy. I’m not all that in love with the idea myself, but I didn’t mean it as literal arguments people will explicitly consider but rather as hidden euristics that might explain it. I’ve seen very few cases where it is explicitly talked about in that lense, and only after starting to read into the subject in more depth, so those are more academic/philosophic digestions than actual world observations
While the main point stands, this particular image seems sort of misleading. The bucket—label analogy suggests that concepts we formulate to navigate the world live in neat, contained and well defined spaces (even if those spaces themselves are not accesible, or even known, to us in a conscious level, which is what I’m reading from this). But, more importantly, one of the traits of buckets is that by finding out something is in this bucket I know it can’t be anywhere else—They are exclusive in that way.
Furthermore, labels themselves seem to be sufficient to model this analogy. Why are not elements (bugs) labeled themselves rather than belong to higher level categories (the Bad-Bucket) which will be the ones carrying the labels?