I declare the Worst Argument In The World to be this: “X is in a category whose archetypal member has certain features. Therefore, we should judge X as if it also had those features, even though it doesn’t.”
Note, however that “X is in a category whose archetypal member has certain features”, is strong evidence that X does in fact have those features. Thus the burden is on the person arguing otherwise to show that it doesn’t.
Keep in mind that your brain’s corrupted hardware is designed to fail in just this kind of “special pleading” situation. Or to put it another way there’s a reason ethical injunctions exist.
Not really, Komogorov complexity difference between various languages is bounded (for everything languages L1 and L2, there is a constant D for which, for every algorithm A, |K(L1, A) - K(L2, A)| < D, D being at most the complexity of writing a L2 compiler in L1 or vice-versa). So while it may not give exactly the same results with different languages, it doesn’t “fall apart”, but stays mostly stable.
Yes, but it’s still true that for any two distinct finite strings S1 and S2, there will always be some description language in which S1 has lower Kolmogorov complexity than S2. So by appropriate choice of language I can render any finite string simpler than any other finite string.
Turing complete languages rarely vary much. If you take the string domain to be binary data, and compare most major programming languages, there will probably be a high between the lengths of equivalent programs.
Any language for which description of 30000 zero bits is longer than say, 30000 bits with zero-separated prime-length clusters of one bits (110111011111011111110...) is not general purpose.
Note, however that “X is in a category whose archetypal member has certain features”, is strong evidence that X does in fact have those features. Thus the burden is on the person arguing otherwise to show that it doesn’t.
Whether this is evidence depends on the category and the archetype.
For example:
Say an alien civilization was familiar with right triangles, but no other kinds of triangles (in Euclidean geometry). Also, they have discovered that a^2 + b^2 = c^2, where a, b & c are the side lengths. Then, they are exposed to a non-right triangle. Using WAW to conclude that a^2 + b^2 = c^2 in the non-right case is wrong 100% of the time. Not evidence in this case.
This example also illustrates that WAW does not require a politically charged statement.
Evidence “includes everything that is used to determine or demonstrate [or possibly just suggest] the truth of an assertion.”
The example illustates a case where the alleged evidence is 100% wrong. In hindsight, it’s clear that the suggestion that a^2 + b^2 = c^2 should have been considered just a hypothesis, not as a statement more likely than not to be true. In this case there are 2 subcategories (right triangles and non-right triangles), and it’s impossible to know without investigation whether the truth of the statement results from inclusion in the main category or the subcategory.
Usually when we say ‘evidence’ we mean ‘Bayesian evidence’. If you examine arbitrary triangles and they all happen to have one side whose length squared is equal to the sum of the squares of the lengths of the other two sides, then being a triangle is evidence that the shape has this property. It was still evidence even if it turns out the triangle didn’t have the property.
If you examine arbitrary triangles and they all happen to have one side whose length squared is equal to the sum of the squares of the lengths of the other two sides, then being a triangle is evidence that the shape has this property.
Agreed. But in this example, it’s known that the new triangle being considered is different from those previously examined because it’s not right. Therefore, the presumption that a sampling of the previously examined triangles is arbitrary, with respect to the larger class that includes the new triangle, is not a rational presumption.
But in this example, it’s known that the new triangle being considered is different from those previously examined because it’s not right. Therefore, the presumption that a sampling of the previously examined triangles is arbitrary, with respect to the larger class that includes the new triangle, is not a rational presumption.
I was assuming that the folks doing the observing did not necessarily realize that all the previous triangles were right and this one is not.
Also, your line of reasoning works equally well if all the triangles you’ve seen so far were written on paper, and this one (also a right triangle) is scratched in the dirt. But in that case, it would be good evidence. So clearly it’s evidence in either case.
I was assuming that the folks doing the observing did not necessarily realize that all the previous triangles were right and this one is not.
In this case, the folks doing the observing do realize that this triangle is different from all those previously considered, but they downplay the significance of this fact, perhaps using the justification: a triangle is a triangle is a triangle.
(I’m actually not making this up as I go along. I had worked out this example some time ago to illustrate what I believe to be a widely-held false belief in finance. I believe that WAW is a good description of the thought process behind this belief.)
Note, however that “X is in a category whose archetypal member has certain features”, is strong evidence that X does in fact have those features. Thus the burden is on the person arguing otherwise to show that it doesn’t.
Keep in mind that your brain’s corrupted hardware is designed to fail in just this kind of “special pleading” situation. Or to put it another way there’s a reason ethical injunctions exist.
Until some other bozo comes up with a different category. Then we get to play tennis.
This problem exists for all reasoning, e.g., Komogorov complexity falls apart when some bozo comes along with a different language.
Not really, Komogorov complexity difference between various languages is bounded (for everything languages L1 and L2, there is a constant D for which, for every algorithm A, |K(L1, A) - K(L2, A)| < D, D being at most the complexity of writing a L2 compiler in L1 or vice-versa). So while it may not give exactly the same results with different languages, it doesn’t “fall apart”, but stays mostly stable.
Yes, but it’s still true that for any two distinct finite strings S1 and S2, there will always be some description language in which S1 has lower Kolmogorov complexity than S2. So by appropriate choice of language I can render any finite string simpler than any other finite string.
Turing complete languages rarely vary much. If you take the string domain to be binary data, and compare most major programming languages, there will probably be a high between the lengths of equivalent programs.
Any language for which description of 30000 zero bits is longer than say, 30000 bits with zero-separated prime-length clusters of one bits (110111011111011111110...) is not general purpose.
Whether this is evidence depends on the category and the archetype.
For example:
Say an alien civilization was familiar with right triangles, but no other kinds of triangles (in Euclidean geometry). Also, they have discovered that a^2 + b^2 = c^2, where a, b & c are the side lengths. Then, they are exposed to a non-right triangle. Using WAW to conclude that a^2 + b^2 = c^2 in the non-right case is wrong 100% of the time. Not evidence in this case.
This example also illustrates that WAW does not require a politically charged statement.
Disagree. It is evidence that turns out to be wrong when one has more evidence.
Evidence “includes everything that is used to determine or demonstrate [or possibly just suggest] the truth of an assertion.”
The example illustates a case where the alleged evidence is 100% wrong. In hindsight, it’s clear that the suggestion that a^2 + b^2 = c^2 should have been considered just a hypothesis, not as a statement more likely than not to be true. In this case there are 2 subcategories (right triangles and non-right triangles), and it’s impossible to know without investigation whether the truth of the statement results from inclusion in the main category or the subcategory.
Usually when we say ‘evidence’ we mean ‘Bayesian evidence’. If you examine arbitrary triangles and they all happen to have one side whose length squared is equal to the sum of the squares of the lengths of the other two sides, then being a triangle is evidence that the shape has this property. It was still evidence even if it turns out the triangle didn’t have the property.
Agreed. But in this example, it’s known that the new triangle being considered is different from those previously examined because it’s not right. Therefore, the presumption that a sampling of the previously examined triangles is arbitrary, with respect to the larger class that includes the new triangle, is not a rational presumption.
I was assuming that the folks doing the observing did not necessarily realize that all the previous triangles were right and this one is not.
Also, your line of reasoning works equally well if all the triangles you’ve seen so far were written on paper, and this one (also a right triangle) is scratched in the dirt. But in that case, it would be good evidence. So clearly it’s evidence in either case.
In this case, the folks doing the observing do realize that this triangle is different from all those previously considered, but they downplay the significance of this fact, perhaps using the justification: a triangle is a triangle is a triangle.
(I’m actually not making this up as I go along. I had worked out this example some time ago to illustrate what I believe to be a widely-held false belief in finance. I believe that WAW is a good description of the thought process behind this belief.)