5 ms·

I don't think it's a paradox by any of those definitions. Why do you think it is?

Sharlin 7y ago
Clearly number 1: an unintuitive, unexpected result that is nevertheless true. Other examples include Simpson's paradox, Braess' paradox, or the mentioned Monty Hall paradox.
- mannykannot 7y ago
  I agree with that as the best fit to Quine's categories, but it is also paradoxical (though not a logical paradox) in that one might think that such a result would have far-reaching implications for cognitive science and AI, but, on reflection, it is not a disruptive result.
- jamesrcole 7y ago
  There are paradoxes that are unintuitive because they appear contrary to other knowledge that we seem reasonably certain of. Then there are things that people find unintuitive or unexpected simply because they run contrary to their intuitions and assumptions. Like, for numerous people in history, the idea of a spherical Earth or how far away the stars really are. These latter cases aren't paradoxes. Is there some established knowledge that the relative difficulties of these AI tasks appear to run contra to? I believe it is just intuition and assumptions they run contra to.
  - pure-awesome 7y ago
    The fact that stars appear close despite being incredibly far away, and the fact that the earth appears flat (and that we don't fall off) despite being spherical are both, indeed, paradoxes.
    - jamesrcole 7y ago
      Why do you think that? Is there, to you, anything unintuitive or unexpected, relative to intuitions, that is not a paradox?
      - pure-awesome 7y ago
        I like that question! Hmm, I'd say to be a paradox, it needs to be so unexpected that it's an apparent contradiction. Merely slightly unexpected is not sufficient. "I did not expect you to arrive so early" is not a paradox. "The left facing arrow on your website takes me to the next page." whilst both unexpected and unintuitive, is not a paradox. Some edge cases: "I am speaking to you in person whilst I am watching you on a live broadcast on television" is maybe a paradox. A statement like "Fruit juice is as unhealthy as sugary soft drinks." could be a paradox for many people.
        jamesrcole 7y ago
        > I'd say to be a paradox, it needs to be so unexpected that it's an apparent contradiction. Thinking about the topic of paradoxes some more, I would say part of my objection is in the following. You could distinguish between two sorts of paradoxes 1) where the phenomenon P itself is genuinely paradoxical 2) where the phenomenon P itself is not itself paradoxical, but where our knowledge of the world is such that our picture of P appears to be paradoxical. In cases of 2), I object to saying that P is paradoxical. The reason for my objection is that doing so would be confusing the map for the territory. What is apparently paradoxical really has nothing to do with P itself. It is all a matter of a particular person's knowledge relating to P. In those cases, P is in no way paradoxical, and it is misleading to call it paradoxical. It would be less misleading to say that some group of people have flawed knowledge relating to P such that there is an apparent contradiction in their knowledge. In short, in cases of 2), P is not paradoxical, rather, certain people's beliefs about P contain illusory contradictions.
        pure-awesome 7y ago
        Calling something a "paradox" is statement about the map, and is relative to a person. I.e., something can be paradoxical to you but not to me. Calling something a "contradiction", on the other hand, is a statement about the territory. > some group of people have flawed knowledge relating to P such that there is an apparent contradiction in their knowledge. > certain people's beliefs about P contain illusory contradictions. These are both (specific forms of) paradoxes. Actual contradiction is also (a different, specific form of) paradox. This is a common usage of the word paradox, and is not incorrect, but "apparent contradiction" is also in common use , also correct, and is the way in which the word is used in the term "Moravec's Paradox". EDIT: Both usages of the term are compatible, in the same way that "dog" and "Labrador" are both correct terms with which to refer to a Labrador (but only one is correct when referring to, e.g., a Husky).
  - Sharlin 7y ago
    There's no clear boundary between assumptions and knowledge. Spherical Earth and distant stars feel no longer paradoxical because we have internalized the more correct model. However, the latter is actually a good example of a result that was paradoxical in its time! Early attempts to measure stellar parallax[1] were unsuccessful, which was at odds with the heliocentric model, unless stars were actually unimaginably far away, something that was deemed implausible at the time. It seems that most of this type of paradoxes result either from having an accurate-seeming model that nevertheless fails to predict an experimental result, or from making an intuitive but incorrect assumption that a model predicts something which, in fact, it does not. Things like the stellar parallax and Olbers' paradox are examples of the former class, whereas Simpson's paradox and the Monty Hall problem are instances of the latter. [1] https://en.wikipedia.org/wiki/Stellar_parallax#Early_theory_and_attempts https://en.wikipedia.org/wiki/Stellar_parallax#Early_theory_...
    - jamesrcole 7y ago
      There doesn't have to be a clear boundary to say that, for example, there's a difference between unfounded assumptions and beleifs that have been tested to different degrees of rigour. What basis is there for the belief that abstract reasoning ought to involve more sophisticated processing? I think it's just an assumption with no solid basis (my initial comment gives the reason I believe that assumption exists). Yes, the stars thing may have felt paradoxical but it isn't itself a paradox. The thing is that if all it takes for something to be considered to be a paradox is for it to feel paradoxical to a sufficient number of people the a lot of well-established bits of scientific knowledge -- that are in no way paradoxes to people who have the relevant undergraduate degrees -- are paradoxes because they feel that way to the population at large.
      - Sharlin 7y ago
        Well, outside of math, "paradox" is not a fundamental ontological category. What is a paradox now may not be so in a hundred years, and hindsight is always 20:20. Paradoxes of this type are definitely paradoxes if they contradict something that appears to be common sense and a consensus position of some sort, irrespective of the level of rigor. The Monty Hall problem confuses even career statisticians, but that's not because the common but wrong answer is somehow based on sound statistical knowledge; it's simply because answer seems so intuitive and self-evident that we don't bother to "shut up and calculate". It seems to me that to count as a paradox, a result has to be both contradictory—not just different—from what is expected; and, the result has to be especially surprising; in Bayesian terms, the expected outcome must have had a high prior probability.
deleted 7y ago
[deleted]

Clearly number 1: an unintuitive, unexpected result that is nevertheless true. Other examples include Simpson's paradox, Braess' paradox, or the mentioned Monty Hall paradox.

mannykannot 7y ago
I agree with that as the best fit to Quine's categories, but it is also paradoxical (though not a logical paradox) in that one might think that such a result would have far-reaching implications for cognitive science and AI, but, on reflection, it is not a disruptive result.
jamesrcole 7y ago
There are paradoxes that are unintuitive because they appear contrary to other knowledge that we seem reasonably certain of. Then there are things that people find unintuitive or unexpected simply because they run contrary to their intuitions and assumptions. Like, for numerous people in history, the idea of a spherical Earth or how far away the stars really are. These latter cases aren't paradoxes. Is there some established knowledge that the relative difficulties of these AI tasks appear to run contra to? I believe it is just intuition and assumptions they run contra to.
- pure-awesome 7y ago
  The fact that stars appear close despite being incredibly far away, and the fact that the earth appears flat (and that we don't fall off) despite being spherical are both, indeed, paradoxes.
  - jamesrcole 7y ago
    Why do you think that? Is there, to you, anything unintuitive or unexpected, relative to intuitions, that is not a paradox?
    - pure-awesome 7y ago
      I like that question! Hmm, I'd say to be a paradox, it needs to be so unexpected that it's an apparent contradiction. Merely slightly unexpected is not sufficient. "I did not expect you to arrive so early" is not a paradox. "The left facing arrow on your website takes me to the next page." whilst both unexpected and unintuitive, is not a paradox. Some edge cases: "I am speaking to you in person whilst I am watching you on a live broadcast on television" is maybe a paradox. A statement like "Fruit juice is as unhealthy as sugary soft drinks." could be a paradox for many people.
      - jamesrcole 7y ago
        > I'd say to be a paradox, it needs to be so unexpected that it's an apparent contradiction. Thinking about the topic of paradoxes some more, I would say part of my objection is in the following. You could distinguish between two sorts of paradoxes 1) where the phenomenon P itself is genuinely paradoxical 2) where the phenomenon P itself is not itself paradoxical, but where our knowledge of the world is such that our picture of P appears to be paradoxical. In cases of 2), I object to saying that P is paradoxical. The reason for my objection is that doing so would be confusing the map for the territory. What is apparently paradoxical really has nothing to do with P itself. It is all a matter of a particular person's knowledge relating to P. In those cases, P is in no way paradoxical, and it is misleading to call it paradoxical. It would be less misleading to say that some group of people have flawed knowledge relating to P such that there is an apparent contradiction in their knowledge. In short, in cases of 2), P is not paradoxical, rather, certain people's beliefs about P contain illusory contradictions.
        pure-awesome 7y ago
        Calling something a "paradox" is statement about the map, and is relative to a person. I.e., something can be paradoxical to you but not to me. Calling something a "contradiction", on the other hand, is a statement about the territory. > some group of people have flawed knowledge relating to P such that there is an apparent contradiction in their knowledge. > certain people's beliefs about P contain illusory contradictions. These are both (specific forms of) paradoxes. Actual contradiction is also (a different, specific form of) paradox. This is a common usage of the word paradox, and is not incorrect, but "apparent contradiction" is also in common use , also correct, and is the way in which the word is used in the term "Moravec's Paradox". EDIT: Both usages of the term are compatible, in the same way that "dog" and "Labrador" are both correct terms with which to refer to a Labrador (but only one is correct when referring to, e.g., a Husky).
- Sharlin 7y ago
  There's no clear boundary between assumptions and knowledge. Spherical Earth and distant stars feel no longer paradoxical because we have internalized the more correct model. However, the latter is actually a good example of a result that was paradoxical in its time! Early attempts to measure stellar parallax[1] were unsuccessful, which was at odds with the heliocentric model, unless stars were actually unimaginably far away, something that was deemed implausible at the time. It seems that most of this type of paradoxes result either from having an accurate-seeming model that nevertheless fails to predict an experimental result, or from making an intuitive but incorrect assumption that a model predicts something which, in fact, it does not. Things like the stellar parallax and Olbers' paradox are examples of the former class, whereas Simpson's paradox and the Monty Hall problem are instances of the latter. [1] https://en.wikipedia.org/wiki/Stellar_parallax#Early_theory_and_attempts https://en.wikipedia.org/wiki/Stellar_parallax#Early_theory_...
  - jamesrcole 7y ago
    There doesn't have to be a clear boundary to say that, for example, there's a difference between unfounded assumptions and beleifs that have been tested to different degrees of rigour. What basis is there for the belief that abstract reasoning ought to involve more sophisticated processing? I think it's just an assumption with no solid basis (my initial comment gives the reason I believe that assumption exists). Yes, the stars thing may have felt paradoxical but it isn't itself a paradox. The thing is that if all it takes for something to be considered to be a paradox is for it to feel paradoxical to a sufficient number of people the a lot of well-established bits of scientific knowledge -- that are in no way paradoxes to people who have the relevant undergraduate degrees -- are paradoxes because they feel that way to the population at large.
    - Sharlin 7y ago
      Well, outside of math, "paradox" is not a fundamental ontological category. What is a paradox now may not be so in a hundred years, and hindsight is always 20:20. Paradoxes of this type are definitely paradoxes if they contradict something that appears to be common sense and a consensus position of some sort, irrespective of the level of rigor. The Monty Hall problem confuses even career statisticians, but that's not because the common but wrong answer is somehow based on sound statistical knowledge; it's simply because answer seems so intuitive and self-evident that we don't bother to "shut up and calculate". It seems to me that to count as a paradox, a result has to be both contradictory—not just different—from what is expected; and, the result has to be especially surprising; in Bayesian terms, the expected outcome must have had a high prior probability.

deleted 7y ago

[deleted]