5 ms·

I concur.

stakhanov 7y ago
It's not ambiguous at all. The statement is perfectly clear. The statement is a contingency, i.e. a statement that is neither valid nor unsatisfiable. (Proof-theoretically: neither p nor not-p is provable. Model-theoretically: some assignment of truth values to p will make it true but not all of them). It would be a far more valuable lesson to teach children that talking about something doesn't will it into existence so that you can start making meaningful statements about it, like how many of them there were. It's like tampering with witness testimony: "Witness: Somebody stole my handbag. Police: Do you remember anything about him? Can you describe him?" All of a sudden the witness remembers that the suspect was male, not female, when the witness may not have seen such a thing at all. ...or like a show I recently saw on History Channel about the zombie apocalypse. Harvard Professor on TV: "Well, scientifically speaking, there is nothing to suggest that a zombie apocalypse would be a scenario we will likely ever be facing. But if there were such a thing as a zombie apocalypse then one of the most important things would be hygiene, so as to minimize the risk of infection, which is a fascinating topic that I have published about quite extensively." Reporter: "Oh, really? Tell me more about the hygiene precautions that we need to use in the event of a zombie apocalypse." Harvard professor: Spends the next 10 minutes of screentime talking about zombie hygiene. Dumb idiot in front of TV: "Honey! Come down here! They're talking about the zombie apocalypse on TV! They have a professor from Harvard and everything!" All of a sudden: The zombie apocalypse is a thing. Conversely: The fact that you can't see something doesn't mean it doesn't exist... (like atoms)! "How many blue cats are there? -> zero." Might sound okay, but "How many atoms are there? -> zero" is quite wrong, since the cats are presumably composed of more than zero atoms but we can't really count them etc etc So when these kinds of presupposition violations come up, then you should teach your little daughter to go "Huh? What the? I can't answer that!" Because "Huh? What the? I can't answer that!" is actually the right answer!
- popnroll 7y ago
  What about "none" instead of zero?
  - stakhanov 7y ago
    ...doesn't help either. The problem is that when you ask "How many blue cats are bouncing?" you are stating that blue cats are in existence. So there'd have to be some, not none. There'd have to be a number strictly greater than zero. So zero/none can't be the answer, or you're somehow breaking the rules of the game of logic, or how the computer game is set up. If, however, you say "How many cats are blue and bouncing?" then the presupposition would only extend so far as to state that cats are in existence, which is reflected on-screen. In that case, it may well be the case that there are zero/no cats that are blue and bouncing. Let me crossindex something I linked in the other thread: https://en.wikipedia.org/wiki/Syllogism#Existential_import https://en.wikipedia.org/wiki/Syllogism#Existential_import When Aristotle describes his logic (All men are mortal...) he never fathoms the possibility that one of these sets that he talks about could be empty. (Empty sets, in that sense, don't belong in the realm of science, as far as he is concerned, but in the realm of fiction and so forth). So, to get back to the original post: If I were doing this for a 2-4 year old, then zero is a can of worms I would try to avoid opening altogether. Or I would make sure that the presupposition-part of any question that is asked is in line with the evidence on screen. If, instead of following Aristotle, you follow the embedding of the syllogism into modern predicate calculus and modern predicate calculus into propositional logic, then you end up with outcomes that will be mindbogglingly counter-intuitive to a 4 year old (but to any person, really). Example: "All flying horses are three-legged." would become a true statement. Since there are no flying horses, this is always an empty set. Ex falso quodlibet. Therefore always true. A valid statement.
    - defanor 7y ago
      I'd think that exercises for small children are based on more mainstream (nowadays) classical logic and ZFC (and likely with finite sets), and certainly are informal. If so, the reasoning can go as "here's a set of cats, take blue ones out of it, then take bouncing ones out of those; how many is there?". I wondered whether what's shown on the screen is also supposed to be a complete representation of the set in question, but apparently the correct answer to every question is 0 and I don't see any cats (maybe it just doesn't work correctly here).
    - 7y ago

I concur.

It's not ambiguous at all. The statement is perfectly clear. The statement is a contingency, i.e. a statement that is neither valid nor unsatisfiable. (Proof-theoretically: neither p nor not-p is provable. Model-theoretically: some assignment of truth values to p will make it true but not all of them). It would be a far more valuable lesson to teach children that talking about something doesn't will it into existence so that you can start making meaningful statements about it, like how many of them there were. It's like tampering with witness testimony: "Witness: Somebody stole my handbag. Police: Do you remember anything about him? Can you describe him?" All of a sudden the witness remembers that the suspect was male, not female, when the witness may not have seen such a thing at all. ...or like a show I recently saw on History Channel about the zombie apocalypse. Harvard Professor on TV: "Well, scientifically speaking, there is nothing to suggest that a zombie apocalypse would be a scenario we will likely ever be facing. But if there were such a thing as a zombie apocalypse then one of the most important things would be hygiene, so as to minimize the risk of infection, which is a fascinating topic that I have published about quite extensively." Reporter: "Oh, really? Tell me more about the hygiene precautions that we need to use in the event of a zombie apocalypse." Harvard professor: Spends the next 10 minutes of screentime talking about zombie hygiene. Dumb idiot in front of TV: "Honey! Come down here! They're talking about the zombie apocalypse on TV! They have a professor from Harvard and everything!" All of a sudden: The zombie apocalypse is a thing. Conversely: The fact that you can't see something doesn't mean it doesn't exist... (like atoms)! "How many blue cats are there? -> zero." Might sound okay, but "How many atoms are there? -> zero" is quite wrong, since the cats are presumably composed of more than zero atoms but we can't really count them etc etc So when these kinds of presupposition violations come up, then you should teach your little daughter to go "Huh? What the? I can't answer that!" Because "Huh? What the? I can't answer that!" is actually the right answer!

popnroll 7y ago
What about "none" instead of zero?
- stakhanov 7y ago
  ...doesn't help either. The problem is that when you ask "How many blue cats are bouncing?" you are stating that blue cats are in existence. So there'd have to be some, not none. There'd have to be a number strictly greater than zero. So zero/none can't be the answer, or you're somehow breaking the rules of the game of logic, or how the computer game is set up. If, however, you say "How many cats are blue and bouncing?" then the presupposition would only extend so far as to state that cats are in existence, which is reflected on-screen. In that case, it may well be the case that there are zero/no cats that are blue and bouncing. Let me crossindex something I linked in the other thread: https://en.wikipedia.org/wiki/Syllogism#Existential_import https://en.wikipedia.org/wiki/Syllogism#Existential_import When Aristotle describes his logic (All men are mortal...) he never fathoms the possibility that one of these sets that he talks about could be empty. (Empty sets, in that sense, don't belong in the realm of science, as far as he is concerned, but in the realm of fiction and so forth). So, to get back to the original post: If I were doing this for a 2-4 year old, then zero is a can of worms I would try to avoid opening altogether. Or I would make sure that the presupposition-part of any question that is asked is in line with the evidence on screen. If, instead of following Aristotle, you follow the embedding of the syllogism into modern predicate calculus and modern predicate calculus into propositional logic, then you end up with outcomes that will be mindbogglingly counter-intuitive to a 4 year old (but to any person, really). Example: "All flying horses are three-legged." would become a true statement. Since there are no flying horses, this is always an empty set. Ex falso quodlibet. Therefore always true. A valid statement.
  - defanor 7y ago
    I'd think that exercises for small children are based on more mainstream (nowadays) classical logic and ZFC (and likely with finite sets), and certainly are informal. If so, the reasoning can go as "here's a set of cats, take blue ones out of it, then take bouncing ones out of those; how many is there?". I wondered whether what's shown on the screen is also supposed to be a complete representation of the set in question, but apparently the correct answer to every question is 0 and I don't see any cats (maybe it just doesn't work correctly here).
  - 7y ago