4 ms·

First of all, logic is a game. A game in the same sense that algebra is a game. Allow me to give you a very simple analogy. AC circuit theory and quantum mecha

by dvt 9y ago

First of all, logic is a game. A game in the same sense that algebra is a game. Allow me to give you a very simple analogy. AC circuit theory and quantum mechanics require the use of complex numbers -- that is, the square root of negative one. In a very real sense, taking the square root of negative one sounds incredibly stupid. In fact, imaginary numbers were a very divisive issue when introduced (not unlike negative numbers before them). What does it really mean to use i? What does i map to in the real world? We're trying to calculate voltages here.. does it make any sense? Well, probably not. I could start talking about how i sort of extends the number line in the second dimension, and so forth, but that would only move the goal post (what about hypercomplex units j or k or l ... ? ). So that's why the best way to see sqrt(-1) = i is as a rule. Second of all, material implication is also a rule. There's nothing to connect to the real world. The problem with logic students is that they often don't understand the differences between abductive, deductive, and inductive logic. You mention atheism vs. religion (I assume you mean theism vs. atheism, as you can presumably have some kind of religion without a deity). When trying to win this kind of debate, you first need to pinpoint what kind of argument you're dealing with. If, for example, you're dealing with an inductive argument, the rules of deduction will not hold -- especially a rule like material implication[1]. I think that your problem is trying to apply formalisms built for one kind of game to another kind of game. Natural language is not logic. Just how Chess is not Checkers. Going back to material implication for a second, what really made material implication "click" for me was studying the Deduction Theorem[2]. This is, of course, a bit more advanced, but understanding MI from a "provability" perspective really clarifies why it's so obviously true. [1] http://ac.els-cdn.com/0888613X94900027/1-s2.0-0888613X94900027-main.pdf?_tid=e265747a-8bc7-11e7-8b1c-00000aacb35d&acdnat=1503907807_40d920a8cae68359ea5e98f028c1a537 http://ac.els-cdn.com/0888613X94900027/1-s2.0-0888613X949000... [2] https://www3.nd.edu/~cfranks/dt.pdf https://www3.nd.edu/~cfranks/dt.pdf

fizixer 9y ago
Okay, here's a concrete example, if you or anyone reading this is up for thinking about it: John's wife Jennifer says the following to her friend, "If John left office by 4:55 pm, he'd be home in a minute" (e.g., she claims that if John's office leaving time is 4:55 pm, he'd be home at 4:56 pm). Now, John never leaves office at 4:55 pm. It is always 5:00 pm or later. If he leaves at 5:00 pm sharp, it takes about 90 minutes on average for him to get home. If there is no traffic, it will still take at least 30 minutes for John to get home. So we know, as a behind-the-scenes knowledge, that if John left at 4:55 pm, there is no way he'd reach home before 5:25 pm. But, since John has never left office before 5:00 pm, and let's assume he never will, according to the rules of logic, Jennifer's claim is True: It is True that if "John left office by 4:55 pm" then "it'll take 1 minute for him to get home". Now, I don't read "A => B" as "A implies B". I find it more convincing to read it as "A => B" being True means "Information about A and B is insufficient to rule out implication". If "A => B" is False, that means it is not true that information about A and B is insufficient to rule out implication. In other words, information about A and B is sufficient to rule out implication. And the only way that's possible is when A is True and B is False. Now, given our problem, if we only look at Jennifer's claim, we would agree with her, because A is False, and B is False. (A: John's office leaving time is 4:55 pm or less, B: John 's travel time is 1 minute). If all we know is that A is False and B is False, we can claim that this is insufficient information to rule out Jennifer's claim. But, we do have extra information, call it C: that it takes John at least 30 minutes to get home, no matter what. The question is, how do we incorporate this extra information, C, in our problem, consisting of A and B, if we wish to refute Jennifer's claim of 'A => B' being True?
- dvt 9y ago
  > But, since John has never left office before 5:00 pm, and let's assume he never will, according to the rules of logic, Jennifer's claim is True: It is True that if "John left office by 4:55 pm" then "it'll take 1 minute for him to get home". A-ha! What logic are you thinking of? Jennifer is making an inductive -- a probabilistic -- claim. So right off the bat, we throw out our deductive rules. There might be an "if" and there might be a "then", but there is no material implication (=>) here. There's a weaker form of something we can call "probabilistic implication" which will naturally lend itself to plenty of holes: there's a nonzero chance that John might be abducted by aliens, for example, and he never makes it home. These probabilities are built into Jennifer's original claim. There's nothing to refute.
  - fizixer 9y ago
    A: John's office leaving time is 4:55 pm or less. B: John's travel time is 1 minute. C: John's travel time is 30 minutes or more. A is False, B is False, C is True (as given). Hence A => B is True (a ridiculous conclusion). I don't see any probability or induction in this problem.
    - dvt 9y ago
      Let me give you a simpler example we can work with. 1: If the sun sets, it will rise. 2: The sun set. Conclusion: The sun will rise. Even though the above might seem like an application of modus ponens, it's actually not. This argument (like yours with John and Jennifer) is inductive -- probabilistic -- in nature. There's some debate when you truly get down to it (is causality empirical?), but almost all claims about the natural world: be they about John's driving or the Sun rising, are inductive; and as such, deductive rules do not apply. In the case above, the sun can, technically, disappear out of existence. Obviously, this is very unlikely but, in fact, guaranteed it will happen at some point by Poincaré and Boltzmann. In Jennifer's case, her argument is inductive because there are a few (actually an infinite number of) assumptions she's making: that he has a full tank of gas, that lightning won't strike him, that he doesn't get abducted by aliens, etc. This differs from a deductive claim, e.g.: 1: Two sets are equal if and only if they contain the same elements. 2: A is a set that contains {a, b, c} 3: B is a set that contains {a, b, c} Conclusion: A = B See the difference?

by dvt 9y ago

fizixer 9y ago

Okay, here's a concrete example, if you or anyone reading this is up for thinking about it: John's wife Jennifer says the following to her friend, "If John left office by 4:55 pm, he'd be home in a minute" (e.g., she claims that if John's office leaving time is 4:55 pm, he'd be home at 4:56 pm). Now, John never leaves office at 4:55 pm. It is always 5:00 pm or later. If he leaves at 5:00 pm sharp, it takes about 90 minutes on average for him to get home. If there is no traffic, it will still take at least 30 minutes for John to get home. So we know, as a behind-the-scenes knowledge, that if John left at 4:55 pm, there is no way he'd reach home before 5:25 pm. But, since John has never left office before 5:00 pm, and let's assume he never will, according to the rules of logic, Jennifer's claim is True: It is True that if "John left office by 4:55 pm" then "it'll take 1 minute for him to get home". Now, I don't read "A => B" as "A implies B". I find it more convincing to read it as "A => B" being True means "Information about A and B is insufficient to rule out implication". If "A => B" is False, that means it is not true that information about A and B is insufficient to rule out implication. In other words, information about A and B is sufficient to rule out implication. And the only way that's possible is when A is True and B is False. Now, given our problem, if we only look at Jennifer's claim, we would agree with her, because A is False, and B is False. (A: John's office leaving time is 4:55 pm or less, B: John 's travel time is 1 minute). If all we know is that A is False and B is False, we can claim that this is insufficient information to rule out Jennifer's claim. But, we do have extra information, call it C: that it takes John at least 30 minutes to get home, no matter what. The question is, how do we incorporate this extra information, C, in our problem, consisting of A and B, if we wish to refute Jennifer's claim of 'A => B' being True?

dvt 9y ago
> But, since John has never left office before 5:00 pm, and let's assume he never will, according to the rules of logic, Jennifer's claim is True: It is True that if "John left office by 4:55 pm" then "it'll take 1 minute for him to get home". A-ha! What logic are you thinking of? Jennifer is making an inductive -- a probabilistic -- claim. So right off the bat, we throw out our deductive rules. There might be an "if" and there might be a "then", but there is no material implication (=>) here. There's a weaker form of something we can call "probabilistic implication" which will naturally lend itself to plenty of holes: there's a nonzero chance that John might be abducted by aliens, for example, and he never makes it home. These probabilities are built into Jennifer's original claim. There's nothing to refute.
- fizixer 9y ago
  A: John's office leaving time is 4:55 pm or less. B: John's travel time is 1 minute. C: John's travel time is 30 minutes or more. A is False, B is False, C is True (as given). Hence A => B is True (a ridiculous conclusion). I don't see any probability or induction in this problem.
  - dvt 9y ago
    Let me give you a simpler example we can work with. 1: If the sun sets, it will rise. 2: The sun set. Conclusion: The sun will rise. Even though the above might seem like an application of modus ponens, it's actually not. This argument (like yours with John and Jennifer) is inductive -- probabilistic -- in nature. There's some debate when you truly get down to it (is causality empirical?), but almost all claims about the natural world: be they about John's driving or the Sun rising, are inductive; and as such, deductive rules do not apply. In the case above, the sun can, technically, disappear out of existence. Obviously, this is very unlikely but, in fact, guaranteed it will happen at some point by Poincaré and Boltzmann. In Jennifer's case, her argument is inductive because there are a few (actually an infinite number of) assumptions she's making: that he has a full tank of gas, that lightning won't strike him, that he doesn't get abducted by aliens, etc. This differs from a deductive claim, e.g.: 1: Two sets are equal if and only if they contain the same elements. 2: A is a set that contains {a, b, c} 3: B is a set that contains {a, b, c} Conclusion: A = B See the difference?