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  1. Poll: There's another way to flip this around. Suppose...

    There's another way to flip this around. Suppose you start at some conclusions and you want a computer to come up with premises from which to derive them. Mathematicians like to do this when they...
  2. Poll: You are wrong on the irrelevance of P3. The...

    You are wrong on the irrelevance of P3. The conclusion follows from P3, P4 and P5 and can be formalized:

    P3) JH != JC
    P4) PM = BJ || PM = JH
    P5) PM = JC
    C) PM = BJ

    From P4 and P5, we have...
  3. Poll: You're just on ignore now. Bye.

    You're just on ignore now. Bye.
  4. Poll: Can you restate the reason for me?

    Can you restate the reason for me?
  5. Poll: It's a good question. But is the status of...

    It's a good question.

    But is the status of validity something which tells of the likelihood, or even the possibility, that something will be accepted as sound? It seems that it's often the...
  6. Poll: Blatant contradictions where one premise is just...

    Blatant contradictions where one premise is just the denial of another? Perhaps there is no good reason. Perhaps all such arguments are stupid. Perhaps we should be so eager to discard them that we...
  7. Poll: To repeat, I like everything you said about...

    To repeat, I like everything you said about stipulative and lexical definitions.

    There are stipulative definitions, such as those in mathematics, which appropriate common terms. Mathematical...
  8. Poll: Ironically, mathematical logicians often use the...

    A sound argument is both valid and has true premises.

    If an argument is valid but has false premises, it’s unsound.
    If an argument is invalid and has true premises, it’s unsound.
    If an argument...
  9. Poll: The argument can be formalized: P1) JC != BJ...

    Thank you to say whether you consider this argument valid or not. P1-P3 are irrelevant. C in no way follows from P4 P5.

    Thank you to abstain from commenting before you voted.
    EB[/QUOTE]

    It is ...
  10. Poll: There are four poll options, with votes split...

    There are four poll options, with votes split evenly on three. If you constructed the poll to give exclusive and exhaustive options, that means that two-thirds of people voted wrong whatever answer...
  11. Poll: To the extent that there is a single correct...

    To the extent that there is a single correct notion of validity, and the poll representative, the results show that two thirds of people are confused.
  12. Poll: I suspect this post is another waste of time....

    I suspect this post is another waste of time. Unlike Angra Mainyu, I don't think anyone is reading these posts other than thread participants.

    One of my first posts to Speakpigeon gave the...
  13. Poll: Let's talk again when you've gone back to school...

    Let's talk again when you've gone back to school and got your degree.
  14. Poll: I enjoyed that post. I made a suggestion...

    I enjoyed that post.

    I made a suggestion above. Mathematical logicians, being mathematicians, aimed to be systematic. And when you are systematic with a bunch of intuitive rules, you sometimes...
  15. Poll: I didn't. I said that some mathematicians argue...

    I didn't. I said that some mathematicians argue that definitions are neither correct nor incorrect, only useful or adequate. I am not one of those.

    My broader point was that mathematicians rarely...
  16. Poll: What distinguishes modern logic more than...

    What distinguishes modern logic more than anything is that, like mathematics, it's highly recursive and systematic. The syntax is recursive, as when we say

    for any proposition P and Q, we can form...
  17. Poll: Does the conclusion need to be an "or" to...

    Does the conclusion need to be an "or" to highlight the issue?

    I need some salt. You have salt and pepper, but they're mixed.
  18. Poll: Which proof is that? The first proof I read of...

    Which proof is that? The first proof I read of Tarski's Theorem was back in 2004 and was not Tarski's original. In fact, I daresay the proof was original to my lecture material. If pressed to provide...
  19. Poll: Far worse for Tarski's Theorem. Anyone claiming...

    Far worse for Tarski's Theorem. Anyone claiming to have falsified it is just stating a logical absurdity. It's a theorem. You can't falsify it.

    The theorem is a fairly easy result of the machinery...
  20. Poll: And you've scored a few more points on the...

    And you've scored a few more points on the crackpot index.
  21. Poll: There you go then. Your results belong in the...

    There you go then. Your results belong in the same place as "falsifications" of Tarski's Theorem.

    If you send such a result to any journal they'll reject it immediately, since any mathematical...
  22. Doing everything without assumptions

    Here's a fairly famous axiom system for propositional logic:

    For any propositional formulas φ, ψ and χ, declare the following to be tautologies

    1) φ → (ψ → φ)
    2) [φ → (ψ → χ)] → [(φ → ψ) → (φ...
  23. Poll: Then how did you decide that the probability of...

    Then how did you decide that the probability of error is maximal?

    No human input is needed to recheck the formalized proof. You can download the source code, run the Makefile, and wait for the...
  24. No. That's as much as you'll get from me. I don't...

    No. That's as much as you'll get from me. I don't care much for the Bayesian take, but it is an attempt to formalize the idea that extraordinary claims require extraordinary evidence.
  25. Some, including WLC and his fans, have taken...

    Some, including WLC and his fans, have taken Bayes' Theorem as a means of talking about evidence.

    The idea is that extraordinary things have low probability. According to Bayes' Theorem, if some...
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