• HermanS
    1
    I never had any formal logic in college, but I find it fascinating, so I bought a used copy of Priest's An Introduction to Non-Classical Logic. I got through the first five chapters with no problems (though the more philosophical questions are above me on first go around), and even most of Chapter 6 (intuitionist logic) was fine, but there are a couple of times where syllogisms are said to be false, but I seem unable to make the tableau rules prove it. If anyone can please point out what I am missing, it would be greatly appreciated.

    6.6.2, First Example (forgive me my useless eraser)
    logic1.jpg

    6.6.2, Second Example
    logic2.jpg

    Exercise 6.10.4c
    IMG-0698.jpg

    Exercise 6.10.4e
    IMG-0697.jpg

    Thanks in advance.
  • Alvin Capello
    89
    HermanS



    Hello! Apologies for the late reply. Here are the places where I think you went wrong. All of these suffer from the same problem it seems:

    In the 2 examples for 6.6.2, you sent both negative conditionals from world 0 to world 1. But this is incorrect: each negative conditional should bring a new world into the tableau. So, for instance, you can send (P -> Q), -0 to world 1, but now you have to send (Q -> S) -0 to a new world, say world 2). Give that a shot and see how it goes :smile:

    Now for exercise 6.10.4c there's a similar problem, when you negate a negative proposition, you need to bring a new world to the tableau. But you sent both of them to the same world. Therefore, after sending -P, -0 to world 1, you need to send -Q, -0 to world 2.

    Same thing with 6.10.4e. You sent both negative conditionals to world 1, but you need to send the first to world 1 and the second to world 2.

    I hope this was helpful. Please let me know if you have more questions.
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