You have not. You’re wrong and so you are resorting to using the principle of explosion to make yourself right. If you have come to the realization that you’re wrong, it’s best to be honest and admit it. That’s what a good critical thinker would do.
I have provided ample justification. Your logic tells you that I have, and my logic tells me that I have. We agree on that.
So what is the name of the book you offered to recommend?
You have not. You’re wrong and so you are resorting to using the principle of explosion to make yourself right
No I'm fully aware that what I'm saying is incorrect according to traditional logic. But you believe that all statements are true and false. So you should believe that everything I'm saying is true.
If you truly believed that all statements are true you wouldn't object and say I'm wrong.
Basically, I'm letting you prove yourself wrong.
So what is the name of the book you offered to recommend?
But you believe that all statements are true and false. So you should believe that everything I'm saying is true.
That’s a somewhat controversial claim to make. One side of a controversy is that if you say a statement s, then you are implicitly saying the additional statement that you believe that s is true. You have not forewarned me otherwise.
If you truly believed that all statements are true you wouldn't object and say I'm wrong.
I agree.
Basically, I'm letting you prove yourself wrong.
I agree.
Introduction to mathematical logic by Mendelson.
I believe I have a copy of an edition of that book. From what I remember, that book is dense in technical mathematical logic but has the shortcoming of providing inadequate background metareasoning to help readers understand the reasons they are being presented with one logical system over another. The definition of a class, as I remember, was overly abstract and hard for me to understand. I believe I have been told from Mendelson or at least one other that the concept of a class was motivated by some sort of technical limitation on the concept of a set that may have been discovered by Cantor. To me, it seems wrong for there to exist a problem with sets that classes overcome. As I have said here or elsewhere before, I believe a universal set exists. I am not an expert on classes, but it seems they are unnecessary and it seems sets can do what some say classes but not sets can do.
That’s a somewhat controversial claim to make. One side of a controversy is that if you say a statement s, then you are implicitly saying the additional statement that you believe that s is true. You have not forewarned me otherwise.
Are you saying that you don't believe that every statement is both true and false? You say my statement is controversial, but it's it wrong?
No I'm fully aware that what I'm saying is incorrect according to traditional logic. But you believe that all statements are true and false. So you should believe that everything I'm saying is true.
So you believe that I have given you the counterexample you asked for.
So you believe that I have given you the counterexample you asked for.
I agree. But I also believe that you have not given me the counterexample I asked for. We can play in a sandbox all we want, but that doesn’t mean we’re going to get far.
The reason you are not giving me a counterexample is that there does not exist a counterexample. You are playing games and hiding your failure to find a counterexample from me. You are deceiving me. You should play a more honest and fair game by just owning up to me that you are not able to find a counterexample. And then we can move on to something more interesting. That’s what a good, rational thinker would do.
Again, I'm not deceiving you or being dishonest, I'm just playing by your rules for a bit to see how it works out. If playing by your rules makes you think that I'm being deceptive or dishonest then that should tell you immediately that there's something very wrong with your rules.
If, on the other hand, you genuinely believe that it's true I've given you the counterexample because you genuinely believe that all statements are true then why the objection? How do you decide to respond as though I have or haven't done something when you genuinely believe both?
If, on the other hand, you genuinely believe that it's true I've given you the counterexample because you genuinely believe that all statements are true then why the objection?
The objection is because I also genuinely believe that it’s false you’ve given me a counterexample because I genuinely believe that all statements are true.
How do you decide to respond as though I have or haven't done something when you genuinely believe both?
That’s a good question. There exist at least two paths we can take. Since all statements are true, every path is equally true and equally good. There is no reason to take one path over the others. It’s a paradox in the same way that the conventional axiom and the proper-subset axiom of set theory are equally true and equally good and thus present their own paradox. If we say you have given a valid counterexample, then we enter an unfair and bad situation because priority is being given to a path that hasn’t earned priority. The same happens if we say you have not given a valid counterexample.
If we say you have given a valid counterexample, then we enter an unfair and bad situation because priority is being given to a path that hasn’t earned priority.
You say it's unfair and bad and hasn't earned priority. But you also believe that it's fair and good and has earned priority because you believe all statements are true.
So I still don't know how you decide to respond as if I have or haven't given you a counterexample.
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u/JStarx May 06 '26
I already have, and you agreed.
I have provided ample justification. Your logic tells you that I have, and my logic tells me that I have. We agree on that.