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I agree with what you have said but have an additional worry. It seems to me that the standard logic we use might be heavily rooted in the real world. It either

I agree with what you have said but have an additional worry. It seems to me that the standard logic we use might be heavily rooted in the real world. It either rains or doesn't rain seems to closely reflect how the classical world works. But would we intuitively accept the same laws of logic if we lived in an universe that was obviously some kind of many worlds universe, where it always rains and doesn't rain?

pdonis 3y ago
> would we intuitively accept the same laws of logic if we lived in an universe that was obviously some kind of many worlds universe, where it always rains and doesn't rain? You don't have to change the laws of logic that you use to do unitary QM (which, taken to extremes, is what gives you a "many worlds universe"). You can describe it just fine using mathematical equations based on the same laws of logic you're familiar with. In other words, what you are calling "standard logic" actually contains many more possibilities than just the simple Boolean "rains or doesn't rain".
- danbruc 3y ago
  Sure, if the system is expressive enough, you can emulate other systems in it, you can build fuzzy logic on top of classical logic. Many worlds was just a random example which is not too far from the classical world. But can we not imagine an universe that is very different from ours, that outright contradicts our logic? After all logic is just build on top of axioms that make sense to us, I don't see that this necessarily grants them some universal truth.
  - pdonis 3y ago
    > can we not imagine an universe that is very different from ours, that outright contradicts our logic? Can you give an example? If you can't, doesn't that in itself answer your question?
    - danbruc 3y ago
      Not necessarily. How and what we can think might be constraint by our brains or maybe even by the universe itself. I don't think any human can make sense of two time dimensions but it seem premature to me to conclude that no universe could have more than one time dimension. Anything I could suggest would by definition not make any sense to us as it defies our logic but could it really not exist? It might of course just be a stupid idea. How would you even think about something like this if you throw out the foundation of our thinking?
      - pdonis 3y ago
        > I don't think any human can make sense of two time dimensions Sure humans can; Greg Egan built a whole sci-fi universe that way: https://www.gregegan.net/DICHRONAUTS/00/DPDM.html https://www.gregegan.net/DICHRONAUTS/00/DPDM.html But two time dimensions doesn't contradict our logic. (It contradicts our best current theories of physics, but that's not the same thing as contradicting our logic. Egan's model is logically consistent.) So this is not an example of what you were claiming. > Anything I could suggest would by definition not make any sense to us In other words, you are saying humans can't imagine a universe that contradicts our logic. I agree. And that is a "no" answer to the question you posed in the GGP post to this one. Whether universes that contradict our logic could "exist", even if we can't imagine them, is a different question from the one you asked in that post. As for that: > How would you even think about something like this if you throw out the foundation of our thinking? Indeed. And if we can't even consistently think about such a thing, what's the point?
        4death4 3y ago
        Our entire logical system is premised on essentially three things: law of identity, law of non-contradiction, and the law of excluded middle. One interesting fact is that there is a school of mathematics called constructive mathematics. This branch of mathematics proves things without using the law of excluded middle.
        danbruc 3y ago
        I am not so sure about the Dichronauts universe - he threw another -1 into the metric but particles still trace out world lines. That seems more like a wired geometry than two time dimensions but that is beyond me to properly judge, whether another -1 in the metric makes a proper second time dimension or whether you would want particles to trace out world surfaces instead of world lines or something completely different. In other words, you are saying humans can't imagine a universe that contradicts our logic. I agree. And that is a "no" answer to the question you posed in the GGP post to this one. Whether universes that contradict our logic could "exist", even if we can't imagine them, is a different question from the one you asked in that post. I mean I could just say let us deny ∀x(x=x) and run with it, see what happens. It really depends on how one understands the word imagine in this context, I could postulate this but I can not really make sense of a thing not being equal to itself. And if we can't even consistently think about such a thing, what's the point? I agree with you that mathematics is pretty much divorced from reality, that mathematics makes up axioms and inspects to consequences of them, and also that some mathematical structures are useful to model aspects of the universe. Some were even specifically invented to model certain aspects of the universe, they were inspired by reality. But at the bottom of mathematics there is somewhere the logic that underpins everything and one can ask the same questions about its relation with reality. Did we arbitrarily pick the axioms of logic or did we pick them because they make sense in our universe? Or are they universal and there can not be any universe that defies our logic? The question is essentially the following. While we - or at least some people - think that mathematics is quite independent of the real world in general, might this be less true than we think because we accidentally introduced aspects of our universe into it by building on top of a logic that reflects how our universe works? Or the other way around, are there other versions of mathematics build on top of other versions of logic that seem illogical to us but only because our universe instilled us with a certain logic.
samus 3y ago
Such systems of logic are quite useful for dealing with our own reality as well. Paraconsistent logics disallow or restrict some of the axioms of classical logics to avoid some contradictions. In turn, it loses completeness to some degree. It has similarities to intuitionistic logic, but intuitionistic logic has other aims.

pdonis 3y ago

> would we intuitively accept the same laws of logic if we lived in an universe that was obviously some kind of many worlds universe, where it always rains and doesn't rain? You don't have to change the laws of logic that you use to do unitary QM (which, taken to extremes, is what gives you a "many worlds universe"). You can describe it just fine using mathematical equations based on the same laws of logic you're familiar with. In other words, what you are calling "standard logic" actually contains many more possibilities than just the simple Boolean "rains or doesn't rain".

danbruc 3y ago
Sure, if the system is expressive enough, you can emulate other systems in it, you can build fuzzy logic on top of classical logic. Many worlds was just a random example which is not too far from the classical world. But can we not imagine an universe that is very different from ours, that outright contradicts our logic? After all logic is just build on top of axioms that make sense to us, I don't see that this necessarily grants them some universal truth.
- pdonis 3y ago
  > can we not imagine an universe that is very different from ours, that outright contradicts our logic? Can you give an example? If you can't, doesn't that in itself answer your question?
  - danbruc 3y ago
    Not necessarily. How and what we can think might be constraint by our brains or maybe even by the universe itself. I don't think any human can make sense of two time dimensions but it seem premature to me to conclude that no universe could have more than one time dimension. Anything I could suggest would by definition not make any sense to us as it defies our logic but could it really not exist? It might of course just be a stupid idea. How would you even think about something like this if you throw out the foundation of our thinking?
    - pdonis 3y ago
      > I don't think any human can make sense of two time dimensions Sure humans can; Greg Egan built a whole sci-fi universe that way: https://www.gregegan.net/DICHRONAUTS/00/DPDM.html https://www.gregegan.net/DICHRONAUTS/00/DPDM.html But two time dimensions doesn't contradict our logic. (It contradicts our best current theories of physics, but that's not the same thing as contradicting our logic. Egan's model is logically consistent.) So this is not an example of what you were claiming. > Anything I could suggest would by definition not make any sense to us In other words, you are saying humans can't imagine a universe that contradicts our logic. I agree. And that is a "no" answer to the question you posed in the GGP post to this one. Whether universes that contradict our logic could "exist", even if we can't imagine them, is a different question from the one you asked in that post. As for that: > How would you even think about something like this if you throw out the foundation of our thinking? Indeed. And if we can't even consistently think about such a thing, what's the point?
      - 4death4 3y ago
        Our entire logical system is premised on essentially three things: law of identity, law of non-contradiction, and the law of excluded middle. One interesting fact is that there is a school of mathematics called constructive mathematics. This branch of mathematics proves things without using the law of excluded middle.
      - danbruc 3y ago
        I am not so sure about the Dichronauts universe - he threw another -1 into the metric but particles still trace out world lines. That seems more like a wired geometry than two time dimensions but that is beyond me to properly judge, whether another -1 in the metric makes a proper second time dimension or whether you would want particles to trace out world surfaces instead of world lines or something completely different. In other words, you are saying humans can't imagine a universe that contradicts our logic. I agree. And that is a "no" answer to the question you posed in the GGP post to this one. Whether universes that contradict our logic could "exist", even if we can't imagine them, is a different question from the one you asked in that post. I mean I could just say let us deny ∀x(x=x) and run with it, see what happens. It really depends on how one understands the word imagine in this context, I could postulate this but I can not really make sense of a thing not being equal to itself. And if we can't even consistently think about such a thing, what's the point? I agree with you that mathematics is pretty much divorced from reality, that mathematics makes up axioms and inspects to consequences of them, and also that some mathematical structures are useful to model aspects of the universe. Some were even specifically invented to model certain aspects of the universe, they were inspired by reality. But at the bottom of mathematics there is somewhere the logic that underpins everything and one can ask the same questions about its relation with reality. Did we arbitrarily pick the axioms of logic or did we pick them because they make sense in our universe? Or are they universal and there can not be any universe that defies our logic? The question is essentially the following. While we - or at least some people - think that mathematics is quite independent of the real world in general, might this be less true than we think because we accidentally introduced aspects of our universe into it by building on top of a logic that reflects how our universe works? Or the other way around, are there other versions of mathematics build on top of other versions of logic that seem illogical to us but only because our universe instilled us with a certain logic.

samus 3y ago

Such systems of logic are quite useful for dealing with our own reality as well. Paraconsistent logics disallow or restrict some of the axioms of classical logics to avoid some contradictions. In turn, it loses completeness to some degree. It has similarities to intuitionistic logic, but intuitionistic logic has other aims.