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It makes perfect intuitive sense if you're used to the way the word "if" is used in classical logic. Remember that it's you who has bent your intuitive sense to

by sid0 16y ago

It makes perfect intuitive sense if you're used to the way the word "if" is used in classical logic. Remember that it's you who has bent your intuitive sense to fit how material implication works. Most people are not going to think it makes intuitive sense, and the fault doesn't lie with them -- it lies with the logic. Logic is like UI: it's Not the User's Fault he doesn't find implication intuitive.

astrofinch 16y ago
Logic is not like UI. UI is a translation layer between the way humans think and the way a machine works. Logic isn't a translation layer. It's more like a theoretical machine. The English terms we use to talk about logic could be considered similar to UI. But I don't think that using the word "if" (instead of making up a new word like "garply") was obviously the wrong design decision for the inventors of English logical terminology. "If" is the word in the English language that most closely maps to the concept the terminology designers wanted to describe.
- sid0 16y ago
  > Logic isn't a translation layer. It's more like a theoretical machine. More precisely, it is a model for human thought. The way logic is similar to UI is that logic's philosophical success is a function of how well human thought maps to it and how intuitive theorems in the logic are, just as UI's success is a function of how intuitive it is. The last hundred years of discourse on philosophical logic have been focused on one thing -- to formalize the human notion of implication better than material implication does. That's why logicians came up with non-classical logics of the modal, counterfactual (which captures the very intuitive notion of mutatis mutandis), fuzzy and intuitionistic varieties.
  - astrofinch 16y ago
    OK, but has anyone managed to construct the real numbers with intuitionist logic? Maybe different logics are like different building materials, each with their own advantages and disadvantages.
    - sid0 16y ago
      > OK, but has anyone managed to construct the real numbers with intuitionist logic? I think it should be possible to do so. As long as you don't need the law of the excluded middle you should be fine. > Maybe different logics are like different building materials, each with their own advantages and disadvantages. I see where you're coming from, but I think logic is more than just a tool.
  - sid0 16y ago
    Sorry, that's more precisely ceteris paribus -- "all else being the same".

by sid0 16y ago

astrofinch 16y ago

Logic is not like UI. UI is a translation layer between the way humans think and the way a machine works. Logic isn't a translation layer. It's more like a theoretical machine. The English terms we use to talk about logic could be considered similar to UI. But I don't think that using the word "if" (instead of making up a new word like "garply") was obviously the wrong design decision for the inventors of English logical terminology. "If" is the word in the English language that most closely maps to the concept the terminology designers wanted to describe.

sid0 16y ago
> Logic isn't a translation layer. It's more like a theoretical machine. More precisely, it is a model for human thought. The way logic is similar to UI is that logic's philosophical success is a function of how well human thought maps to it and how intuitive theorems in the logic are, just as UI's success is a function of how intuitive it is. The last hundred years of discourse on philosophical logic have been focused on one thing -- to formalize the human notion of implication better than material implication does. That's why logicians came up with non-classical logics of the modal, counterfactual (which captures the very intuitive notion of mutatis mutandis), fuzzy and intuitionistic varieties.
- astrofinch 16y ago
  OK, but has anyone managed to construct the real numbers with intuitionist logic? Maybe different logics are like different building materials, each with their own advantages and disadvantages.
  - sid0 16y ago
    > OK, but has anyone managed to construct the real numbers with intuitionist logic? I think it should be possible to do so. As long as you don't need the law of the excluded middle you should be fine. > Maybe different logics are like different building materials, each with their own advantages and disadvantages. I see where you're coming from, but I think logic is more than just a tool.
- sid0 16y ago
  Sorry, that's more precisely ceteris paribus -- "all else being the same".