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A case against Boolean logic

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Re: A case against Boolean logic

#91

Post by matt_kantor »

carodgers wrote: post #90
matt_kantor wrote: post #88

Earlier quoted context omitted.

> No, not every statement requires assumptions in order to hold. "The assumptions A implies B and B implies C, taken together, yield A implies C." This statement contains assumptions and makes observations about them, but it is true regardless of whether the assumptions it describes are true. The statement as a whole is "true" in the exact sense that the no counterexample to it can ever be given in any universe, unde…

Modus ponens holds regardless of whether it is assumed correct or not. By that, I mean that excepting contradictions, not only are no counterexamples known, but it is known that none will ever be found. So I decline to adopt your convention of classifying it as an assumption. It might be more accurate to call it an observation.

The domain of your claim was "in any universe, under any set of assumptions". I now take it that you assume (see what I did there?) that all universes are sound according to classical logic and can admit no contradictions. You might be interested in https://plato.stanford.edu/entries/impossible-worlds>, an overview of philosophical thinking on that subject.

Separately, if you scrub "plus rules like modus ponens" from my previous comment, do you agree with the rest of it?

Re: A case against Boolean logic

#92

Post by carodgers »

matt_kantor wrote: post #91
carodgers wrote: post #90

Earlier quoted context omitted.

Modus ponens holds regardless of whether it is assumed correct or not. By that, I mean that excepting contradictions, not only are no counterexamples known, but it is known that none will ever be found. So I decline to adopt your convention of classifying it as an assumption. It might be more accurate to call it an observation.

The domain of your claim was "in any universe, under any set of assumptions". I now take it that you assume (see what I did there?) that all universes are sound according to classical logic and can admit no contradictions. You might be interested in https://plato.stanford.edu/entries/impossible-worlds >, an overview of philosophical thinking on that subject. Separately, if you scrub "plus rules like modus ponens" fro…

No, again, I have made no assumptions. I have made the observation (as others may, just as easily) that no one will ever succeed in describing a scenario or a universe where modus ponens is violated.

Re: A case against Boolean logic

#93

Post by matt_kantor »

carodgers wrote: post #92
matt_kantor wrote: post #91

Earlier quoted context omitted.

The domain of your claim was "in any universe, under any set of assumptions". I now take it that you assume (see what I did there?) that all universes are sound according to classical logic and can admit no contradictions. You might be interested in https://plato.stanford.edu/entries/impossible-worlds >, an overview of philosophical thinking on that subject. Separately, if you scrub "plus rules like modus ponens" fro…

No, again, I have made no assumptions. I have made the observation (as others may, just as easily) that no one will ever succeed in describing a scenario or a universe where modus ponens is violated.

It seems like you don't actually want to engage with me in discussion. If I'm mistaken about that, please correct me (I enjoy talking about stuff like this and would love to understand your perspective). If not, that's fine too, but I don't want to waste my time.

Re: A case against Boolean logic

#94

Post by smaudet »

rhdunn wrote: post #76
gobdovan wrote: post #46

This blog is one of the most confused and inaccurate collection of writing that I recurrently find on HN. The account spams a deeply flawed blog post about 'Category theory illustrated' (also referenced from this article) where it misstates central theorems in CT and this 'Case against boolean logic' article, which promises an alternative to Boolean logic, but never formulates one. The article instead gestures toward…

A better formulation would be something like Fuzzy Logic [1]. That represents floating point values from 0 (false) to 1 (true), so 0.5 could be "unsure", 0.9 could be "very likely", etc. However, that doesn't make boolean logic invalid. Boolean logic is also the foundation of computing: logic gates, circuits like BCD, etc. [1] https://en.wikipedia.org/wiki/Fuzzy_logic

Yeah, this (the OPs) reads like a confused teenagers post, who has just started to explore the intracacies of logic. The whole post disproves itself...

Fuzzy logic is fine, I suspect they saw something like this and got confused. I would recommend they think harder about how very pertinent boolean logic is to everything they are doing before dismissing it...

Re: A case against Boolean logic

#95

Post by carodgers »

matt_kantor wrote: post #93
carodgers wrote: post #92

Earlier quoted context omitted.

No, again, I have made no assumptions. I have made the observation (as others may, just as easily) that no one will ever succeed in describing a scenario or a universe where modus ponens is violated.

It seems like you don't actually want to engage with me in discussion. If I'm mistaken about that, please correct me (I enjoy talking about stuff like this and would love to understand your perspective). If not, that's fine too, but I don't want to waste my time.

On other topics I imagine the conversation would flow better and, I hope, be just as lively and engaging. But to be direct, no, I'm not eager to continue when universes that admit contradictions are on the table. A conversation that permits contradictions is not likely to be productive. So I'll be content to just restate my point. Cheers!

Re: A case against Boolean logic

#96

Post by danbruc »

dTal wrote: post #87
danbruc wrote: post #56

Earlier quoted context omitted.

Which is exactly what I wrote. [...] two dependent binary questions [...] The second one is meaningless if the first one is false. Considered generally, though, if I ask a true/false question then read your answer from a single bit, it may be the case that there is no possible way for you to not lie to me. Then you are not asking a binary question. If there is, for example, the possibility that I might not know the a…

Have you stopped beating your wife?

Two question, have you ever beaten your wife, if so, did you stop? You can not stop something that never started. Alternatively, if you know from context that the wife has been beaten in the past, then yes or no are perfectly fine as the only options.

That question is obviously made as a trap because you can defend both answers. Yes, I am not beating her and actually never have, focusing on the current state. No, I did not stop because I never started, focusing on the state change. And the other party can do the same. No, so you did not stop beating your wife, so you are beating her. Yes, so you stopped beating your wife, then must have beaten here in the past.

The correct response is of course that the question is not applicable because it assumes a state - the wife has been beaten in the past - that does not match reality. And not applicable is not a third answer to the question, it is a statement about the question itself. So in contexts where non-applicable binary question might occur, you have to first determine whether the question is applicable before proceeding to answer the question.

Re: A case against Boolean logic

#97

Post by danbruc »

somat wrote: post #89
kqp wrote: post #50

Earlier quoted context omitted.

The known/unknown question is not separate in the real world, computing avoids it by asking binary questions only when they’re answerable. Considered generally, though, if I ask a true/false question then read your answer from a single bit, it may be the case that there is no possible way for you to not lie to me.

As a specific example. If I ask the true/false question "Have you stopped murdering people?" an entirely valid response is "that question is wrong" It is reasonable to map the world in binary logic. but the map logic must be correct and raising an error when it is not is important.

The crucial point here is the difference between response and answer. Saying that the question is not applicable because you never started murdering people is a response but not an answer to the question. And that response answers an omitted binary question, is the actual question applicable in the current context, is the implied assumption - you started murdering people at some point in the past - satisfied?
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