The word "is", maps to the logical "equals" operator. I agree with the example, but I don't agree it is relevant. There is no implies operator.
The statement "Math is Language", where A is Math and B is Language, maps to the logical assertion: "A = B".
If we are going to really be kinda twisty and non-standard, we could interpret the english "is" to be "is an equivalence class of". Which would map to your example pretty well: language is indeed an equivalence class of math, but math is not an equivalence class of language. Though, nobody is talking about implies operator or equivalence class here.. It's a "is" relationship, logical *equals*
You point out the "is a" relationship, not the "is" relationship, they are different. [0]
Find examples with two singular nouns and just the word 'is'.
The phrase in question: 'Math is language' is an example, or something like 'food is love' is too. I concede you could interpret those last few sentences with poetic license to be read more like: "A is a form of B", or "A is a B" - though that is not what was written and this is not a place to expect that much poetic license.
*edit*: a minute later, thought of a good example. "ice is water". True that "ice is a form of water", but strictly speaking no, "ice is not water". I'll concede there could exist an implied "is a", or an implied "is a form of", but that is poetic license IMO.
[0] Google AI summarized it pretty well: google "logical "is a" vs logical "is"
> In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things
> You point out the "is a" relationship, not the "is" relationship, they are different.
Well, what you reacted to was, let me copy'n'paste, "Math is a language". It was you who insisted that "is" in this sentence maps to "equals" relation, so thanks for agreeing that you were wrong.
I'm reacting to: "Math is language. 'Everything' is language. Language is the image of reality."
There are other discussions which say:
- Math is a subset of language, surely
- It's easily argued that languages are subsets of math.
Given that context, the distinction seems to be very important.
I find the following idea (paraphrasing) to be very interesting: "not only is math a subset of language, but the language and math are equal sets." I also think it's not true, but am curious how a person would support this assertion. So, my challenge is, because the logical "is" relationship is reflexive and the reflexive property does not hold here - how can this be true? The most satisfying answer has been (paraphrasing) "cause I'm using non-precise language and you should just infer what I meant." Which is fine I guess..
I literally copied "Math is a language." from your quote that started this subthread. Nobody here has typed "Math is language" - except you. Just open https://news.ycombinator.com/item?id=43873113, press CTRL+F and see for yourself. I can't fathom how can you still deny being so obviously wrong.
Honestly I don't think his point even stands. We were using English to communicate and English doesn't have the strict rules of mathematics. That's literally why we created math (which I'll gladly call "a class of languages"). He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection.
The problem here all comes down to seadan83 acting in bad faith and using an intentional misinterpretation of my words in order to fit them to their conclusion. I'm not going to entertain them more because I won't play such a pointless game. The ambiguity of written and spoken language always allows for such abuse. So either they are a bad faith actor "having fun" (trolling) finding intentional misinterpretations to frustrate those who wish to act in good faith or they are dumb. Personally, I don't think they're dumb.
> We were using English to communicate and English doesn't have the strict rules of mathematics.
Agree.
> He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection.
I agree. So, why can't either interpretation be valid? Perhaps, because one is obviously not true? Yet, it seemed like there was a clarification that the obviously not true relationship was the intended one!!!
Godelski previously wrote: "Coding IS math. Not "coding uses math".
I interpreted that clarification to mean you intended "is" to be a strict "is". Particularly given the other context and discussion of "is a" in other threads. I suspect now you were perhaps emphasizing "uses a" vs "is a", rather than "uses a" vs "is". Not a satisfying conclusion here. It would be a lot more interesting if the precision could have been there and had we been able to instead talk about whether all coding languages form an abstract algebra or not. Or perhaps use that line of reasoning to explain why all coding is a form of math. That would have been far more interesting..
It's such an absurd thing to argue about that I just assumed that some massive brainfart happened there. It happens to everyone, not everyone doubles down on it though.
The statement "Math is Language", where A is Math and B is Language, maps to the logical assertion: "A = B".
If we are going to really be kinda twisty and non-standard, we could interpret the english "is" to be "is an equivalence class of". Which would map to your example pretty well: language is indeed an equivalence class of math, but math is not an equivalence class of language. Though, nobody is talking about implies operator or equivalence class here.. It's a "is" relationship, logical *equals*