If you really want to get technical, integer math is even just an abstraction.
Well, yes, in a certain sense. But I don't think it is in the sense you're using.
Absoluteness in quantity is very hard to prove, just based on perspective alone. One person may say they have three apples. I say they have 2.95 apples because the stem is missing from one of them.
I'm at a bit of a loss here. Are you not aware that apples and integers are vastly different things? You are talking about using integers as an abstraction for counting physical objects, but while that can be useful, that doesn't mean that integers
are physical objects, or that physical objects are integers.
To understand what I'm talking about, you need to stop trying to correlate mathematical concepts with physical objects and understand that there are mathematical ideas
per se that one can manipulate with logic, regardless of whether the real world is capable of "living up" to these or not. And those are the answers I'm looking for from an intelligent analysis.
Is the Intel 8080 manual wrong when it says that the CPU always clears the carry when I execute an AND instruction? Well, yes, because it doesn't always. If I run the CPU on 3.5 V rather than the required 5 V, perhaps it malfunctions. But any intelligent being would know that going down that road of argument is counterproductive; we want to talk about things as they
should work, and consider the above a failure of use, and bugs as a failure of design, rather than going for the nihilistic, "the world is random; we can't try to do anything" approach.
The integral nature of a calculation is for convenience....
No. It may be convenient for you to use integers in certain situations as a good enough approximation of what you need to calculate, but integers in math are not a "convenience"; they are a real thing that lives in logic.
...but an integer is an abstraction, not a concrete thing based in some unquestionable reality.
I'm not sure where or how the "reality" comes into this or not. Integers are a concept, based in certain rules, and if you follow these rules you can come up with valid results. That is unquestionable, because the rules are there, and they have no necessary connection with the physical world. You may choose to apply these ideas to the physical world, but do not mistake your application to mean that integers now must match and have all the failings of the physical world.
It holds very well with how we analyze our universe, but in reality the universe is not required to operate on integer anything.
Yes, exactly. But how does this matter when I am dealing with mathematical and logical concepts, and ChatGPT is failing to do so?
This would be a big part of my expectation of "intelligence": it can understand abstract systems and work within those rules. Which LLMs clearly can't.
Most facts you know because someone told you. You don't have the ability to personally verify them all.
When I'm doing logic, there's no need to verify anything. I simply look at the rules, work within those rules, and come up with a result. And that's where the LLMs entirely fail. You tell them, "assume X is true, tell me about Y" and they reply with, "You are right, X is true," and then give you something that by logic only works if X is false.
The universe is a big complex place, and we often have false beliefs. But the ability to work out
valid conclusions, whether they're true or false, is a huge part of why we've come as far as we have. And LLMs, apparently, have
no way to do that. You can give them all the facts in the world, but if they've been trained on more "the sun goes around the earth" text than "the earth goes around the sun" text, they'll come out with the former. (And even if they've been trained on the latter, they will still occasionally come out with the former.)
I don't see why teaching an LLM prevents it from ever knowing facts, but teaching a kid does not.
You can train a child to follow rules. You cannot train an LLM to follow rules.