“The law of non contradiction exists”. Even Aristotle couldn’t “prove it” exists yet logic uses it all the time. I hardly think logic is about what exists but rather a tool, born out of interlocution.
Aristotle indeed couldn’t prove it, that is, to derive it as a conclusion step by step from the evidence of the senses. His reasons for this are sound: 1) an attempt to do so has to rely on PNC already, and 2) we can’t assume infinite regress.
Asking a proof of PNC would imply proving non-contradiction by some means that assumes that contradictions do exist.
PNC doesn’t need a proof; it needs validation: a process of establishing an idea’s relationship to reality, whether through deductive reasoning, inductive reasoning, or sense perception.
> logic is [not] about what exists but rather a tool
If logic describes something that is not real, then our ideas and even institutions are detached from reality, and so some people claim a right to secede from “established truths” and place anyone who disagrees outside the circle of rational dialogue. That would be a harmless academic issue if the last two centuries weren’t a living record of that detachment playing out in politics, ideology, and culture.
To get into a radiation tech program, there are 260 applicants, almost all with all As, for 20 slots at my local community college.
Maybe in the very first instant you’d think it’s merit based. But, EVERYONE is playing the game. Getting homework and tests from friends who already took the class, taking classes at several different schools to get the easier teachers, paying multiple times the tuition cost on tutors and other study aides (eg $2k+ for all the anatomy models), every demographic is using paid ChatGPT. We all know which teachers to take. We spend much of class strategizing like this.
Every single student. It’s just another game to play or you lose.
Real question: If people are that good at grinding (it is a legit skill), why don't they go for something better, like a 4-year university degree in STEM or medicine? They can make much more money.
Also, how do they decide which students to pick? And I would love to know the gender ratio.
I thought there has been a huge increase in need-based scholarships for US university fees in the last 15 years. More than just rich schools. Many state universities also offer quite good need-based scholarships based upon your own income + net worth and that of your parents.
Yes state schools are. That’s why it’s so competitive as well. $4-$6k at the state school vs $50K+ at private.
There’s one state school for my program within 100 miles of me (physical therapy assistant)
And a four year program is still 2 extra years of tuition even at the subsidized amount, and most would work fewer hours if at all because they need high GPAs.
Even among trades where you can move up the initial ranks simply by showing up sober and working once you get to the point where you want to level up by striking out on your own it's all the same shit. Instead of paying a tutor you're paying a consultant and/or an accountant to tell you the answer. Instead of the school or licensing board asking you questions where wrong answers will have an opportunity cost of many dollars it's the government.
Just out of curiosity, where do all those hyper-competitive 260 applicants expect to work after graduating "radiation tech program" in a community college? And how much approximately do they expect to get paid for it?
1) True believers
2) Hype
3) A way to wash blatant copyright infringement
True believers are scary and can be taken advantage of. I played DOTA from 2005 on and beating pros is not enough for AGI belief. I get that the learning is more indirect than a deterministic decision tree, but the scaling limitations and gaps in types of knowledge that are ingestible makes AGI a pipe dream for my lifetime.
This is how I feel with AI math proofs. I’m not sure where they’re at now, but a year ago it took so much more time to check if an LLM proof was technically correct even if hard to understand, compared to a well structured human proof.
Maybe it was Timothy Gowers who commented on this.
Lots of human proofs have the unfortunate “creative leap” that isn’t fully explained but with some detectable subtlety. LLMs end up making large leaps too, but too often the subtle ways mathematicians think and communicate is lost, and so the proof becomes so much more laborious to check.
Like you don’t always see how a mathematician came up with some move or object to “try”, and to an LLM it appears random large creative leaps are the way to write proofs.
Just because those things don't contribute to your final grade doesn't mean you don't do them.
At Oxbridge, for CS we still had lab work. We still had problem sets assigned for CS and for math which were graded. We had one large CS group project in, I want to say, our second year. Humanities students were still assigned essays. It's just that none of this stuff contributed to your final degree classification which was based entirely on your exams (although if you didn't do your CS practicals you wouldn't be allowed to pass).
Obviously Oxbridge isn't exactly representative but certainly my experience showed me that the American style is not the only way of making education work.
The “it does X for you” aspect of technology is not completely without its downsides, for various values of X.
For example, take “X” to be “walking”. Do we have the technology that allows us to pretty much never have to walk? Sure. As far as I am aware, though, we do not generally favour a lifestyle of being bound to a mobility aid by choice, and in fact we have found that not walking when able in the long run creates substantial well-being issues for a human. (Now, we have found ways to alleviate some of those issues for those who aren’t able, but clearly it is not sufficient because we still walk.)
The problem is exacerbated immensely as the value of X approaches something as fundamental to one’s humanity as “thinking”.
> "It does X for you" is the point of many technologies. You still require knowledge to work around it.
When running water replaced the need to pump water out of the ground yourself, were people urged to "learn faucets"? You kind of just need to twist a knob and water comes out, right?
Maybe there was an intermediary stage where running water was slightly more complicated and there were more steps to learn, but devoting time to learning those steps would have been a waste of time, since the end goal of the system was for it to function without much input.
Not at all. It’s a tool. It can be used well and it can be used badly, the difference often being others things thought in a CS curriculum. But a well trained engineer using the tool will be more productive than that engineer doing everything by hand, so leaving that tool out of the curriculum is doing a disservice to the students
This distinction seems more arbitrary over time. Growing up I was taught different species couldn’t interbreed. But what about Neanderthal and Sapiens?
I don't think you could have chosen a worse example. Dogs are themselves a subspecies, and are split into many different breeds, of wildly different character and physiology: https://en.wikipedia.org/wiki/Dog#Taxonomy
Grammar seems like you’re talking about LLMs specifically. Well, isn’t Sudoku just math? LLMs suck at Sudoku last I checked. When told not to code a solver, its very first deduction was wrong.
Generally when people talk about using LLMs to do mathematics research they’re not talking about the LLM alone, but the LLM + a harness for it to write and execute theorem provers such as Lean or Coq to validate their results.
I guess I just don’t have the experience or optimism that a harness around an LLM, which can’t make the first, bare deduction on its own, is a good use of compute.
I got out of RLHF, including games and puzzles, before agents took off and maybe I have outdated info. But we estimated RLHF’ing a single hard full sized sudoku was ~25 hours worth of work.
https://plato.stanford.edu/entries/aristotle-noncontradictio...
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