What has Gödel incompleteness to do with that? We can just take any sentence φ as an axiom, and we’ve a trivial proof thereof.
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What has Gödel incompleteness to do with that? We can just take any sentence φ as an axiom, and we’ve a trivial proof thereof.
This is not, generally, true. Cambridge tends to have higher offers, and I had a friend offered 5A*+S1 (STEP), but that’s mostly because he buggered up his interview (and he was taking 5 A-levels). The standard offer at Oxford for mathematics is A*A*A, which is exactly what those applying from any public school will be asked to achieve.
> or just 3 As from state schools
Not for maths. For easy courses like PPE, someone who misses a standard offer of A*AA might be let off by a few grades. People at public schools who miss their offers are much likelier to be a bit thick.
In any case, this project seems to me to be no more extraordinary than the redistributive effects of e.g. Medicaid or Pentagon spending, or the construction of Interstates. The Interstates, in the present US political environment, might indeed seem extraordinary; but the question is then not how one convinces people from state A to spend on state B, but how to convince people to make large long-term investments in the first place.
1: https://web.archive.org/web/20130111042126/http://archiviost...
It is also hard to see what these drafting habits have to do with the common law system. Points 1–5 could be true of a legislature in pretty much any legal tradition.
Others may misidentify respectable, good, or correct arguments as ‘attacks’ in narrower senses, but that no more makes the underlying categories meaningless than the misapplication of such descriptions as ‘true’, ‘valid’, ‘scientifically established’, or ‘by definition’. I have no general pithy answer to what one should do about the sorts of attack I have described, but I venture that it is reasonable to talk or attempt to do something about them. What term would you prefer?
Yes, often.
There is nothing wrong with the use of ‘an’ before ‘history’ and the forms of that lemma. It is unusual, and perhaps pretentious or otherwise silly, but only in the same way as ‘connexion’ is an unusual (&c) but perfectly correct spelling.
If you want to make a different point about the majority, or a very big majority, or two people, you should make that point instead. Obviously the Chinese with whom I interact are of a certain class and intellectual formation of which I must remain aware; in particular, the closeness of some to the party breeds a unique type of contempt. That is why I am not trying to generalise; seemingly, you are.
https://www.bbc.co.uk/blogs/magazinemonitor/2009/09/how_to_s...
Second, I am not sure that this is a ‘small’ minority. Even ignoring the Channel 14 polls (which do seem to be made up) the current coalition is on about 50 seats (looking at https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_I...). And then I am not really convinced that Sa’ar or Lieberman would really be opposed to this specific action, which would make a majority. For that matter, I saw one poll saying a Sa’ar+Cohen+Bennett tie-up would hit a whole thirty-two seats and reduce the Likud to twelve (that's the one labelled ‘Merger of Gideon Sa'ar, Naftali Bennett and Yossi Cohen & Labor and Meretz under Yair Golan’…) Admittedly maybe Lieberman would say that it’s stupid but that’s different from saying it’s disgraceful.
I’d say this is the murky case because on the fixed training data and query distribution X ≈ 1 and we know that even though we don’t know the value of X on other training data and other query distributions. I think that might be where the disagreement lies.
I think that this might be a nice way of getting round my objection, but there is one worry, which is that X is relative to a distribution on the questions we ask when we aren’t dealing with Encyclopedia Eric but with an LLM. I don’t actually use LLMs very much myself, partly out of arrogance and Luddite tendencies. But I suspect that the value of X for some sorts of questions (simple quiz questions, maybe?) and some LLMs (maybe not Google’s) will be high enough to end up in the murky case.
Of course, both you and I agree that there /is/ clearly a difference. I can see the attraction of appealing to the intuitive or pretheoretic notion of knowledge, since it’s a fairly straightforward way of stating the difference and it’s not obvious how else one might put it (I suppose ‘LLMs don’t explicitly think through the facts stored when deciding what to say’ is one way of putting it.)
I remember some time ago rather sleepily watching John Hawthorne talk about conditionals; my sole memory was of his banging on about ‘the little logician in the brain’ (I think the point was something like: some conditionals seem [in]felicitous in virtue of form because the little logician in the brain is reading them; others seem infelicitous because we examine them more closely and look e.g. at the referents involved, in which case e.g. Gricean considerations apply). One difference at least in the case of LLMs that makes sense to me is that there is no ‘little logician’ in LLMs.
The point you make might be regarded as an argument about the first question. In each case, the ‘chain of custody’ (as the parent comment put it) is compared and some condition is proposed. The condition explicitly considered in the first question was reliability; it was suggested that reliability is not enough, because it isn’t justification (which we can understand pretheoretically, ignoring the post-Gettier literature). My point was that we can’t circumvent the post-Gettier literature because at least one seemingly plausible view of justification is just reliability, and so that needs to be rejected Gettier-style (see e.g. BonJour on clairvoyance). The condition one might read into your point here is something like: if in the ‘chain of custody’ some text is generated by something that is incapable of belief, the text at the end of the chain loses some sort of epistemic virtue (for example, beliefs acquired on reading it may not amount to knowledge). Thus,
> text from an LLM is more suspect than text from a dictionary.
I am not sure that this is right. If I have a computer generate a proof of a proposition, I know the proposition thereby proved, even though ‘the text is entirely generated by an entity which is not capable of having justified true beliefs’ (or, arguably, beliefs at all). Or, even more prosaically, if I give a computer a list of capital cities, and then write a simple program to take the name of a country and output e.g. ‘[t]he capital of France is Paris’, the computer generates the text and is incapable of belief, but, in many circumstances, it is plausible to think that one thereby comes to know the fact output.
I don’t think that that is a reductio of the point about LLMs, because the output of LLMs is different from the output of, for example, an algorithm that searches for a formally verified proof, and the mechanisms by which it is generated also are.
Beliefs derived from the output of LLMs that are ‘right most of the time’ pass one facially plausible precisification of ‘justification’ in that they are generated by a reliable belief-generation mechanism (see e.g. Goldman). To block this point one must engage with the post-Gettier literature at least to some extent. There is a clear difference between beliefs induced by reading the outputs of LLMs and those induced by the contents of a reference work, but it is inessential to the point and arguably muddies the water to present the distinction as difference in status as knowledge or non-knowledge.