If we're limiting ourselves to deductive reasoning, then yes – the facts as stated do not give enough information to deduce that Greg must be white.
If instead we use abductive inference, we might seek the simplest and most likely explanation given our universe of observations. Sherlock Holmes was a big fan of abduction!
Much of real-world reasoning is abductive to a greater or lesser extent. There is a well-known joke about some motley band of engineers, logicians, mathematicians, statisticians, etc etc catching a train through the Highlands. They see a black sheep, the engineer says "look, all sheep in Scotland are black!", the statistician says "no, you can't say that – just that MOST sheep in Scotland are black", another says "no, we can only say that at least ONE sheep is black", another says "no, it's only black on at least one side", then the one you're stuck next to at the party says "you're all wrong, we can only say that at least one sheep in Scotland is black on at least one side at least some of the time". The last statement is fully deductive; the rest of them are abductive, and more-or-less useful.
This is why I think the ability to ask good questions is a better indication of understanding and intelligence than the ability to generate answers.
As a gauge for how far we are from AI you can consider what sort of modeling capacity is required until an AI can ask, when presented with such a sequence: "What country is the swan from?" or, even more impressively: "Do you know where this took place and what country the swan's parents were from?" For the first question it would then abduce a color. Same for the second but perhaps it could include probabilities based on estimated number of each color and the genetics of swan color.
This post is a rotation meant to provide a better sense of scale for the problem at hand.
> This is why I think the ability to ask good questions is a better indication of understanding and intelligence than the ability to generate answers.
Certainly! Synthesis rather than reformatting (or, more commonly, regurgitation). Analysis and abduction are more than just "put it in your own words". More useful too.
There is something of a rush on at the moment to generate chat-bots to replace FAQs. Every Slack/Fleep/Blern/Crank channel appears to have five or six memoisation bots. Seems to be largely a solved problem!
When we can start having bots that can be sensibly interrogated for a summary (or even a "hey, you've been away for several hours: here's the key points"), we can finally abandon the chatrooms and let the generative bots flood them with abductive content, and the precis bots can then ping you every couple of weeks when something important comes up.
I would hypothesize abductive reasoning works better for collectives which accept mistakes as one means of learning. For today's AI, it might be better to ask for a bit of context from your observers before making conclusions.
"Am I in the United States around the first part of the 21st century?"
"Yes."
"Oh, how unfortunate - now I have to ask another question or you may think I'm not sentient."
Correct answer should be "possibly white", but "insufficient data for meaningful answer" should also be right:) There's a high chance of being right with swans, not so much with humans.
* Assume it is provable that ( l e. S /\ l e. W ) implies for all l ( l e. S /\ l e. W ), and assume that g e. S . Then it is provable that if ( l e. S /\ l e. W ) then g e. W .
h1::whiteswans.1 |- ( ( l e. S /\ l e. W ) -> A. l ( l e. S -> l e. W ) )
h2::whiteswans.2 |- g e. S
3:1:bnj1361 |- ( ( l e. S /\ l e. W ) -> S C_ W )
5:3:sseld |- ( ( l e. S /\ l e. W ) -> ( g e. S -> g e. W ) )
That would make it a classic logic "puzzle". I think these Babi tests are meant to incorporate more fuzzy concepts. If you read this sentence to a 4-year-old, she would probably answer 'white', right?
I would hope that she would answer "white...?" -- eg., demonstrate the ability and willingness make a useful provisional inference, with the understanding that it is provisional and the curiosity to know more. That, it seems to me, would be the answer that is most useful and correct.
But you're probably right, the answer would be 'white', at least until a black swan comes along and utterly fucks with her worldview. Humans prefer certainties and binaries, and eschew uncertainties, probabilities, and multiplicities. So they employ all sorts of cognitive errors to avoid these things. This s a problem, because the universe rarely comes in binaries or delivers enough information for real certainty. I would hope that machine consciousness would avoid these errors, as I think they are the foundations of some of our nastier tendencies.
> Humans prefer certainties and binaries, and eschew uncertainties, probabilities, and multiplicities. So they employ all sorts of cognitive errors to avoid these things.
I wonder how general is that. I'd like to believe it's more of a mindset thing - I definitely saw people reasoning this way, but I also know some that handle uncertainty pretty well. I'd like to include myself in the second group - personally, I'm actually suspicious of anything that sounds binary in the real world - it means I'm being fed some artificial boundaries.
If instead we use abductive inference, we might seek the simplest and most likely explanation given our universe of observations. Sherlock Holmes was a big fan of abduction!
Much of real-world reasoning is abductive to a greater or lesser extent. There is a well-known joke about some motley band of engineers, logicians, mathematicians, statisticians, etc etc catching a train through the Highlands. They see a black sheep, the engineer says "look, all sheep in Scotland are black!", the statistician says "no, you can't say that – just that MOST sheep in Scotland are black", another says "no, we can only say that at least ONE sheep is black", another says "no, it's only black on at least one side", then the one you're stuck next to at the party says "you're all wrong, we can only say that at least one sheep in Scotland is black on at least one side at least some of the time". The last statement is fully deductive; the rest of them are abductive, and more-or-less useful.