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August 23

"Proof" of the principle of skepticism?

In AI, a logic-based agent is one which represents knowledge/beliefs as a set of sentences. A key aspect of logic-based agents is that they only admit a sentence if they are 100% sure it's true. I call this the "principle of skepticism". It forgoes the need for unlearning. It is usually assumed that deciding what to unlearn is hard, and it is better just make sure that you never believe anything false in the first place.

I have a sketch informal justification for this principle:

Suppose there were a 1% chance you would admit a belief if it were false.

You would go around gaining knowledge, perhaps much faster than you would if you demanded 100% certainty.

However, sooner or later, you would admit a belief which was false.

Because that belief is used as the basis for making new inferences, the probability of admitting another false belief increases.

If you didn't manage to unlearn the false belief, then, more quickly than it did before, you will admit another false belief, and the probability of you admitting a false belief increases again, and your ability to unlearn weakens again.

It's obvious what happens. Sooner or later, your inference system is quickly destroyed, and it admits false sentences as often as it rejects them, from which there is no hope for recovery.

Is this justification sound? And in any case, I was wondering if there could be made a formal "proof" or sorts of the skepticism principle, in the context of AI or computer science, or in general. PeterPresent (talk) 18:21, 23 August 2017 (UTC)[reply]

You may find a larger number of people who know about this kind of question in the AI StackExchange. 87.112.201.156 (talk) 20:08, 23 August 2017 (UTC)[reply]

I don't think that would be appropriate. It's not really an AI question. It's just trying to find a justification for being a skeptic. PeterPresent (talk) 02:25, 24 August 2017 (UTC)[reply]

Note that fuzzy logic specifically deals with the cases where 100% certainty is impossible. StuRat (talk) 20:49, 23 August 2017 (UTC)[reply]

Probability deals with cases where 100% certainty is impossible. In fuzzy logic, beliefs are still only admitted if they are definitely true; it's just that the beliefs are imprecise. A fuzzy sentence would be "Bob is tall" as opposed to "Bob is 190cm". It's still that we accept "Bob is tall" only if we are 100% sure of that fact. Incidentally, I think most AI professionals don't think very highly of fuzzy logic. It is only covered briefly in the standard textbook, certainly to a much lesser extent than non-fuzzy logic or probability.

As for probability, it's still the case that beliefs are only admitted when we are 100% sure they are true; it's just that beliefs are of the form "the probability that Bob's height is >180cm is 0.8 given the current evidence" and things like that. They are easily amenable to being updated with new evidence, but it's still the case that we admit a statement like "the probability that Bob's height is >180cm is 0.8 given the current evidence" only when we are 100% sure that statement itself is true. If we didn't, the problem I described in my OP would still occur. In other words, the laws of probability follow the laws of logic. PeterPresent (talk) 02:25, 24 August 2017 (UTC)[reply]

Fuzzy logic has it's place, like in medical diagnosis. StuRat (talk) 02:42, 24 August 2017 (UTC)[reply]

You're describing the Principle of explosion. The article has a nice writeup with both informal and formal proofs. As it turns out, we are certain about very few things in the world, so nearly all practical AI agents nowadays are built upon statistical inference/Bayesian learning instead of classical/deductive logic. C0617470r (talk) 09:32, 27 August 2017 (UTC)[reply]

Why do none of the 3 New York commuter railroads go to Downtown Manhattan?

Manhattan's widest river was tunneled under by 1908 so why not, after going c. 50-110 miles from the outer suburbs/exurbs you can't go 1-3 miles more to reach the Wall Street region? Sagittarian Milky Way (talk) 22:01, 23 August 2017 (UTC)[reply]

It's still expensive to tunnel under rivers, so you can expect them to save money by doing this as few times as possible. StuRat (talk) 22:05, 23 August 2017 (UTC)[reply]

It has to do with the bedrock for one part. Look up the construction of the Twin Towers (New York City) which had to have special underground retaining walls built due to the unsuitability of the loose soil. The skyscrapers in Manhattan are built where the bedrock is close to the surface.

Secondarily, many of the buildings at the time those railroads were built were not structurally stable enough to have heavy freight train traffic. :Finally, there is indeed the Path Train system which had a terminus at the WTC (I haven't been on that train since the 90's, so I don't know its disposition since 9/11), and the a multitude of smaller subway trains and above ground bus routes that will get you to Wall Street.

In any case, Wall Street is a cobblestone anachronism, almost all business is conducted in the skyscrapers in midtown, the only sort of things of interest downtown that far are tourist attractions, city hall and the court buildings and the diamond district with some shopping on Fulton Street--there's simply no call for major rail to the area. μηδείς (talk) 02:52, 24 August 2017 (UTC)[reply]

I don't follow the question; there's 4-5 New York City Subway lines that go through downtown Manhattan; the IRT Broadway–Seventh Avenue Line goes all the way to The Battery. Of course, the commuter rail doesn't have many stops in the city, but that's because that's not what a commuter rail does. In every city in the world with a commuter rail system similar to New York, the commuter rail's purpose is to gather people from the suburbs and exurbs and get them into large hub stations in the city center; from THERE people take local light rail/bus/etc. to their exact destination. The New York commuter rail systems get everyone to places like Grand Central Terminal and Penn Station. From there, commuters distribute on local public transportation to their destination. You see the same system in Boston, Philadelphia, Chicago, Washington, DC, London, Paris, etc. The question is based on a false premise. I don't know why the OP would think that the commuter rail would have many stops in Downtown or other parts of the city center, because that's not what commuter rail is for... --Jayron 32 11:23, 24 August 2017 (UTC)[reply]

The OP omitted that the river tunnels were for heavy-grade freight trains. His question may be naive, but can be answered once one makes that assumption. The commuter rails (subways like the IRT) you mention were never freight trains. μηδείς (talk) 20:30, 24 August 2017 (UTC)[reply]

London has seen the inadequacy of that arrangement: Crossrail. 81.151.100.122 (talk) 10:45, 25 August 2017 (UTC)[reply]

If I read that article correctly, the Elizabeth Line is still a commuter, and not local, line. There are only a few stops in Central London; the line still serves the purpose of bringing travelers from afar to central London, and most of those will take other transportation options once there. That's the point, commuter rail is not a "metro", it's not designed to get around a city. It's designed to get to a city from the suburbs. --Jayron 32 14:36, 25 August 2017 (UTC)[reply]

But the point is that it goes through the City and West End, whereas all the old termini are peripheral. The stop at Tottenham Court Road station in the heart of the West End, and Farringdon station in the City are going to be within easy walking distance of many workplaces. Alansplodge (talk) 12:13, 27 August 2017 (UTC)[reply]

@Sagittarian Milky Way: The answer to your question ultimately goes back to the history of the various private railroads that built the rail lines that were eventually consolidated into the system we have today. For trains arriving from the north (upstate New York and Connecticut), the tracks end at Grand Central Terminal, previously the site of the Grand Central Depot. The Depot (and hence the terminal that replaced it) was built on 42nd Street because in the nineteenth century, the authorities prohibited railroad tracks further south than that, because having trains run in what was then the built-up part of the City was disruptive (air pollution, scaring horses, etc.). Pennsylvania Station was built in its current location because it was most convenient for the Pennsylvania Railroad, which owned some of the lines that are now part of NJ Transit, as well as the Long Island Rail Road. Newyorkbrad (talk) 21:24, 27 August 2017 (UTC)[reply]

The same reasoning applies in London and, I believe, in Paris and elsewhere. Trains from the north stopped at Marylebone, Euston, King's Cross and Broad Street. Trains from the east stopped at Liverpool Street. Trains from the south east stopped at Waterloo, those from the south at Victoria. Trains from the west stopped at Paddington. Each railway company built its own terminal. The Metropolitan Railway was an underground line which linked these terminals. The Elizabeth Line is a proper railway which utilises main line tracks. It is one of a series - we already have Thameslink which runs north to south stopping at Farringdon and City Thameslink and on the drawing board is Crossrail 2, originally conceived as the Hackney - Chelsea line. 92.8.219.206 (talk) 13:08, 28 August 2017 (UTC)[reply]

(A minor correction to the above from an ageing Brit (and former railway periodical editor) who was using these services as far back as the sixties. Trains from the south-east stopped mainly at Charing Cross (which replaced London Bridge as the main SER terminus), with some still terminating at London Bridge or going on to Waterloo East. It was Waterloo (which succeeded the much earlier Nine Elms) that served mainly the south and south-west (though much of Paddington's services also came from the south west as well as west). {The poster formerly known as 87.81.230.195} 90.204.180.96 (talk) 20:57, 28 August 2017 (UTC))[reply]