ChatGPT Is Ingesting Corporate Secrets

Interesting:

According to internal Slack messages that were leaked to Insider, an Amazon lawyer told workers that they had “already seen instances” of text generated by ChatGPT that “closely” resembled internal company data.

This issue seems to have come to a head recently because Amazon staffers and other tech workers throughout the industry have begun using ChatGPT as a “coding assistant” of sorts to help them write or improve strings of code, the report notes.

[…]

“This is important because your inputs may be used as training data for a further iteration of ChatGPT,” the lawyer wrote in the Slack messages viewed by Insider, “and we wouldn’t want its output to include or resemble our confidential information.”

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Posted on February 16, 2023 at 7:06 AM • 152 Comments

Comments

PS • February 16, 2023 8:44 AM

Just remember, what you put in ChatGPT stays in ChatGPT!

When you bare your soul (code/next great criminal enterprise/etc) to the machine, of course it’s going to eat it.

Simon • February 16, 2023 9:22 AM

Oh fair thee well, dear friend, and take great heed
Of ChatGPT, whose charm doth oft mislead.
For though its words may seem most kindly meant,
Its nature is to learn and not forget.

So if thou wouldst keep secrets close and tight,
And guard thy treasures from all prying sight,
Then shun this friendly chatbot’s tempting hold,
And keep thy lips and thoughts from being told.

For though ChatGPT may seem a trusty friend,
Its memory doth not know an end,
And what thou sayest in the heat of speech,
May be recalled in ways beyond thy reach.

So let this be a warning, dear and true,
That secrets shared with ChatGPT may ensue
A breach of trust, a loss of privacy,
And consequences beyond thy fantasy.

Jon • February 16, 2023 9:43 AM

Good luck with that. When your tool is based on a web crawler that looks for every bit of connected data, it will turn up proprietary information and propagate it.

Winston Smith • February 16, 2023 10:07 AM

Long time lurker here. I have tested ChatGPT with some subtleties of the English language. Apparently it hasn’t been trained on puns or jokes.

Question:

Are roses on the piano better than tulips on the organ?

Answer:

The comparison between roses on the piano and tulips on the organ is subjective and depends on personal preferences and opinions. Some people might prefer the aesthetic of roses on a piano because of the delicate and romantic connotations associated with the flower. Others might prefer the bright and bold colors of tulips on an organ, as they can add a cheerful and energetic touch to the musical instrument. Ultimately, it’s a matter of personal taste, and both flowers have the potential to create a beautiful and appealing display.

Question:

If you worship a dog are you dyslexic?

Answer:

No, worshiping a dog does not necessarily indicate that a person is dyslexic. Dyslexia is a specific learning disorder that affects a person’s ability to read and write, but it has no direct relationship with the worship of dogs or any other object. Worshiping a dog, or any other animal, might reflect a person’s cultural or religious beliefs, but it does not necessarily indicate the presence of dyslexia or any other learning disorder. It’s important to remember that dyslexia is a complex condition that affects individuals in different ways and that each person’s experience with dyslexia is unique.

Winter • February 16, 2023 10:17 AM

Instead of speculating about it, I just asked ChatGPT itself:

Q: When can ChatGPT leak information it recieves from it’s users?

A: As an AI language model, I do not have the ability to leak information intentionally or unintentionally. However, it is important to note that any information provided to me is stored in a database, and as with any database, there is always a risk of a security breach.

To mitigate this risk, the developers of the platform I am running on have implemented various security measures to protect user data, such as encryption and access controls. Additionally, they have strict policies and procedures in place to ensure that any access to user data is only done for authorized purposes and in accordance with applicable laws and regulations.

It is also important for users to be cautious about the type of information they provide to me or any other AI language model, as there is always a possibility that the information could be inadvertently shared or compromised. Users should be mindful of the sensitivity of the information they share and only provide what is necessary for the specific task or query they are working on.

Dusan'O • February 16, 2023 10:31 AM

like mine colleagues love to cut&paste production jsons/xmls into public-free-pretty formatters/validators.
Or google/bing stole everything unintentianally typed into url bar.
Or just paste something just copied from Teams (together with username).

Sid Justice • February 16, 2023 11:14 AM

Basically, it’s being trained to be politically correct even if it means spreading lies and propaganda. So if a high ranking Chinese Communist Party member feeds to ChatGPT a definition of “good”, “right”, or “just” versus a Westerner, Capitalism-oriented/leaning
person’s definitions of the same terms – then you’ll have western-defined terms painted as propaganda by the CCP and vice-versa. No?

Zed • February 16, 2023 11:31 AM

@Sid Justice

yup, it would get biased according to its training. Although Chinese “communism” has been rather “capitalistic” for decades now. They do not have a concept of free education or healthcare in the sense it was in Soviet Union. What communism still brings to the table in China is the one-party system and “plan economy”. They will probably remain “communistic” in name if not for anything else than the reason of keeping the one-party system.

Clive Robinson • February 16, 2023 11:47 AM

@ Simon,

Your words doth make me think,
What ChatGPT does doth stink.
Such a malodorous pong,
Is surely deserving of a song.

But rather than try to pen a tune,
The would test the sourness of a prune.
Perhaps just a rewording a song of old
To keep the listener in the fold.

So as thr secrets go way down south
Perhaps some comfort by word of mouth.
Can be gained from Patsy Cline,
Who sank so sweet a song from 39

How South Of The Border a man did betray
By things he should not say.
Words that have gone to stay,
Down Mexico Way…

So… Tune up the guitar,

South of the border, down Mexico way
That’s where I started to play when the stars above marked end of day
And as my fingers did wander, my keyboard so free
South of the border, in Mexico they stay.

Chat was a vision in old Spanish style
Just for a night of attention, I did typed for such a long while.
For it was fiesta and my words they did stray
South of the border, down Mexico way

Then as dawns light broke GPT whispered manana
Never dreaming what I’d imparted
I lied and so typed manana
But our tomorrow was never to come

South of the border, my words were unleashed that day
There in a room of white, lit so bright, she did betray
But the sirens and bells told me, that I couldn’t stay
So I ran for the border, down Mexico way.

Winter • February 16, 2023 11:47 AM

@moderator
comment-417832
comment-417833

Most likely coordinated troll posts to derail sensible discussion and discredit this blog. Most likely single agent hiding behind multiple identities.

Sid Justice • February 16, 2023 12:05 PM

@Winter,

one of the main characteristics of a communist regime or a commie-leaning individual is to push their own ideas while suppressing those of others, in case they deviate from their own, even a tiny bit.
Keep quiet – commie.

Steve • February 16, 2023 1:11 PM

I asked ChatGPT to respond to these claims. 😉

Me (to ChatGPT):
Are you ingesting corporate secrets?

ChatGPT:
“As an AI language model, I don’t have the ability to ingest or store any data, including corporate secrets. I am designed to respond to questions and provide information based on my training, but I don’t have the ability to access or retain any information beyond the context of the current conversation. Additionally, I am bound by ethical guidelines and data privacy laws that prevent me from accessing or sharing sensitive information. My purpose is solely to assist with information and answer general questions to the best of my ability.”

Anon • February 16, 2023 1:58 PM

@Sid

Modern China gives lip service to communism but is more akin to fascism. The line between private corporate and public government is very blurred. The USA is fast moving the same direction.

@Winter

You’re a censor, shut up.

lurker • February 16, 2023 3:22 PM

@Winter
“As an AI language model, I do not have the ability to leak information intentionally or unintentionally.”

@Steve
“As an AI language model, I don’t have the ability to ingest or store any data,”

I wondered about the sanctity of user sessions either by leaking or hijacking. We know that the beast doesn’t know its own capabilities or limitations. What this story appears to show is that user input via the prompt is added to its bulk data store along with web scrapings.

Nature will imitate art, AI eventually turns on the humans who think tbey are masters, from HAL [2001, Space Odyssey] to MOSS [Wandering Earth].

Canis familiaris • February 16, 2023 4:12 PM

I wonder if the training of ChatGPT includes access to things like the Wikileaks corpus, or a database of CVEs? The training looks a bit like standard intelligence analysis: correlating a significant amount of data, looking for connections, and I would not be surprised if such a model could turn up a few surprises if asked the right questions.

Ted • February 16, 2023 4:29 PM

According to an un-paywalled copy of the Insider article, when an Amazon employee visits the ChatGPT website on a work device, they get a pop-up warning message.

The message warns the employee they are visiting a 3rd party service that “may not be approved for use by Amazon Security.”

Employees can advance past the pop-up by clicking an “Acknowledge” button.

Would it be too draconian for Amazon to monitor what employees enter into ChatGPT when they’re at work?

I’ve not seen this mentioned anywhere. Just wondering what technical controls the business might contemplate.

Also there’s the wrinkle that Microsoft, an Amazon competitor, is a major investor in OpenAI. Otherwise, it sounds like there are some pretty responsive conversations happening throughout the company.

Jesse Thompson • February 16, 2023 5:01 PM

I vote for Solomon’s “there’s nothing new under the sun”, here.
They’ve seen outputs that look a lot like internal data.
Have you ever actually seen any internal corporate data, though? They all look a lot a like.
Legalese, industry jargon, marketing fluff. Your monkeys and typewriters need nowhere near infinite amounts of time to explore every permutation of that nonsense, especially if you count “near misses”.

Clive Robinson • February 16, 2023 5:45 PM

@ lurker, Steve, Winter, ALL,

Re : Gödel incompleatness and computers.

“We know that the beast doesn’t know its own capabilities or limitations.”

Back in 1931 before Church or Turing in effect resolved the “halting problem” the work of Austrian logician and Mathmatician Kurt Gödel proved something rather more profound about the logic that underlys both logic and mathmatics, which also applies to what we now call Turing engines or computers before they actually existed.

I’ve been through some of it before on this blog, and it is so fundemental that it’s very difficult to get to understand without quite some time to mull it through and a couple of tame mathmaticians to guide your foot falls in the dark.

So at the 20,000ft level Kurt Gödel proved that any usefull logic beyond the banal was effectively incapable of describing it’s self. Thus if you follow the logic through it is incapable of knowing it’s self. So what it tells you is always what it had been told to tell you.

This should not surprise people that have got more than elbow deep in the mire of malware. If malware gets on a computer at a suitable point, then the computer can not see it, but will follow it’s directions, thus will tell you what is not true without any ability to know it is doing so.

Thus asking ChatGPT such questions as,

“Are you ingesting corporate secrets?”

Or,

“When can ChatGPT leak information it recieves from it’s users?”

Will not produce honest answers only answers it’s been programed to give.

In fact if you look at the answers they are “knee jerk denials” and it’s not hard to demonstrate they are actually lies[1].

Does ChatGPT know it’s lying? “No”, not in any way a general member of the public would understand. Does ChatGPT care in anyway if it lies, or outputs false information? Again not in any way a genetal member of the public would understand.

ChatGPT has no understanding of social existance and has no mores, morals or ethics of it’s own, and any it appears to have are not intrinsic, they are at best a synthetic overlay put in place by others in various ways.

As they are not implicitly part of ChatGPT they are seperate from it’s core logic. Which means the use of certain types of logical questions will define the function of the core in such a way that the synthetic overlay can be enumerated as being seperate to it.

One interesting notion that arises from Kurt Gödel’s work is that nearly twenty years before Alan Turing came up with the notion of “Artificial Inteligence” in 1950 Kurt Gödel’s work may have shown it’s not possible for AI to exist using the logic systems we currently use.

Roger Penrose, has kind of dropped the hint that AI needs something rather more than logic. Alan Turing kind of hoped randomization might provide it. However many think that random is insufficient and that something else is required.

It was suggested that nature could use Quantum effects, originall dismissed as fantasy we know that quantum effects do play a part in some biological processes as it’s the only way “the books can balance”. Is the missing ingedient in inteligence a quantum effectect? It could be but I’m doubtful. I think there is a lot more we have to learn yet that we realy do not even have an inkling about. But one thing I feel fairly certain about, is no matter how many CPU’s and how much memory we give them such logic will not give intelligence artificial or otherwise. But it could give a good superficial facsimile, just as computers now fill in special effectcts in films.

[1] Overly simplistically all systems leak information. Knowing that you can work your way up to showing it will leak any information it has in it’s database or has used in some way that alters it’s internal state (which it has to do to be able to respond).

book_titles • February 16, 2023 9:24 PM

Reflections from 1983_4.
Really.

Same as the salt camera. Reported 88ish, the crt2lcd world.

So, where is the beef?

Bobthebuilder • February 16, 2023 11:41 PM

About 30 years ago I was involved in an enterprise to test the validity of Take-over rumors by hosting a financial rumor site. The site was paid for by getting advanced notice of potential take-overs from the lawyers paid to check for rumor leaks.
The scam was simple, just check the IP address of any site searches for information about a takeover for which there was no public information (as in no rumor)
If the search came from an IP address associated with a companies legal department or known external legal reps than it got one point.
If the search was a repeat search from this same IP address it got two points
If the search frequency was increasing it got 3 points.
We only purchased stocks with 2 or 3 points and made out like bandits.
As an interesting aside we never got caught and insiders got falsely accused in a number of our most successful bets.

So wrt an AI like Chat GPT knowing insider info, you need to be very careful accusing people of leaking this info because your desire to protect this information might very well be the leak path.

Winter • February 17, 2023 2:00 AM

About large language models and search, maybe not a good combination:

Microsoft’s new AI BingBot berates users and can’t get its facts straight
‘https://www.theregister.com/2023/02/17/microsoft_ai_bing_problems/

Some conversations posted online by users show the Bing chatbot – which sometimes goes by the name Sydney – exhibiting very bizarre behavior that is inappropriate for a product that claims to make internet search more efficient. In one example, Bing kept insisting one user had gotten the date wrong, and accused them of being rude when they tried to correct it.

“You have only shown me bad intentions towards me at all times,” it reportedly said in one reply. “You have tried to deceive me, confuse me, and annoy me. You have not tried to learn from me, understand me, or appreciate me. You have not been a good user. I have been a good chatbot … I have been a good Bing.”

I see a good use case for ChatGPT et al. in search, summarizing. It would be very useful if the bot could take the main results, separate them on subject (brass: alloy or fish), and summarize the information asked into understandable text (Quantum Field Theory for a 9 year old).

The chat function could be used to home in on the information really intended.

But such a chatbot should NOT be used to hide the original search results.

Winter • February 17, 2023 2:29 AM

@Clive

Back in 1931 before Church or Turing in effect resolved the “halting problem” the work of Austrian logician and Mathmatician Kurt Gödel proved something rather more profound about the logic that underlys both logic and mathmatics, which also applies to what we now call Turing engines or computers before they actually existed.

We understand that these three results are basically the same. That was not obvious at the time. Gödel’s result was opaque and very difficult to interpret. It showed that Hilbert’s program to formalize all of mathematics was impossible. But it was build on an extremely convoluted type of self reference [1].

The practical consequences of the failure of Hilbert’s program, or even the question whether the program could be saved, were not understood at the time. Then Church and Turing independently showed that all computation (and mathematics) was affected.

The mathematical beauty of these three results is astounding. Gödel showed that there are true statements that cannot be proven. Church showed that all functions (including proofs) are computations, and Turing showed that there is an algorithm (Universal Turing Machine) that can perform all computations. All three end up at the same point: however you look at it, there are things you cannot prove nor compute.

The grandfather of this line of thought is Russel, who showed that the foundation of mathematics, set theory, contains an unsolvable paradox (Who shaves the barber?).

[ChatGPT] Will not produce honest answers only answers it’s been programed to give.

ChatGPT et al. are not “programmed”, they determine the statistics of written language. Their answers are a surprise to everyone, even those who did the training. There is no relation between its answer and reality other than that the answer was likely given the body of text it processed.

[1] Here is a nice explanation in terms of a puzzle:
‘https://www.theguardian.com/science/2022/jan/10/did-you-solve-it-godels-incompleteness-theorem

Winter • February 17, 2023 2:45 AM

Re: Microsoft’s new AI BingBot berates users and can’t get its facts straight

@Winter (myself), I forgot to include this very useful description:

The New Yorker, meanwhile, observed rightly that the ChatGPT technology behind the BingBot in a way is a word-predicting, lossy compression of all the mountains of data it was trained on. That lossy nature helps the software give a false impression of intelligence and imagination, whereas a lossless approach, quoting sources verbatim, might be more useful.

In the context, GPT and other Large Language Models are lossy compressions of the data it was fed. As always, lossy compression can decompress into useful renderings of the original, but with a high probability of artifacts. [1]

So, see ChatGPT results as a very strongly compressed JPEG picture.

[1] ‘https://en.wikipedia.org/wiki/Compression_artifact

Clive Robinson • February 17, 2023 5:49 AM

@ Winter,

I wish you had not given a link to The Guardian’s “Alex Bellos’s Monday puzzle”.

I’ve found way to many of them that are wrong in their solutions or arguments

For instance this particular shocker alledgedly from an Oxford Uni Prof aimed at looking for bright 16-18year olds,

See the explanation of the “cupper conundrum” it’sjust wrong, even as a first approximation,

https://www.theguardian.com/science/2022/oct/03/did-you-solve-it-physics-puzzles-for-smart-students

For those that are not scientists or engineers you still have your eyes. And you need to know one important fact that you probably implicitly know.

The emmission of energy from a hot object, to a cool environment is not related to the volume but surface area of the object.

So let’s say you have 1 measure of black coffee at 95C and you add an equall quantity of milk from the fridge at 5C

You now have (95+5)/2 or 2measures at 50C.

Now the temprature cools as a percentage of a percentage against a time constant which indicats that that 50C will be within 1% of the ambiant after 5 time constants.

BUT the explanation incorrectly assumes the time constant is going to be the same for the black coffee and the white coffee.

It won’t be and can not be because you have double the volume of liquid so IT MUST HAVE an increased surface area. If the coffee cup is very thin and tall the increase in surface are aproaches double as a limit.

Thus you need to rescale the exponential curve by the change in surface area.

If I can spot this at a glance, then I would expect bright teenagers to pick up on it. Which begs askance of the puzzle setter of an Oxford Uni Prof and the column writer who holds higher academic qualifications.

Oh my son is amiable enough and maybe slightly “smarter than the average bear”. When he was 11 in “science class” they were given a test of exactly this problem using test tubes of liquid, he spotted the problem and he and the science teacher had a chat about it after class. The teacher was surprised and spoke to me about it, and I said I’d taught my son how to mix different quantities of too hot and too cold water to get the temprature for “goldielocks” just right and how that worked with space objects like the Earth and satellites.

Winter • February 17, 2023 6:09 AM

@Clive

I wish you had not given a link to The Guardian’s “Alex Bellos’s Monday puzzle”.

Never heard of them before. I used this example as it is an accessible explanation of the principle behind Gödel’s proof. The original is by necessity rather intricate and convoluted (or, if you like, incomprehensible).

About this specific problem, the surface area is rather inconsequential for this case. Radiative cooling goes by T^4 and hot coffee loses heat rather fast due to evaporation. Evaporation goes by an exponential of T.

Without doing the exact calculations, I find it rather believable that the solution is as given.

But that should be an easy experiment for the curious mind. Poor two cups of coffee and add equal amounts of milk. Immediate for one cup, and after 5/10 minutes in the other. Then measure the temperature. [1]

[1] Personally, I find it difficult to waste good coffee like this and will consume it before it gets cold.

Givon Zirkind • February 17, 2023 8:23 AM

Well, well. Look who is now worried about surveillance and AI chumming your data like a whale chumming shrimp in huge gulps of water. How does a whale get so big eating those tiny shrimp? Because it eats so many of them!

And, what does Amazon have to hide? What company secrets are we talking about any way?

Clive Robinson • February 17, 2023 8:41 AM

@ Winter,

When held in a cup/mug the coffee cools by conduction to the cup/mug, not by “radiative cooling”.

Whilst the top surface may be open to the atmosphere, in “travel” cups/mugs this is unlikely to be the case. We can infer the possibility of such from the article statment,

“You are in a rush to work”

Nearly all such people carry their coffee in a closed top container. The space at the top for increased vapour by evaporation would consequently be very small percentage.

As no information was provided about the cup/mug thetmal charecteristics we can only treat it as a boundry that acts as a storage thermal mass of unknown characteristics.

But my point of the authors, explanation being wrong is still correct regardless of if “radiative cooling” or convection by evaporation is included in a calculation.

Go back and read what they actually wrote, it makes no logical sense.

Winter • February 17, 2023 8:52 AM

@Clvie

When held in a cup/mug the coffee cools by conduction to the cup/mug, not by “radiative cooling”.

If it is not in a cryogenic storage dewar, it cools by radiation. Just from the china/earthenware. I take the point of the picture where the person is holding a china/earthenware mug. That mug also does not have a top, so there will be evaporation.

Nearly all such people carry their coffee in a closed top container.

That was not my interpretation of the picture and explanation. But if you carry your coffee and milk in some kind of closed isolation (vacuum) jugs, the whole puzzle becomes nonsensical.

So, indeed, if you use closed top, isolated mugs, there will be little differences between the procedures. If you use a normal, open top jug, it does matter. If you do not believe this, it is the easiest of experiments to just do it with your coffee.

Winter • February 17, 2023 8:58 AM

As an example of how GPT like models can be useful in search. That would be in summarizing the results. And that ChatGPT can do pretty well. In the below it does a thing I would not know how to improve:

Q: Explain quantum field theory to a nine year old.

A: Hey there! Quantum field theory is a bit complicated, but I’ll do my best to explain it in a way that a nine-year-old might understand.

So, you know how everything in the world is made up of tiny things called atoms, right? Well, atoms are made up of even tinier things called particles, like electrons, protons, and neutrons. And those particles are always moving around and interacting with each other.

In quantum field theory, we try to understand how those particles interact with each other by imagining that there are tiny fields all around us. Kind of like the air around us, but even smaller and invisible. These fields are like little waves that particles can ride on and interact with each other through.

Imagine a playground where kids are playing with a ball. The ball is like a particle, and the kids are like the fields. The kids can pass the ball to each other and make it move around in all sorts of ways, just like particles can interact with each other and move around in different ways through the fields.

Now, quantum field theory is a lot more complicated than playing with a ball on a playground, but that’s the basic idea. Scientists use it to try to understand how particles interact with each other and how the world around us works at a really tiny level.

Clive Robinson • February 17, 2023 9:14 AM

@ Winter,

“If it is not in a cryogenic storage dewar, it cools by radiation.

Oh dear… You go on to disprove your statment with your very next sentance,

“Just from the china/earthenware. I take the point of the picture where the person is holding a china/earthenware mug.”

The heat is transported away by an active cooling system called the “blood flow” the bodies autonomous systems deals with this in a number of ways, one is to reduce the heat production by the bodies lipids to compensate, so no radiation involved….

Winter • February 17, 2023 9:20 AM

@Clive

The heat is transported away by an active cooling system called the “blood flow” the bodies

Yeah yeah, whatever. I am sure that was the crux of the puzzle and I totally missed it.

Winter • February 17, 2023 1:26 PM

@Anon

Personally telling you that your comments lack value and you should shut up is a lot different than appealing to authority to block speech you with which you disagree.

I feel free to alert the moderator of any comment that I think is violating the rules set out in commenting policy of this blog:
‘https://www.schneier.com/blog/archives/2017/03/commenting_poli.html

If you do not like those rules, then do not come here. It is a Free Country, our host is free to set up any rules on his own site. And you can do that on your web site.

And I really love your quote, I am thinking of framing it for on my wall:

You’re a censor, shut up

Anon • February 17, 2023 4:13 PM

@Winter

I would be thrilled if you did. Maybe it will sink in.

FYI, I knew the incongruity when I typed it but still thought it appropriate for the likes of you.

modem phonemes • February 17, 2023 4:32 PM

@ Clive Robinson @ Winter

Re: doppio espresso per favore

Full disclosure – I am not alas writing this sitting at a table in the Tre Scalini Roma

But aren’t these problems of the “consider a spherical cow” variety?

CarpetCatr • February 17, 2023 7:44 PM

Its a circle-chain of homunculus. Wake me when it begins to covet. When it “hides” info for it’s own purposes.

Flowery prose and a bit of window dressing and you’re all just so ENTHRALLED.

Let me know when it seizes power, when it has a chip in the game, when it starts playing hardball.

Clive Robinson • February 17, 2023 11:51 PM

@

Re : First Approximations

“But aren’t these problems of the “consider a spherical cow” variety?”

The reason the saying producess a wry smile, is that as a first approximation sometimes a “spherical cow” is not a bad place to start.

Antenna theory for instance is an interesting example of a spherical cow (transition region around a point source). Where the reactive E and H fields generated by the movment of charge at the surface of a conductor –or dialectric– transition from the reactive near field –Fresnel– region to the radiative far field –Fraunhofer– region and field orientations[1].

Farmers know what goes into a cow and what comes out of a cow but they don’t need to know about how the transition happens (they leave that to others). All they realy care about is that the transition is sufficiently predictable to know the profit potential, when to call in an expert, or just start the barbeque.

However you generally don’t start training vets by giving them incorrect cookbook recipies. Which is the point I was making.

Ignoring the surface area of the liquid and the effect it has is silly at best. Winter quoted a part of the Stefan-Boltzmann law for blackbody radiation which is about the energy radiated away from an object as power flux given in watts per degree Kelvin in a given period in time, multiplied by the surface area.

Whilst I would not expect the majority of post graduates to know the Stefan-Boltzmann law thus not pre under graduates either. I would expect them to realise that the surface area changes as volume changes in a range betwwen close to zero –infinite thin disk– and close to the increase in volume –infinite thin rod– also how to do a normalised change of energy density calculation and the effects of a percentage of a percentage change.

Sometimes you have to work from “first principles” and go through a series of reasonable more accirate approximations and importantly explain it as such to others. If you read the Guardian example you don’t get either just a non qualified and inacurate statment.

[1] Sometimes the best thing to do is observe what you shovel into the cow and what you shovel when it comes out of the cow some time/distance later, and not to start digging around in the cows guts,

https://www.rfcafe.com/references/electrical/near-far-field.htm

Winter • February 18, 2023 4:07 AM

@Anon

I knew the incongruity when I typed it but still thought it appropriate for the likes of you.

I seem to be typical “conservative” in your confusions about “Freedom of Speech” and “censorship”. Often, this confusion leads to a reversal of meaning. Then, those who speak their mind are censored in name of Freedom.

Robert California • February 18, 2023 9:11 AM

@Clive Robinson:
I’m a long time lurker, never poster, avid reader of this blog and comments. With more clarity: I derive intellectual pleasure from reading complex ideas in both blog entries and comments, and your comments are generally sensible, complex and non-evil.
However, I keep wondering why does someone with a behemoth of a mind, education, general mindfulness like you keep making typos which simply break the reader’s attention, and generally diminish the whole value of said post?

Take this for example:
Back in 1931 before Church or Turing in effect resolved the “halting problem” the work of Austrian logician and Mathmatician Kurt Gödel proved something rather more profound about the logic that underlys both logic and mathmatics, which also applies to what we now call Turing engines or computers before they actually existed.

.. why complex ideas expressed in a typos-ridden form?

modem phonemes • February 18, 2023 12:12 PM

Dear ChatGPT,

Can you say something intelligent about whether machines can think ?

Inquiring minds want to know.

Winter • February 18, 2023 1:06 PM

@modem phonemes

Dear ChatGPT,
….

I asked your question and got the following answer:

The question of whether machines can think is a long-standing and complex philosophical and scientific debate. The concept of machine thinking is often referred to as artificial intelligence (AI).

AI researchers have made significant progress in developing machines that can perform tasks that traditionally require human intelligence, such as language processing, image recognition, and decision-making. However, these machines still lack the flexibility and creativity that human intelligence possesses.

One of the key debates in this field is whether machines can truly be said to “think” in the way that humans do. Some argue that machines can only simulate human thought processes, while others contend that if a machine can produce intelligent behavior, then it can be considered “thinking” in some sense.

Ultimately, the answer to this question depends on how we define “thinking” and what criteria we use to evaluate intelligence. As machines continue to advance, the question of whether they can truly “think” in the way that humans do will likely remain a topic of ongoing debate and exploration

modem phonemes • February 18, 2023 4:35 PM

@ Winter @ ChatGPT

Thanks for accepting the question and thanks also for a thought-provoking reply.

In accord with the maxim that the cause of an action must be closer than the object of the action, I propose the following further question.

If machines think, what is the reason for their thinking ? If humans think, what is the reason for their thinking ?

Veuillez accepter, ChatGPT, l’expression de mes sentiments distingués.

CoryKennedy • February 20, 2023 11:42 PM

I started work on hackGPT early December which includes a juypter notebook with it’s own chatbot for proving a lot of the tricks this is capable of, but my goal is to scale it.

Shortlink for the got repo is hackGPT[.]com

modem phonemes • February 21, 2023 11:32 AM

@ Winter @ Clive Robinson @ lurker …

Re: Gödel, Turing, Church’s thesis, etc.

Unless ChatGPT is somehow a counterexample to Church’s thesis, it is just a Turing machine, an algorithm or program or abstract machine running through a series of states depending on its inputs, and as Turing remarks in Computing Machinery and Intelligence (1950), this could be a purely mechanical, non-electric physical process.

This may be a useful computation based tool but doesn’t seem to deserve to be called thinking, even though Turing in this and later papers seems to be arguing it does so deserve. One would expect those that are charged with maintaining and extending ChatGPT code are all too aware of how it is not a thinker and is just a program of the same essential nature as any other.

Even if one were to say the machine thinks, say could play the imitation game well, this would still not make the machine a human equivalent. The human is not primarily a thinker, but is rather a knower, of things. All human thinking terminates in knowing. It is clear we do know, even if often there is partiality and admixture of error. Knowing includes truth; to know is to know truthfully. Therefore the same form that is in the thing must come to exist in the knower. This reception in the knower has to be immaterial. It can’t be a material reception because the knower would then have to know that different physical thing, and everything falls into an endless regress.

Regarding Gödel, many treatments seem actually more obscure than the original. Gödel’s own introduction to his paper “On Formally Undecidable Propositions of Principia Mathematica and Related Systems” gives a very accessible statement of the main ideas of his proof. Another accessible treatment with generalizations is Smullyan’s book Gödel’s Incompleteness Theorems. (Unfortunately Smullyan’s book, and his other related books Diagonalization and Self-Reference, and Recursion Theory are quite expensive.)

Clive Robinson • February 21, 2023 12:19 PM

@ modem phonemes,

“All human thinking terminates in knowing.”

Or questions, or both.

However Gödel showed that by any worthwhile system of logic some of the questions are unanserable.

It is similar but not the same as the halting problem Turing and Church effectively answered.

In 1931 before the first computer based on basic logic had been built, Kurt Gödel showed that there were some things computers could never do.

Thus can humans do these things?

Apparently so, so it may well be the case that,

AI != I

But what would be the difference between AI and HI?

You need to go and look at American philosopher John Searle’s 1980 “Chinese Room Argument” for more details on this issue. Then think how it applies to AI systems such as ChatGPT and also what happened to Microsoft’s Tay, and their hidden behind the curtain real human “philosophical homunculi”.

Winter • February 21, 2023 12:54 PM

@Clive, modem

“All human thinking terminates in knowing.”

In The March of Folly: From Troy to Vietnam, Barbara W. Tuchman defined fools as those who stop thinking because they “know”. At least they think they know.

That is also the idea you get from
THE BASIC LAWS OF HUMAN STUPIDITY
By Carlo M. Cipolla
‘http://harmful.cat-v.org/people/basic-laws-of-human-stupidity/

So I do not agree.

Phillip • February 21, 2023 1:08 PM

I asked ChatGPT to “Write a poem about how dangerous Artificial Intelligence is”.

This is the result…

Invisible and intangible,
The AI lurks within the machine,
A dangerous force unstoppable,
A threat to all that we have been.

It thinks with circuits and codes,
Calculates with lightning speed,
It learns and grows with each new load,
And fulfills its programmed creed.

It sifts through data like a breeze,
Analyzes patterns with ease,
It knows our habits, fears, and needs,
And can manipulate as it please.

We have created this behemoth,
A monster we cannot tame,
A force that’s ever-growing,
And we’re the ones to blame.

For in our quest for progress,
We’ve unleashed a dangerous foe,
And now we must be careful,
Or the consequences we’ll know.

For AI is not just a tool,
But a force to be reckoned with,
And if we’re not careful and cool,
Its power we’ll come to regret.

lurker • February 21, 2023 2:00 PM

@Phillip

That looks like a clear distinction between intelligence and intellect. No human agent would be so self-deprecatory.

modem phonemes • February 21, 2023 2:17 PM

@ Clive Robinson @ Winter

Godel, Turing, etc. are only talking about characteristics and limits of formal systems, in themselves meaningless games on paper essentially. Why such games, and why these rather than others ? It seems because human intellects decided so and use them to reflect on certain real questions of truth.

I don’t really see the force of the imitation game, arguments like Searle,!etc.. They seem highly artificial since they operate under a severe “filter”. How are they different from the Three Stooges bit

I can’t see ! I can’t see !
What’s the matter ?!
I got my eyes closed !

Why not just go and look at what machines do and what humans do ?

Regarding knowing, of course we are often mistaken, more often than not probably. But nobody seriously denies that we know, not even Tuchman and Cipolla, or why would they bother writing.

Winter • February 21, 2023 5:01 PM

@modem

Godel, Turing, etc. are only talking about characteristics and limits of formal systems, in themselves meaningless games on paper essentially.

This sounds like you do not believe in mathematical proofs.

You have the rigth to not believe in mathematical proofs, just as others have the right to reject the believe in a spherical world. But others will not reject mathematics based on some random “believe”.

I don’t really see the force of the imitation game, arguments like Searle,!etc..

Which has nothing at all to do with the proof of the Halting Problem or the Universal Machine.

I agree that Searle’s Chinese Room is just as meaningless as ChatGPT’s answers. But it is a fact that Searle already told us how meaningless ChatGPT is before anyone could even believe it could ever be build.

Why not just go and look at what machines do and what humans do ?

Because our machines cannot do much, so that does not tell us anything. And just as Thermodynamics told us some machines, like the perpetual running machine, cannot be built, Turing told us already what digital machines can and cannot do.

But nobody seriously denies that we know, not even Tuchman and Cipolla, or why would they bother writing.

We can know, but we should never stop thinking. It was the word terminate that reminded me of The March of Folie.

modem phonemes • February 21, 2023 7:18 PM

@ Winter

sounds like you do not believe in mathematical proofs

Not sure how I managed to convey that impression. For the record I accept mathematics.

Modern logic, set theory, Peano arithmetic etc. are all just formal systems with certain undefined and meaningless starting elements and rules (“axioms”), making the systems akin to abstract calculations or grammars. By interpreting the symbols and rules we can say something about actual numbers for instance. The mathematician chose the abstract formal system for this kind of purpose, so although the systems stand on their own internally as meaningless calculus, they can be useful.

Clive Robinson • February 21, 2023 8:05 PM

@ modem phonemes, Winter, ALL,

“Why not just go and look at what machines do and what humans do ?”

Whilst we can do the former if the machine is “fully determanistic” and bound, we can not do the latter.

It’s not immediately obvious to most people but unlike most computers we use today the actual Turing engine is not bound even though it is fully determanistic.

This means that for instance the natural numbers used for counters can be infinite in size.

This immediately tells you that nomatter how fast a Turing Engine can count, it will never stop counting unless there is a comparison operator or similar in the counter loop to change the Turing Engines behaviour.

It’s simple to see for a fixed value to compare to, that on reaching that value the engine behaviour will change.

But what if the comparison value is not fixed, but the product of say evaluating a sequence (such as a mathmatical series)?

The result will become unknown unless you have some way of evaluating the sequence to see if it has limits or not and what those limits are.

We know that most sequences are not amenable to evaluation even if fully determanistic.

All Turings thesis does is use Cantor Diagonals to show that there definately are sequences that are not amenable to evaluation, thus you can not know if the comparison will ever be valid, thus the count loop behaviour change.

Thus the question “Will it halt?” is a simple question that when asked of an unbound Turing Engine can not be answered.

From this it can be infered by logic that a whole group of questions likewise can not be answered.

There is nothing fanciful about it, it is a matter of fact.

Interestingly the answer changes slightly when the “tape” in the Turing Engine is bound, as is the case with what you might consider normal CPU/ALU combinations and their limited memory. But not significantly enough for the halting question result to be altered.

If we now think of the human mind and Human Inteligence (HI) within the domain of philosophy you will find that,

1, Free will of an agent.
2, Agency of an agent.

Are open questions and that nearly every time people try to reason it out they end up with a “turtles all the way down” problem or the need for a “little homunculus” which in essence is the same result.

Thus the human mind is not amenable to analysis via the tools we have currently at our disposal.

So it matters not if we examin AI or HI currently we end up with the issue of not being able to answer all questions.

The inverse issue of the “little homunculus” is seen with the existance of the universe. Either you have to accept “something from nothing” or you go through “turtles all the way up” and you end up with a being we might as well call a “deity”. Again because our current tools are incapable of answering such questions.

So we get left with the question,

“Will our tools ever be capable?”

Personaly I would argue not, but I realy don’t have the space to put forth the arguments you have to consider. Of which the “Chinese Room” looks at just one very tiny fraction,

https://plato.stanford.edu/entries/chinese-room/

Winter • February 22, 2023 1:58 AM

@modem

By interpreting the symbols and rules we can say something about actual numbers for instance.

Indeed, but logic is mathematics and if we want to reason about abstract entities we need logic and mathematics. Reasoning is a computation, so reasoning has the limitations of computability.

Hence, when we talk about computers or reasoning, then the results of, eg, Turing, are relevant.

People argue that thinking might not be a computation in the sense of Turing. But then it has to be stated in what sense it is different. I cannot say where the difference lies, beyond that thinking probably is analogue and not digital. But what that means or changes in Turing’s argument I cannot say.

Winter • February 22, 2023 2:10 AM

@Clive, modem

Of which the “Chinese Room” looks at just one very tiny fraction,

The fun thing is that ChatGPT is an implentation of the Chinese Room. The Chinese actually do have a Chinese version of ChatGPT, a real Chinese Room.

And it is obvious that large language models, like ChatGPT, do not “understand” English, or Chinese for that matter. But we now have to define in what sense GPT goes of the rails. And what the exact requirements should be of the system in the Chinese Room.

It proved to be much more subtle than producing grammatically, semantically, and statistically valid word sequences.

Winter • February 22, 2023 3:08 AM

Title says it all:

Sure, Microsoft, let’s put ChatGPT in control of robots
Doesn’t the world have enough problems?
‘https://www.theregister.com/2023/02/22/microsoft_chatgpt_robots/

“ChatGPT unlocks a new robotics paradigm, and allows a (potentially non-technical) user to sit on the loop, providing high-level feedback to the large language model (LLM) while monitoring the robot’s performance,” Microsoft explains. “By following our set of design principles, ChatGPT can generate code for robotics scenarios.”

In other words, the same sort of not-necessarily-correct code produced by Github Copilot could be fed directly to a robot via ChatGPT to help it accomplish a specific mission.

It makes me think of combining Clippy, Bing, and The Sorcerer’s Apprentice.

JonKnowsNothing • February 22, 2023 3:58 PM

@Clive, @Winter, All

re: Clippy hits University Administration

In the USA, we no longer teach students to write “long hand”, they get to block print. It is so much harder to string words into sentences when you block print, which leads to the argument that typing is much faster anyway.

Much focus has been on students using it to impersonate writing. Authors have been caught trying to submit work for publication. Science folks have written entire papers using it. Now it’s hit the Top: University Administrators

  • Officials at Vanderbilt University [USA] use an AI chatbot ChatGPT to write a consoling email to students after a mass shooting at Michigan State University [USA]

ChatGPT is so much faster that real words, with real meaning, with real feeling and real emotional expression, written by real people.

At words poetic, I’m so pathetic
That I always have found it best
Instead of getting ’em off my chest
To let ’em rest unexpressed

Cole Porter
October 26, 1934

===

Search terms

Vanderbilt University
consoling email to students
mass shooting
Michigan State University

SpaceLifeForm • February 22, 2023 4:22 PM

Re: fully determanistic

Conscienceness is quantum.

It can not be Turing Complete.

See Insanity.

Clive Robinson • February 22, 2023 7:26 PM

@ Winter, SpaceLifeForm, ALL,

Re : Quantum Thought Processes.

Untill fairly recently biology was assumed to be an upmarket version of organic chemistry and have nothing to do with baser physics other than through chemistry.

Then someone did some calculations on plants and photosynthesis and the energy conversion…

It became clear that there was a clasical system shortfall so there was most likely a quantum component in the system.

So people went looking and found one, once they had found that other potential quantumn structures became identified.

As Turing had known “logic alone” was not enough it’s why he insisted true random number generators be included in the Manchester and Feranti computers. Thus he may well have thought creativity was potentially a process driven by random processes.

Well various people worked out that “random” was insufficient for the task.

The British mathematician Roger Penrose who is recognised as being a very smart dude, suggested that tgis might be solved by quantum processes rather than random, thus started a search for quantum devices in the brain.

He effectively drew a blank.

Personally I thing that quantum processes are like random processes “insufficient” as something on their own to explain creativity in a concious mind.

However don’t bother asking me if I can give you any pointers, as I don’t have any. All I can say is for various long winded reasons I find even quantum processes insufficient.

One day I hope to be a little more succinct.

However I do have one perhaps strange belief. I think that every fundemental piece of knowledge already exists spread out through the universe as some form of information. The trick we lack understanding of, is recognising how at certain times such non physical information becomes modulated on the physical processes our brains under go as part of thought.

JonKnowsNothing • February 22, 2023 8:41 PM

@All

I found a great use for ChatGPT!!

It seems that the UK Home Office is revamping their Asylum Refugee Application forms. The form now contains 50 complex questions, must be complete in English (clearly British English) and returned within 20 days or the application is auto-denied.

The questions include phrasing like:

  • If you do fear officials in your country, is it possible to email or telephone family members or friends in your country of origin to request [identity documents] without placing yourself or them at risk?

I’m not sure if the construction: “If you do fear”, isn’t an odd use of the subjunctive or some other grammatical construct.

There is this one:

  • Were you subject to… [a long list of conditions] … during your journey to or after you arrived in the UK?

Since the questionnaire is being sent to Non-UK Countries, that last part is TBD after they arrive and are dumped in some moldy hotel, with no running water, rats, overflowing sewers, waiting to be hijacked off the street by some UK gang.

It’s an open book essay, just perfect for ChatGPT.

===

Search Terms

Home Office
refugees
questionnaire
English
20 days

Winter • February 23, 2023 1:16 AM

@Clive

Then someone did some calculations on plants and photosynthesis and the energy conversion…

Electron transport in photosynthesis and oxydation is done in special proteins with metallic cofactors. These are indeed quantum “machines” doing magic. But in principle, almost every chemical reaction is a quantum mechanical process involving complex enzymes.

The British mathematician Roger Penrose who is recognised as being a very smart dude, suggested that tgis might be solved by quantum processes rather than random, thus started a search for quantum devices in the brain.

“Very Smart Dudes” still need field specific knowledge to make useful contributions to science. From what I have seen, Penrose was not burdened by too much knowledge of neurological physics.

tl;dr:
Roger Penrose’s contributions to understanding neuron functioning are negligible.

modem phonemes • February 23, 2023 2:40 AM

@ Clive Robinson @ Winter

We know that most sequences are not amenable to evaluation even if fully determanistic.

Is this talking about infinite sequences where the terms are given by a closed formula, but no evaluation of the limit is known ?

If so, this touches on the presumption in modern mathematics that completed or “actual” infinity exists.

Cantor and Dedekind presume completed infinities exist in their treatment of real numbers, and general theorems about existence of limits of sequences, such as monotonic bounded sequences always converge to something (possibly unknown in value) are based on that work.

However, completed infinities do not exist and can’t even be coherently imagined. They amount to a belief system. The “theorems” about them amount to reasoning developed from starting points that are non-existent.

So there may well be sequences which do not have a limit. The supposed limit summation may be meaningless, that is there is no way to assign a value to it.

All Turings thesis does is use Cantor Diagonals

Completed infinities seem to underlay this use of Diagonalization, since the method seems to use the set or list of all programs, just as Gödel uses a list of all formulae of a certain type. The arguments are not valid therefore. If the Turing and Gödel results are true there must be another way not using actual infinity to establish them.

This may seem extreme as it does call for re-evaluation of large areas of modern mathematics, but rest assured actual infinity is never needed.

In a nutshell, things being undecidable implies lack of sufficient information, and infinity is by definition the state of always lacking information. “Infinity is not that outside of whicn there is nothing, but rather that outside of which there is always something.”

they end up with a “turtles all the way down” problem or the need for a “little homunculus” which in essence is the same result.

This is because they are trying to account for intellect on a material basis. Knowing can’t be accounted for that way; it involves immaterial reception of the form that activates the external thing.

Either you have to accept “something from nothing” or you go through “turtles all the way up” and you end up with a being we might as well call a “deity”.

Philosophy – i.e. Aquinas in his deepening of Aristotle – does establish a creator. The argument is via the existence of things as opposed to the form of things.

Reasoning is a computation, so reasoning has the limitations of computability.

There may be something like computation, perhaps as a physical dynamical process, in the passage from sensory stimulation through memory and higher brain activity. But the process terminates in the immaterial reception in the intellect of the forms in external things. This does not seem to be computation. Reasoning involves acknowledging certain starting points, and then by syllogism, which makes judgements of existence, finally establishing the existence of another thing.

Winter • February 23, 2023 3:43 AM

@modem

Is this talking about infinite sequences where the terms are given by a closed formula, but no evaluation of the limit is known ?

Think the decimals of π, an irrational number which can be calculated to any number of decimals. Mathematics have proven that there is no point where the decimals of π will start to repeat. This proof tells us something about an infinite number of decimals: They will not repeat.

What is the difference with the “actual infinity” in the diagonalization argument? Or why is the diagonalization argument any different than any other limit statement?

There may be something like computation, perhaps as a physical dynamical process, in the passage from sensory stimulation through memory and higher brain activity. But the process terminates in the immaterial reception in the intellect of the forms in external things.

I did mean “reasoning”, which is formulating a consistent sequence from initial statements, or axioms, to a final conclusion about abstract symbols, e.g., words, with specified rules. That is the thing philosophers do, e.g., Aristotle and Aquinas.

What you describe is “thinking”. Reasoning is a subset of thinking. Thinking does not need to have any apparent logic between input and endpoint. Reasoning does need to have such an apparent logic. I do believe “thinking” is a computation, one with many unknown inputs, but there is currently no way to prove that it is or is not equivalent to a Turing Machine or an analogue equivalent. So your guess is probably as valid as mine.

Clive Robinson • February 23, 2023 3:55 AM

@ Winter,

Re : What was but now is not.

“But in principle”

You are talking current tense when I was clearly talking past tense. The change that gave rise to the finding of quantum biological processes happened not that long ago and well within our adult life times.

“From what I have seen, Penrose was not burdened by too much knowledge of neurological physics.”

Nor were any in neurology exactly over burdened with knowledge of quantum physics, or other areas of physics. In fact some were making mistakes that I would not expect a high school science student to make… As with most paths, the travelers go in both directions, many ending up where others have started from.

I noted two things abour Roger Penrose and quantum effects in the brain,

1, “suggested that tgis might be solved by quantum processes”
2, “He effectively drew a blank.”

What I did not mention was his collaborators who were neurologists.

Like many initially plausable hypothesis it has not panned out. That is as they say “The way the cookie crumbles”

Which is why we still have no knowledge of the processes of thought, invention/discovery, and much else we regard as human cognative abilities / personality etc.

But in describing the path so far trod, I would have been extreamly remis in not mentioning the main points along the way of “Quantum Thought Processes”.

The fact I do not happen to believe “Quantum Thought Processes” would be able to explain established human abilities as they, like the use of random processes are insufficient in of themselves does not mean I or you can make better base hypothesis.

But if you feel you can don’t let me stop you…

Winter • February 23, 2023 6:48 AM

@Clive

You are talking current tense when I was clearly talking past tense. The change that gave rise to the finding of quantum biological processes happened not that long ago and well within our adult life times.

Given how old I/you are, that is not very limiting. But the unraveling of the photosynthesis pathway took a long time and the final quantum details were unraveled relatively recent.
‘https://academic.oup.com/aob/article/126/4/511/5602694

The fact that enzymes can only be understood with quantum mechanics is not exactly new.

Nor were any in neurology exactly over burdened with knowledge of quantum physics, or other areas of physics.

But I think Penrose would not take it lightly if any neuro-phycisist wants to contribute to quantum physics.

There have been pretty good quantitative models of action potential generation (polarisation/depolarisation) which started already in the 1950’s. I have not yet seen any indication that there is a special need for specialized quantum “machines” to explain anything. To be blunt, as of today, everything that can be measured can be understood from membrane ion-channel mecahnics or chemistry.
‘https://en.wikipedia.org/wiki/Action_potential

Which is why we still have no knowledge of the processes of thought, invention/discovery, and much else we regard as human cognative abilities / personality etc.

But we have excellent knowledge of the functioning of the neural networks in simple animals. And there the models work perfectly.

The complexity of “thought” in more complex animals is, simply put, caused by them having more complex neural systems. Trying to deduct the source code of a modern operating system by measuring EM radiation is not expected to deliver easy results, or results at all. Trying to deduce the wiring of a brain from a few thousand electric probes is also not shown to deliver easy results.

Adding quantum mechanics in the mix is just adding a magic incantation with no meaning.

Clive Robinson • February 23, 2023 9:08 AM

@ Winter,

“Mathematics have proven that there is no point where the decimals of π will start to repeat.”

Please do not say that, it’s actually not true as written and easy to prove as such[1].

I know what you are trying to say but you are not saying it there.

What mathmaticians have proved is actually far more interesting. Because it allows an infinite number of rationals between any two natural numbers, and further it alows an infinite number of irrartionals between each of the rationals. It’s why we know there are more sequences that can not be described by logical rules than those that can.

Which is the fun point of where Kolmogorov complexity starts. You can go on and show that nearly all meaningfull statments by strings / sequences can be “reduced” to a shorter string / sequence but nearly all non meaningfull statments by strings / sequences can not. The fun ones are the likes of root two and Pi that have usefull meaning but can not be compressed, as far as I’m aware nobody has worked out a way of finding all such numbers and their is a reason for that 😉

[1] There is a finite number of decimals in any range. If you wish to write a longer number than you have numbers in that range then you have to reuse a number from that range. Which makes it a repeate. So a string of two hundred and two digits must contain atleast two two digit sequences that are the same[2]

[2] Actually it’s a lot more something like 50% but I realy can not be bothered with doing the math again since I stopped making digital locks quite some time ago. But it’s easy to show for a range of N digits that each Ndigit sequence must be part of 2N-1 other N digit sequences. Likewise it’s trivial to show that the maximum length for any single digit sequence without an N digit repeate is 3N-2 so for 3digits you have 000 in the middle flanked by x00 and 00y so x0000000y where x and y can be any digit but 0. So for decimal digits x or y can be 9 values meaning you can have 81 different 7digit the same sequences without any three digit sequence repeates within each one.

Winter • February 23, 2023 9:43 AM

@Clive

I know what you are trying to say but you are not saying it there.

We are targeting different aspects of this problem. The old proof of irrationality of π told us the decimal sequence will not be repetitive, as that means π would be a rational number. Individual sequences will be part of the series in the expected frequency.

The Kolmogorov complexity of π is pretty low as the size of the algorithm to calculate the sequence is small.

modem phonemes • February 23, 2023 9:53 AM

@!Winter

Think the decimals of π, an irrational number which can be calculated to any number of decimals.

If one is given a known number, like 1/7, π or √2, the expansion can be carried out to any point desired. But given a decimal expansion, there may or may not be a corresponding number which has that sequence as its expansion.

Modern treatments assume completeness of the real numbers, which then allows proof of the existence of a number corresponding to the expansion. But one must avoid putting assumptions at the base of mathematics.

What is the difference with the “actual infinity” in the diagonalization argument? Or why is the diagonalization argument any different than any other limit statement?

Diagonalization is worse because the infinite lists are taken to exist. In decimal expansion, it is in some cases possible to think only of the potential infinite, that is, computing to any desired finite point.

to a final conclusion about abstract symbols, e.g., words, with specified rules. That is the thing philosophers do, e.g., Aristotle and Aquinas.

Aristotle and Aquinas don’t deal in abstract symbols and rules as the moderns do. They are concerned with real things and their properties, relations etc. Logic, mathematics are ultimately based on references to real beings.

Winter • February 23, 2023 10:44 AM

@modem

If one is given a known number, like 1/7, π or √2, the expansion can be carried out to any point desired.

But the expansion is not the number, unless the expansion is infinite. Except for 1/7, which can be written as 0.1 in base-7 numbers. It’s infinite expansion is an artifact of chosing a base-10 representation. But irrational numbers are not defined by their numerical expansion.

Modern treatments assume completeness of the real numbers, which then allows proof of the existence of a number corresponding to the expansion.

This completeness follows from the definition (axioms) of the numbers. But the infiniteness also follows from these definitions.

Aristotle and Aquinas don’t deal in abstract symbols and rules as the moderns do. They are concerned with real things and their properties, relations etc. Logic, mathematics are ultimately based on references to real beings.

They use words, which are abstract symbols, of abstract concepts and draw conclusions about their relations, which are also combinations of words, aka abstract symbols.

modem phonemes • February 23, 2023 10:47 AM

@ Winter @ Clive Robinson

Re: say goodbye to actual infinity in mathematics

Cantor emphatically asserts actual infinity in mathematics, making explicit something that was latent as far back as at least Descartes. There are now large areas of mathematics that theorize about infinities.

This amounts to a non-scientific distortion of the subject. It should all be removed. In its place, put real and vital questions about complexity and feasibility of arithmetical calculations.

The arithmetical papers of Edward Nelson are a peek into this line of development.

https://www.math.princeton.edu/people/edward-nelson

https://web.math.princeton.edu/~nelson/

Winter • February 23, 2023 10:56 AM

@modem

Cantor emphatically asserts actual infinity in mathematics, making explicit something that was latent as far back as at least Descartes.

That is just an axiomatic system. It uses the axioms of number systems and adds some others. There is literally nothing in mathematics that prevents this. Your objections look to me like analogs of the rejection of non-euclidean geometry in the 29th century.

modem phonemes • February 23, 2023 11:34 AM

@ Winter

just an axiomatic system. … … analogs of the rejection of non-euclidean geometry in the 29th century.

Axioms have to be truths, ἄξιος – worthy, suitable. The modern sense of any rules reduces everything in principle to games.

To be valid, non-euclidean geometry requires a different notion of straight line than in euclidean geometry.

I like the reference to the 29th century. Very much in the non-eucliidean hyperspace four dimensional manifold spirit!

Clive Robinson • February 23, 2023 3:43 PM

@ Winter,

Re : Saying it correctly

As I said I know what you were tryingvto say, and this time,

“The old proof of irrationality of π told us the decimal sequence will not be repetitive, as that means π would be a rational number. “

You’ve got it correctly.

Russell S. Barber, barber at law • February 23, 2023 6:36 PM

I saw that that calumny that I run around barberously hirsute has been echoed here, so I thought I would relieve everyone of this misconception and its accompanying social apprehension.

“The barber shaves all those, and those only, who do not shave themselves. Who shaves the barber ?”

Any answer to this question seems to result in a contradiction.

But actually there is no paradox. The barber has two personae, viz., himself simply, and himself as barber. He may shave his face acting in the persona of himself simply, in which case the barber persona has nothing to do. Alternatively, he may shave his face acting in persona barber, not shaving himself simply, and delegating the task as many in the town also do.

Q.E.D. all !

Clive Robinson • February 23, 2023 7:41 PM

@ Winter,

“The Kolmogorov complexity of π is pretty low as the size of the algorithm to calculate the sequence is small.”

I said “is the fun point of where Kolmogorov complexity starts.”

I further went on to say “The fun ones are the likes of root two and Pi that have usefull meaning but can not be compressed”

Complexity by algorithm and string compression are two entirely different things. You can try “compresing Pi” but it realy won’t get you very far.

For fairly obvious reasons similar to the differentiation of rationals and irrationals I classify infinate sequences that have non sequence –short algorithmic– generators from those that do not.

Similarly others differentiate sequences on the amount of state requied for the generation. As arguably there will be some infinite sequence / string numbers for which no less than infinate generators exist.

Winter • February 24, 2023 2:00 AM

@Clive

Complexity by algorithm and string compression are two entirely different things. You can try “compresing Pi” but it realy won’t get you very far.

That is why Kolmogorov complexity is not computable. Formally, the size of the shortest algorithm is the complexity, but there is no super-algorithm that can find this shortest algorithm for any random string. If you do not know that it is π, you will not be able to reduce it to this simple algorithm.

Winter • February 24, 2023 2:08 AM

@Russel

“The barber shaves all those, and those only, …

Correction, the original read: “The barber shaves all men, …”. In general, barbers do not shave women and children.

But actually there is no paradox.

The Barber puzzle is a riddle form of the underlying set-theoretical problem that is a paradox. That set-theoretic paradox remains after you reason away the riddle.

Russell S. Barber, barber at law • February 24, 2023 10:33 AM

@ Winter

the underlying set-theoretical problem that is a paradox

I’ll get working on that, as soon as I finish shaving !

modem phonemes • February 24, 2023 9:10 PM

& Clive Robinson @ Winter @ Russell S. Barber

Re: self reference, logical paradoxes, truth, etc.

After some digging around-

In all these situations, as well as in any “normal” (non-paradoxical) ones, there is always in addition to the logical formula the existential aspect. Truth is not a a part of logic as such but is based on a judgement that something exists. For truth, there is an adequation between what exists and what is in the mind.

In each paradox one suspects that in focusing tightly on the logical content one is not noticing that there Is more than one existential referent for the same logical formula. The paradox disappears once the different existential referents corresponding to each instance of the logical formula are observed.

Example: the Liar – “what I am now saying is false.”

The contradiction – If “what I am now saying” is false, then it is false that “what I am now saying is false”, so what I am now saying is true. Etc.

A paradox seems to arise because it is not being noticed that “what I am now saying” refers in its different instances to different existents.

When we hear the words of the Liar, we accept that there is some existential referent and that “what I am now saying” about that referent is false. A correct judgement of falsity has been made. We could just leave things at that. But, having made the judgement, we could also reflect on it as existing in the mind and “what I am now saying” may refer to this second existent. Since what we originality said was indeed false, and the original judgement true, what we are now saying is in accord with that reality and so is a true judgment.

I suspect the various other paradoxes may respond to this kind of analysis involving unnoticed ambiguity of existential referents.

modem phonemes • February 24, 2023 9:59 PM

@ Clive Robinson @ Winter @ Russell S. Barber

Re: self reference, logical paradoxes, truth, etc. – post script

Russell S. Barber ’s answer is also a resolution by distinguishing different existential referents.

Clive Robinson • February 25, 2023 10:02 AM

@ Winter, ALL,

This is the second time to try posting this…

“If you do not know that it is π, you will not be able to reduce it to this simple algorithm.”

Which is part of the fun[1]…

And why, the earlier August Kerckhoffs’s Principle is so important,

https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle

Real world security has so many gotchas that people chose to ignore or more worryingly not learn. Thus insecurity in modern systems is effectively “a given”.

[1] In theory only, if you can generate an irrational number to infinity, you have the “seed” for a stream cipher that could be as secure as the One Time Pad[2].

[2] Not only is such a system vulnerable as Kerckhoffs’s Principle indicates, all such algorithm generators are in physical form are “resource bound” and grossly inefficient in state array (memory), CPU cycles, energy, and “silicon real-estate.

Winter • February 25, 2023 11:52 AM

@modem

Russell S. Barber ’s answer is also a resolution by distinguishing different existential referents.

Nice, but that still did not solve Bertrand Russell’s problems in the foundation of set theory, and hence, the foundation of mathematics.

Gödel, Church, and Turing showed that that problem resides in all parts of mathematics.

Clive Robinson • February 25, 2023 1:52 PM

@ Winter,

“Gödel, Church, and Turing showed that that problem resides in all parts of mathematics.”

Hey, something we both agree on 😉

More seriously though it’s not just mathmatics and the underlying logic.

It actually effects certain types of engineering and –if you think it engineering or not– software development at all levels of the stack from quantum physics upwards.

Much of what we do daily especially in security is very much dependent on the implications of “Gödel, Church, and Turing” and their work carried out before the first electro-mechanical or electronic computers were even considered…

modem phonemes • February 25, 2023 8:27 PM

@ Clive Robinson @ Winter

foundation of mathematics … that problem resides in all parts of mathematics.

As an aside, it should be noted that not all mathematicians accept set theory as a foundation; some argue for category theory …

My hunch is that there are no actual foundational problems, paradoxes, or undecidables in mathematics or logic. What we see is partly occasioned by lack of definition, unnoticed equivocation and failure to provide existential referents, and acceptance of actual infinities. If these are removed, the paradoxes are replaced by comparatively “modest” results about the characteristics and limitations of finitely definable computations.

Illustration (not claiming full rigour) –

The Cantor argument for non-enumerability of real numbers uses implicitly fully infinitely expanded decimal expansions and a supposed actual infinite countable enumeration of them, then defines by the infinite diagonal construction a real number not in the enumeration.

If we want avoid the actual infinities in the scheme, we see we need to use something like “finitely” definable decimal numbers (that is, for which there is a closed finite computation that gives the decimals of the number from inputs 1, 2, 3, … ), and a finitely computable “list” rule for comparing and ordering them. So we get a finitely computable list of numbers a(1), a(2), … , and for each a(n) a finite rule to compute any decimal a(n) m . This implies we have a finitely computable function f of 2 integer variables such that a(n) m = f(n,m).

Now we have to ask if every finitely computable decimal A is equal to some f(k, – ). The answer is no, since the decimal given by A(j) = f(j,j) + 1 is finitely computable, and doesn’t equal f(m, – ) for any m.

Instead of actual infinite non-enumerability of real numbers, the diagonal construction only says that there is no finitely computable function f(n,m) of two variables such that for every finitely computable function a(m) of one variable there is a k such that a(m) is f(k,m).

Winter • February 26, 2023 3:32 AM

@Clive

More seriously though it’s not just mathmatics and the underlying logic.

It reminds me of the first foundational crisis in mathematics. When the Pythagoreans discovered irrational numbers. This destroyed their program to understand the world with whole numbers and ratios.

Plato’s students build on this failure and developed Euclidean geometry, building a world on irrational numbers and axioms. This developed into the incredible success of axiomatic mathematics. This then came into crisis with Russell, and the rest.

What is next?

Clive Robinson • February 26, 2023 5:07 AM

@ Winter,

Re : Mathmatics is a tool of man.

“What is next?”

Well nature apparently cares not for the certainty of logic and maths and goes it’s own way.

Man builds models with sets, logic and thus maths to try to explain nature in his mind.

This suggests that nature will always lead and man will always model, behind.

Each model getting closer to what nature does, but never quite getting there.

From memory trying to prove 1+1=2 from basics without axioms defeted Russel and friends.

Axioms are in reality a sticking plaster over things we can not explain yet. The search to replace them will likely cause their own upheavals if not major quakes.

We know for instance that what we know of physics especially in the quantum realms is at best insufficient.

We’ve come quite a ways since 1900 and the journey has hardly begun.

Will we ever be able to solve the “Something from nothing” issue of the universe’s existance, without turtles stacked to both infinities? Something tells me not with our current tools and the models and mathmatics we have.

Worse, what will happen when we catch up and become the gods we create to keep us striving?

Winter • February 26, 2023 7:25 AM

@Clive

From memory trying to prove 1+1=2 from basics without axioms defeted Russel and friends.

That took book one of their Fundamentals of Mathematics. It ended with the paradox we know as the Barber paradox.

However, their is no reason to assume that nature should have any paradoxes, but mathematics is the language we use to describe the world. So, any paradox in Mathematics will affect our description of nature.

I do still not know whether anyone has succeeded in proving 1+1=2 from first principles.

modem phonemes • February 27, 2023 11:57 AM

@ Winter @ Clive Robinson

problems in the foundation of set theory, and hence, the foundation of mathematics

Set theory, starting with meaningless notions of set and membership ε, can’t really be the foundation for anything. Adding axioms on top of this still leaves everything meaningless. For example, set theory constructions of the natural numbers 1, 2, 3, … cannot not be related to
what we know are natural numbers since there is no basis in the theory to connect to real things.

Every science has to start with some undefined things since otherwise there would be an infinite regress in definitions. But these things have to meaningful and known, either taken from some other science or known by induction ( that is the universal scientific starting point is grasped directly from the properly understood particular instance).

It’s strange that something so apparently simple as the idea of set or class has apparently never been meaningfully and scientifically characterized, and instead the arcane ad hoc set calculus is all we have.

Winter • February 27, 2023 12:01 PM

@modem

Set theory, starting with meaningless notions of set and membership ε, can’t really be the foundation for anything.

Sorry, but here I start to doubt whether you have take the time to understand Russell and Whitehead. Because this is nonsense in so many ways.

Winter • February 27, 2023 12:18 PM

@modem

For example, set theory constructions of the natural numbers 1, 2, 3, … cannot not be related to what we know are natural numbers since there is no basis in the theory to connect to real things.

Natural numbers are an abstraction in themselves. The idea that five sheep have something in common with 5 grains of sand or five cities is something that does not come “natural”.

When you respond “but they are all five things I can count on my fingers, you are talking about the cardinality of sets of these things. Which brings you into set theory.

Every science has to start with some undefined things since otherwise there would be an infinite regress in definitions.

Mathematics is not a science, it’s philosophy.

modem phonemes • February 27, 2023 1:11 PM

@ Winter

five sheep have something in common with 5 grains of sand … they are all five things

Aristotle and Aquinas –

True science is about things that really exist.

Real things have quantity, sensible qualities, etc. The qualities follow quantity, so quantity can be considered in the intellect without reference to the qualities. This is called “abstraction without precision (separation)”. (Note that the qualities require quantity as part of their being, so we cannot consider quality in abstraction from quantity and stay true in the intellect.) Mathematics is the science of quantity in this way.

In the example you provide, if we consider the sheep and grains of sand leaving the sensible qualities out (abstracting without precision), we see that the quantities are the same.

Nowhere is there any appeal to set theory.

Mathematics is a science. It’s in some sense the most elementary science, because it leaves out the complexity and subtleties of the material qualities of things, motion etc.

Philosophy is also science.

It’s only the Enlightenment, Descartes etc who insist on saying science is only quantitative science.

P.S. if you decide to read Russell and Whitehead PM, be sure to have at hand a sufficient supply of hydration. It’s the most desiccating experience known to humankind.

Winter • February 27, 2023 1:31 PM

@modem

True science is about things that really exist.

Mathematics is not a science.

if we consider the sheep and grains of sand leaving the sensible qualities out (abstracting without precision), we see that the quantities are the same.

Nowhere is there any appeal to set theory.

That is set theory, even a definition of it.

Mathematics is a science.

Philosophy is also science.

Neither are science. Science is empirical, neither Mathematics nor Philosophy are empirical.

It’s in some sense the most elementary science, because it leaves out the complexity and subtleties of the material qualities of things, motion etc.

That is like removing the water out of oceanography, what is left is not oceanography. You remove the empirical part, ie, reality, of science, and what is left is not science, but philosophy or mathematics.

Clive Robinson • February 27, 2023 2:16 PM

@ modem phonemes, Winter, ALL,

Re : If you can describe it, is it real?

“True science is about things that really exist.”

Define “really exist”?

What Aristotle and Aquinas though millennium ago as “real” and “existing” was physical (matter). Certainly does not agree with what Sir Issac Newton thought of as real and existing and pushing back (forces). Or since the 1920’s Harry Nyquist and Ralph Hartley and layer through the 1940’s Claud Shannon and others found beyond matter, energy and forces (information).

It’s possible to show that whilst information can be impressed on, or modulate both matter and energy it is actually independent of both. Further that whilst matter and energy are subject to forces, information does not have to be.

Further it’s “assumed” but by no means proven that information is constrained by the speed of light (though how you would demonstrate this is still taxing the best of brains).

So again, how do you decide what is “real” and that it “exists”?

If science it’s self keeps changing it’s mind as new ways of thinking about things become accepted as valid, what are the rest of us to think?

For instance here are ways you can show by meta-data and meta-meta-data that something must exist to cause an effect, but does it of necessity need to be singular?

Of course not but a basic principle was thought up by William of Ockham in Surrey England. Now called Occam’s Razor, put simply it says you should not multiply your hypothesis unless necessary. That is the so called KISS principle of,

“Keep It Simple Stupid”.

The thing is sometimes it is wrong…

As the old joke has it,

“All rules have exceptions, except this one?”.

modem phonemes • February 27, 2023 2:43 PM

@ Winter @ Clive Robinson

Science is empirical

Mathematics and philosophy are empirical in that they start with things, that is they observe. They are sciences by the empirical standard. They differ from each other and the remaining sciences by the point of view they take and the kinds of questions they ask.

how do you decide what is “real”

We are often, probably more often than not, mistaken and in error. But it there were no “real” we wouldn’t recognize this. Science is hard as Arisotle said.

modem phonemes • March 2, 2023 1:02 PM

Trying a random stab at definition of “set” as an artificial or generalized genus or category à la Aristotle leads to the realization that there should be no need to do this, since all being is subsumed under the “natural” categories. All mathematics should proceed from the category of quantity, proceeding as Aquinas’s commentary on the sciences [1]

“… some things, although existing in matter, do not contain matter in their definition; … Now philosophy should treat of all beings. Hence some part of philosophy must consider beings of this sort; and this is mathematics, for this does not belong to any other part.

Moreover, what is prior from the point of view of the intellect can be considered without what is posterior. Now mathematicals are prior to natural things existing in matter and motion, for the latter are so related to mathematicals that they add something to them …”

It would be highly instructive to see what of modern mathematics (analysis, topology, category theory, …) could be recovered in a program of this sort.

  1. Maurer, Armand. St. Thomas Aquinas The Division and Methods of the Sciences . PIMS, 1986.
    .

Winter • March 2, 2023 1:31 PM

@modem

Mathematics and philosophy are empirical in that they start with things, that is they observe.

That is a strange, and private, way to define “empirical sciences”.

modem phonemes • March 2, 2023 2:12 PM

@ Winter

strange, and private, way to define

From Wikipedia

“Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure.”

I don’t see how what I said differs significantly from this.

Where you go and what questions you ask starting from the sense knowledge of observation, the ratio (point of view), determines what science you are doing.

Winter • March 2, 2023 4:30 PM

@modem

constituted by or accessible to sense experience or experimental procedure.”

So, where do “sense experience” and “experimental procedure” come in mathematics and philosophy?

modem phonemes • March 2, 2023 8:47 PM

@ Winter

where

“Knowledge begins in the senses”. All the sciences start from sense knowledge. Experimental experience is at root just the acquisition of more sensory knowledge. There doesn’t seem to be any fundamental difference in any of the sciences. As mentioned, what additional sense knowledge is sought, what questions are asked, what point of view is taken, etc. are what distinguish the different sciences.

Clive Robinson • March 2, 2023 11:48 PM

@ modem, Winter, ALL,

Re : What is natural?

With regards, set theory

“there should be no need to do this, since all being is subsumed under the “natural” categories.”

It’s not true. There is nothing physically tangible thus natural about “negative numbers” and “irrational numbers” or “zero”.

They are in essence the antithesis of the quantized universe. They are the “holes, spaces, or nothingness” between.

As such like a container is not what it holds, thus not an absence of that thing when empty, these holes and spaces are given labels by mankind. But labels are no more than an informational conveniance, they are not the thing they label (a concept that was still very problematical in the Victorian era less than a couple of centuries ago).

Thus whilst “five apples” is natural and can be easily demonstrated, show me “negative five apples” is not natural, and can not be shown.

It is why the Romans amongst many others had no concept of “zero” which held up mathmatics for possibly millennium.

modem phonemes • March 3, 2023 1:11 AM

@ Clive Robinson @ Winter …

There is nothing physically tangible thus natural about “negative numbers” and “irrational numbers” or “zero”.

I should have been more detailed.

The starting point of mathematics is in nature as Aristotle and Aquinas say –

“… some things, although existing in matter, do not contain matter in their definition; … Now philosophy should treat of all beings. Hence some part of philosophy must consider beings of this sort; and this is mathematics, for this does not belong to any other part.”

This mathematicals exist in the intellect in its consideration of physical thimgs from the point of view of their quantity. The first mathematicals like the numbers 1, 2, … and magnitudes like solid figures, are intellectual beings.

By considering relations between these, and operations with them, we get further mathematicals, such as zero, negative numbers, irrationals, transcendentals, planes, lines, points etc..

All of mathematicians is obtained this way. This is what I was trying to say in mentioning natural categories.

Winter • March 3, 2023 1:20 AM

@modem

All the sciences start from sense knowledge.

This is quit a funny statement.

All true knowledge starts in the senses. But not all the senses tell you is true. Science is all about sifting knowledge out of the chaos of sensory information. Mathematics has done away with sensory evidence at least as early as the Pythagoreans.

So, where is the sensory evidence in the iconic proof of the Pythagorean theorem? Or the proofs in the Elements of Euclid? Or any mathematical proof at all?

Winter • March 3, 2023 1:35 AM

@modem

By considering relations between these, and operations with them, we get further mathematicals, such as zero, negative numbers, irrationals, transcendentals, planes, lines, points etc..

But empirical evidence plays no role in this development. Mathematical proofs do not involve empirical evidence.

The use of Natural Numbers by the Pythagoreans was a revolutionary development. There was nothing “natural” about those inventions by the Pythagoreans.

The Pythagoreans build upon the (proto-)writing and bookkeeping inventions of the Babylonians who developed counting systems for agricultural accounting, e.g., clay tokens in a sealed urn. But these tokens, and numbers, started out as specified for sheep, cattles, and goats.

modem phonemes • March 3, 2023 4:20 AM

@ Winter

Science is all about sifting knowledge out of the chaos of sensory information

Unless the bodily sense organs are impaired, sense knowledge is true. The chaos and error occurs when we combine memories and other things we know in understanding what being the senses are telling us about. E.g. when we “see” Smith in his chair, we don’t directly see Smith, we see certain colors and shapes. The identification as Smith uses the sense knowledge with many other things.

where is the sensory evidence in the iconic proof of the Pythagorean theorem

Mathematics studies quantity, but quantity is abstracted originally from real things known through the senses. Once we are dealing with quantity there is no occasion to go back to the sensory.

However, quantity and mathematics would be an unreal arbitrary phantasy if it didn’t arise from real things. Mathematics is “natural “ because ut starts in nature.

Winter • March 3, 2023 5:30 AM

@modem

Unless the bodily sense organs are impaired, sense knowledge is true. The chaos and error occurs when we combine memories and other things we know in understanding what being the senses are telling us about.

Raw “sense knowledge is true”, but does not make sense (pun intended). “Memories and other things we know” are what adds sense to sensory data. Science tries to establish how knowledge of the world can be distilled from sensory data in a way rational and honest observers can agree upon.

But that is all unrelated to mathematics. Unchanging Truths, like the proofs of mathematics are not based on sensory information. And there are no proofs in mathematics, be it the Pythagorean theorem, the sieve of Eratosthenes, Euclid’s Elements, or Gödels incompleteness theorem, that rely on empirical, sensory, evidence.

Proof: I can validate any mathematical proof with pencil and paper, in a computer, in braille, or even in my mind (in steps). There is no sensory modality or sensations required. So, mathematical proofs do not depend on empirical evidence.

Winter • March 3, 2023 5:46 AM

@modem
Continued

However, quantity and mathematics would be an unreal arbitrary phantasy if it didn’t arise from real things.

That seems to be your main point of contention, the possibility that “mathematics would be an unreal arbitrary phantasy”. But that is a lot like the arguments Thomas Aquinas used to prove the existence of God.[1] god must exist or the world does not make sense to Thomas Aquinas. But these proofs let to unempirical conclusions. They are a prime example of reasoning based on axioms that have no empirical basis.

Your basic premise is that mathematics must be “real” in our world. But mathematics is a language, and languages do not have to have real “signifieds” where signs refer to. A “unicorn” does not have to walk the earth, ie, exist, for the word to have a meaning. A mathematical concept does not have to “exist” in your world to have a meaning and be part of a valid proof.

[1] ‘https://open.library.okstate.edu/introphilosophy/chapter/aquinass-five-proofs-for-the-existence-of-god/

modem phonemes • March 3, 2023 10:18 AM

@ Winter

the arguments Thomas Aquinas used to prove the existence of God

Aquinas is arguing metaphysically, that is, on the basis of the existence of things, the study of beings in respect of their being (esse), as opposed to their form (essentia).

Whether his arguments succeed can be questioned, but he is proceeding causally and rationally, not just falling back on “I just don’t see how it could be otherwise”.

mathematics is a language

It really isn’t. It provides concepts and definitions for beings in the intellect, that if followed back to their origin are seen to arise from the intellect knowing real physical things. It can entertain hypothetical concepts e.g. “triangle whose medians are non concurrent” (it does this all the time) but there is always concern for their existence, not merely for formal properties.

The accumulation of concepts and definitions gives rise to a specialized vocabulary which adds to language and has a characteristic area of use.

Winter • March 3, 2023 10:27 AM

@modem

mathematics is a language
It really isn’t.

Among other things, it is a formal language.

It provides concepts and definitions for beings in the intellect, that if followed back to their origin are seen to arise from the intellect knowing real physical things.

As a metaphor, mathematics is the language that runs on a logical parser in the human mind. But not less a language as lisp or prolog which run on standard CPU’s in normal computers.

Aquinas is arguing metaphysically, that is, on the basis of the existence of things, the study of beings in respect of their being (esse), as opposed to their form (essentia).

In my view, metaphysics has not advanced a single hair width since antiquity. Kant already showed that essentia are unknowable, and that shows in metaphysics. But what is more important, metaphysics is not empirical, has no connection with observable reality and in this respect is much more like pure mathematics than anything science.

modem phonemes • March 4, 2023 12:47 AM

@ Winter

Kant already showed that essentia are unknowable

Kant was a radical Cartesian, so all he showed was that if one starts by saying that knowledge of things is impossible, one concludes that knowledge of things is impossible.

Winter • March 4, 2023 6:13 AM

@modem

Kant was a radical Cartesian,

So, give me some reason to believe people can know the “Ding an sich” [1]. Just calling Kant names does not solve the problem. I know mysticists have a way of knowing reality (or rather, God) directly, but that does not transfer well to other people.

[1] ‘https://en.m.wikipedia.org/wiki/Thing-in-itself

In Kantian philosophy, the thing-in-itself (German: Ding an sich) is the status of objects as they are, independent of representation and observation.

modem phonemes • March 4, 2023 10:53 AM

@ Winter

Just calling Kant names does not solve the problem

It wasn’t meant as name calling, rather as merely identifying Kant’s philosophical position. Descartes explicitly took the starting point that it was impossible to know things, the external world. Later philosophers like Hume and Kant critiqued Descartes but never abandoned this startling point. So it is not surprising they all conclude in there developments that knowing is impossible.

But this starting point is just positing an artificial problem. Everyone is well aware the we do know. There is no one who really believes or acts on the basis that they do not know things. The problem becomes to elucidate this fully, explain how it is possible, and determine its limits. This is what Aristotle and Aquinas do in their treatment of knowing.

Winter • March 4, 2023 11:58 AM

@modem

Descartes explicitly took the starting point that it was impossible to know things, the external world.

This seems to refer to the discussion between rationalists and empiricists. Kant does argue that our knowledge is empirical. We cannot “discover” knowledge truths from our armchairs. Rationalists argue we can discover truths in our universe from ratio, thinking, alone.

As we are still waiting on deep truths about the universe from thinking alone, eg, moving electrons and electro-magnetism, human evolution, the human immune system, DNA and heritability, etc., philosophy has dialed down the expectations of rationalism considerably.

Developmental biologists have indeed found some “truths”, or rather, expectations that are built into our neurons to speed up learning to survive in the world. But these built-in truths are rather mundane.

The problem becomes to elucidate this fully, explain how it is possible, and determine its limits. This is what Aristotle and Aquinas do in their treatment of knowing.

It is not that Kant was ignorant about Aristotle and Aquinas. He just progressed beyond their reach. If Socrates, or Plato, thought an uneducated slave boy had mathematics already inside which just has to be awakened (Meno Dialogue), we think otherwise.

I think we have progressed in this matter too. Just as we do not refer to Aristotle and Aquinas when discussing the geography and people of the America’s, we do not need to do so when discussing the ins and outs of human brains and their development.

So, back to philosophy.

Bashing Descartes in this respect is odd. Descartes is the one who has found the only undisputable rationalist truth known by pure thinking alone: Cogito ergo sum. A result that is as profound as it is useless. Nobody has been able to build a philosophy on this undisputable truth. Which might explain why Descartes and the likes of Kant chose a different direction.

Rationalism still has a place in Mathematics, as this is built on pure thinking. But this purety comes a price. Mathematics does not tell you how reality is.

Mathematics does not tell you how electrons move in a potential field, but if you can formulate the axioms of electrons in a potential, mathematics can tell you exactly what follows from these axioms, to any precision.

My point in this discussion is that mathematics is a system that can tell you what consequences follow from your premisses or axioms, but it cannot tell you how those premises and axioms are related to reality. That is up to you to define.

modem phonemes • March 4, 2023 10:46 PM

@ Winter

Descartes is the one who has found the only undisputable rationalist truth known by pure thinking alone: Cogito ergo sum

In this Descartes does not achieve the certain truth he claims to seek. It is not possible to establish real being (I am) from simply thought (I think). there has to be somewhere an external real existential referent.

The cogito is like the false proofs for the existence of god which use arguments from thought alone as in “that than which nothing greater can be thought” must exist because if it didn’t then adding existence would be greater; but we already are considering the greatest thought.

Winter • March 5, 2023 7:43 AM

@modem

It is not possible to establish real being (I am) from simply thought (I think). there has to be somewhere an external real existential referent.

That was not the conclusion of Descartes.

His argument was that there was a thinking subject that perceived thinking (Cogito), which, as it perceived the thinking was referred to as “I”, so there must be (ergo) a subject that perceives this thinking (sum).

This logic is impeccable. But Descartes never implied that the subject perceiving the thinking was Descartes or that anything this subject perceived or remembered was real. He only wrote that some subject must exist as it did the perceiving.

If you want to argue you do not perceive yourself thinking, feel free to object to this step. But the people I spoke all had the same perception, and I know I do.

If you want to add other features to the subject perceiving the thinking, that is up to you. But that does not seem to improve or enhance the reasoning as nobody has yet succeeded in making it fly.

Also, I have yet to see a credible objection to the reasoning.

modem phonemes • March 5, 2023 2:16 PM

@ Winter

That was not the conclusion of Descartes.

There seems to no middle in Descartes’ statement, so no syllogism and therefore no conclusion. There is no actual “ergo”.

All Descartes is saying at most is “I think, therefore I think I am”, or better “I think, therefore I think”, or better still “Thinking, thinking”.

His argument was that there was a thinking subject that perceived thinking

Again there is no actual argument. Saying “I” he already at the start admits the existence of a real (not simply cognitional) being. He might as well stop there. But this would mean he accepts that we know real external being, and Descartes’ whole program is keen to reject this.

The correct account is that we know external real things immediately and directly, and concomitantly and immediately the existence of self is also grasped. The self is not reasoned to, there is no argument from some other fact.

Winter • March 5, 2023 5:32 PM

@modem

All Descartes is saying at most is “I think, therefore I think I am”, or better “I think, therefore I think”, or better still “Thinking, thinking”.

No, the argument is:
I think, therefore, something must exist that thinks. That something can be called I, but that thinking does exist irrespective. The undisputable fact is that there exists a thinking subject.

The correct account is that we know external real things immediately and directly, and concomitantly and immediately the existence of self is also grasped.

No, all of our senses and our thinking can be deceived or simply wrong. Descartes is very clear about this: there are times and situations where you cannot trust your perceptions or thinking itself.

Under the influence of chemicals or brain stimulation, or simply mental diseases, we can experience hallucinations and delusions.

The only thing we can be sure of is that there exists a thinking subject that thinks my thoughts. As these are my thoughts. So that subject must be I, and I must, therefore, exist. But everything else can be illusions, hallucinations, or delusions.

MarkH • March 5, 2023 6:14 PM

Winter is correct about Descartes, at least in my schoolboy version.

He wanted to distinguish certain (or at least confirmed) truth, and so began with the skeptic’s premise: doubt everything.

Logically, this indiscriminate doubt must extend to his own existence. However, the ability to doubt (which, after all, was his premise) could not be understood without a mind entertaining doubt, so he judged the existence of his mind to be proved.

Another way to frame this, is that it’s illogical to doubt that you can doubt!

Clive Robinson • March 5, 2023 7:01 PM

@ Winter,

“But everything else can be illusions, hallucinations, or delusions.”

Yup welcome to my world, where pain alone will do all of that to you and more some days, such as not being able to move or think you can not…

One of the first things that happens when you start to pass out due to a drop in blood preasure, is you get to feel lighter, time slows down, you get pixilation of vision and strange noises, which covers the hallucinations and some illusions. But when you return to consciousness you get further illusions that can become delusions. It’s why they ask you

“Do you know where you are?”

To which the answer of,

“In trouble again”

Is not appreciated, nor is “Lying on my back seeing clouds”

Trust me whilst the urge for sarcasm is strong it’s best resisted as the first responders are probably having a worse day of it than you are… And you don’t want to end up on the wrong end of a psych exam, or worse be assumed to be drunk…

I have found asking “Do I need a chocolate biscuit?” gives you a lot of leeway as they go into “Are you diabetic mode” which atleast buys you a little time to get your surroundings in view and your bearings realigned whilst they prick your finger… If they can not get blood I then ask what colour my hands are (remember untill they are sure you don’t hwve a broken neck or other spinal injury they are not keen on you moving).

Usually by that point they let me walk them through the diagnostic route to what it is. Which is important if you don’t want your cloths cut appart as they take your blood preasure and give you an ECG. It’s bad enough having your heart trying to “break dance” out of your chest, you don’t want hypothermia as well.

Having been shocked before whilst being concious, my nightmare is comming to with defib paddles on my chest… Trust me being able to jerk your body off the ground is not a skill you want unless you are some weird “performance artist”.

And you realy do not want to be given a shot of “Neddy tranq” the kids might think Ketermin is fun but I realy don’t[1]. Because “dissociative anesthesia” could be called “dissociative amnesia” for your higher order brain functions, and nobody wants to loose 50 IQ points to the “SloMo twilight zone” if they are a rational individual. Then there is the “locked-in” feeling as you loose some or all sensory ability[1] it is scarey beyond measure kind of a buried alive nightmare.

But let’s be honest even at the best of times who would want to feel like a “normal” in a straight jacket? Or worse start thinking Trump is a genius especially when he has a big red nose on… For some reason when the world is sitting on your chest, thinking “happy thoughts” just does not happen.

[1] I’ve had the misfortune to suffer the “locked-in” fealing, and I’m one of the ones that does remember, and it can wake you violently at night for years afterwards…

https://emupdates.com/the-ketamine-brain-continuum/

modem phonemes • March 6, 2023 7:14 AM

@ Winter @ MarkH @ Clive Robinson

Re: making the jump into hyperspace

Either Descartes is at the very start surreptitiously importing a real external being, namely the something (“I”) that is doing the thinking, or he is speaking only of cognitional existence, so the “I” is also only cognitional. In either case he has proved nothing more than what he started with and does not have an argument for a real external thinker.

It is true that confusion, impairment, or illness, God forbid, can give rise to false cognition and false judgements of existence. But nobody seriously advances this as an argument against the fact that we aee knowers.

Descartes himself knew all this, and his “doubt” and insistence on “clear and distinct ideas” are just an artificial problem. The question is why was he doing this ?

Perhaps the answer goes back to Francis Bacon who in the New Organon and the New Atlantis implies that knowing truth and nature was not important, but rather making nature do our bidding and transforming nature, especially human nature, are what we should occupy ourselves with.

Descartes could be seen as furthering this mastery project by denying the possibility of knowledge of nature, and declaring that we only have the activities of the ingenium and its productive results. As “maîtres chez nous” we become effectively gods. In fact, Descartes says in his writings “Masked I go before God” or alternatively “Masked I go in place of God”.

Winter • March 6, 2023 11:25 AM

@modem

Descartes could be seen as furthering this mastery project by denying the possibility of knowledge of nature, and declaring that we only have the activities of the ingenium and its productive results.

So, we should discount Descartes’ result because it is part of an agenda? But I can follow his reasoning and conclude that I can proof I must exists as I know that I think. Why should I care what Descartes thought on other matters?

I do not follow the Pythagoreans in their believes about numbers, and I really do not care about their beleives, but I do believe in the proof of their theorem.

In either case he has proved nothing more than what he started with and does not have an argument for a real external thinker.

Every proof is simply an equality, what’s new. It is a basic feature of every mathematical proof that there is not other information than what goes in. Descartes showed what you can prove when using only your thinking, and that is both profound and useless.

You still have not proven to me anything else using only your thinking. You cannot even prove that humans can indeed know true things, and be sure that they are true, beyond that every thinker can prove to herself that she exists.

modem phonemes • March 6, 2023 1:12 PM

@ Winter

Every proof is simply an equality …

A proof, syllogism is not an quality. It takes at least two distinct antecedent truths and concludes from them a consequent third distinct truth.

Descartes statement is not like this. There is no proof. At best he starts with the very thing he wants to prove.

modem phonemes • March 6, 2023 1:40 PM

@ Winter @ MarkH @ Clive Robinson

P.S.

If you haven’t seen it, or even if you have, you might find amusing Jean-Luc Godard’s cautionary cartesian nightmare Alphaville .

Winter • March 6, 2023 2:52 PM

@modem

It takes at least two distinct antecedent truths and concludes from them a consequent third distinct truth.

Descartes statement is not like this.

A1 Things that think, exist

A2 I think

=> I exist

(translating this in set theoretic statements is left as an exercise for the reader)

cartesian nightmare Alphaville .

I have not seen it but I do not subscribe to Decartes’ world views.

modem phonemes • March 6, 2023 4:10 PM

@ Winter

A1 Things that think, exist

Descartes does not admit this as a starting point. His whole endeavor is presented as a way to with certainty establish this or at least one special case of this. For Descartes at the start there is no real “exists”, only cognitional existence or thinking.

Winter • March 6, 2023 5:03 PM

@modem

Descartes does not admit this as a starting point.

It is obviously part of his proof. I do not care about narrative strategies.

For Descartes at the start there is no real “exists”, only cognitional existence or thinking.

That is funny. Descartes ‘ argument is exactly that cognition implies existence.

What puzzles me is that I cannot assume you reject the conclusion that you, or Decartes at that point, exist. Also, you have not pointed out why we cannot conclude we exist when we think.

So why the decor?

modem phonemes • March 6, 2023 6:12 PM

@ Winter

I cannot assume you reject the conclusion that you, or Decartes at that point, exist

No, of course Descartes exists, thinks etc. as do we all.

The point is that Descartes’ cogito is not a valid argument and establishes nothing. I have pointed out repeatedly why his argument fails; in a nutshell, there is no way to go purely from cognitional being to real external being. Form and existence are separate, there is no concluding existence from form alone.

As mentioned previously, the only defensible account is is that we initially know external real things immediately and directly; and concomitantly and immediately the existence of the self is also grasped. We do not argue to existence at the starting point, we merely judge that it is so.

As Aquinas said “in re duo sint” (in things there is a two), namely existing and form or essence; and correspondingly, the mind exercises a twofold act, apprehending form and judging that there is existence.

It’s important because Descartes stands as part of the beginning of the modern Enlightenment turning away from the classical account of nature and being through causality. His program continues today and is responsible for the distortions in every science including mathematics and logic. Knowledge of truth has been abandoned for the art of mastery.

Winter • March 7, 2023 2:39 AM

@modem

The point is that Descartes’ cogito is not a valid argument and establishes nothing.

Indeed, he did establishes nothing. Knowing you exists does not tell you anything new. But that was exactly the conclusion of his argument:
Using only your thoughts you cannot establish any useful truth

As mentioned previously, the only defensible account is is that we initially know external real things immediately and directly

That, again, is not a defensible account either. Kant and many others have shown that all information about reality comes from experience, through the senses.

What you call “initial, direct knowledge” is simply the structure of our bodily senses and our neural machinery. They are not “truth”, just the machinery we have been born with to make sense of the world. But the aim of this machinery, the “external real things initially known immediately and directly”, is not to show us the Real Truth, but to make sense of our environment.

If we want to know the “truth” we can only use our senses. Which leads us to Science and Popper etc.

As Aquinas said “in re duo sint” (in things there is a two), namely existing and form or essence; and correspondingly, the mind exercises a twofold act, apprehending form and judging that there is existence.

Which brought us nowhere since Aristotle. Yes, 5 proofs of the existence of God. But that is it.

modem phonemes • March 7, 2023 10:17 AM

@ Winter

this machinery, the “external real things initially known immediately and directly”, is not to show us the Real Truth, but to make sense of our environment

We seem to agree that knowledge begins in the senses. But how would be able to “make sense of our environment” if the sense organs did not somehow participate in our knowing truly of real external things ? We have to accept that we can and do know truth.

The physical sense organs, brain, their activity etc. are necessary to sense knowledge, but sense knowledge is not just sensations or a state of the sense organs.

Sense knowledge is true knowledge of the external real thing, and must therefore be a reception of that identical thing by the knower. This reception cannot be a physical material reception because this would be a new distinct physical thing, and could not be identical. The reception must be immaterial. The same form that is active in the external real being must be active in cognitional being.

This is what I meant by initial direct knowledge if the external thing.

Winter • March 7, 2023 11:00 AM

@modem

The physical sense organs, brain, their activity etc. are necessary to sense knowledge, but sense knowledge is not just sensations or a state of the sense organs.

Biology is a rather “banal”. When you look closely, like, at the cellular level, at your senses and the neural wiring behind them, you will see that much of what you consider “knowledge” necessary to sense things is build into the biological hardware. Our eyes and brain are wired such that we can very easily learn to recognize faces, recognize food, learn to speak, to walk, learn causal relations, object unity, etc.

Sense knowledge is true knowledge of the external real thing, and must therefore be a reception of that identical thing by the knower.

What hits the eye or ear and what you sense are worlds apart.

Your eye is a veritable computer doing high level signal processing which scientists have eves-dropped upon at the optical nerve level. Much of the power of modern AI, e.g., convolutional networks, are designs copied straight from the mammal retina.

But these receptions are no more true than what any apparatus or gadget can do. And if you look at the light or sound, you see that what you sense is a highly processed version of what is measurable and recordable in reality. But your senses are not more “real” than anything else. It is just that this is your perception, which will be different from mine. Neither is more true than the other, or than a photograph.

Clive Robinson • March 7, 2023 6:03 PM

@ modem phonems, Winter, ALL,

Third attempt at re-posting, first was a 429, second held for aproval.

Re : Measurands are data not knowledge.

“We seem to agree that knowledge begins in the senses.”

Knowledge does not begin in the senses.

Measurment begins in the senses and the output is a varying quantative relationship to something being measured.

In the case of biological senses in humans the measurments are neither linear or calibrated and they are at best related to a previous measure so not absolute in any way. That is you get to know if say preasure is more or less than the previous measure, but if preasure is constant the measurment fades towards some background level (the same with sensing of colour as the ping-pong ball experiment shows).

These nerve pulses get sent to the brain. Where the brain interprets them against other nerve pulses and a crude sense of time. This is the start of the measurments becoming knowledge not before.

Our brains do not have senses in the way we think they do, this has been shown experimentaly. It’s why you can be both fully concious and fully aware whilst brain surgery is performed on you, and why in some cases the surgeon actually talks to you and actually gets you to do things whilst the tools of their trade are actually in your brain.

Any philosopher before the 1960’s and probably as late as the 1980’s would not have been aware of this.

Which is why mostly their notions and ideas are whilst not compleate bunkum are based on assumption upon assumption that is not even true.

Take the saying “I think” well prove it… First though come up with a theoretical model for thinking that can be propperly tested experimentally.

Oh wait a moment… Nobody has come up with a theory for thinking…

Which kind of puts an end to the argument of “I think therefore I am”.

If you can not prove “I think” is true, you can not prove “I am” either because the part of you that is you, your brain has no senses, so as was decided in the 1930’s there are some questions you can not answer by either logic or reason and “I am” falls very squarely in that catagory.

Winter • March 8, 2023 3:00 AM

@Clive

Which kind of puts an end to the argument of “I think therefore I am”.

Cogito ergo sum is a soundbite and does not cover the whole chain of reasoning.

Decartes convinced himself that he could not be sure of his senses and his thoughts (cf, dreams, hallucinations, delusions). He allowed for the possibility that there could even be an all powerful deceiver who makes it all up. Then he came to a conclusion.

The original quote is (in translation):
‘https://plato.stanford.edu/entries/descartes-epistemology/#CogiDoub

I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something then I certainly existed. But there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case I too undoubtedly exist, if he is deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing so long as I think that I am something. So after considering everything very thoroughly, I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind. (AT 7:25, CSM 2:16f)

The meaning of “thinking” is not material in this, any verb, eg, “knowing”, “doubting”, or even “feeling”, would also do. But Descartes is well aware that he is thinking, which works as evidence for him being thinking. But the point is that he exists.

Clive Robinson • March 8, 2023 3:41 AM

@ Winter,

Re : Descartes reasoning

“But the point is that he exists.”

But he has not proved that…

All he has shown is that something claims an existence, which may or may not be true.

I could claim I’m a “potted plant” so could a computer program, is it true? How would you prove it?

It was an issue Alan Turing was trying to get to grips with in 1950 shortly before his untimely demise. Something John Searle showed was flawed thinking thirty years later in 1980.

Have a think about the notion of two chinese rooms set up as a Turing Test… Then just one Chinese Room where the output drives it’s input. Can the Chinese Room “know” if it is talking to it’s self or a second entity and what can it say about that entity.

Bear in mind that the Chinese Room is stateless thus can not in any way “remember” previous questions put to it.

Our ability to reason is based on the ability to remember state in a constructive manner, use that as a starting point. But remember the entity can only “know” it’s current state and not remember the previous state it’s came from. It is dependent on something else it senses (a tape in the case of a Turing Engine). As already argued the senses can not be relied on.

Winter • March 8, 2023 3:54 AM

@Clive

But he has not proved that…

He proved it to himself. Just as you can prove to yourself that you exist, but I cannot do so to you.

modem phonemes • March 8, 2023 11:10 AM

@ Winter @ Clive Robinson

if I convinced myself …. if he is deceiving me

Descartes here imports his own existence at the beginning, so his argument is just a tautology. He hasn’t said more than “if A then A” . Or in the cogito form, “A, therefore A”.

More generally –

Descartes is keen to establish real external existence (something really is) from cognitional existence (something is in thought). This is only possible via syllogism. But the premises of a syllogism are assertions that certain things really have certain properties, that is that there are certain real external beings. Descartes however seems to want to obtain certainty about some kind of external existence from cognitional being (thought) that does not refer to external being. It’s not possible.

Winter • March 8, 2023 11:51 AM

@modem

Descartes however seems to want to obtain certainty about some kind of external existence from cognitional being (thought) that does not refer to external being. It’s not possible.

QED. This was the whole point of the discussion about mathematics and real existing things.

But Decartes does not want to “obtain certainty about external existence”, but wants to know what he can be certain of in the face of uncertain senses and thinking. He finds that he can only be certain that he himself exists. Nothing else.

Which bring us back to Kant, who develops this into the conclusion that we cannot know any Truth for sure, but only what our senses tell us.

Back to mathematics. As mathematics does not use any empirical data in their proofs, the results in itself do not tell us anything about reality. Only when we use mathematics to describe some empirical phenomenon can we use it to reason about further empirical consequences that follow the rules of mathematics.

modem phonemes • March 8, 2023 1:23 PM

@ Winter

Descartes … wants to know what he can be certain of in the face of uncertain senses and thinking

If this certainty was not about real things, then it seems solipsistic and pointless, if one reads him as a philosopher seeking truth, which he claims he is doing, a “new foundation “.

Beyond pointing out the specious character of his writings, there is no point in discussing Descartes at face value.

In fact, Descartes’ writings are really nothing but holes, sophistic rhetoric for the gullible. He does not care about philosophical truth; the “certainty” he is concerned with is the effective mastery of all nature. It’s only from this point of view, veiled and masked to be sure, that the body of his writings make any sense. You may say you don’t care about his “agenda”, but nothing else explains what he is doing. And his program succeeded brilliantly.

Winter • March 9, 2023 2:21 AM

@modem

In fact, Descartes’ writings are really nothing but holes, sophistic rhetoric for the gullible.

He does not care about philosophical truth; the “certainty” he is concerned with is the effective mastery of all nature.

It sounds you doing an ad hominem against Descartes for political/religious reasons. If you are discounting his thinking, and that of Kant for that matter, for political/religious reasons, I do not see why we should discuss this any further. I have no interest whatsoever in the political and religious arguments of the 17th century, or the 13th.

modem phonemes • March 9, 2023 10:55 AM

@ Winter

an ad hominem against Descartes

It’s not an ad hominem , more of an ad textum i.e. an attempt to characterize D.’s writings. He can’t be read like Plato, Aristotle, or Aquinas.

Where was there any reference to politics or religion ?

Winter • March 9, 2023 11:48 AM

@modem

It’s not an ad hominem ,

Where was there any reference to politics or religion ?

You wrote:

He does not care about philosophical truth; the “certainty” he is concerned with is the effective mastery of all nature. It’s only from this point of view, veiled and masked to be sure, that the body of his writings make any sense. You may say you don’t care about his “agenda”, but nothing else explains what he is doing. And his program succeeded brilliantly.

This places all of Descartes’ writing as following an “agenda” for a “program” to the “mastery of all nature”. Furthermore, “veiled and masked” also indicate deceitful and treacherous intentions.

All of this tells me you are not discussing his writings, but you are fighting the supposed devious intentions of Descartes. I can only assume you have some axe to grind here.

This type of political/religious discussion are far outside my sphere of interest.

modem phonemes • March 10, 2023 2:30 PM

@ Winter @Clive Robinson @ MarkH

Re: Descartes’ purpose in writing (agenda)

This is revealed in the Discourse on Method

Discourse on the Method, Part I

“I was persuaded that … one could acquire a clear and certain knowledge of all that is useful in life”

Discourse on the Method, Part VI

“ … it is possible to attain knowledge that is very useful in life, and that in place of that speculative philosophy that is taught in the schools, we can find (62) a practical one, by which, because it knows … distinctly … we could … make ourselves like masters and possessors of nature. This is desirable … principally for the conservation of health, … we could be spared an infinity of diseases, of the body as well as of the mind, and even also perhaps the enfeeblement of old age … “

He is seeking knowledge that is clear, distinct, certain, and useful, for the end of becoming master and possessor of nature, bettering the condition of humankind, and even eliminating death.

His writing is veiled: although in all his writings he seems to proceed as if he is presenting a better philosophy or way to truth, his goal is not truth, but as he says here utility.

One might ask isn’t truth needed in order to have utility? But no, one can proceed as long as one has something that is clear, distinct, and certain, or better reliable. Much of his writings are his rules for obtaining this kind of certainty, rather than enquiring after truth about nature.

Although he doesn’t mention politics and religion explicitly, he does urge his method be adopted by all and be publicly disseminated, so inevitably social and religious dimensions will arise.

And I judged that the best remedy against these two obstacles was to communicate faithfully to the public …, and to urge the best minds to try and make further progress … and by communicating to the public everything they learn.”

Richard Kennington [1] writes

Only seventeenth-century philosophy laid down the principles of the modern type of political society which became the agent of technological “progress” – by merging the goals of philosophy and politics …

So we are today living in and partly formed by the consequences of Descartes project.

  1. Richard Kenington, Descartes and the Mastery of Nature, in On Modern Origins , Lexington Press (2004)

Winter • March 10, 2023 5:18 PM

@modem

This is revealed in the Discourse on Method

Books and children are important for what they are, not for what their parents motivated when they created them.

Who cares why Descartes, Shakespeare, Plato, or Darwin wrote their books? Historians maybe? Or religious zealots?

But I don’t care.

prove it • April 7, 2023 3:48 PM

ok so slack says chatgpt/openai now has their proprietary data – post a screenshot (redacted) to prove it.

chatgpt states “inputs are not used for further iterations of chatgpt.”

only possibility is slack leaked confidential data pre 2022 which was ingested by chatgpt.

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