# [ExI] e: GPT-4 on its inability to solve the symbol grounding problem

Giovanni Santostasi gsantostasi at gmail.com
Mon Apr 17 03:42:23 UTC 2023

```Let's stick to math because it is easier to think about. Are you aware that
the entire sequence of natural numbers can be derived from the null set?
Have you ever seen the proof?
You can read it here, there are several references.
https://math.stackexchange.com/questions/4039712/how-do-you-generate-the-numbers-from-an-empty-set

You do need something, the idea that the null set exists. Ok, I can concede
you need nothingness and then you can derive everything as a
re-arrangement (relationships) of this nothing. By the way, as I pointed
out before you can build a universe in this way. So no, nothing is required
to establish a language besides the symbols in the language. Maybe you are
thinking of Godel incompleteness theorem but that is another thing. In that
case, is about truth but language doesn't require to have the perfect truth
that mathematics logic seeks. Language is fuzzy, it has to be just
approximately (or probabilistically true) to have meaning.

Giovanni

On Sun, Apr 16, 2023 at 8:25 PM Gordon Swobe <gordon.swobe at gmail.com> wrote:

> “5” can be expressed formally also as “V”, I meant. These symbols point to
> what we really mean by 5, which is outside of the language of mathematics.
> It’s the same with English words.
>
> -gts
>
> On Sun, Apr 16, 2023 at 9:18 PM Gordon Swobe <gordon.swobe at gmail.com>
> wrote:
>
>>
>>
>> On Sun, Apr 16, 2023 at 7:43 PM Giovanni Santostasi <
>> gsantostasi at gmail.com> wrote:
>>
>>>
>>> *To know the difference, it must have a deeper understanding of number,
>>> beyond the mere symbolic representations of them. This is to say it must
>>> have access to the referents, to what we really *mean* by numbers
>>> independent of their formal representations.*What are you talking about?
>>>
>>
>>
>> Talking about the distinction between form and meaning. What applies to
>> words applies also to numbers. The symbolic expression “5” for example is
>> distinct from what we mean by it. The meaning can be expressed formally
>> also as “IV” or ”five.”
>>
>>
>> LLMs have access to and are trained only on the formal expressions of
>> both words and numbers, not their meanings.
>>
>>
>> -gts
>>
>>
>>> *“1, 2, 3, 4, Spring, Summer, Fall, Winter” and this pattern is repeated
>>> many times.   *
>>> Yeah, this is not enough to make the connection Spring==1, Summer==2 but
>>> if I randomize the pattern 1,3,4,2, Spring, Fall, Winter, Summer, and then
>>> another randomization eventually the LLM will make the connection.
>>>
>>> On Sun, Apr 16, 2023 at 3:57 PM Gordon Swobe via extropy-chat <
>>> extropy-chat at lists.extropy.org> wrote:
>>>
>>>>
>>>>
>>>> On Sun, Apr 16, 2023 at 2:07 PM Jason Resch via extropy-chat <
>>>> extropy-chat at lists.extropy.org> wrote:
>>>>
>>>>
>>>> To ground the symbol "two" or any other number -- to truly understand
>>>>>> that the sequence is a sequence of numbers and what are numbers -- it needs
>>>>>> access to the referents of numbers which is what the symbol grounding
>>>>>> problem is all about. The referents exist outside of the language of
>>>>>> mathematics.
>>>>>>
>>>>>
>>>>> But they aren't outside the patterns within language and the corpus of
>>>>>
>>>>
>>>>
>>>> But they are. Consider a simplified hypothetical in which the entire
>>>> corpus is
>>>>
>>>> “1, 2, 3, 4, Spring, Summer, Fall, Winter” and this pattern is repeated
>>>> many times.
>>>>
>>>> How does the LLM know that the names of the seasons do not represent
>>>> the numbers 5, 6, 7, 8? Or that the numbers 1-4 to not represent four more
>>>> mysterious seasons?
>>>>
>>>> To know the difference, it must have a deeper understanding of number,
>>>> beyond the mere symbolic representations of them. This is to say it must
>>>> have access to the referents, to what we really *mean* by numbers
>>>> independent of their formal representations.
>>>>
>>>> That is why I like the position of mathematical platonists who say we
>>>> can so-to-speak “see” the meanings of numbers — the referents — in our
>>>> conscious minds. Kantians say the essentially the same thing.
>>>>
>>>>
>>>> Consider GPT having a sentence like:
>>>>>  "This sentence has five words”
>>>>>
>>>>> Can the model not count the words in a sentence like a child can count
>>>>> pieces of candy? Is that sentence not a direct referent/exemplar for a set
>>>>> of cardinality of five?
>>>>>
>>>>
>>>> You seem to keep assuming a priori knowledge that the model does not
>>>> have before it begins its training. How does it even know what it means to
>>>> count without first understanding the meanings of numbers?
>>>>
>>>> I think you did something similar some weeks ago when you assumed it
>>>> could learn the meanings of words with only a dictionary and no knowledge
>>>> of the meanings of any of the words within it.
>>>>
>>>>
>>>>>>>
>>>>> But AI can't because...?
>>>>>
>>>>
>>>>
>>>> An LLM can’t because it has no access to the world outside of formal
>>>> language and symbols, and that is where the referents that give meaning to
>>>> the symbols are to be found.
>>>>
>>>> -gts
>>>> _______________________________________________
>>>> extropy-chat mailing list
>>>> extropy-chat at lists.extropy.org
>>>> http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
>>>>
>>>
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