
Depends upon what the meaning of the word “is” is - feross
https://meaningness.com/eggplant/formal-logic
======
nojs
It’s interesting to think how fundamentally impossible it is to parse a
sentence without a background corpus of knowledge about the world:

> I dropped the hammer on the table and it smashed

> I dropped the vase on the table and it smashed

Exact same grammatical structure but if you switch the noun the way you parse
the sentence changes. This is why machine learning with huge datasets wins in
NLP, translation etc.

~~~
baddox
And I wonder how you parse, let's say, "I dropped the pencil on the table and
it smashed."

~~~
naniwaduni
You reject it as semantically implausible.

~~~
paganel
Not necessarily, in this case I didn't reject the phrase "I dropped the pencil
on the table and it smashed." as semantically implausible because of its
context (it was used close to similar-looking phrases). Of course that it
doesn't inform us anything about any "pencil" nor "table", but it does inform
us about the limits (or non-limits) of AI.

------
avindroth
One of the most influential philosophical concepts for me from the last decade
was from this very blog called “Nebulosity”. It just speaks to the nature of
reality that is misinterpreted with overlays of meaning.

-

‘Nebulosity’ refers to the insubstantial, amorphous, non-separable, transient,
ambiguous nature of meaningness.

From a distance, clouds can look solid; close-up they are mere fog, which can
even be so thin it becomes invisible when you enter it.

Clouds often have vague boundaries and no particular shape.

It can be impossible to say where one cloud ends and another begins; whether
two bits of cloud are connected or not; or to count the number of clouds in a
section of the sky.

If you watch a cloud for a few minutes, it may change shape and size, or
evaporate into nothing. But it is impossible to find an exact moment at which
it ceases to exist.

It can be impossible to say even whether there is a cloud in a particular
place, or not.

[from]
[https://meaningness.com/nebulosity](https://meaningness.com/nebulosity)

~~~
aidenn0
Maybe I'm missing a subtlety of your meaning here (how appropriate) but I know
that philosophers have discussed such things for centuries; e.g. 2 grains of
sand is not a pile, 1000 grains is, but where is the transition?

~~~
FeepingCreature
So much effort wasted based on trying to derive fundamental meaning from
coincident attributes of our brains' neurological implementation of abstract
concepts.

"The transition is wherever your 'pile' classifier neuron fires."

~~~
aidenn0
I think you are selling at least some of the philosophers short. What is a
pile and isn't a pile is not entirely subjective (i.e. we all agree that 1
grain of sand is not a pile), nor is it entirely objective (in the sense that
different people will probably draw the line at different places). On top of
that, the transition even for a single individual is not abrupt.

Understanding and dissecting these sorts of ambiguities with something as
inoffensive as piles of sand can be useful for better understanding
disagreement that stems from ambiguity when things are more contentious.

~~~
FeepingCreature
Yeah but those properties are exactly what you would expect from imitation
learned fuzzy neuronal classifiers. As such, they have no deeper meaning than
saying "does the fact that the deep learning model thinks this traffic cone is
a penguin reveal to us a deep truth about traffic cones and penguins?" No.. It
just used some shortcut feature that's not universally applicable. Just like
us.

The heap classifier works to tell that obvious heaps are heaps. It works to
tell that single items are not heaps. In between, there is no meaning but
noise.

------
mynegation
English is a language with pretty reduced inflection mechanisms and overloaded
word meanings. Translated into Russian you would be forced to use different
builds for different meanings: “St. trinian’s is a pretty (in female gender,
nominative case) school for little (in female gender, genitive case) girls” or
“St. Trinian’s is a school for pretty little (both female gender, genitive
case) girls”.

~~~
sdigital
It's true that languages with case declensions (beyond the vestigial declined
pronoun forms in English) would be less ambiguous in expressing that example
sentence.

English is an analytic language, meaning that more information is conveyed
through syntactic patterning involving closed classes of words like particles,
prepositions, and articles. These words could be considered "overloaded" as
you said, but for non-closed classes of words though, as far as I know English
is not known to be more or less polysemic than other languages.

------
clairity
bill clinton, is that you?!

but seriously, in contrast to natural language, the article lays out the
basics of mathematically-based logic, not for its own accord, but as
groundwork for the more interesting later sections talking about context-
dependence and reasonableness.

the reason natural language has so much ambiguity is not because our brains
couldn't have come up with a rigorously logical language, but because the
world is ambiguous and language reflects that.

~~~
foldr
>but because the world is ambiguous and language reflects that.

This doesn't seem like a very satisfying explanation. Take one particular
example of a structurally ambiguous sentence of English:

"The company couldn't make the car fast enough".

The two meanings are completely distinct (speed of production vs. speed of the
car). There's no fuzziness about this distinction out there in the world. The
speed at which a car travels and the speed at which it's made are two
completely distinct properties.

~~~
eindiran
That is an interesting example because it looks like semantic ambiguity rather
than syntactic ambiguity. But actually it is about structure as you commented
-- something like this:

[S [DP [D The [N company]]] [VP [AuxP [Aux couldn't] [V make]] [DP [D the] [NP
[N car] [AdjP [Adv fast] [A enough]]]]

vs

[S [DP [D The [N company]]] [V' [VP [AuxP [Aux couldn't] [V make]] [DP [D the]
[N car]]] [AdjP [Adv fast] [A enough]]]

Regarding the meat of your comment, it is quite difficult to banish all
ambiguity from natural language for a variety of reasons, but we don't really
need to: humans are incredibly good at handling linguistic ambiguity. There
has been a lot of fascinating research on the topic: in particular, I
recommend reading up about anaphora resolution[0] and garden path sentence
repair[1], because the literature includes some info on what is happening in
the brain, which is significantly more detailed than what exists for most
other types of linguistic ambiguity.

All of this ambiguity in natural language is something that continues to be
huge hurdle for NLP: it turns out that fetching the right information from the
context to resolve all the ambiguities that arise in a single conversation is
completely non-trivial, despite how easy humans make it look!

An interesting case study in the opposite direction (ie attempting to remove
ambiguities from natural language) is Ithkuil[2]: it is a conlang that
attempted to completely banish (semantic and lexical) ambiguity and it ended
up being ridiculously hard to use or learn at all.

[0]
[https://en.wikipedia.org/wiki/Anaphora_(linguistics)](https://en.wikipedia.org/wiki/Anaphora_\(linguistics\))

[1] [https://en.wikipedia.org/wiki/Garden-
path_sentence](https://en.wikipedia.org/wiki/Garden-path_sentence)

[2]
[https://en.wikipedia.org/wiki/Ithkuil](https://en.wikipedia.org/wiki/Ithkuil)

If anyone is curious, you can plug those trees into here
([http://mshang.ca/syntree/](http://mshang.ca/syntree/)) and it will draw them
for you. But my tree drawing skills are very rusty, so they are pretty
basic/bad.

~~~
baddox
I'm confused about your sentence parse notation. Isn't "fast" an adjective in
one of the interpretations (namely the one parsed the same as "The company
couldn't make the car safe enough")?

Doesn't that "safe" example point out something else? The example with "fast"
is only ambiguous because it's common to use "fast" as both an adjective and
an adverb? The sentence with "safe" doesn't sound to me like an acceptable way
to say that the company's manufacturing process was too dangerous.

~~~
pwinnski
For the alternative meaning, I think you'd say, "The company couldn't make the
car safely enough." So yeah, adjective and adverb, I think you're right. For
that matter, "The company couldn't make the car quickly enough" would resolve
the ambiguity in one direction, but I guess not the other.

------
guerrilla
Frege did not in general reject intuition. The rules of what became first-
order logic are accepted on the grounds that they are intuitively undeniable
and provide the results we need. That's the actual lesson of Russel's paradox
in response to Basic Law V: that blatantly obvious things can be problematic.

For anyone interested in the semantic analysis of the verb "to be", I
recommend Andrea Moro's book "A Brief History of the Verb To Be."

Also note that analytic philosophy is the philosophical tradition the author
is referring to, not rationalism [2]. This is an ahistorical use of the latter
word. They did define their terms in the glossary but that won't help you in
searching.

[1].
[https://en.m.wikipedia.org/wiki/Analytic_philosophy](https://en.m.wikipedia.org/wiki/Analytic_philosophy)

[2]. [https://plato.stanford.edu/entries/rationalism-
empiricism/](https://plato.stanford.edu/entries/rationalism-empiricism/)

------
Rumperuu
Related:
[https://en.wikipedia.org/wiki/E-Prime](https://en.wikipedia.org/wiki/E-Prime)

------
thelazydogsback
I just saw this sign yesterday and was thinking how many ways it could be
parsed:

"Big golf factory sale opening"

Seems like at least 8:

"Big (golf factory)" vs "(Big golf) factory"

"(factory sale) opening" vs. "factory (sale opening)"

"... opening:V(PresentProgressive)" vs "... opening:N"

Only two of which are semantically likely, and one of which is pragmatically
likely - unless you're really rich and in the market for golf factories.

------
sawaruna
Forgive the dumb question but what is False about ‘∀x eggplant(x) ⇒ fruit(x)’

~~~
nerevarthelame
I think it's a poor example, because whether or not an eggplant is considered
a fruit depends on your perspective and context. It is a fruit botanically,
but it is not typically considered or used as one for culinary purposes.

That distinction of ambiguity adds an interesting complexity to "meaningness,"
but I agree that it's confusing in relationship to the rest of this specific
article.

~~~
sawaruna
Alright, that was the only thing I could thing of that would cause my
confusion here. I viewed it simply as 'it's False to say all eggplants are
fruits' but I guess the author's intention was 'because people consider
eggplants to be culinarily a vegetable, saying all eggplants are fruits is
False'.

It's an interesting addition to the disgusting about meaning in linguistics,
but according to formal logic as used by linguistics, is the eggplant example
even correct? It seems as though no matter what, 'an eggplant is a fruit' is
True, and perhaps there is a different logical notation to imply it could be
considered otherwise depending on context.

------
danielam
"We want our beliefs to be true, but if we don’t even know what they mean,
we’re in trouble. A single sentence might be true in some sense, false in some
other sense, and meaningless in a third. If you believe 'St. Trinian’s is a
pretty little girls’ school,' what do you believe?"

When someone claims they believe that statement, they have a meaning in mind.
Amphiboly is a feature of syntax and spoken language, not beliefs. Confusion,
on the other hand, is.

"In 'the eggplant is a fruit,' probably what is meant is that all eggplants
are fruits. In 'the dog is a Samoyed,' probably what is meant is that some dog
is a Samoyed."

What he's describing is equivocation. However, something similar occurs when
words or phrases are analogical (for example "healthy body" vs. "healthy
sandwich"). Which brings me to...

"This problem is pervasive. Linguists catalog many distinct ways a sentence
can be ambiguous. On analysis, almost any sentence can be read with multiple
meanings. [...] natural languages—English, Chinese, Tamil—are hopelessly
broken. They are incapable of adequately expressing true beliefs."

Why broken? By what measure? And why? That we must grapple with ambiguities
doesn't mean natural language isn't serving its proper purpose. And incapable?
I do hope that's hyperbole because, as the author has no doubt noticed, the
entire article, including the quoted claim, is written in English.

"Modern rationalism’s first major improvement on traditional logic replaced
natural language sentences with mathematical formulae."

Modern rationalism? Also formal languages can help, but they aren't magic
bullets. I am still vulnerable to equivocation.

And why the dismissal of Aristotelian logic for which the author offers no
tangible justification, like:

"Frege’s 1879 invention of modern formal logic fixed several outstanding
defects in traditional, Aristotelian logic"

"Outstanding defects" is, to riff on the article's fixation, ambiguous. Three
features of Aristotelian term logic that Fred Sommers identifies as "missing"
are the inability to deal with particulars in a systematic way, the absence of
relations and the absence of compound propositions. If those are defects, then
fine, but even without those features, the logic is immensely useful in a
broad range of applications. Also, recall that it dominated logic for two
millennia (I highly recommend (Joyce 1916)). I think it deserves a bit more
credit. Furthermore, Sommers updated term logic with his own "algebraized"
term functor logic which accounts for these three "deficits". Worth also
noting is that Sommers saw Fregean logic as a regression to Platonic views of
subject and predicate and rejects putting them in separate universes (Sommers
1982).

"He solved several long-standing technical problems, in which Aristotelian
logic gave outright wrong answers"

Wrong answers? Like?

"In Fregean epistemology, we can eliminate the ambiguity of 'is' [examples
follows]"

How does that depart from the copula in term logic in any relevant way?
Chapman's examples transcribed into term logic are "every Eggplant is a Fruit"
and "some Dog is a Samoyed". Each is governed by laws of immediate inference.
So what ambiguity is he talking about here that his FOL examples don't also
suffer from?

"But what if you see a dog, and it’s obviously a Samoyed, but you don’t know
its registry number? What do you believe then?"

You believe exactly what you've described.

------
chewxy
So Bill Clinton invented n-categories huh

------
mjh2539
Todays sneak-peak at dilettantism in the philosophy of language, logic, and
formal semantics. Brought to you by YC!

~~~
Smaug123
Would you say this if this were a blog post about someone's first steps in
discovering Haskell?

