Dear Martin,
I must admit that I cannot easily answer large e-mails that mix up several
issues.
Yes, sorry for the mess.
Firstly, a philosophical question for the below: Why do make the distinction of
known knowledge? The CRM FOL are explicitly about being, not (only) about
knowing. If you implicitly argue that the CRM should describe only known
knowlegde, I'd recommend you to read the paper by Carlo Meghini (and me)
formalizing the CRM, and we discuss details!😁
I did read it. I skipped the skolemisation part and only read the Wikipedia
article, though :-)
The term "known knowledge" was not good. Let's go with "current knowledge"
instead.
I don't say that the CRM should describe only current knowledge. I do say specifically about P7
that it should make up its mind whether it is about being or about knowing. Concretely, I suggest
that P7 statements should only describe what is currently known, especially since it is so
important to you to model finding the best known approximation of the phenomenal place. In other
words, I see P7 as a "declarative property" that encodes explicit attestations and
inferred knowledge. P161, on the other hand, is a "phenomenal property" and about being
rather than knowing. Both are fundamentally different. I think it is pointless to soften this up by
saying that all places between the phenomenal place and an attested P7 are also P7. Then one has to
distinguish between known and as-yet-unknown P7. Take this scale of P7 statements from small to big:
phenomenal place
… P7 places that are as-yet-unknown
… the smallest inferrable P7
… some inferred P7
… an explicit attestation
… more inferred P7
… the largest explicit attestation that we know of and still regard as P7
… places that are regarded as too big to be P7
… planet Earth
So, my point is that the "P7 places that are as-yet-unknown" part at the
beginning of the scale obscures the semantics of P7 and is neither useful nor necessary.
It is enough to be able to find the smallest inferrable P7.
In particular, I used to think that the relationship between P161 and P7 is vaguely similar to
"has current X" and "has former or current X", but I now think it is pointless
to say P161(x,y) ∧ E4(x) ⇒ P7(x,y) because it says that the phenomenal place is automatically the
best P7 approximation of itself, only that it can never actually be known.
Even if you see it differently, would you agree that my interpretation of P7 is
consistent and "does the job"?
Secondly,
I am a bit at loss what you mean by S1,S2,S2a.
Perhaps my description was too terse.
S1: P7 contains P161 (not "P7 => P161" as I wrote earlier)
* this is the first statement in the FOL block of P7 (after the domain and
range statements)
* S1 states that each P7 provides an approximation of P161
* the exact form of S1 is discussed at length below
S2: P7 => all places between phenomenal place and P7 are also P7
* this is the second statement in the FOL block of P7
* S2 covers the scale above from "phenomenal place" to "the largest explicit
attestation that we know of and still regard as P7"
* i.e. mixing up being and knowing
S2a: S2 but with P7 instead of P161
* this is the version of the second statement where the term P161(x,z) is
replaced by P7(x,z)
* S2a covers everything between pairs of known P7
* if we can reach "the smallest inferrable P7", it covers the scale above from "the smallest
inferrable P7" to "the largest explicit attestation that we know of and still regard as P7"
* i.e. purely about knowing
F: the (explicitly named) intersection of two P7 is also P7
* F makes sure that we can indeed reach "the smallest inferrable P7"
* i.e. purely about knowing
I regard that P7(x,y) ∧ E53(z) ∧ P161(x,z) ⇒ P89(z,y) is wrong. It is
definitely that P7 implies that there exists a spatial projection inside the y
in the same reference space. NOT, that if a spatial projection exists, it is
inside the Y.
P161 is one of the thingies that behave like a function. It depends on x and a
reference system, and it exists independently of any P7. Let's call this
function F161. It is defined as
z = F161(x) ⇔ P161(x,z)
The reference system is conveniently left out here but could easily be added as
a second variable u, as in F161(x,u). With the usual implicit (∀x,y), all the
following statements are equivalent:
P7(x,y) ⇒ (∃z) [E53(z) ∧ P161(x,z) ∧ P89(z,y)]
P7(x,y) ⇒ (∀z) [E53(z) ∧ P161(x,z) ⇒ P89(z,y)]
P7(x,y) ∧ E53(z) ∧ P161(x,z) ⇒ P89(z,y) with an implicit (∀z)
P7(x,y) ⇒ (∃z) [z = F161(x) ∧ P89(z,y)]
P7(x,y) ⇒ (∀z) [z = F161(x) ⇒ P89(z,y)]
P7(x,y) ∧ z = F161(x) ⇒ P89(z,y) with implicit (∀z)
P7(x,y) ⇒ P89(F161(x), y)
We haven't introduced function symbols yet. From the remaining versions I chose the one
with P161 on the left-hand side because then I don't need to write down the implicit
"for all" and can pretend there is no quantifier for z at all.
Best,
Wolfgang
Am 26.10.2022 um 21:18 schrieb Martin Doerr via Crm-sig <[email protected]>:
Dear Wolfgang,
I must admit that I cannot easily answer large e-mails that mix up several
issues.
Firstly, a philosophical question for the below: Why do make the distinction of
known knowledge? The CRM FOL are explicitly about being, not (only) about
knowing. If you implicitly argue that the CRM should describe only known
knowlegde, I'd recommend you to read the paper by Carlo Meghini (and me)
formalizing the CRM, and we discuss details!😁
Secondly,
I am a bit at loss what you mean by S1,S2,S2a.
I regard that P7(x,y) ∧ E53(z) ∧ P161(x,z) ⇒ P89(z,y) is wrong. It is
definitely that P7 implies that there exists a spatial projection inside the y
in the same reference space. NOT, that if a spatial projection exists, it is
inside the Y.
Please clarify!
Best,
Martin
On 10/24/2022 11:15 AM, Wolfgang Schmidle via Crm-sig wrote:
Dear Martin,
Thank you for your insightful comments! Yes, I agree on your points about
fuzziness and about FOL for outer bound approximations.
The "creation" of a spatial projection is probably a misunderstanding.
Fair enough, my words were not chosen well. My point was that the intersection belongs to
a group of phenomenal or unique declarative thingies that behave like functions. I was
trying to elaborate that we can introduce a function symbol representing the intersection
even if FOL doesn't "know" about intersections.
And let's forget about the union of attested places. My point was simply that we shouldn't argue
with wobbly terms like "reasonable" or "context". For example, especially in
the case of Caesar's murder one could argue that the context is in fact the whole Roman Empire. I
am fine with S2 on that end of the scale if we don't burden it with semantic ballast.
On the other end we have, assuming a shared reference system:
S1: P7 => P161
S2: P7 => all places between phenomenal place and P7 are also P7
S2a: S2 but with P7 instead of P161
F: the (explicitly named) intersection of two P7 is also P7
We know S2 => S2a and F
With the help of your comments I can now sharpen my point to this: S1 plus S2a
plus F are enough to describe the known knowledge. Everything else that could
theoretically be inferred by S2 is not known knowledge.
Take your example about detecting inconsistencies:
Ceasar dying on the Forum Romanum has an empty intersection with the Theatrum
Pompeii, on the Mars Field. Obviously inconconsistent.
Consequently, Curia Iulia must be wrong.
This can be done with F.
Best,
Wolfgang
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