The ORM Foundation

Note to Niels: Your original proposition was asserted in the "Extensions to ORM" thread but the proposition is about the Philosophy of ORM so I moved the discussion to this new thread in the "Philosophy" section. 

In this thread, you asserted the following proposition:

"A fact is nothing more and nothing less than a proposition, irrespective of who said it, and in what language it is stated."

This proposition can be considered in parts:
1: A fact is a proposition that is either true, false or meaningless.
2: Propositions do not appear out of thin air - they are made by people.
3: When a person makes a proposition, the person must use a language to express the proposition.

Niels, you used the following argument to support your case:  

Let's look at two propositions expressed by some person in a language:

Ken said: "Lee Harvey Oswald killed John F. Kennedy" 

Niels said "Lee Harvey Oswald vermoordde John F. Kennedy" 

Note: "vermoordde" is the Dutch equivalence of "killed", and in this particular context has exactly the same meaning.

Obviously the two statements are not equal, one is expressed by a person named Ken, the other by a person named Niels, and they are even expressed in different languages, yet they both make the same factual statement about the killer of John F. Kennedy. 

  "yet they both make the same factual statement about the killer of John F. Kennedy. "

Now it seems to me that this needs a bit of clarification:

1: Both propositions are about the same event.
2: Each proposition is made about the same event by a different observer.

So, it is true that each proposition is about the same event.
It is also true that each proposition was uttered by a different person - probably at a different point in time that was after the event itself.

Then you say:  "...yet they both make the same factual statement.. "

Here, you seem to be using the term "factual statement" to mean the same thing as "the event that was observed", which is clearly not the case.

Events don't speak for themselves, it is people who utter propositions about the events that they observe.

Thus, I argue that your claim that both propositions make the same "factual statement" is false.
There is no third proposition that can be considered to be the "factual statement" to which you refer.
Nobody uttered this "factual statement" so it does not exist.

What is true is that both propositions refer to the same event.
So we have one event, two observers and two propositions - and that's it!

Which, seems to me to be rather goedzooi.

Ken

 Hello Ken,

Having had a night to think about our discussion yesterday, I realized my argument wasn't as precise as it should have been.

Let's start again with the statement "Lee Harvey Oswald  killed John F. Kennedy".

In the thread you referred to, I wanted to make clear that the question whether it is a proposition depends on the context. 

Before, October 18, 1939,  the day Lee Harvey Oswald was born, the statement is clearly not a proposition, since one of the terms in the statement is undefined. 

Unlike you say, I don't subscribe to the notion that a proposition can be meaningless. A statement that has the structural form of a proposition, but one of its referents is undefined, is not a propositions. Propositions in classical logic (and ORM is based on classical logic), unlike values in a relational database have only two possible values: true or false. In SQL terms: propositions are NOT NULL.

Between the day Lee Harvey Oswald was born and the event in Dallas, November 22, 1963, the statement "Lee Harvey Oswald  killed John F. Kennedy", is a proposition. Both referents Lee Harvey Oswald and John F. Kennedy are defined (and let's for arguments sake assume that there is no ambiguity as to whom we are referring to). Let's also assume that the verb "to kill" is well defined, making the statement "Lee Harvey Oswald  killed John F. Kennedy" a valid proposition.

Its truth value however is false. Between October 18, 1939 and November 22, 1963 John F. Kennedy was alive, so he could not have been killed.

This is where I'd like to correct my earlier argument. Even though the statement "Lee Harvey Oswald  killed John F. Kennedy" is a proposition when stated between October 18, 1939 and November 22, 1963, it is not a fact.

Facts are propositions that are held to be true.

The statement "Lee Harvey Oswald  killed John F. Kennedy" is only a fact after November 22, 1963. 

Now that I have rectified my original argument, let me address your message.

"A fact is a proposition that is either true, false or meaningless"

No, as I just explained a fact is a proposition that is true. Meaningless propositions don't exist.

"Propositions do not appear out of thin air - they are made by people."

Although propositions do not appear out of thin air, they don't necessarily have to be made by people. Two interacting theorem provers may well exchange propositions that have never been conceived by humans. 

The focus on people smacks a bit like insisting that consciousness is somehow necessary in the Copenhagen interpretation of quantum mechanics.

How a proposition comes about is irrelevant for its truth value, while the context in which a proposition is used may change its truth value, or even render a statement that is considered a proposition in another context into something that is not considered a proposition.

 "When a person makes a proposition, the person must use a language to express the proposition."

While this is true, it also applies to non-humans that create propositions, also the language a proposition is stated in is irrelevant for the truth value of the proposition.

Under every condition "Lee Harvey Oswald killed John F. Kennedy" behaves exactly like "Lee Harvey Oswald vermoordde John F. Kennedy". Each statement is meaningless and therefore not a proposition before October 18, 1939. Each statement is a preposition after that date, with false as its truth value until 22 November 1963, after that date both prepositions are held to be true (at least to the extent that people believe the official reading of the case). 

Since we can't distinguish  "Lee Harvey Oswald killed John F. Kennedy" from "Lee Harvey Oswald vermoordde John F. Kennedy" on any logical ground, they are equivalent. There are no two propositions, there is only one, it is just uttered in two different languages.

On top of that, none of us was there as an observer (I presume), so it's all hearsay anyway. 

Niels

A quick question, Ken.

Are there 2 posts preceding this one in this thread, or are there two posts preceding this one in this thread?

Niels 

 Hi Niels,

There are two posts preceeding your "quick question" post.
Your quick question post is the third in the thread and this one is the fourth.

Let me know if this solves your problem and I will removethis post and your quick question post.

Ken

 Are you sure it's two and not 2?

Hello Niels,

Thanks for the clarification.
It seems that when I first read your first post, my perceptive processes "saw" the two propositions as being identical.
At the time, I wondered why you were making two identical statements separated by an "or".
Which led me to ask myself "Did Niels make a mistake here?"
Now however, I get your point and I see my perceptive error.

Amazing what tricks human perception can play!
(Aside: One of the best bits of evidence I have seen on the vagaries of human perception is the "The invisible gorilla" experiment.)

Of course, some people might argue that what "my mind" was doing was "extracting" a "naked fact" which in turn might lead to the conclusion that both propositions are making the same "factual statement".

However the invisible gorilla experiment (and related experiments and evidence) suggest a different explanation.

Here is what I think happened to me:
My perceptive process used the first few words of your question to establish "a conceptual framework" and, once that was set in my head, I used that initial conceptual framework to interpret the "meaning" of the rest of your question. In other words, the first few words "framed" the question.

So as I now understand it, your question is:
Is the proposition: "There are two posts preceding this one in this thread."
The same as          "There are 2 posts preceding this one in this thread."

Well from the perspective of an alien who has never been to Earth before, each proposition uses a different set of characters so they are not the same.
So if the propositions are different, why would some people think that they are conveying the same message?

Well, I hope I have already answered that with my explanation of how the human perceptive process works.

The two propositions are not the same.
However, within the specific context in which you used them, and in the light of the linguistic structure of the sentence, I agree that in this case, they mean the same thing.

But the "trick" of making two different propositions mean the same thing has more to do with the human perceptive process and linguistic structures than it has to do with the symbols that are used to represent a state of affairs.

Thanks for pointing this out.
It really made me think!

Ken  

 Hello Ken,

It was not my intention to trick you, my question was meant as rhetorical device, and I am glad upon clarification you picked up on that. It was an attempt to demonstrate that two propositions, either written in different languages or formulated using different symbol sets, can in fact be completely equivalent. I assume, you verified the fact that there are two messages before my question, by counting, just like I did when I posted the question, and you would use the same method of verification, independent of whether the number was written as "2" or as "two".

Niels 

Hello Niels,

Sorry for any misunderstanding but when I used the word "trick" it was not my intention to refer to your behaviour or intentions in any way.  

My purpose in using the word "trick" was to refer to the "natural" behaviour of the human perceptive process.
For example, I mentioned the "invisible gorilla" link to illustrate one of these "tricks", specifically the seeming "trick" that we play on ourselves as a result of "selective attention" - which in the invisible gorilla example causes some people not to "see" the gorilla when it is in "plain view".
 
So back to the issue of propositional equivalence.

When I read the first few words of your question, my perceptive process set up a "a conceptual framework" which I then (unwittingly) used to interpret the rest of the text. So I did not detect that you had used "2" in one part and "two" in another. (Which is why I was puzzled)

As I see it, this was not an example of propositional equivalence, it was an example of me getting an idea of "meaning" from the first part and then "casting" my initial idea of "the meaning" over the second part.

The point that is relevant to our discussion is that I did not use any reasoning process to separately evaluate the "2" part and the "two" part- simply because I did not detect the differences. 
So, the aparrent "sameness" of the two parts was a function of the "trick" that my own perceptive process played on me rather than the result of any reasoning process based on the anaylys of the propositions.

Now I'm still thinking about your claim of "complete equvalence".
My intution is telling me that they are not equivalent but I must confess that I have not (yet) developed a reasoned argument as to why or why not.

My library contains quite a few academic books on logic and philosophy so I'll get back to you on this after I have reviewed the points that the authors make about the equivalence of propositions.

Ken

Hello Niels,

Thanks for a great example of why a lexical representation of a value is not the value itself. I've never liked the NIAM-era notion of LOT vs. NLOT (Lexical Object Type vs Non-Lexical Object Type), which evolved into Value Type and Entity Type in ORM. The problem is that the focus is on the wrong thing, namely a lexical representation of a value, not the value itself.

The fundamental difference between a value type and an entity type is that an instance of the value type is self-identifying. There are a number of concepts that correspond to a self-identifying object such as immutability of values (a value cannot change because if it changes it is a different value), equivalence of copies of the value, etc. However, as you demonstrate with "2" vs. "two", self-identification does not mean that there is exactly one lexical representation of this value. A lexical representation of a value is clearly not the value, so the emphasis in naming should be on the value (Value Type) instead of how the value is represented (Lexical Object Type).

Another example of the disconnect between a lexical representation and the value it represents is the difference in decimal separators on different sides of the pond: "1.000" means "one thousand" on your side, but over here is it just a fancy way of writing "one". Clearly, language is important in interpreting a lexical representation.

So, I'm totally on board with you on this. Just as readings in different languages--or multiple readings in the same language--do not change the represented fact, different lexical representations (combined with the means of interpreting that representation, such as a language) represent the same immutable value. In both cases the thing being represented (fact and value) are the central concepts. The representation is always secondary, and the equivalence of the underlying objects is not determined solely by the equivalence of their representations.

-Matt

 Hello Matt,

 Thank you for your kind words. I liked learning the evolution from NIAM to ORM from you.

 Niels 

Hello Niels,

Sorry for the delay in getting back to you on this. There was more technical work to do than I anticipated and there is still quite a bit more I have to do. However, I have done the urgent work so here is a short but considered response.

Firstly the idea that two propositions that use different words have the same "meaning" or are "equivalent" in some way, seems to be based on the Platonic notion that, in addition to the written or spoken sentences, there is some abstract idea that the sentences represent - aka their "meaning".
But this idea that there exists some separate "abstract meaning" in addition to the written propositions can be neither proven nor disproven. 

In your example, what we can agree on is that there are two propostions - one written in Dutch and one written in English.
And there is evidence to suggest that both propositions are true.

We could assert a third proposition: "Lee Harvey Oswald a tué John F. Kennedy" and the evidence suggests that this proposition is also true.
So now we have three propositions, each of which we can consider to be true.

However, I do not see the need to assert the existence of a separate and inaccessible abstraction called "meaning".

So my conclusion is that each of the three propositions stands on its own and there is no separate thing called "meaning".
This conclusion also applies to the "2" and "two" example.

Now I will confess that I do feel a sense of "propositional eqivalence" but from a logical perspective I don't see a need for "propositional equvalence" to exist.

Ken

Hello Ken,

Without propositional equivalence there would be no logic. In fact, every logic starts with certain axioms that are written as equivalence relations.

This document lists the axioms of propositional logic. You may disagree with some of these axioms, and feel more at ease with something like intuitionistic logic, but there too the logic is based on axioms that are written as equivalence relations.

Equivalence is a rare phenomenon in the physical world, where every object has an identity and two discernable objects have different identities. This is argued to break at the quantum level, but in the macroscopic world that we perceive, objects generally have an identity.

This is even true for the actual lexical representation of abstract entities. We could say that the statement "2 = 2" is blatantly false, because the first 2 is written on the left hand side of the = sign and the other is written on the right hand side, so the the two 2s are anything but equal. In other words, in the actual lexical representation of abstract entities, we can give each symbol an identity.

However, in the logics we use, we don't care about these identities. For every logic I have ever come across, the statement "a = b" is exactly the same as the statement "a = b", even though in the physical world we can discern the first occurrence in the sentence from the second.

Even stronger, a written expression would be nothing more than dots on a screen or blots on a piece of paper, but for the meaning that is expressed, just like a vocal expression would be nothing more than slightly hotter air, but for the meaning of the expression.

Expressions, whether written or spoken exist because of the meaning they denote, and one of the most fundamental things we do with logic is try to establish or refute equivalence between expressions. 

Niels

 I basically agree with Niels on how to conceive of propositions. In philosophy, there are different schools of thought on the precise nature of propositions, but I subscribe to one of the more popular viewpoints that treats propositions as extra-linguistic entities that are are always true or false (and hence truth-bearers). Their truth or falsity is determined by states of affairs (truth-makers).

Different sentences (in the same or different languages) may be used to assert the same proposition. For example :

Honshu is an island of Japan. 

Honshu is one of the islands of Japan.

Honshu wa Nihon no shima desu.

Depending on the communication context (e.g. speaker, time, place etc.), the same sentence may be used to express different propositions. For example:

Albert Einstein is alive.    True when stated in 1900 and referring to the famous scientist with this name.

Albert Einstein is alive.  False when stated in 2000 and referring to the famous scientist with this name.

Here we have one sentence but two propositions. 

Cheers

Terry 

 Hello Niels,

I have no disagreement with the rules of propositional logic as shown in the document you linked to.

However, I do disagree with your assertions that:
 "every object has an identity"  and "two discernible objects have different identities".

The concept of an "object" is something that humans have invented for the convenience of talking about their experiences.
The names that we use for objects and object categories are useful for acting as "pointers" to "things" that we perceive.
For example, the cup of coffee on my desk does not know that it is a cup of coffee. It is only a cup of coffee because (a) I assert that it is and (b) by human convention many other people would agree with the proposition that it is a cup of coffee. 

So, it seems to me that what you call "objects" and their "identities" are nothing more than linguistic conveniences for humans to use to discuss their experiences and ideas.

Does 2=2? 
It is true that in the "Magritte" paradigm that you mention, "2=2" is indeed false.

However, in the arithmetic paradigm, the proposition 2=2 is true and what makes it true are the rules of arithmetic that have been invented by humans and nothing else.

The meaning of expressions
I'm going to use the word "sign" as a shorthand to refer to all manner of things that such as written words, road signs and noises uttered by humans.

Signs invented by humans do not have any intrinsic meaning. So, as you mention, signs such as written words are just marks on paper or on a screen or on a tablet of stone... To the degree that a sign has "meaning" such "meaning" is or has been assigned by human convention alone.

Your phrase "but for the meaning they express" is worded in a way that seems to carry the hidden proposition that signs themselves somehow "contain" or "carry" meaning. I think that this is a false notion. It seems to me that any meaning that a sign may or may not have is based on human conventions and nothing else.

Niels Hoogeveen:

Expressions, whether written or spoken exist because of the meaning they denote

If you accept that signs do not have any intrinsic meaning then you must also accept that this proposition is false.
Propositions are asserted by people, they don't appear out of thin air.

• Intended "meaning" exists in the mind of the person who utters the proposition.
• Perceived "meaning" exists in the mind of the person who sees or hears the proposition. (or feels as in the case of braille)

This is it. There is nothing else.

Niels Hoogeveen:

one of the most fundamental things we do with logic is try to establish or refute equivalence between expressions. 

That's not the way it seems to me.
As I see it, Logic is a method of reasoning according to certain rules.

Ken 
 

Hi Terry,

At the risk of being a little bit off topic here, the communication contexts are a point of interest to me with regard to fact based modelling. We already touched on it in the thread about Postgresql's exclusion constraints and how that can be used for example with respect to temporal information. 

There are however other communication contexts than temporal ones. We could eg. look at phylogenetics where one taxon is said to descend from another taxon, according to some phylogeneticist. Others in that field may (gently or not so gently) disagree, and define a different lineage. This may lead to different propositions about the lineage of a particular taxon, and may even lead to difference of opinion about the existence of certain taxa. At the same time, there is agreement that in fact there is only one lineage (as long as we are talking about organisms where horizontal gene flow plays no significant factor), but due to limited information, different proposals for a lineage may coexist at the same time. There is also agreement that proposed taxa are only valid if they are part of an actually lineage. Once agreement is reached about some part of the taxonomy, certain taxa are claimed to no longer exist (other than for historical purposes).

I would find it interesting to learn what types of communication contexts exist and if there are modelling patterns that can be reused to properly model facts and even entities, whose existence depends on the communication context.  

Niels