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What is a fact?

Last post 03-28-2014 15:02 by Terry Halpin. 21 replies.
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  • 03-26-2014 9:00 In reply to

    Re: What is a fact?

    Hello Ken,

    You say: "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.

    Depending on the exact meaning of "invented" I may agree or disagree with you on this one. The rules of arithmetic have been "invented" many time over the course of human history. Egyptians and Sumerians may have learned it from each other, but it is likely that the Mayan "invention" of arithmetic is independent of the "invention" that happened in the Middle-East/North Africa.

    Instead of calling it an invention, we could also call it a discovery.Arithmetic is based on a set of patterns that are useful to count things. Entities with the ability to discern patterns and find it useful to count, may therefore discover the usefulness of these patterns.

    Is the rule that the sum of the angles of a triangle in Euclidian space has a constant value, a discovery or an invention?

    The people that first learned this rule may have called it a discovery. Maybe they were playing with sticks and ropes, and found out that no matter how they positioned their sticks, something remained invariant (that which we call the sum of the angles). 

    Certainly there are human elements in how we symbolize these rules. In most of the world we tend to write angles in some base 360 notation, a convention borrowed from the Sumerians, but the invariance of the sum of the angles under transformation of the triangle is just as true had we used a base 10 notation for angles. 

    Even some artists go so far as to call their creation a discovery. There have been sculptors who claimed that the statue they created, was already present in the marble, and the artist merely unveiled that presence. I don't necessarily subscribe to that idea, since the exact shape of the statue is defined by the statue itself, unlike physical representations of mathematical objects like circles and rectangles, which are always an approximation of some ideal. 

    The usage of the word ideal in this specific context doesn't necessarily make me a Platonist. A mathematical circle can be precisely defined and when measuring a physical representation of a circle we can, up to quantum uncertainty, at least in principle state how that physical representation deviates from that ideal. The same can not be said about categories. It is impossible to define an ideal chair, let alone measure a physical chair and state how the two differ from one another.

    Later on you state: "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. 

    If it comes through that way, then I have not been clear enough. Signs do not contain or carry a meaning, but they do by convention map to a particular meaning. The human element in this is the convention. In fact, I am inclined to view your notion that "killed"  and "vermoordde" are not equivalent in the statements used earlier in this discussion, smells like a hidden proposition that signs themselves "contain" or "carry" meaning. If not, then how does meaning come into play in your thinking, or is meaning an entirely meaningless concept. And if that is the case, how can we have a meaningful discussion?

    Near the end of your message you say: "As I see it, Logic is a method of reasoning according to certain rules.".

    I don't necessarily disagree with you on this one, but if we look more closely at what those methods of reasoning are, then we see that substitution plays an important role, and substitution is only possible if we accept equivalence relations.

    Finally, I'd like to return to the start of your message. You say: The concept of an "object" is something that humans have invented for the convenience of talking about their experiences. 

    While the word "object" is certainly a human invention and not a discovery, the universe we live in somehow seems to behave in such a way that two things that we call objects have the property of never being in the same place at the same time. Again, this notion breaks down at the quantum level, where probability waves can overlap, but for macroscopic objects we generally deal with, this seems to hold true. In that sense, two cups of coffee are discernible from one another by the fact that they are not located at the same place at the same time. Even ants seem to acknowledge this rule of nature, since they do not regularly have the habit of trying to walk through cups of coffee, even though they might be tempted to get in your coffee, if it contains sugar.

    Niels

  • 03-26-2014 9:00 In reply to

    Re: What is a fact?

    Hi Niels,

    As an alternative to thread drift, it may be useful for you to to start another thread with a title that meets your needs.
    If you want to do this, then I suggest that you phrase the title of the thread in the form of a question such as:  

    "How can fact based modeling be used to resolve phylogenetic disputes?" or something similar - It's up to you.

    I'd also like to share with you my three step approach to fact based modeling:

    The first step is to "Get the Facts" from the experts. And by "facts" I mean sentences that are in a form that we can classify as "propositions".  
    The second step is to use ORM to model the facts. Terry proposes a method called the "Conceptual Schema Design Procedure" (CSDP) for doing this.
    The third step is to convert the object-role model to an artefact that programmers can use. For example, the object-role model can be used to generate DDL for an RDBMS.     

    So for me, whether you want to model a situation in phylogenetics or any other domain, the procedure is the same. You start by helping the domain experts to express themselves using facts in the form of propositions that have a truth value.

    In practice, steps 1 and 2 tend to be done fact-by-fact. You get the domain experts to agree on a fact and then you use the fact to create the model. 
    It's useful to use an ORM tool because the tool helps to prevent you from making an inconsistent model by enforcing certain rules on the facts as you enter them.

    So, if I was creating a "phylogenetic model" then I would start by asking the experts just one question:
    What are the facts?

    In practical sessions, the object-role modeling process itself will help to expose disputes.

    And, as each dispute arises, the modeler uses his or her "moderator skills" to get the parties to agree on the facts. 

    Ken 

    PS: In this post I use the term "facts" to mean "fact types". 

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  • 03-26-2014 15:39 In reply to

    Re: What is a fact?

     Hi Niels

    You are probably aware that communication act theory (formerly, and sometimes still, known as speech act theory) has been an active field of study for many years, with Austin and Searle being the main early contributors. For a concise overview, see http://en.wikipedia.org/wiki/Speech_act. 

    Your phylogenetics example reminds me of a genealogy model that Andy Carver and I developed many, many years ago. In that model (unfortunately, I no longer have a copy of it) we included Proposition and AssertionAct as entity types.This enabled us to record who asserted what proposition, and what degree of certainty was attached etc. I expect something similar could be done with your phylogenetics example.

    Cheers

    Terry 

     

  • 03-26-2014 16:59 In reply to

    Re: What is a fact?

     

    Terry Halpin:
    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).

     Hi Terry,

    Of course I agree that there are physical things in the world, such as those things that we call cars, houses, cats, dogs and so on. And, one might choose to call such things "extra-linguistic entities". However, I feel that it is better to call them "extra-linguistic states of affairs" or just "states of affairs".

    States of affairs can exist without anyone ever making an utterance about them. However, propositions do not utter themselves in some timeless void and in some form that is not a language. So it seems to me that there is a problem with the term "extra-linguistic proposition" because it seems to refer to something that is not expressed in a language and that was not expressed by a person. 

    I don't see how a proposition can be anything other than "an utterance expressed by a person in some language at some point in time that conforms to the rules that enable the utterance to be classified as 'a proposition'".

    If you remove the person (the utterer) and time of utterance from a proposition then you may still have some symbols (or sounds) which may conform to the rules that enable them to be classified as a sentence. However, it may not be possible to assign a truth value to the sentence that remains. 

    Regarding your "Honshu" example, I agree that:

    1: In the physical world, there is "something that exists" that people classify as an "island" and to which people have assigned the name "Honshu".
    2: It is possible for a person to use language to make assertions about this "something that exists". 

    For example: 

    On 25 March 2014, Terry Halpin asserted three propositions about the island of Honshu.
    Each of the three propositions stands alone.
    Each proposition refers to the same "something that exists" or "state of affairs."
    However, the "state of affairs" that we call "The Island of Honshu" is quite independent of any propositions that any person might make about it. The state of affairs that we call "Honshu" is an extra-linguistic state of affairs. It is not an extra-linguistic proposition.

    Regarding your example "Albert Einstein is Alive."

    I agree that this is a sentence in the English language. However, its truth value can only be determined by asking "When was this sentence uttered?" And since sentences don't utter themselves, then it seems to me that before you can classify a sentence as a proposition with a truth value, then you also have to say who uttered the sentence.

    Consider this photograph taken at the first Solvay Conference that took place in 1911. Suppose that, at the time that the photograph was taken, Marie Curie had said to Henri Poincaré: "Albert Einstein is alive." Henri Poincaré would surely have agreed that this was a true statement because Albert Einstein was standing behind him.

    So whilst I'm happy to accept that the words "Albert Einstein is alive." form a sentence in the English language, I hold that the sentence "Albert Einstein is alive" has an indeterminate truth value and is not a valid proposition.

    Consider some similar sentences:

     Terry Halpin is in England.
     Ken Evans is in Australia.
     Norma is in America.
     Elvis is alive.

    All of these sentences have been true at some time in the past but they are not true today (26 March 2014). Thus, on their own, they have an indeterminate truth value.  So it seems to me that to be classified as a "Proposition" a sentence must be expressed in such a way that it has a "direct" truth value.  But I feel that more is needed.

    For example, at first sight, the sentence: "Albert Einstein attended the Solvay Conference in 1911" seems to be acceptable as a proposition.

    However, suppose that in 2015, someone writes a book about the states of affairs that pertained in the 15th century. And in this book, the author asserts that "Christopher Columbus said 'Albert Einstein attended the Solvay Conference in 1911'."

    We would have to classify the author's assertion as meaningless because, in the 15th century, this utterance would be about persons who had not yet been born and about an event that was several centuries in the future. 

    Propositions do not appear out of thin air. Propositions are made by people at a particular point in time about a state of affairs.
    This would seem to exclude anything of an “extra-linguistic” nature.

    Ken


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  • 03-27-2014 15:58 In reply to

    Re: What is a fact?

    Hi Ken

    Sentences are linguistic, but propositions are not.

    Utterances are speech acts, not propositions. A proposition is what it is that is asserted when a declarative sentence is uttered or inscribed. Of course, to determine the precise proposition expressed by an utterance or inscription of a sentence, one has to know the relevant context of that communication act. Depending on the sentence, this might require knowledge of the time it was uttered/inscribed. For example, if I say now that "You are now in the UK" this time-deictic and person-deictic sentence expresses a true proposition if we agree that "you" denotes you (i.e. Ken Evans, the administrator of the ORM Foundation website). If I uttered that same sentence when you were at the ORM Workshop in Montpellier, I would be expressing a different, and false proposition. There are many deictic aspects (e.g. time, person, place etc.) that can be relevant depending on the sentence.

    Concrete entities such as the island of Honshu are not states of affairs. Abstract entities such as ideas or numbers are not states of affairs. 

    You claim that my utterances of the following three sentences resulted in three different propositions. This is not the case. My utterances of those sentences all express the same proposition, which is made true by corresponding to an actual, current state of affairs. The "is" (or "desu") is present tense, and you know the time of my utterance. They all "say the same thing" (express the same proposition).. 

    Honshu is an island of Japan. 

    Honshu is one of the islands of Japan.

    Honshu wa Nihon no shima desu.

     

    I hope this clarifies what I said earlier. 

    Cheers

    Terry 

     

  • 03-28-2014 12:10 In reply to

    Re: What is a fact?

    Hi Terry,

    Thanks for your clarification from which I infer that your view is that:   “Propositions exist independently of any declarative sentences that may be uttered to assert the proposition.”

    As a student of philosophy and logic, I have read many websites and books to find out what others have said about “propositions” and here are two sentences from my research: 

    “We mean by a “proposition” primarily a form of words which expresses what is either true or false.” Russell (1920) 

    “A proposition is a written or uttered sentence which is declarative and which we agree to being true or false but not both.”  (Epstein 2001):

    Epstein then contrasts his own view with what he calls the “Platonist view” that “Propositions are abstract objects and a proposition is true or is false but not both independently of our even knowing of its existence.”  Epstein continues: “For me to reason with a Platonist, it is not necessary that I believe in abstract propositions or thoughts or meanings. It is enough that we agree that certain sentences are, or from his view represent propositions.”

    So from this, would I be right in concluding that your view is that of the Platonist?

    Maybe I have misunderstood you but for my part, I cannot agree that:  “There exists a class of things called unknowable truth bearers.” because it seems to me to contain the contradiction: “There exists an x such that x is unknowable.”  

    So, regarding your three sentences, I accept that they are all true but I find it hard to accept that they all say the “same thing” because to do so seems to require that I accept the existence of an abstraction called an “unknowable thing”.

    Ken

    References
    Epstein R. L. 2001: Propositional Logic:  The Semantic Foundations of Logic
    Russell B. 1920: Introduction to Mathematical Philosophy

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  • 03-28-2014 15:02 In reply to

    Re: What is a fact?

    Hi Ken

    Although I am not a fully fledged Platonist, I could be classified as one kind of realist, as the term is currently used in philosophy.

    Your quote from Russell (1920) where he treated a proposition simply as a declarative sentence represents a position that few philosophers (other than Epstein, apparently) would agree with nowadays. Russell dropped that viewpoint later in his life, and instead treated propositions basically as mental acts.

    In case you have not already read it, I recommend chapter 4 of Loux, M. J. (2002), Metaphysics: A contemporary introduction, 2nd edition, Routledge for a reasonable overview of the many different viewpoints on the nature of propositions (though Loux's discussion of the term "fact" in the sense of a state of affairs differs from the way I use "fact" in ORM). 

    Regarding my 3 sentences about Honshu, my utterances of them did all "say the same thing" in that they meant the same, and they acknowledged the same state of affairs.

    Maybe we can simply agree to disagree on these issues, just as many philosophers do nowadays. I don't think it matters a great deal on how one does data modeling.

    Cheers

    Terry 

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