John, Edwina, List,
I have questions abot the terms "model", "truth", "fuzzy":
"Model": I used to think it was synonymous with "theory". But now I guess, it is an abstraction (like your (John´s) network graph in the pdf-link) of a special situation to which a general theory applies. Is that so?
"Truth": Are there two (or more?) kinds of it, one about the past in which a truth (about what has happened) exists, and one about the future, where it doesn´t, due to object change, why Maturana replaced it with "viability" I think?
"Fuzzy(ness)": Are there two (or more, think of others) reasons for fuzziness: Graduality, subjectivity...?
Best, Helmut
On 3/25/2018 5:08 PM, Edwina Taborsky wrote:
> I think that it's very difficult to correlate theory to model to
> the real world - and I think that Peirce specifically didn't want
> to do such a thing, not because of the difficulty but because of
> the resultant 'lack of truth' in these correlations.
Yes. I have used that diagram with a two-stage mapping between
theories and the world for a long time. When I talk to logicians,
I get very strong opinions, pro and con. Some say that it's
obvious, and others claim that it's totally wrong.
Following is a response I sent some time ago to a logician who
strongly disagreed with that diagram. He never replied to my
request for a better diagram or explanation.
John
_____________________________________________________________________
To XXX,
I agree with (1) the definition of model theory and your comments
about it; (2) that names in a logic may refer to aspects of the
world; and (3) that logicians, scientists, engineers, and ontologists
may talk about sets that contain physical entities.
But the issues about symbol grounding and identity conditions
are critical. Unless there is some way of relating a domain D
to the real world, there is no difference between a real D and
a hypothetical, virtual, imaginary, or fictional D.
XXX
> Model theory itself provides no account of this, of how symbols are
> grounded. It was never supposed to do that: it simply assumes that
> they refer, and gives an account of truth-conditions based on that
> assumption. it simply assumes that they refer, and gives an account
> of truth conditions based on that assumption.
Again, we are in complete agreement.
XXX
> But that observation does not lead to your curious distortion
> of model theory itself.
I have not distorted model theory in the slightest. As you said,
model theory "simply assumes that [the symbols in the logic] refer".
I drew that diagram to show that model theory, by itself, ignores
the questions about how well the model describes the world.
For an example of the way I discuss that diagram, see the quotation
below. I have never seen a diagram with a shorter, clearer, and more
accurate description of that mapping. If you can find or draw a better
one with a better description, I would love to see it.
John
________________________________________________________________________
>From page 5 of http://jfsowa.com/pubs/fuzzy.pdf
> Figure 3: Relating a theory to the world
>
> To bridge the gap between theories and the world, Figure 3 shows a model
> as a Janus-like structure, with an engineering side facing the world and
> an an abstract side facing a theory.
>
> On the left is a picture of the physical world, which contains more
> detail and complexity than any humanly conceivable model or theory can
> represent. In the middle is a mathematical model that represents a
> domain of individuals D and a set of relations R over individuals in D.
>
> If the world had a unique decomposition into discrete objects and
> relations, the world itself would be a universal model, of which all
> accurate models would be subsets. But the selection of a domain and its
> decomposition into objects depend on the intentions of some agent and
> the limitations of the agent’s measuring instruments. Even the best
> models are approximations to a limited aspect of the world for a
> specific purpose
-----------------------------
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> I think that it's very difficult to correlate theory to model to
> the real world - and I think that Peirce specifically didn't want
> to do such a thing, not because of the difficulty but because of
> the resultant 'lack of truth' in these correlations.
Yes. I have used that diagram with a two-stage mapping between
theories and the world for a long time. When I talk to logicians,
I get very strong opinions, pro and con. Some say that it's
obvious, and others claim that it's totally wrong.
Following is a response I sent some time ago to a logician who
strongly disagreed with that diagram. He never replied to my
request for a better diagram or explanation.
John
_____________________________________________________________________
To XXX,
I agree with (1) the definition of model theory and your comments
about it; (2) that names in a logic may refer to aspects of the
world; and (3) that logicians, scientists, engineers, and ontologists
may talk about sets that contain physical entities.
But the issues about symbol grounding and identity conditions
are critical. Unless there is some way of relating a domain D
to the real world, there is no difference between a real D and
a hypothetical, virtual, imaginary, or fictional D.
XXX
> Model theory itself provides no account of this, of how symbols are
> grounded. It was never supposed to do that: it simply assumes that
> they refer, and gives an account of truth-conditions based on that
> assumption. it simply assumes that they refer, and gives an account
> of truth conditions based on that assumption.
Again, we are in complete agreement.
XXX
> But that observation does not lead to your curious distortion
> of model theory itself.
I have not distorted model theory in the slightest. As you said,
model theory "simply assumes that [the symbols in the logic] refer".
I drew that diagram to show that model theory, by itself, ignores
the questions about how well the model describes the world.
For an example of the way I discuss that diagram, see the quotation
below. I have never seen a diagram with a shorter, clearer, and more
accurate description of that mapping. If you can find or draw a better
one with a better description, I would love to see it.
John
________________________________________________________________________
>From page 5 of http://jfsowa.com/pubs/fuzzy.pdf
> Figure 3: Relating a theory to the world
>
> To bridge the gap between theories and the world, Figure 3 shows a model
> as a Janus-like structure, with an engineering side facing the world and
> an an abstract side facing a theory.
>
> On the left is a picture of the physical world, which contains more
> detail and complexity than any humanly conceivable model or theory can
> represent. In the middle is a mathematical model that represents a
> domain of individuals D and a set of relations R over individuals in D.
>
> If the world had a unique decomposition into discrete objects and
> relations, the world itself would be a universal model, of which all
> accurate models would be subsets. But the selection of a domain and its
> decomposition into objects depend on the intentions of some agent and
> the limitations of the agent’s measuring instruments. Even the best
> models are approximations to a limited aspect of the world for a
> specific purpose
-----------------------------
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----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
