Talk:Formal interpretation/Archive 1

different word

Could we use a different word than reasonable? Maybe satisfactoryCSTAR 19:40, 28 Jun 2004 (UTC)

abstract

Do we need to specify 'abstract'? Isn't that already in the word 'Model' (at lesat, in this specific meaning of the word).

There are other articles on specific kinds models: physical models, economic models. Some name was necessary to distinguish this sense from other senses.CSTAR 13:30, 30 Jun 2004 (UTC)

excuse me if i disagree. models are inherently and basically a (useful) abstraction of reality. this is a tautological article (with lots of annoyingly distracting redundancies, i might add). the above question is justified in all respects. -- Kku 17:29, 17 April 2006 (UTC)

Re: A model, such as a digital or analog simulation, isn't normally considered an abstract model in the sense of this article. The adjective "abstract" served as a disambiguation from other meanings.

Re: "annoyingly distracting redundancies". Please remove them, then. Though it might be useful to you to feel assured that you know more than the rest of us about this, it would be better for all if you actually attempted to share this knowledger in the article. WP is a cooperative effort. --CSTAR 18:14, 17 April 2006 (UTC)

ok. my emphasis was on the "abstract" thing. s.a. my discussion page reply -- Kku 22:33, 17 April 2006 (UTC)

wht does economics deal wtih?

A model is an object used as representation of another object which is called "the real object"

Recent edits

Model is a description of a complex entity or process. - Ajay Lakhani, 03 Decemeber 2005

The section Abstract models vs mathematical models of article is now a mess. The main point of that section was to differentiate the model (as a relation between syntax and semantics) and model as used in the article. That distinction has been obliterated by recent edits.--CSTAR 05:08, 27 November 2005 (UTC)

I reverted the page based on these comments.--CSTAR 05:13, 27 November 2005 (UTC)

The section now discusses the controversy in contrast to the previous version which violated NPOV because it didn't discuss the controversy. So I will revert back. Sorry,--Carl Hewitt 05:34, 27 November 2005 (UTC)

The article Model theory already discusses a relationship between syntax and semantics.--Carl Hewitt 05:41, 27 November 2005 (UTC)

What controversy? That there is a distinction between model (as in Model theory)and abstract model and makeing that distinctiuon clear? Why are you opposed to discussing this in the article? --CSTAR 06:03, 27 November 2005 (UTC)

The question is: What is the relationship between mathematical models and abstract models?--Carl Hewitt 06:32, 27 November 2005 (UTC)

How can you claim there is a controversy regadrding the nature of abstract models? There are numerous models in political theory and economics which are not mathematical, yet they are abstract.--CSTAR 06:12, 27 November 2005 (UTC)

The question is whether these abstract models in political theory and economics can be made precise enough to be scientific without being made into mathematical models. In this regard it is important to remember that some define mathematics as precise reasoning.--Carl Hewitt 06:32, 27 November 2005 (UTC)

Certainly workers in these fields (and others, such as psychology) think that their work is precise. Philosophers have models; epistemology constructs models of knowledge. Do you dismiss all this as junk science? that's certainly POV! Why shouldn't the models used in these fields be sufficently precise to provide useful predictions?--CSTAR 07:37, 27 November 2005 (UTC)

This is what the controversy is about! If a model is precise enough to make precise predictions then it is arguably mathematical.--Carl Hewitt 08:48, 27 November 2005 (UTC)

Reply to Hewitt

Right, it may be controversial to you, but is it really considered significantly controversial by a substantial part of researchers?. I just picked up a book (more or less) at random from by library: David H. Fischer Historians Fallacies, 1970.

• p xvi: The resultant explanatory paradigm may take many different forms: a statistical generalization, or a narrative or a causal model, or maybe an analogy

• p 3 Moreover, there can be no questioning in a sophisticated sense without hypothesising, and noo systematic testing of hypotheses without th econstruction of hypothetical models which can be put to the test.

and so on. There are lots of other examples in other areas. Again I disagree it's controversial.--CSTAR

Dispute

Recently User:CarlHewitt has substantially changed the section Abstract models vs models in mathematics (which he renamed it to What are abstract models and mathematical models?) as follows:

• He removed the distinction between the notion of model as used within mathematics, as a model of a formal theory (such as models of set theory of models of first order arithmetic) and the notion of abstract model as discussed in this article. Since the two are often confused (in fact, Hewitt has introduced a category which is now considered for deletion in which the two are conflated), it is important that this distinction be clearly made.

The article says (now with a third additional sentence added at the end):

Certainly the notion of conceptual model used in physical or social sciences is different from the notion of model as used in mathematical model theory. On the other hand, there are mathematical models such as domain theory that do not fit within model theory. Therefore the fact that some scientific models do not fit within model theory is not a good argument that they are not mathematical models.

Regards,--Carl Hewitt 19:52, 27 November 2005 (UTC)

Please note that the article never made the argument that model theory and mathematical models were any way similar concepts, or that by the fact they were dissimilar, that any conclusion could be reasonably inferred. I don't see where you get this idea. You seem to be setting up a straw man argument.--CSTAR 20:37, 27 November 2005 (UTC)

You have a good point. Is there some way we could word this better? Regards,--Carl Hewitt 20:46, 27 November 2005 (UTC)

• He added the claim that the fact the assertion that some abstract models are not mathematical is "controversial". Hewitt's claim is itself highly controversial, since it contradicts the known existence of non-mathematical models in the social sciences. Whether or not these models can be formalized using mathematics (and maybe even be made into better models) is irrelevant. It is a completely non-controversial fact that non-mathematical models recognized as non-mathematical and are widely used.

This is the kind of controversy that has occurred in many disciplines. In Artificial Intelligence, it was the "neats" versus the "scruffies".--Carl Hewitt 20:03, 27 November 2005 (UTC)

Based on these facts, I will place an appropriate dispute banner on the article. --CSTAR 16:12, 27 November 2005 (UTC)

While this may initially have been done out of ignorance and possibly vanity (undoubtedly to create another place to put the actor model) it has been sufficiently explained to him now, making this vandalism. —R. Koot 16:34, 27 November 2005 (UTC)

Dispute (cont'd)

There are two issues under discussion:

• Removal of the distinction between the notion of model as used within mathematics, that is as a model of a formal theory (such as models of set theory of models of first order arithmetic) and a mathematical model to formalize some phenomenon.

This distinction should be put back into the article.

The above does not state a distinction. Could you please be more precise? Thanks,--Carl Hewitt 23:24, 27 November 2005 (UTC)

OK I forgot to finish the sentence. Now I did.--CSTAR 23:43, 27 November 2005 (UTC)

As per previous dicussion, the above characterization is too narrow for mathematical models. There are mathematical models (such as domain theory) that are not models of formal theories (such as models of set theory of models of first order arithmetic).--Carl Hewitt 23:50, 27 November 2005 (UTC)

Good point. Your point seems to be that they are still models in the sense there is a class of syntactic objects (such as lambda expressions) which are mapped into objects in the domain (e.g., models of the lambda calculus). The objects aren't formulas (which are true or false). However, I think it is appropriate to treat the two the two kinds separately at least for purposes of this article, precisely because I have often seen the two confused. I think we should let others weigh in on this point.--CSTAR 00:41, 28 November 2005 (UTC)

• Addition of the claim that the assertion that some abstract models are not mathematical is not controversial. Specifically, the claim in the article is the following:

Since mathematics is seen by some to be precise reasoning, it is argued that any abstract model that is precise to be scientific must necessarily be a mathematical model.

I contend that this claim is generally regarded as false. In other words, in WP parlance, the majority view is that this claim is false. To show why this is so, it suffices to consider almost any work on political science, sociology or psychology (which, for better or worse are all regarded as science). In these disciplines, non-mathematical models are constructed all the time. Moreover, the claim that these models can be formalized or could be improved if they were formalized is irrelevant. Here we are talking about actual practice in these areas. Now it may be the case that many philosophers of science argue the contrary position; that these are useless constructs etc., etc. Fine. Adding that fact would be a useful addition to the article, but it has to be stated, in my view, as the minority opinion.

--CSTAR 22:46, 27 November 2005 (UTC)

Dear CSTAR,

Per your suggestion, I have changed the sentence in the article to the following:

Since mathematics is seen by some to be precise reasoning, some philosphers of science have argued that any abstract model that can produce precise scientific predictions must necessarily be a mathematical model.

Regards, --Carl Hewitt 23:24, 27 November 2005 (UTC)

Sorry, your "fix" is not good enough. The positions have to be clearly stated as majority and minority positions.--CSTAR 23:19, 27 November 2005 (UTC)

Do you have any suggestions how to word this? Thanks, --Carl Hewitt 23:27, 27 November 2005 (UTC)

Proposal

I propose that the section under dispute be deleted and be entirely rewritten by a third party.--CSTAR 00:46, 28 November 2005 (UTC)

Since the section under dispute is an improvement over what was there before, perhaps it should remain until a third party shows up with some new ideas. Regards, --Carl Hewitt 02:00, 28 November 2005 (UTC)

Why is it an improvement? I don't think it's an improvement even if you do.--CSTAR 02:02, 28 November 2005 (UTC)

Which statements do you want to delete? Regards, --Carl Hewitt 02:49, 28 November 2005 (UTC)

What is the section in dispute, exactly (as CSTAR has resigned, I'm going to try to take over his position here, to the extent I can.) Arthur Rubin | (talk) 00:43, 1 December 2005 (UTC)

Here's a suggestion. If a model is precise enough to be rigorous and make predictions, then it's mathematical. If it's not, then it's metaphorical. This does not make it useless. Sciences like sociology, psychology, economics can still have their useful models, but precision, I think, entails mathematics. The distinction I always remember about models is that some were quantitative and some were qualitative. Qualitative can still be mathematical.

On the model theory vs. math model distinction, that seems to be too esoteric to be widely held. Can someone explain what it entails that is of more consequence than just domain of math objects vs domain of real world objects? Is that the distinction? If that's not it then I don't understand what you're arguing about. Montalvo 00:29, 29 November 2005 (UTC)

I am not so sure, if you are just fighting over the wrong place: maybe the conflict can be solved, if you describe the language used for specifying the model in more detail? In the end it is not a question of the representation format (e.g., English vs. Propositional Logic), but of the complexity and formality of what is expressed. Many models in e.g. political science (formulated in plain English) satisfy the requirements of an abstract model, whereas some other ('pre-model', exploratory) papers cannot offer s.th. similar. Sometimes formal non-natural languages can help with checking a model for inconsistencies. I believe that to call it a model, it has to be explicated (wouldn't count emergence as a model). Fridolin Wild, 14:48, 23 February 2006 (CET)

As Carl seems to conflate the usages -- I believe the paragraph

Certainly the notion of conceptual model used in physical or social sciences is different from the notion of model as used in mathematical model theory. On the other hand, there are mathematical models such as domain theory that do not fit within model theory. Therefore the fact that some scientific models do not fit within model theory is not a good argument that they are not mathematical models.

should be omitted entirely, but any sentence which refers to model theory, directly or indirectly, should also be omitted. (And I, at least, am familiar enough with model theory to find them.) -- Arthur Rubin | (talk) 00:43, 1 December 2005 (UTC)

Look at - http://www.genealogy.ams.org/html/id.phtml?id=10490

Thanks, anonymous edit by 198.208.159.20, for that vote of confidence. (It wasn't me.) Arthur Rubin | (talk) 17:55, 13 December 2005 (UTC)

OK, I'm removing the paragraph mentioned above. I don't think there's a clause there that belongs in this article. I'll see if I can come up with a good version of the preceding paragraph. Arthur Rubin | (talk) 18:34, 13 December 2005 (UTC)

In the Enterprise Modeling domain, most of the modeling tools used are essentially graphical, used to describe objects, relationships, and processes (or activities). These abstract models are used and useful, although the only way they are tested, so far as I know, is to convert them into software and execute the software. Yet they are formal, and I suppose with sufficient motivation, one might come up with an explicit mathematical formalism for them. In fact, such a formalism might be extremely useful, although it probably would require so many additional assumptions as to make it impractical. In fact, for complex systems these kinds of models will always retain some ambituity, some process which is essentially "call Joe to fix this". They are useful, nonetheless. In any case, I believe that many non-mathematicians will find the distinction between "abstract" and "mathematical" a useful one, and I urge the debaters here to come to a resolution which preserves this distinction.66.32.228.219 16:00, 29 December 2005 (UTC)

prediction vs. specification

The 66.32.228.319 example doe fully reflect the matter of dispute, I think. If a domain is an object of mathematics, and if the enterprise-modeler classifies entities, there we go. (Is that an entity-relationhip type of graph? That is exactly what most people would think of as the mathematics-aspect, the captured view, of the real-world.)

The problem with a domain, is the abstraction. When/if your modeling-tool is not rich enough, you lump, or if that tool is excessively-elaborate to the point that most of the people do not get what each category would stand for, then we would find a lot of spurious (and wrong, that is) "finer classification."

For a vote, I would limit the term 'mathematics' to only those models which allow computation-automation, without a further (emotional, real-world) reflection by a human. e.g: The computation as a spreadheet, or a Petri net verifier, would both fit.

After the model is there, other people may work through that, with some computational-tool, that is. We may contrast model-through-mathematics vs. model-through-linguistics. The latter need not mean "vague." In fact, the domain theory is vague, if that domain-ort is not appropriate. For example, the student vs. waiter example, in view of the need for specification, is thoroughly human.

Prediction vs specification. The computational-model would allow prediction, whereas what most people would not think as a math-model, may allow really wise specification. e.g: As in that example I had mentioned, no tool of mathematics that I know, would think up the rule "do not warn the waiters about that, if they never put their fingers in the soup" is not derivable with a tool/method of matematics. That is human reflection/wisdom for a rule.

FerzenR 00:49, 5 January 2006 (UTC)

oops! on prediction

The word 'prediction' is not the issue. If there is a model, that is that. The point I stated is the computational vs. intuitive/verbal. (Even the word specification is doubling. A break-even level is a specification-of-min-level, for your spreadsheet-based budget model.)

right information/wisdom > mathematics

And 'mathematics' is not necessarily so predictive. Do we mean statistics? What else? Most of [social] science (as opposed to engineering, or philosophy), is with statistics, if to predict. Psychology (see JPSP), medicine (see JAMA), etc. As opposed to graphics (see CG&A) -- even graphics is with statistics, if to infer/re-construct a shape, from sample-data. Right?

Right there, please reflect on what your popular exam-guide suggested you, about SAT, GRE, etc. That is, if you may eliminate any, then you may guess. That is termed an educated-guess. There, if statistics is the math-type tool, fit for the computational model, the type of abstract/human/intuitive-model as with the student vs. waiter example, is the really fitting, at other.

Is that vaporware? No. Think about the poster "do not have a rugby tournament in the lecture hall." That is most likely never the case, either. Why would no one object to that? The answer is that, that is not pejorative. Is pejorativeness "mathematical?" No. When we successfully guess based on that, We know what that is, though.

Two that I had read, may relate

• Kelley had written in an old annals-of-psyschology, the article "commonsense psychology. There, he pointed out that, lay people guess most of psychology. (Even tough there exist also fallacies, as we all know.) Do they work through mathematics? No.
• I had read (on a web page of a U.S. business school? I cannot find that again, now.) that in an experiment, some other people (academics/students) guessed finer than game-theorists. Game-theory is mathematics. What is wrong, then?

Not each information is mathematical. How could each model exist only in mathematics? What to make of the rest?

FerzenR 06:24, 5 January 2006 (UTC)

Found that reference: The less-accuracy of game-theorists

FerzenR 06:43, 5 January 2006 (UTC)

Is there still a dispute? Isn't there a maintainer for this article?

The history shows a banner as of 16:12, 27 November 2005 CSTAR (Dispute banner)

So, has this been resolved yet? I turn my back, and the article is whacked. --Ancheta Wis 14:12, 21 March 2006 (UTC)

This was one of the (many) articles that were affected by the Carl Hewitt dispute. I was inactive for a couple of momnths as a result of it. --CSTAR 15:15, 21 March 2006 (UTC)

Are you (CSTAR) OK with the article, or should we just kill the section What are abstract models and mathematical models? ? Tentatively, I could go either way, although I lean toward killing the section, as it's now too short to be a separate section, but too difficult to integrate it into an existing section — in addition to possible disputes as to content. I think that was the only CH dispute in this article. — Arthur Rubin | (talk) 18:24, 21 March 2006 (UTC)

Kill. Less work.--CSTAR 20:25, 21 March 2006 (UTC)

Done. Copied below, in case someone wants to salvage it. — Arthur Rubin | (talk) 21:42, 21 March 2006 (UTC)

Deleted section

Can sum1 plz tell me bout models in science??????????

What are abstract models and mathematical models?

Some argue that the key difference between the two notions of model is this: whereas in mathematical models, interpretation (and validity) occurs entirely within mathematics, for an abstract model, interpretation and validity requires the following two activities:

1. An expression (or perhaps more realistically, an explanation) of the model's ontology (that is what the model deals with) in terms of ordinary language.
2. A test of the validity of the model's assumptions. These tests of validity are set up by experimental procedures such as laboratory tests, statistical data gathering or polling. In some cases, both of these activities can be expressed by operational definitions.

Sometimes it is possible to interpret one abstract model in terms of another abstract model in such a way that validity of assertions is preserved. This relation between models can actually be used to justify the validity of a model based on the validity of another more refined model.

Anon question

218.111.219.207 asked the following question on the article mainpage :

"what model is using for e-learning?"

Can anyone provide any e-learning examples of models? Cheers, --Plumbago 08:54, 27 April 2006 (UTC)

Is this page really necessary?

At least half the material on this page is either duplicated on the page Mathematical model or could be moved over to that one. Material that does not belong on that page could easily be merged into appropriate pages on psychological models, economic models, etc. While I normally tend to argue against merging/deleting pages, I think this page seems a bit superfluous. What do others think? Cazort 00:56, 15 October 2007 (UTC)